SB: Math 1

Short Answer What function is the inverse of y = 3x + 4?

ANSWER: y = (x-4)/3

Specifying whether your answer is open or closed, what is the interval of angles in degrees whose terminal sides are in the second quadrant?

THE OPEN INTERVAL FROM 90 TO 180

All multiple choices are in what format?

W X Y and Z

Bonus: What is 4 to the power of log base 2 of 5? W) 1/5 X) Square root of 5 Y) 5 Z) 25

Z) 25

BONUS MATH Short Answer: If $10,000 is placed in a savings account that pays 5% interest compounded annually, what is the total amount of money in the account at the end of 2 years, to the nearest dollar?

$11,025

BONUS MATH Short Answer: Factor the following expression completely: 81x² + 180xy + 100y²

(9x + 10y)²

Short Answer Factor the following polynomial completely over the real numbers: x3 + 3x2 - 5x - 15.

(x + 3)(x + 5)(x - 5) (IN ANY ORDER)

What is the sine of 270 degrees?

-1

What is the complex conjugate of -4 -36i?

-4 + 36i

MATH Short Answer: Name a real number that does not have a multiplicative inverse.

0

MATH Short Answer: Assuming that the natural log of 5 = 1.6, find, to the first decimal place, the natural log of 5¹/³ :

0.5

Bonus: What is the sum from n = 0 to 2016 of the cosine of open parenthesis pi times n divided by 2 close parenthesis?

1

Short Answer According to Descartes's Rule of Signs, what are the possible numbers of positive real roots that the following equation might have: x5 - 7x3 + 15x2 + 3 = 10?

1 OR 3 (MUST GIVE BOTH ANSWERS)

Identify all of the following three integer operations that are commutative: 1) Addition; 2) Subtraction; 3) Multiplication.

1 and 3

Bonus: Identify all of the following four properties that are preserved under a translation: 1) Distance; 2) Collinearity; 3) Midpoint; 4) Angle measure.

1, 2, 3, 4 (ACCEPT: ALL)

BONUS MATH Short Answer Cards numbered 1 through 10 lie on a table. If two cards are picked at random, without replacement, what is the probability, as a fraction in lowest terms, that the two cards will have values within one of each other?

1/5 (Solution: 9/(10 nCr 2) = 9/45 = 1/5)

Bonus: A bag contains 18 socks: 4 are red, 6 are white, and 8 are blue. How many socks must you take out to be certain that you will have at least one pair of blue socks?

12

MATH Short Answer: If the shortest leg of a 30-60-90 right triangle is 6 inches, what is the measure, in inches, of the other 2 sides?

12 AND 6√3

BONUS MATH Short Answer Factor the following expression completely: 12x² + 24x - 36

12(x + 3)(x - 1) (ACCEPT: 12(x - 1)(x + 3))m

BONUS MATH Short Answer: If y varies directly as x and z, and y = 12 when x = 4 and z = 5, find y when x = 10 and z = 20:

120

What is the degree measure of each interior angle in a regular hexagon?

120

BONUS MATH Short Answer: Simplify the following expression by combining like terms: 12.03A - 4.03B - 0.03(A - 40)

12A - 4.03B + 1.2

Given f(x) = 3x-5 and g(x) = 4x, what is f of g of x?

12x-5

How many terms does the binomial expansion of open parenthesis x²+ 3y³ close parenthesis to 13th power contain?

14

BONUS MATH Short Answer: Find the sum of all interior angles, in degrees, in a regular polygon having 100 sides:

17,640

Bonus: Special water for a 600-liter aquarium is only sold in35-liter containers. What is the minimum number of these 35-liter containersyou would need to buy tobe able to completely fill the tank?

18(DO NOT ACCEPT: 17 1/7 or 120/7)

BONUS MATH Short Answer Convert the angle, 18º18'36" (read as: 18 degrees, 18 minutes, 36 seconds) to degrees, to the second decimal place:

18.31

Bonus: Find the circumference of a circle with area equal to one over pi.

2

If all of the prime factors of 444, including multiple occurences, are added, how much greater will the result be than that for 222?

2

What is the greatest common factor of 18 and 142?

2

MATH Short Answer Simplify the following, giving your answer in proper scientific notation: (6.0 × 10¹²)(2.0 × 10¹⁰)²

2.4 × 10³³

BONUS MATH Short Answer: Multiply the following 4 numbers and give your answer in scientific notation: 30,000 × 3,000 × 30 × 0.1

2.7 × 10⁸

BONUS MATH Short Answer Considering the function f(x) = x2 , use a left Riemann sum with 4 equal subintervals to estimate the integral from 2 to 10 to the nearest integer.

240

BONUS MATH Short Answer: Find the sum of the first 10 terms of the arithmetic sequence whose first three terms are 7, 11, and 15:

250

BONUS MATH Short Answer An object is launched straight up from the ground with an initial velocity of 176 feet per second. What is the height of the object above the ground, in feet, 2 seconds into the flight?

288

BONUS MATH Short Answer: Find the following product, giving your answer in standard form: (4x³ + x)(7x³ + 4x² )

28x⁶ + 16x⁵ + 7x⁴ + 4x³ (ACCEPT: x³ (28x³ + 16x² + 7x + 4))

MATH Short Answer: In what quadrant does θ (read as: theta) terminate if sine θ is positive and secant θ is negative?

2nd (ACCEPT: 2)

What is the distance between the points (0, 1) and (2, 3)?

2√2

MATH Short Answer: What is the smaller of two integers whose sum is 19 and whose product is 48?

3

Determine all of the prime factors of 111.

3 AND 37

What is the derivative with respect to x of -5 divided by x⁶?

30/x⁷(DO NOT ACCEPT: 30x⁻⁷)

BONUS MATH Short Answer Find the numerical value of the geometric mean of the following 4 values: 2¹ ; 2³ ; 2⁸ ; 2⁸

32 (DO NOT ACCEPT: 2⁵ )

MATH Short Answer Evaluate the following expression when a = 1/3 , b = 4, c = -1, and d = -5: 2[3a - (b + c) - 4d]

36

What is the second derivative with respect to x of 2x^3-12 evaluated at x = 3?

36

MATH Short Answer: What is the greatest common factor of the terms in the expression 3x⁵y² + 6x³y⁵ (read as: 3 x to the fifth y squared plus 6 x cubed y to the fifth)?

3x³y²

How many lines of symmetry does a square have?

4

BONUS MATH Short Answer: Solve the following equation for x: -2|3 + ( x/2 )| = -10 (read as: negative 2 times the absolute value of 3 plus, open parenthesis, x divided by 2, close parenthesis, close absolute value, equals negative 10)

4 AND -16

MATH Short Answer: A jar of 100 marbles contains only 2 colors of marbles, red and blue. If there are 13 red marbles for every 12 blue marbles, how many blue marbles are in the jar?

48

Bonus: Expressing your answer in terms of m, evaluate the functionf(x) = 4x²-9x+ 11 when x is m-7.

4m²-65m + 270

MATH Short Answer: There are 10 people on a bus who, when ranked from youngest to oldest, all differ from those on the bus closest in age to them by the same number of years. If the youngest is 6 and the oldest is 51, what is the common difference in their age?

5

Bonus: A right triangle has hypotenuse of length 46 and one leg of length 44. What is the length of the third side?

6√5

BONUS MATH Short Answer: If the area of a regular pentagon is 280 square centimeters, what is the length, in centimeters, of each side if the apothem is 16 centimeters?

7

BONUS MATH Short Answer If $10,000 is placed in a savings account that pays 5% interest compounded annually, what is the total amount of money in the account at the end of 2 years, to the nearest dollar?

ANSWER: $11,025 (Solution: A = P[1 + (r/n)]^(nt); = $10,000[1 + (0.05/1)]^(1x2) = $11,025)

BONUS 21) MATH Short Answer After a 20% increase, the new price of a tennis racket is $180.00. What was the original price of the racket?

ANSWER: $150.00

BONUS MATH Short Answer Mother Goose divided her estate among her four favorite friends according to the following specifications: • Humpty Dumpty shall receive half of the estate, less $9000; • Simple Simon shall receive one third of the estate, less $3000; • Little Jack Horner shall receive exactly one fourth of the estate; • Little Miss Muffet shall receive one sixth of the estate, plus $3000. What was the total dollar value of Mother Goose's estate?

ANSWER: $36,000

BONUS MATH Short Answer A store has been buying a certain type of calculator at $25 and selling them at $40. At this price, they have been selling 50 calculators per month. The owner of the store wishes to increase the price of the calculator and estimates that for each $1 increase in price, 3 fewer calculators will be sold each month. Determine the price, to the nearest dollar, that maximizes profit.

ANSWER: $41

MATH Short Answer If a point has polar coordinates (3, π), what are the rectangular coordinates?

ANSWER: (-3, 0) (Solution: x = 3 cos π = -3 and y = 3 sin π = 0)

MATH Short Answer Starting with point (4, 2) in the coordinate plane, reflect it across the xaxis, then rotate it 180 degrees around the origin, and finally, translate it vertically up by 2 units. What are the coordinates of the point's final location?

ANSWER: (-4, 4)

Math - Short Answer The point (3, -7) is reflected through the y-axis, with the result then translated 2 units left. What are the coordinates of the final image?

ANSWER: (-5, -7)

BONUS MATH Short Answer Giving your answer as an ordered pair, find the solution of the system of the following 2 equations: x = (2/3)y - 2 and x = y - 3:

ANSWER: (0, 3)

[bonus] Short Answer Giving your answer as an ordered pair, find the solution of the system of the following 2 equations: 2x + 3y = 8, and 3x - 2y = -1

ANSWER: (1, 2) (ACCEPT: 1 AND 2)

BONUS23) Math - Short Answer In a three-dimensional coordinate system, the point (1, 2, 3) is reflected in the xy-plane, then the result is rotated by 180 degrees about the x-axis, and finally that image is translated by 5 units in the positive y direction. What are the final coordinates of the final image?

ANSWER: (1, 3, 3)

BONUS MATH Short Answer The point (3, 2) is reflected across the graph of y = 6 and the resulting point is then reflected across the graph of y = x. What are the coordinates of the final point?

ANSWER: (10, 3) (Solution: the 1st reflection → (3,10); 2nd reflection interchanges the x and y coordinates)

Short Answer Simplify the following radical expression, giving your answer in standard bi form: √(-144/49)

ANSWER: (12/7)i

BONUS MATH Short Answer What are the coordinates of the hole in the graph of the function, g(x) = (2x² − 8)/(x − 2)?

ANSWER: (2, 8) (Solution: simplifies to 2(x + 2); graph looks like a line except at the indicated hole)

MATH Short Answer If the height of a cone is equal to the diameter of its base, express the volume of the cone in terms of its radius r and as a fraction in terms of pi.

ANSWER: (2/3) πr³ (ALSO ACCEPT: : 2πr³ /3)

BONUS MATH Short Answer What is the reciprocal of the complex number 2 + i?

ANSWER: (2/5) - (1/5)i (ACCEPT: 0.4 - 0.2i)

Short Answer Giving your answer in simplest radical form, rationalize the denominator of the following expression: 1/ (3-√x)

ANSWER: (3+√x)/(9-x)

MATH Short Answer Give the coordinates of the point where the line 3x + 2y = 18 intersects the x axis.

ANSWER: (6, 0)

BONUS MATH Short Answer Factor the following expression completely: 81x^2 + 180xy + 100y^2

ANSWER: (9x + 10y)^2

[Bonus] Short Answer: Multiply the following, giving your answer in standard form and without negative exponents or radicals: (a^(2/3) + b^(2/3))^2

ANSWER: (a^(4/3) + 2a^(2/3) * b^(2/3) +b^(4/3))

BONUS 5) MATH Short Answer Factor completely the expression: 5rs + 25r - 3s - 15.

ANSWER: (s + 5)(5r - 3)

BONUS 14) Math - Short Answer Assuming x is a value for which the denominator is defined, simplify the fraction with numerator 6x2 + 4x - 2 and denominator 12x2 - 4x.

ANSWER: (x +1)/(2x)

BONUS MATH Short Answer The three vertices of a triangle have coordinates (4, 8), (−2, 5), and (3, 1). The longest side of the triangle is opposite which of these three vertices?

ANSWER: (−2, 5)

MATH Short Answer Find an antiderivative for 𝑙n(𝑒^−𝑥^2 ) [the natural log of the quantity e to the power of negative x squared].

ANSWER: -(1/3)x3 (ACCEPT: GIVEN ANSWER PLUS ANY CONSTANT)

BONUS MATH Short Answer Simplify the following rational expression by combining like terms, assuming x is not equal to 4: (x^2-16)/(4x-x^2)

ANSWER: -(x+4)/x (ACCEPT: other forms)

BONUS MATH Short Answer Simplify the following expression: sec^2 3𝜋/4 − csc^2 𝜋/4 − cos^2 4𝜋 [secant squared of 3 pi over 4 minus cosecant squared of pi over 4 minus cosine squared of 4 pi].

ANSWER: -1

MATH Short Answer For the function ƒ(x) = 1/x, what is ƒ'(5)?

ANSWER: -1/25

MATH Short Answer What is the determinant of a 2-by-2 square matrix whose rows are 4, 2 and -3, -4?

ANSWER: -10 (Solution: D = ad - bc = 4(-4) - (-3)(2) = -10)

BONUS MATH Short Answer If the first four terms of an arithmetic sequence are a, 2a, b, and a - 6 - b, find the 100th term.

ANSWER: -100

Math - Short Answer If theta is an angle in the third quadrant and the cosine of theta equals negative five-thirteenths, what is the sine of theta?

ANSWER: -12/13

BONUS Math - Short Answer Find the product of the following three complex numbers: 2i, -11 + 2i, 4 - 5i

ANSWER: -126 - 68i

TOSS-UP18) Math - Short Answer Determine the maximum of the function f(x) = x^2 - 22 on the closed interval from -3 to 2.

ANSWER: -13

Math - Short Answer What is the dot product of 4i - 6j and -3i + j?

ANSWER: -18

[Bonus] Short Answer Solve the following equation for x: (x+9)/(x+10) = (20/18)

ANSWER: -19

MATH The average of a and b is x. The average of b and x equals the average of a and (b + 1). Find a - b.

ANSWER: -2

TOSS-UP12) Math - Short Answer For what values of x does the function f(x) = the fraction with numerator x - 2and denominator x² - 4 have a vertical asymptote?

ANSWER: -2

BONUS MATH Short Answer Solve the following inequality for x: |3 - 2x| ≤ 7 (read as: the absolute value of, 3 minus 2x, close absolute value, is less than or equal to 7)

ANSWER: -2 ≤ x ≤ 5 (ACCEPT: 5 ≥ x ≥ -2)

BONUS MATH Short Answer If f(x) = 2x - 1 and g(x) = 6 + 2x - x^2 , what is the standard polynomial form for g(f(x)) (read as: g of f of x)?

ANSWER: -4x^2 + 8x + 3

BONUS MATH Short Answer Find all values of c such that the given function is continuous from negative infinity to infinity: f(x) = c2 x when x ≤ 2, and f(x) = (5/4)cx2 + 3 when x > 2.

ANSWER: -½, 3

MATH Short Answer What is the solution set of the inequality (x - 1)² ≤ 0 [the quantity x minus one squared is less than or equal to zero]?

ANSWER: 1

BONUS MATH Short Answer Providing your answer in simplest form, give the volume in terms of π of a solid generated by revolving the region bounded by the graph of y = ln(x) (read as: y equals the natural log of x), the x-axis, the lines x = 1, and x = e, about the y-axis.

ANSWER: 1 2 π (e2 + 1) [ACCEPT: π( e^2/2 + 1/2 )]

MATH Short Answer In the algebra of real-valued functions, give the name or number of all of the following 3 choices that the implied domain usually excludes: 1) numbers causing division by zero 2) numbers causing imaginary numbers in the range 3) numbers causing irrational numbers in the range

ANSWER: 1 AND 2

MATH Short Answer If two 6-sided fair dice are rolled, providing your answer as a fraction in lowest terms, what is the probability that both numbers will be even?

ANSWER: 1/4

Math - Short Answer For what integer value of k is 2015 cubed closest to 10^k ?

ANSWER: 10

[Bonus] Short Answer: Rounded to the nearest centimeter, if side A of a right triangle measures 2 centimeters and side B measures 10 centimeters, what is the length of the hypotenuse?

ANSWER: 10 (Solution: 2² + 10² = c² ; c = 10.20 = 10)

MATH Short Answer Providing your answer to one decimal place, find the value of the following fraction: 63!/(3!*62!) [the numerator is 63 factorial; the denominator is 62 factorial times 3 factorial].

ANSWER: 10.5

BONUS Math - Short Answer A box contains 10 red marbles and 5 black marbles. A marble is randomly selected from the box. If the marble is red, it is returned to the box. If the marble is black, it and 3 additional black marbles are put in the box. Then a second marble is randomly selected. What is the probability that the second marble selected is black?

ANSWER: 10/27

BONUS21) Math - Short Answer A box contains 10 red marbles and 5 black marbles. A marble is randomly selected from the box. If the marble is red, it is returned to the box. If the marble is black, it and 3 additional black marbles are put in the box. Then a second marble is randomly selected. What is the probability that the second marble selected is black?

ANSWER: 10/27

BONUS MATH Short Answer How many three-digit numbers can be made using digits 0 through 4, provided the first digit is not zero?

ANSWER: 100

[Bonus] Short Answer: Giving your answer in terms of pi, what is the area of a circle whose circumference is 20?

ANSWER: 100/π (Solution: C = πd; A = πr² = π(10/π)² = 100/π)

MATH Short Answer If the exterior angle of a base angle of an isosceles [eye-SOS-uhlees] triangle measures 141º, what is the measure of the vertex angle?

ANSWER: 102°

MATH Short Answer Express 600º in radians as a reduced fraction in terms of π:

ANSWER: 10π/3

BONUS10) Math - Short AnswerWhat is the smallest positive angle, in degree measure, between the vectors i + 2j + 3k and 2i - 3j - k?

ANSWER: 120

BONUS MATH Short Answer What is the area, in square feet, of a triangle whose perpendicular height is 20 feet with a base of 12 feet?

ANSWER: 120 (Solution: A = ½ bh = ½ (12)(20) = 120 ft^2 )

BONUS MATH Short Answer If y varies directly as x and z, and y = 12 when x = 4 and z = 5, find y when x = 10 and z = 20:

ANSWER: 120 (Solution: y= kxz; 12 = k(4)(5); k = 3/5; y = 3/5(10)(20) = 120)

BONUS MATH Short Answer A right triangle has sides with lengths of 8, 15, and 17 meters. As a fraction in lowest terms and in meters, what is the length of the altitude to the hypotenuse?

ANSWER: 120/17

BONUS3) Math - Short Answer Convert 291 in base 10 to base 6.

ANSWER: 1203

BONUS MATH Short Answer Simplify the following expression by combining like terms: 12.03A - 4.03B - 0.03(A - 40)

ANSWER: 12A - 4.03B + 1.2

BONUS MATH Short Answer After 40 times at bat, BJ has 9 hits. What is the least number of hits he would need in his next 30 times at bat so that he has hits in at least 31% of his total at-bats?

ANSWER: 13

MATH Short Answer Find the magnitude of the vector 5i - 12j.

ANSWER: 13

MATH Short Answer What is the numerical value of 1152 ?

ANSWER: 13225

MATH Short Answer What is the angle formed, in degrees, between the hour and minute hand of an analog clock at 10:30 AM?

ANSWER: 135

Short Answer Subtract the following complex numbers, giving your answer in standard form: (11 - 4i) - (-3 + 3i)

ANSWER: 14 - 7i

TOSS-UP2) Math - Short Answer Jora models a series of 28 six-sided dice rolls as a binomial distribution based on whether a roll is 6 or not. If she repeated this series of dice rolls multiple times, what is the average number of times that the dice will land on six?

ANSWER: 14/3 ACCEPT: FOUR AND TWO THIRDS

[BONUS] Short Answer: Giving your answer in centimeters to the first decimal place, if one leg of an isosceles right triangle is 100 centimeters long, how long is the hypotenuse?

ANSWER: 141.4 (Solution: c = a 2 = 100 2 - 141.4cm)

BONUS3) Math - Short Answer Robert is asked by his teacher to subtract 3 from a number and divide the result by 9. Instead, he subtracts 9 and then divides the result by 3, giving him 43. What is the correct answer to the teacher's question?

ANSWER: 15

BONUS 4) MATH Short Answer A coin is tossed 10 times. Providing your answer as a fraction in lowest terms, what is the probability that there are 3 heads and 7 tails?

ANSWER: 15/128

MATH Short Answer What is the probability that at least one head appears in 4 tosses of a fair coin?

ANSWER: 15/16 (ACCEPT: 0.9375)

MATH Short Answer Providing your answer as an improper fraction in lowest terms, what is the area under the curve bounded by the x-axis, x = 4 and y = √x?

ANSWER: 16/3

BONUS 25) MATH Short Answer Evaluate the following: ∫(0,2) ((1/t)*(e^ln(t)))dt[the integral from 0 to 2 of 1 over t times e to the power of the natural log of t dt].

ANSWER: 2

BONUS 3) Math - Short Answer If the line tangent to the graph of the function f(x) at the point (1, 3) passes through the point (-1.5, -2), then what is value of the derivative of f(x) when x = 1?

ANSWER: 2

MATH Short Answer What is the area of the region bounded by the curve: y = sinx [y equals sine of x] and the x-axis from x = 0 to x = π?

ANSWER: 2

MATH Short Answer For what values of x is the function f(x)=x²/(x²-4x+4) [f of x equals the fraction with numerator x squared and denominator x squared minus 4 x plus 4] NOT defined?

ANSWER: 2

[BONUS] Short Answer: If Emily can paint a fence in 4 hours but Kathy takes 6 hours, how many hours will it take them to paint the fence if they work together?

ANSWER: 2 (5/ 2) (ACCEPT: (12/5) or 2.4) (Solution: 1/x = 1/4 + 1/6; x = 12/5 hrs or 2 2/5 hrs)

BONUS 4) MATH Short Answer Solve for x: 5 + √(x+14) = x + 7 [5 plus the square root of the quantity x plus 14 equals x plus 7].

ANSWER: 2 (DO NOT ACCEPT: -5)

TOSS-UP 5) MATH Short Answer On a blueprint, if three-quarters of an inch represents 1 foot, then 2 inches will represent what distance, in feet, expressed as the most reduced compound fraction?

ANSWER: 2 3 2 (ACCEPT: 2.66)

BONUS Math - Short Answer A particle moves along a curve with equations x = 4cos t; y = 4sin t; z = 6t. What is the speed of the particle at time t = π/2?

ANSWER: 2 times the square root of 13

BONUS17) Math - Short Answer A particle moves along a curve with equations x = 4cos t; y = 4sin t; z = 6t. What is the speed of the particle at time t= π/2?

ANSWER: 2 times the square root of 13

[bonus] Short Answer Find the sum of all interior angles, in degrees, in a regular polygon having 14 sides:

ANSWER: 2,160 (Solution: (14 - 2)(180) = 2,160º)

MATH Short Answer Simplify the following, giving your answer in proper scientific notation: (6.0 × 10^12)(2.0 × 10^10)^2

ANSWER: 2.4 × 10^33

BONUS MATH Short Answer Multiply the following 4 numbers and give your answer in scientific notation: 30,000 × 3,000 × 30 × 0.1

ANSWER: 2.7 × 10^8

BONUS 16) MATH Short Answer Providing your answers as fractions in lowest terms, what are the x-intercepts of the graph of y = 12x² - 5x - 2?

ANSWER: 2/3 AND -1/4

BONUS MATH Short Answer Find the inverse of the 2-by-2 matrix whose rows are 3, 5 and 7, -2. Give your answer in rows.

ANSWER: 2/41, 5/41, 7/41, -3/41

BONUS MATH Short Answer Find the following quotient of complex numbers: (4 + i)/(1 - 2i).

ANSWER: 2/5 + (9/5)i (ACCEPT: 0.4 + 1.8i)

BONUS MATH Short Answer Given 2 two by two matrices A = [ 1 3 2 1 ] [row one: 1, 3; row 2: 2, 1] and B = [ 3 4 1 0 ] [row 1: 3, 4; row 2: 1, 0]. Find the determinant of the product AB.

ANSWER: 20

BONUS MATH Short Answer What is the degree measure of the angle formed by 2 secants intersecting outside a circle if the measures of the intercepted arcs are 80º and 34º?

ANSWER: 23 (Solution: ½(80º - 34º) = 23º

BONUS 4) MATH Short Answer If the length, width, and height of a right rectangular prism are in the ratio of 3:4:12 [3 to 4 to 12], find the height in meters of the solid if the diagonal of the solid is 26 meters long.

ANSWER: 24

MATH Short Answer What is the surface area of a cube with volume 8?

ANSWER: 24

[BONUS] Short Answer: What is the least common multiple of the following 4 numbers: 12, 15, 16, 20

ANSWER: 240

Short Answer Solve the following logarithmic equation for x: log₄ x = 4 (read as: log base 4 of x equals 4)

ANSWER: 256 (Solution: 4⁴ = 256)

MATH Short Answer The perimeters of two similar figures have a ratio of 5:7. What is the ratio of their areas?

ANSWER: 25:49 (ACCEPT: 25/49)

BONUS6) Math - Short Answer If you made a checkerboard with 23 squares on each side with black squares in every corner and alternating red and black along every row and column, how many red squares do you have on your checkerboard?

ANSWER: 264

BONUS 16) MATH Short Answer Todd the Tortoise is 268 years old, while Sammy the Snail is 32 years old. How many years will it take for Todd's age to be exactly 5 times Sammy's age?

ANSWER: 27

Math - Short Answer How many different sequences of 26 coin tosses result in at least 25 'heads'?

ANSWER: 27

MATH Short Answer Let 𝑦 = 𝑒^𝑥^2 [e to the power of x squared]. Find dy/dx.

ANSWER: 2𝑥𝑒^𝑥^2

[BONUS] Short Answer: Solve the following equation for x: -10 |(x + 2)| = -50 (read as: negative 10 times the absolute value of, open parenthesis, x + 2, close parenthesis, equals negative 50)

ANSWER: 3 AND -7

Short Answer If a 6-foot tall person who is standing next to a vertical pole casts a shadow of 8 feet and the pole casts a shadow of 40 feet, how many feet tall is the pole?

ANSWER: 30 (Solution: x/40 = 6/8; x = 30ft)

BONUS MATH Short Answer It takes 20 minutes for Janis to prepare lunch. When Kristen helps, it only takes 12 minutes. How many minutes would it take Kristen to prepare the same lunch if she worked alone?

ANSWER: 30 (Solution: 12/20 + 12/x = 1, x = 30 min)

Short Answer Solve the following trigonometric equation for x, giving your answer in degrees such that 0º ≤ x < 360º: 2 sin x - 1 = 0

ANSWER: 30º AND 150º

Short Answer: Solve the following radical equation for x, when x is a real number: (x+1)^(1/5) = 2

ANSWER: 31

BONUS MATH Short Answer Find the numerical value of the geometric mean of the following 4 values: 2¹ ; 2³ ; 2⁸ ; 2⁸

ANSWER: 32 (DO NOT ACCEPT: 2⁵ ) (Solution: 1 + 3 + 8 + 8 = 20/4 = 5; 2⁵ = 32)

BONUS MATH Short Answer How many distinct permutations can be made from the letters in the word INFINITY?

ANSWER: 3360

[Bonus] Short Answer Consider a 6-sided irregular polygon whose perimeter is 100 centimeters. If 4 of the sides have a length of 7 centimeters each, what is the length, in centimeters, of each of the remaining two sides if they are congruent?

ANSWER: 36 (Solution: 100 - 28 = 72; 72/2 = 36cm)

BONUS MATH Short Answer Solve the following equation for x: 2² x 2^[x²-2] = 2²¹

ANSWER: 4 OR -4 (ACCEPT: x = ±4 )

BONUS MATH Short Answer Assuming that log 2 = 0.7 and log 3 = 1.1, find the value of log 72 to the nearest tenth.

ANSWER: 4.3

MATH Short Answer Providing your answer in decimal form, what is the area under the curve y = x between 0 and 3?

ANSWER: 4.5

MATH Short Answer Each side of a cube is white. Two sides are selected at random and painted green. What is the probability that two selected sides will have a common edge?

ANSWER: 4/5

BONUS MATH Short Answer What is the coefficient corresponding to x3 in the binomial expansion of (x + 2)5 (read as: the quantity x plus 2 to the power of 5)?

ANSWER: 40

BONUS MATH Short Answer How many integers between 1 and 1000 inclusive are NOT divisible by either 2 or 5?

ANSWER: 400

BONUS 16) MATH Short Answer If the radius of a spherical balloon is expanding at the rate of 5 inches per second, assuming the initial volume is 0 and providing your answer as an improper fraction in lowest terms, what is its volume in inches cubed in terms of π after 2 seconds?

ANSWER: 4000π/3

[BONUS] Short Answer: One-half of a number added to one third of the same number is 68 less than the number. What is the number?

ANSWER: 408 (Solution: x/2 + x/3 = x - 68; x = 408)

TOSS-UP1) Math - Short Answer While waiting at a train crossing, Gayle decided to time how long it took for a 1-mile long train to pass her directly. If it took exactly 75 seconds for the train to pass, at how many miles per hour was the train traveling?

ANSWER: 48

MATH Short Answer A jar of 100 marbles contains only 2 colors of marbles, red and blue. If there are 13 red marbles for every 12 blue marbles, how many blue marbles are in the jar?

ANSWER: 48 (Solution: 12/25 = B/100, B = 48)

BONUS 6) MATH Short Answer If the squared length of the diagonal of one face of a cube is 162, what is the surface area in square units of the cube?

ANSWER: 486

BONUS 12) Math - Short Answer f(x) is a twice differentiable function where f prime of x is less than 0 and f double prime of x is less than 0 for all real numbers. If f(4) = 12 and f(5) = 9, what is the largest possible integer value for f(6)?

ANSWER: 5

MATH Short Answer A drawer contains 30 socks: 10 brown, 9 black, 6 blue, and 5 red. What is the fewest number of socks I must pick from the drawer without looking to be absolutely certain I have 2 socks of the same color?

ANSWER: 5

TOSS-UP20) Math - Short AnswerAn exam has 5 equally-weighted true/false questions. How many distinct ways are there to score an 80% on the exam?

ANSWER: 5

[bonus] Short Answer Given the function f(x) = x ³ + 3x - k and f(3) = 31, solve for k:

ANSWER: 5 (Solution: 31 = 3³ + 3(3) - k; k = 5)

[bonus] Short Answer Solve the following equation for x over the set of complex numbers, giving your answer in simplest form: x² - 10x + 34 = 0

ANSWER: 5 ± 3i (ACCEPT: 5 + 3i AND 5 - 3i)

BONUS MATH Short Answer A farmer has three hens of varying weights. When the hens are weighed in pairs, they weigh 11.3, 11.8, and 12.1 pounds. What is the weight in pounds of the lightest hen?

ANSWER: 5.5

BONUS MATH Short Answer Find the following limit: lim𝑥→2 (𝑥^5− 32)/(𝑥^4− 16) [the limit as x approaches 2 of the fraction with numerator x to the fifth minus 32 and denominator x to the fourth minus 16].

ANSWER: 5/2 (ACCEPT: 2 ½ OR 2.5)

MATH Short Answer Given that 𝑓(𝑥) = (2𝑥)/(𝑥−1) [f of x equals the fraction with numerator 2x and denominator x minus 1] is a one-to-one function, find x so that f^(-1)(x) = 5 [f inverse of x equals 5].

ANSWER: 5/2 (ACCEPT: 2.5 OR 2 1/2)

TOSS-UP 23) MATH Short Answer Given that 𝑓(𝑥) = 2𝑥/(𝑥−1) [f of x equals the fraction with numerator 2x and denominator x minus 1] is a one-to-one function, find x so that f -1(x) = 5 [f inverse of x equals 5].

ANSWER: 5/2 (ACCEPT: 2.5 OR 2 1/2)

BONUS Math - Short Answer Consider rolling a six-sided die three times. What is the probability that the three results are strictly increasing?

ANSWER: 5/54

BONUS12) Math - Short Answer Consider rolling a six-sided die three times. What is the probability that the three results are strictly increasing?

ANSWER: 5/54

MATH Short Answer Giving your answer as a proper fraction, what is the cube root of 125/343 ?

ANSWER: 5/7

BONUS MATH Short Answer If each interior angle of a polygon is 14 times the size of each exterior angle, what is the sum in degrees of the interior angles of this polygon?

ANSWER: 5040°

BONUS MATH Short Answer Mary travels for 110 miles averaging 55 miles per hour and for 150 miles averaging 50 miles per hour. What is Mary's average speed in miles per hour for the trip?

ANSWER: 52

BONUS MATH Short Answer Giving your answer in inches and in simplest radical form, if the hypotenuse of a 45-45-90º triangle is 10 inches, find the length of the other sides:

ANSWER: 5sqrt(2) ACCEPT: BOTH 5sqrt(2)

BONUS Math - Short Answer What is the tens digit in the sum from n = 6 to 2015 of n factorial?

ANSWER: 6

BONUS14) Math - Short Answer What is the tens digit in the sum from n = 6 to 2015 of n factorial?

ANSWER: 6

MATH Short Answer Given 𝑔(𝑥) = 5 + (𝑥^2)/(sin(𝑥^2)) [g of x equals 5 plus the fraction with numerator x squared and denominator sine of the quantity x squared], find lim 𝑥→0 𝑔(𝑥) [the limit as x approaches zero of g of x].

ANSWER: 6

MATH Short Answer Find a value for a such that the lim(x->∞) (ax⁵-x³+x)/(x-x³+2x⁵)=3[limit as x approaches infinity of the fraction with numerator ax to the fifth minus x cubed plus x and denominator x minus x cubed plus 2 x to the fifth equals 3].

ANSWER: 6

MATH Short Answer What is the radius of the circle with equation x² + 6x + y² - 8y 11= 0?

ANSWER: 6

TOSS-UP3) Math - Short Answer What is the integer part of the log base 3 of 2015?

ANSWER: 6

MATH Short Answer Find 2 mean proportionals between the numbers 3 and 24:

ANSWER: 6 AND 12 (Solution: 3r³ = 24, r = 2)

BONUS MATH Short Answer Assuming y^2 + 3x^(2)y = 7x^2 - 5 implicitly defines y as a function of x, find dy/dx at the point (3, 2).

ANSWER: 6/31

[Bonus] Short Answer: What is the least common denominator of the following 3 fractions: 2/5, 7/6, and 7/12

ANSWER: 60

[BONUS] Short Answer: What is the sum of the first 5 terms of the geometric sequence in which the first term is 2 and the common ratio is 2?

ANSWER: 62 (Solution: 2 + 4 + 8 + 16 + 32 = 62)

MATH Short Answer Expressing your answer in simplest form, if y = (x⁶) ln(x) [y equals x to the sixth power times the natural log of x], what is the derivative of y with respect to x?

ANSWER: 6x⁵ ln(x) + x⁵

MATH Short Answer In a circle with diameter AB, if the radius is 6 centimeters, find the length in centimeters, giving your answer in terms of π, of the arc AB:

ANSWER: 6π (Solution: AB = ½(2πr) = 6π cm)

BONUS17) Math - Short AnswerWhat is the largest prime factor of the quantity 4²⁰¹³ + 4²⁰¹⁴ + 4²⁰¹⁵?

ANSWER: 7

MATH Short Answer If f(x) = 3^x [f of x equals 3 to the power of x], find the value of f(log3 7) [f of log base 3 of 7].

ANSWER: 7

MATH Short Answer What is the degree of the polynomial: (x - 3)³(x - 7)⁴ [open parenthesis x minus 3 close parenthesis cubed times open parenthesis x minus 7 close parenthesis to the power of 4]?

ANSWER: 7

TOSS-UP21) Math - Short AnswerA basketball player makes 6 baskets during a game, each worth 2 or 3 points. How many different possible values exist for the total points scored by the player?

ANSWER: 7

BONUS MATH Short Answer If the area of a regular pentagon is 280 square centimeters, what is the length, in centimeters, of each side if the apothem is 16 centimeters?

ANSWER: 7 (Solution: A = ½ ap; 280 = ½ (16)(p); p = 35/5 = 7 cm)

BONUS MATH Short Answer If the area of a regular pentagon is 280 square centimeters, what is the length, in centimeters, of each side if the apothem is 16 centimeters?

ANSWER: 7 (Solution: A = ½ ap; 280 = ½ (16)(p); p = 35/5 = 7 cm)

BONUS MATH Short Answer Providing your answer in decimal form, what is the limit of 3n+ 4n 5n ∞ n=0 (read as: the summation of n equals 0 to infinity of [pause] open parenthesis 3 to the n plus 4 to the n close parenthesis over 5 to the n)?

ANSWER: 7.5

Math - Short Answer If the radius of a sphere is doubled, by what percent does the volume increase?

ANSWER: 700

TOSS-UP10) Math - Short Answer If the radius of a sphere is doubled, by what percent does the volume increase?

ANSWER: 700

MATH Short Answer In how many different ways can a president, vice president, and secretary be elected in a club of 10 members if no one may hold more than one office?

ANSWER: 720

BONUS MATH Short Answer Giving your answer in millimeters squared, find the lateral surface area of a right pentagonal prism whose altitude is 12 millimeters and base has sides of length 8, 10, 12, 14, and 16 millimeters, respectively:

ANSWER: 720 (Solution: LA = (P)(h) = (8+10+12+14+16)(12) = 720 mm² )

BONUS MATH Short Answer A flagpole casts a 100-foot long shadow. If a 6-foot tall person standing at the base of the pole casts an 8-foot shadow, how many feet tall is the flagpole?

ANSWER: 75 (Solution: (100 × 6)/8 = 75 ft)

[bonus] Short Answer Find the 9th term of the geometric sequence whose first 3 terms are 3, 6, and 12:

ANSWER: 768 (Solution: ax= a(r)^(x-1);a₉ = 3(2)⁸; a=768

MATH Short Answer Convert 420 degrees to radians as an improper fraction in terms of pi.

ANSWER: 7π/3

BONUS 19) MATH Short Answer For Valentine's Day, Adam bought several dozen roses and several dozen carnations. The roses cost $15 per dozen, and the carnations cost $8 per dozen. Adam bought a total of 17 dozen flowers and paid a total of $192. How many dozen roses did he buy?

ANSWER: 8

MATH Short Answer How many subsets are there of a set whose elements are the composite numbers less than 9?

ANSWER: 8

[bonus] Short Answer Multiply the following complex numbers, giving your answer in standard form: (2 + i√ 2 )(3 - i √2 )

ANSWER: 8 + 2√ i (ACCEPT: 8 + i √2 )

BONUS MATH Short Answer A horse is enclosed in a square field of side 100 meters. The horse eats grass along the outside edges of the field, forming a border of uniform width inside the field. If the area of the border is 9/25 of the area of the field, what is the width in meters of the inside edge of the border?

ANSWER: 80

BONUS 13) MATH Short Answer If the average of 5 numbers is 16, what is the sum of the 5 numbers?

ANSWER: 80

MATH Short Answer A population has a mean of 73 and a standard deviation of 8. If the distribution is standardized to create a new distribution with a mean of 100 and a standard deviation of 20, what is the new value of a score of 65 from the original distribution?

ANSWER: 80

Short Answer What is the degree of the following monomial: -6x²y⁴z³

ANSWER: 9

[bonus] Short Answer Find the number of sides in a regular polygon if each interior angle measures 176 degrees:

ANSWER: 90 (Solution: (n - 2)180º = 176n; n = 90)

MATH Short Answer A circle has a diameter of 32 meters. Find the degree measure of the central angle of a sector of the circle if its arc length measures 8π meters:

ANSWER: 90 (Solution: arc/circumference = nº/360º; n = 90º or (8π/2π16)(360º) = 90º)

MATH Short Answer A circle has a diameter of 32 meters. Find the degree measure of the central angle of a sector of the circle if its arc length measures 8π meters:

ANSWER: 90 (Solution: arc/circumference = nº/360º; n = 90º or (8π/2π16)(360º) = 90º)

MATH Short Answer Find the measure in degrees of the largest angle of a triangle with sides of 24 centimeters, 7 centimeters, and 25 centimeters.

ANSWER: 90°

BONUS MATH Short Answer Giving your answers in terms of π and in inches squared, find the total surface area of a closed right circular cone whose altitude is 8 inches and radius is 6 inches:

ANSWER: 96π (Solution: l² = 8² + 6² , l = 10 in; LSA = πrl = π(6)(10) = 60π; SA = LA + B = 60π + π(6)² = 96π in²)

MATH Short Answer Giving your answer in terms of π and in inches, what is the arc-length of a semi-circle whose diameter is 18 inches?

ANSWER: 9π (Solution: C = πd; ½(18π) = 9π)

BONUS MATH Short Answer Give the resulting vector for the cross product of vector <1,0,0> with vector <0,0,1> :

ANSWER: <0,−1,0>

BONUS MATH Short Answer The curve defined by the equation, Ax² + Bx + Cy² + Dy + E =0, can be an ellipse if which of the constants are positive?

ANSWER: A AND C

MATH Short Answer By words or number, name all of the following 3 statements that are TRUE for the function, f(x) = -3x² - 2x - 2 = 0: 1) there are no real zeros 2) the graph is a parabola opening downward 3) the graph has no x-intercepts

ANSWER: ALL

Short Answer: Solve the following inequality for x: |(x + 5)| > -7 (read as: the absolute value of, open parenthesis, x + 5, close parenthesis, is greater than -7)

ANSWER: ALL REAL NUMBERS (ACCEPT: + INFINITY TO -INFINITY)

BONUS MATH Short Answer What are, respectively, the amplitude, period, horizontal shift, and vertical shift of y = -5 + 7cos [π/6 (x + π/12)] (read as: y equals negative 5 plus 7 cosine of open bracket pi over 6 open parenthesis x plus pi over 12 close parenthesis close bracket)?

ANSWER: AMPLITUDE = 7, PERIOD = 12, HORIZONTAL SHIFT = - π/12 (ACCEPT: π/12 LEFT), VERTICAL SHIFT = -5 (ACCEPT: 5 DOWN)

BONUS MATH Short Answer Consider triangle ABC, where the measure of angle A = 20º, B =117º, and C = 43º. Arrange the 3 sides in order of increasing length:

ANSWER: BC; AB; AC (Solution: the longer side is opposite the greater angle)

MATH Short Answer What term BEST describes 2 angles with 90º as the sum of their measurements?

ANSWER: COMPLEMENTARY

MATH Short Answer Find the cotangent and cosecant, respectively, of a 90º angle:

ANSWER: COTAN = 0; COSECANT = 1

TOSS-UP3) Math - Short Answer What is the limit as x approaches zero of the fraction with numerator x + 1 and denominator x?

ANSWER: DOES NOT EXIST (ACCEPT: DNE, NON-EXISTANT; DO NOT ACCEPT: INFINITY, MINUS INFINITY, PLUS or MINUS INFINITY)

BONUS 6) MATH Short Answer Given the equation 9x² + 4y² + 54x - 8y + 49 = 0, what kind of shape is its graph, and what are the coordinates of its center?

ANSWER: ELLIPSE, (-3, 1)

Math - Short Answer The graph of the function f(x) lies in the first quadrant. The function g(x) equals negative 2 times f(x). In what quadrant does the graph of the function f(x) + g(x) lie?

ANSWER: FOURTH (ACCEPT: 4)

MATH Short Answer Identify the type of conic section represented by the equation, x² - 16y² = 64:

ANSWER: HYPERBOLA

MATH Short Answer The graph of the following equation is an example of what conic section: 2𝑥^2 = 2𝑦^2 + 13?

ANSWER: HYPERBOLA

MATH Short Answer If the graph of the function f lies in quadrant IV, then in which quadrant does the graph of the inverse of f lie?

ANSWER: II (ACCEPT: 2 OR SECOND)

BONUS MATH Short Answer The graph of the polar equation, r = 5 - 5 cosine θ, is a cardioid. In which two quadrants is most of the area of this cardioid?

ANSWER: II AND III (ACCEPT: 2 AND 3 or SECOND AND THIRD)

TOSS-UP 14) Math - Short Answer In what quadrants does the graph of the equation y = -2x - 3 lie?

ANSWER: II, III, AND IV (ACCEPT: SECOND, THIRD, AND FOURTH OR ALL BUT FIRST)

MATH Short Answer What is the specific name for a common tangent that intersects the segment joining the centers of 2 circles?

ANSWER: INTERNAL COMMON TANGENT (ACCEPT: INTERNAL or INTERNAL TANGENT)

TOSS-UP17) Math - Short Answer Classify the roots of the equation 2x² - 4x - 3 = 0 as imaginary, rational, or irrational.

ANSWER: IRRATIONAL

MATH Short Answer What are the leading coefficient and degree, respectively, of the following polynomial: 3x² - 6x⁵ + 7

ANSWER: LEADING COEFFICIENT = -6; DEGREE = 5

MATH Short Answer Giving your answer as up, down, left, or right, the graph of the equation x = 5y - 8y² - 1 opens in what direction?

ANSWER: LEFT

Math - Short Answer The Seven Bridges of Konigsberg was a historically notable problem in graph theory and topology that was resolved by what mathematician?

ANSWER: LEONHARD EULER

TOSS-UP17) Math - Short Answer The Seven Bridges of Konigsberg was a historically notable problem in graph theory and topology that was resolved by what mathematician?

ANSWER: LEONHARD EULER

MATH Short Answer Given that g(𝑥) ≤ f (𝑥) ≤ h(𝑥) for all x, the lim𝑥→a 𝑔(𝑥) = M [limit as x approaches a of g of x is M], and the lim𝑥→a ℎ(𝑥) = M [limit as x approaches a of h of x is M], what is the lim𝑥→a 𝑓(𝑥) [limit as x approaches a of f of x]?

ANSWER: M

(General Science) [Bonus] Short Answer: What is the Roman numeral equivalent of the year 1776?

ANSWER: MDCCLXXVI

BONUS 21) MATH Short Answer What are the median, mean and mode of the following set of numbers: 2, 3, 3, 8, 8, 8, 10, 14

ANSWER: MEDIAN = 8.; MEAN = 7; MODE = 8

MATH Short Answer What is the solution to the following system of three equations: equation one: 2x - y + 3z = 8; equation two: x - 6y - z = 0; and equation three: -6x + 3y - 9z = 24?

ANSWER: NO SOLUTION

TOSS-UP 1) Math - Short Answer A scientist is designing an experiment in which she will determine if there is a correlation between drinking tea and contracting cancer. What statistical term is used to describe the assumption that drinking tea does not correlate with contracting cancer?

ANSWER: NULL HYPOTHESIS

BONUS 4) MATH Short Answer How many real solutions does the following equation have: (x² + 1)² + 2(x² + 1) - 3 = 0 [x squared plus 1 quantity squared plus 2 times open parenthesis x squared plus 1 close parenthesis minus 3 equals zero]?

ANSWER: ONE

BONUS23) Math - Short Answer In a 30-60-90 right triangle, the 60 degree angle is bisected. What is the ratio of the lengths of the segments into which the bisector divides the opposite leg?

ANSWER: ONE HALF (Accept: 2, 1:2, 2:1)

BONUS MATH Short Answer Find the radius and the center, respectively, of the circle with the equation: x2 + y2 − 16x + 12y + 75 = 0?

ANSWER: RADIUS = 5; CENTER = (8, -6)

BONUS7) Math - Short Answer In 2004, February 29th was a Sunday. On what day of the week will February 29th be in 2020?

ANSWER: SATURDAY

BONUS MATH Short Answer The terminal side of angle θ (read as: theta) in standard position passes through the point (-5, 12). Find the sine, cosine and tangent, in fractional form:

ANSWER: SIN = 12/13; COS = -5/13; TAN = -12/5

Math - Short Answer What is the minimum distance between the graph of y = x + 1 and the origin?

ANSWER: SQUARE ROOT OF 2 OVER 2

TOSS-UP21) Math - Short Answer What is the minimum distance between the graph of y = x + 1 and the origin?

ANSWER: SQUARE ROOT OF 2 OVER 2

BONUS Math - Short Answer What is the standard deviation of the following list of 4 numbers: 3, 3, 9, 17?

ANSWER: SQUARE ROOT OF 33

TOSS-UP3) Math - Short AnswerWhat adjective describes two angles that sum to 180 degrees?

ANSWER: SUPPLEMENTARY

BONUS 8) COMPUTER SCIENCE Short Answer What is the name for the measure of memory or storage capacity that is equal to 2 to the 40th power bytes or, in decimal, approximately a thousand gigabytes?

ANSWER: TERABYTE

BONUS11 ) Math - Short Answer If July had five Mondays, August must have had five of what day?

ANSWER: THURSDAY

TOSS-UP 7) Math - Multiple Choice Which of the following is NOT equal to a × log base b of c? W) 1/a × log base b of the fraction a/c X) -a × log base b of the fraction 1/c Y) -log base b of open parenthesis c^(-a) close parenthesis Z) Natural log of (e^a) × log base b of c

ANSWER: W) 1/a × log BASE b OF THE FRACTION a/c

MATH Multiple Choice Find the radius of a circle in which a 30° arc is 2𝜋 units long. W) 12 X) 15 Y) 15 𝜋 Z) 60 𝜋

ANSWER: W) 12

BONUS 15) MATH Multiple Choice What is the volume of a cube that has a space diagonal of 3√3? W) 27 X) 27√3 Y) 54 Z) 81

ANSWER: W) 27

MATH Multiple Choice Which of the following is a second quadrant angle in standard position: W) 500º X) -180º Y) -680º Z) 930º

ANSWER: W) 500º

MATH Multiple Choice For f(x) = x² + 2x + 4, which of the following statements is NOT true? W) f(x) has a maximum value X) The graph of f is not a line Y) The graph of f has no x-intercepts Z) The graph of f has a y-intercept

ANSWER: W) f(x) HAS A MAXIMUM VALUE

MATH Multiple Choice Given 𝑓(𝑥) = √(7𝑥^2 − 3) [f of x equals the square root of the quantity 7 x squared minus 3], which of the following are u(x) and g(u) such that f(x) = g(u(x)) [f of x equals g of u of x]? W) u(x) = 7x^2 − 2 and 𝑔(𝑢) = √(𝑢) X) u(x) = √(𝑥) and g(u) = 7u^2 − 3 Y) u(x) = √(7𝑥^2 − 3) [u of x equals the square root of the quantity 7 x squared minus 3] and 𝑔(𝑢) = √(𝑢) Z) u(x) = √(7𝑥 − 3) and g(u) = 𝑢^2

ANSWER: W) u(x) = 7x^2 − 2 and 𝑔(𝑢) = √(𝑢)

MATH Multiple Choice Which of the following is the equation for the tangent line for y = x⁴ at the point (1, 1): W) y = 4x - 3 X) y = 4x - 1 Y) y = 4x + 1 Z) y = 4x + 3

ANSWER: W) y = 4x - 3 (Solution: using the derivative, y' = 4x³ , the slope of the tangent line at x = 1 is 4. The line must pass through (1, 1) so y - 1 = 4(x - 1))

MATH Multiple Choice What is the general solution to the differential equation: dy/dx = 2x + 1 [dy dx equals 2x plus 1]? W) y = x^2 + x + c X) y = ½ x^2 + c Y) y = 2 + c Z) y = 2x + c

ANSWER: W) y = x^2 + x + c

MATH Multiple Choice What is the largest possible real domain of the function h(x) = ln(x^2 - 9) [h of x equals the natural log of the quantity x squared minus 9]? W) (−∞, ∞) X) (−∞, −3) ∪ (3, ∞) Y) (−3, 3) Z) (3, ∞)

ANSWER: X) (−∞, −3) ∪ (3, ∞)

BONUS MATH Multiple Choice A tourist begins a city stroll at an intersection. He walks north one block and then flips a coin. If the coin shows heads, he turns right; if it is tails, he turns left. In all, he walks a total of four blocks, flipping the coin at each corner to decide which way to turn. What is the probability that he ends at the starting point? W) 1/8 X) 1/4 Y) 1/3 Z) 1/2

ANSWER: X) 1/4

BONUS 22) MATH Multiple Choice A jar contains 50 marbles. Exactly 10% are green, 20% are blue, 30% are yellow, and the rest are orange. Which of the following is the probability of randomly picking first a blue marble, replacing it, and then picking an orange marble? W) 1/25 X) 2/25 Y) 3/25 Z) 4/25

ANSWER: X) 2/25

TOSS-UP15) Math - Multiple Choice A continuous function f has domain the closed interval from 1 to 25 and range the closed interval from 3 to 30. If f prime of x is less than 0 for all x in the closed interval from 1 to 25, what is f(25)? W) 1 X) 3 Y) 25 Z) 30

ANSWER: X) 3

MATH Multiple Choice Which of the following is an even function? W) Sine X) Cosine Y) Tangent Z) Cotangent

ANSWER: X) COSINE

MATH Multiple Choice The hyperbola with equation y²/25-x²/36 = 1 possesses which of the following characteristics? W) It opens left and right and has asymptotes y = (5/6)x and y = -(5/6)x X) It opens up and down and has asymptotes y = (5/6)x and y = -(5/6) x Y) It opens left and right and has asymptotes y = (6/5)x and y = -(6/5) x Z) It opens up and down and has asymptotes y = (6/5)x and y = -(6/5)x

ANSWER: X) IT OPENS UP AND DOWN AND HAS ASYMPTOTES y = (5/6)x AND y = -(5/6)x

BONUS7) Math - Multiple Choice Which of the following ratios represents the ratio of the diagonal of a cube to a diagonal of one of the faces of cube? W) 2 to the square root of 3 X) the square root of 3 to the square root of 2 Y) the square root of 3 to 1 Z) the square root of 6 to the square root of 3

ANSWER: X) THE SQUARE ROOT OF 3 TO THE SQUARE ROOT OF 2

BONUS MATH Multiple Choice Which of the following statements is NOT true? W) cos(-x) = cos(x) [cosine of negative x equals cosine of x] X) tan(-x) = tan(x) [tangent of negative x equals tangent of x] Y) The amplitude of y = -2 cos(t) is equal to 2 Z) The range of y = -5 sin(t) is [-5 , 5] [the closed interval from negative 5 to 5]

ANSWER: X) tan(-x) = tan(x)

BONUS MATH Short Answer Find the x and y intercepts of the line passing through the point (4, 8) that is perpendicular to the line 3x - 6y - 12 = 0:

ANSWER: X-INTERCEPT = (8, 0) (ACCEPT: 8); Y-INTERCEPT = (0, 16) (ACCEPT: 16)

Multiple Choice Which of the following are coterminal angles in standard position (read slowly): W) 550º and 185º X) 80° and -190° Y) 1160° and 800° Z) 181° and -118°

ANSWER: Y) 1160° AND 800° (Solution: 80 +3(360º) = 1160º; 80 +2(360º) = 800º

MATH Multiple Choice What is the coefficient of the xy^2 term in the expansion of (x + 2y)^3 [open parenthesis x plus 2y close parenthesis to the power of 3]? W) 3 X) 8 Y) 12 Z) 18

ANSWER: Y) 12

BONUS Math - Multiple Choice A regular decagon is inscribed in a circle with radius 8. Which of the following is the length of one of its sides? W) 8 sine of 36° X) 8 cosine of 36° Y) 16 sine of 18° Z) 16 cosine of 18°

ANSWER: Y) 16 sine of 18°

MATH Multiple Choice If 5 x e = 30, which of the following is the value of x, assuming that the natural log of 2 = 0.7, and the natural log of 15 = 2.7: W) 15 X) 16 Y) 17 Z) 18

ANSWER: Y) 17 (Solution: x/5 = ln 15 + ln 2 = 3.4; x/5 = 3.4; x = 17)

MATH Multiple Choice If e^(x/5) = 30, which of the following is the value of x, assuming that the natural log of 2 = 0.7, and the natural log of 15 = 2.7: W) 15 X) 16 Y) 17 Z) 18

ANSWER: Y) 17 (Solution: x/5 = ln 15 + ln 2 = 3.4; x/5 = 3.4; x = 17)

BONUS18) Math - Multiple Choice How many two digit positive integers have at least one 5 as a digit? W) 16 X) 17 Y) 18 Z) 19

ANSWER: Y) 18

BONUS 5) MATH Multiple Choice Which of the following numbers is divisible by 9: W) 3191 X) 3527 Y) 212,526 Z) 439,327

ANSWER: Y) 212,526 (Solution: sum of the numbers divisible by 9)

BONUS MATH Multiple Choice Which of the following numbers is evenly divisible by both 11 and 3: W) 7791 X) 7553 Y) 5181 Z) 8769

ANSWER: Y) 5181

MATH Multiple Choice What is the principal value in radians for cos^−1(−√(3)/2 ) [inverse cosine of negative square root of 3 over 2]? W) − 𝜋/6 X) − 𝜋/3 Y) 5𝜋/6 Z) 11𝜋/6

ANSWER: Y) 5𝜋/6

MATH Multiple Choice Box A contains 4 chips numbered 1 through 4 and Box B contains 5 chips numbered 1 through 5. A chip is drawn from each box and the product of the two values drawn is denoted by x. What is the probability that x is even? W) 1/2 X) 2/3 Y) 7/10 Z) 3/4

ANSWER: Y) 7/10

MATH Multiple Choice In how many ways can a committee of 7 be seated along one side of a table if the chair of the committee must sit in the middle? W) 49 X) 120 Y) 720 Z) 5040

ANSWER: Y) 720

MATH Multiple Choice Which of the following is NOT true of matrices: W) a square matrix that has an inverse is called invertible X) a matrix does not have to have an inverse Y) a matrix that does not have an inverse is called non-singular Z) a matrix must be square in order to have an inverse

ANSWER: Y) A MATRIX THAT DOES NOT HAVE AN INVERSE IS CALLED NONSINGULAR (Solution: it's called singular)

MATH Multiple Choice Which of the following statements is NOT true about Taylor series? W) Taylor series are defined for infinitely differentiable functions X) All Taylor series are power series Y) All Taylor series are convergent Z) The first n terms of a Taylor series approximate a function with a polynomial

ANSWER: Y) ALL TAYLOR SERIES ARE CONVERGENT

4) MATH Multiple Choice Which of the following is equivalent to sin24ºcos17º + cos24ºsin17º [sine of 24 degrees times cosine of 17 degrees plus cosine of 24 degrees times sine of 17 degrees]? W) Sine of 7º X) Cosine of 41º Y) Sine of 41º Z) Tangent of 41º

ANSWER: Y) SINE OF 41º

MATH Multiple Choice Which of the following is NOT true: W) all central angles in a regular polygon are equal X) irregular polygons are not considered to have centers and have no central angles Y) the circumcircle of a regular polygon is the circle that passes through at least one vertex Z) all regular polygons are convex

ANSWER: Y) THE CIRCUMCIRCLE OF A REGULAR POLYGON IS THE CIRCLE THAT PASSES THROUGH AT LEAST ONE VERTEX

BONUS 10) MATH Multiple Choice If function f is defined by f(x) = (4x² - 12x)/(x² - 9) [f of x equals a fraction with numerator 4 x squared minus 12 x and denominator x squared minus 9], then at x = 3, which of the following is true? W) The graph of f has a vertical asymptote X) The graph of f has a hole on the x axis Y) The graph of f has a hole at (3, 2) Z) f(x) = 0

ANSWER: Y) THE GRAPH OF F HAS A HOLE AT (3, 2)

BONUS18) Math - Multiple Choice Telesha and Chrissy each have a bag that contains one ball of each of the colors blue, green, red, purple, and pink. If Telesha takes one ball at random out of her bag and places it in Chrissy's bag and then Chrissy takes one ball at random out of her bag and places it in Telesha's bag, what is the probability that the two bags have the same contents? W) 1/10 X) 1/6 Y) 1/5 Z) 1/3

ANSWER: Z) 1/3

BONUS 20) MATH Multiple Choice Which of the following is the volume of the solid created by revolving the area bounded by semicircle y=√(16-(x-4)²)[y equals the square root of open bracket 16 minus open parenthesis x minus 4 close parenthesis squared close brackets] and the x-axis around the x-axis? W) 16π X) 64π/3 Y) 64π Z) 256π/3

ANSWER: Z) 256π/3

TOSS-UP 12) Math - Multiple Choice The average value of a continuous function f(x) on a closed interval from 2 to 6 is 8. What is the value of the definite integral from 2 to 6 of f(x) dx? W) 4 X) 8 Y) 24 Z) 32

ANSWER: Z) 32

BONUS2) Math - Multiple Choice A square ABCD has a side length of 10. Point E lies on BC and the area of the triangle ABE is 40. What is the length of BE? W) 5 X) 6 Y) 7 Z) 8

ANSWER: Z) 8

MATH Multiple Choice One-fifth of 0.04% is equal to: W) 8 × 10^(-2) X) 8 × 10^(-3) Y) 8 × 10^(-4) Z) 8 × 10^(-5)

ANSWER: Z) 8 × 10^(-5) (Solution: (0.2)(0.0004) = 0.00008)

TOSS-UP8) Math - Multiple Choice In the expansion of open parenthesis 2x - y close parenthesis to the 5th power, what is the coefficient of the term that contains (x^3)(y^2)? W) -80 X) -8 Y) 8 Z) 80

ANSWER: Z) 80

BONUS6) Math - Multiple Choice Which of the following is never TRUE? W) Absolute value of a plus absolute value of b equals absolute value of open parenthesis a + b close parenthesis X) Absolute value of open parenthesis a + 1000 close parenthesis is less than absolute value of Y) Negative absolute value of a equals absolute value of a Z) Absolute value of open parenthesis a - b close parenthesis is less than absolute value of a minus absolute value of b

ANSWER: Z) ABSOLUTE VALUE OF OPEN PARENTHESIS a - b CLOSE PARENTHESIS IS LESS THAN ABSOLUTE VALUE OF a MINUS ABSOLUTE VALUE OF b

Multiple Choice Which of the following is the contrapositive of the conditional statement: If p, then q? W) If q, then p X) If not p, then q Y) If not p, then not q Z) If not q, then not p

ANSWER: Z) IF NOT Q, THEN NOT P

MATH Multiple Choice Which of the following statements is NOT an advantage of a repeated-measures design compared to an independent-measures design to compare two treatment conditions? W) It requires fewer subjects X) It is better suited to study development that takes place over time Y) It reduces problems caused by individual differences Z) It reduces the confounding effects of other factors

ANSWER: Z) IT REDUCES THE CONFOUNDING EFFECTS OF OTHER FACTORS

MATH Multiple Choice Which of the following is lim(x->0)|x|/x [the limit as x approaches 0 of the absolute value of x over x]? W) -1 X) 0 Y) 1 Z) The limit does not exist

ANSWER: Z) THE LIMIT DOES NOT EXIST

Multiple Choice If a population distribution is illustrated as a symmetrical bell shape curve, then the median and the mean are: W) not the same X) uncertain Y) variable Z) the same

ANSWER: Z) THE SAME

MATH Multiple Choice If the line y = 2 is reflected over the y-axis, what is the equation of the image? W) x = -2 X) y = -2 Y) x= 2 Z) y = 2

ANSWER: Z) y = 2

BONUS15) Math - Short Answer Simplify cosine open parenthesis x+ π/3 close parenthesis + sine open parenthesis x+ π/6 close parenthesis.

ANSWER: cos x

BONUS MATH Short Answer Express the following in terms of a single trigonometric function, given that all fractions are defined: (sec x + csc x)/(1 + tan x) [the fraction with numerator secant of x plus cosecant of x and denominator 1 plus the tangent of x].

ANSWER: csc x (ACCEPT: 1/sin x)

MATH Short Answer Solve for x: ln(x + 1) - 1 = 0 [the natural log of open parenthesis x plus 1 close parenthesis minus 1 equals 0].

ANSWER: e - 1

MATH Short Answer What is the derivative with respect to x of x(e)^2 [x times e squared]?

ANSWER: e^2

BONUS MATH Short Answer Evaluate the following limit: limn→∞ 1+ 3 n n (read as: the limit as n approaches infinity of open parenthesis 1 plus 3 over n close parenthesis to the power of n).

ANSWER: e^3

BONUS MATH Short Answer For a function f(x), suppose that you know that f(-1) = -2 and that f(3) = 2. What would you need to know about f in order to invoke the Intermediate Value Theorem to conclude that there is at least one zero of f on [-1, 3] [the closed interval from negative 1 to 3]?

ANSWER: f IS CONTINUOUS ON [-1, 3] (ACCEPT: F IS CONTINOUS ON THE INTERVAL)

MATH Short Answer Simplify i¹⁷ (read as: i to the 17th power):

ANSWER: i (Solution: i¹⁷ = i¹ = i)

BONUS MATH Short Answer Find the nonzero value of k that will result in exactly one real solution to the equation kx^2 + 7x - 5 = 0.

ANSWER: k = -49/20 (ACCEPT: -2 9/20 OR -2.45)

BONUS18) Math - Short Answer What is the limit as n approaches 0 of the fraction with numerator 2ⁿ - 1and denominator eⁿ - 1?

ANSWER: ln 2

Short Answer Convert log base 4 of 53 into a base 10 expression:

ANSWER: log 53/log 4 Accept: (log₁₀53/ log₁₀4)

BONUS MATH Short Answer Let g(x) = (x − 1)^2 [g of x equal the square of the quantity x minus 1]. What is the set of all real values of x for which g(x) > 4 [g of x is greater than 4]?

ANSWER: x < -1 OR x > 3 (MUST GIVE BOTH ANSWERS)

BONUS MATH Short Answer What are the equations of all asymptotes -- vertical, horizontal, or oblique -- for the graph of the function 𝑓(𝑥) = (𝑥^2 − 3𝑥)/(𝑥 − 1) [f of x equals the fraction with numerator x squared minus 3x and denominator x minus 1]?

ANSWER: x = 1, y = x - 2

[bonus] Short Answer Solve the following inequality for x, giving your answer in fractional form: (1/3)x + (2/3) < (5/6)x -2

ANSWER: x > (16/3) Accept: (x>5(1/3)

BONUS MATH Short Answer Determine the largest possible real domain of y = √(𝑥−1)/√(x^2-1) [y equals the fraction with numerator the square root of the quantity x minus 1 and denominator the square root of the quantity x squared minus 1 ].

ANSWER: x > 1

BONUS MATH Short Answer The polynomial p(x) = x⁴ + 5x³ - 2x² - 24x has a zero at x = 2. Factor p completely. [NOTE: EXPRESSIONS IN ANSWER CAN BE IN ANY ORDER]

ANSWER: x(x - 2)(x + 3)(x + 4)

BONUS Math - Short Answer Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = x - x 4 and y = 0.

ANSWER: π/3

BONUS MATH Short Answer A circle of radius 2 is centered at the point (2, 3). What is the slope of the line tangent to the circle at the point where x = 3 and y is greater than 3?

ANSWER: −√3/3 (DO NOT ACCEPT: −1 √3 )

TOSS-UP3) Math - Short Answer If a 52 foot-long wire is bent to form a square, what is the length of the square's diagonal?

Answer: 13 times the square root of 2

TOSS-UP12) Math - Multiple Choice A right triangle with one angle of 45º is inscribed in a circle of radius 10. What is the area of the triangle? W) 50 X) 50 times the square root of 2 Y) 100 Z) 100 times the square root of 2

Answer: Y) 100

TOSS-UP1) Math - Multiple Choice Consider the graph of the function 4x² - 4y² = 0. Which of the following shapes most resembles the graph of this function? W) Circle X) Hyperbola Y) Pair of intersecting straight lines Z) Ellipse

Answer: Y) PAIR OF INTERSECTING STRAIGHT LINES

Multiple Choice Which of the following has a graph that is a parabola that opens downward: W) f(x) = 3x + 1 X) f(x) = x² - 2 Y) f(x) = -x² Z) f(x) = x³

Answer: Y) f(x) = -x²

MATH Short Answer: What are the leading coefficient and degree, respectively, of the following polynomial: 3x² - 6x⁵ + 7

LEADING COEFFICIENT = -6; DEGREE = 5

Short Answer A triangular prism has a base that is an equilateral triangle with sides of length x. If the height of the prism is x, express the volume of the prism in terms of x.

V=( x^3 3)/4

BONUS MATH Short Answer: Find the x and y intercepts of the line passing through the point (4, 8) that is perpendicular to the line 3x - 6y - 12 = 0:

X-INTERCEPT = (8, 0) (ACCEPT: 8); Y-INTERCEPT = (0, 16) (ACCEPT: 16)

MATH Multiple Choice Which of the following represents the inverse function of f(x) = x³ + 5: W) (x - 5)³ X) x³ - 5 Y) (x − 5)¹/³ Z) (1/(x-5)³

Y) (x − 5)¹/³

MATH Multiple Choice: Which of the following is NOT a Pythagorean triple: W) 15, 20, 25 X) 10, 24, 26 Y) 16, 24, 30 Z) 33, 44, 55

Y) 16, 24, 30

MATH Multiple Choice If e×/⁵ = 30, which of the following is the value of x, assuming that the natural log of 2 = 0.7, and the natural log of 15 = 2.7: W) 15 X) 16 Y) 17 Z) 18

Y) 17

Four students and two moderators sit at a circular table. How many distinct arrangements are there of these 6 people if the two moderators must sit opposite each other? W) 4 X) 6 Y) 24 Z) 48

Y) 24

MATH Multiple Choice: Which of the following is NOT true of matrices: W) a square matrix that has an inverse is called invertible X) a matrix does not have to have an inverse Y) a matrix that does not have an inverse is called non-singular Z) a matrix must be square in order to have an inverse

Y) A MATRIX THAT DOES NOT HAVE AN INVERSE IS CALLED NONSINGULAR

Multiple Choice Which of the following decreases when 5 is subtracted from each item of a data set? W) Standard deviation X) Range Y) Mean Z) Variance

Y) MEAN

When working with three coordinate axes, what rule determines the orientation of the z-axis in relation to the x-and y-axes? W) Left-hand rule X) Octant rule Y) Right-hand rule Z) Three-space rule

Y) RIGHT-HAND RULE

MATH Multiple Choice Which of the following is NOT true: W) all central angles in a regular polygon are equal X) irregular polygons are not considered to have centers and have no central angles Y) the circumcircle of a regular polygon is the circle that passes through at least one vertex Z) all regular polygons are convex

Y) THE CIRCUMCIRCLE OF A REGULAR POLYGON IS THE CIRCLE THAT PASSES THROUGH AT LEAST ONE VERTEX

MATH Multiple Choice Which of the following is TRUE about any two successive terms in the Fibonacci sequence: W) their product is a Fibonacci number X) they are either both odd or both even Y) they are relatively prime Z) their quotient is the golden ratio

Y) THEY ARE RELATIVELY PRIME

Bonus: What are the linear factors of the polynomial 2ab+ 3a-8b-12?

a-4 AND 2b+ 3

MATH Short Answer Simplify i¹⁷ (read as: i to the 17th power):

i

BONUS MATH Short Answer Find an antiderivative for 𝑦 = xe^-x

ANSWER: -(x + 1) e^-x (ACCEPT: -xe^-x - e^-x , OR EITHER ANSWER +/- ANY CONSTANT)

Math - Short Answer In 2004, February 29th was a Sunday. On what day of the week will February 29th be in 2020?

ANSWER: SATURDAY

BONUS Math - Short Answer Convert 291 in base 10 to base 6.

ANSWER: 1203

TOSS-UP 13) MATH Short Answer In order, what are the prime numbers between 30 and 50?

ANSWER: 31, 37, 41, 43, 47

Bonus: What is the derivative evaluated at x= 7 of the fraction with numerator (x^3)-1 and denominator x-1?

15

DO NOT answer until you are...

verbally recognized

MATH Short Answer What is the sum of the smallest prime number and the smallest composite number?

ANSWER: 6

Math - Short Answer What is the integer part of the log base 3 of 2015?

ANSWER: 6

BONUS MATH Short Answer If y varies directly as x, and y = 42 when x = 30, find y if x = 45:

ANSWER: 63

BONUS 6) MATH Short Answer Evaluate [the integral from the square root of 2 to the 3 times the square root of 2 of the quantity 3 x squared plus 6 dx] in simplest radical form.

ANSWER: 64√2

Short Answer Remove all negative exponents and simplify the following expression for all non-zero values of x: (-32x⁵)^(-2/5)

ANSWER: (1/4x²)

MATH Short Answer What is the scalar product of the vectors 2i - 3j + 2k and i + 2j + 2k?

ANSWER: 0

TOSS-UP MATH Short Answer What is the remainder of (148 + 10) / 7 ?

ANSWER: 4

BONUS MATH Short Answer Given: x^2 + y^2 = 34 in the first quadrant and dx/dt = 5, find dy/dt when x = 3.

ANSWER: -3

BONUS 20) MATH Short Answer What is the remainder when 2x³-x²+3x-4 is divided by x+3?

ANSWER: -76

BONUS MATH Short Answer A curve is defined parametrically by x = cos t [x equals cosine of t] and y = tan t [y equals tangent of t]. What is dy/dx when t = π/6?

ANSWER: -8/3

TOSS-UP2) Math - Short Answer Evaluate the following expression: -i^25

ANSWER: -i

MATH Short Answer What is the limit of x^x as x approaches 0?

ANSWER: 1

TOSS-UP6) Math - Short Answer Express the repeating decimal 0.131313, with repeating part 13, as a fraction written in lowest terms.

ANSWER: 13/99

BONUS 16) MATH Short Answer Solve 3x - 2ix = 5 for x in standard a+bi form.

ANSWER: 15/13 + 10i/13

TOSS-UP 3) Math - Short Answer How many faces does a regular icosahedron have?

ANSWER: 20

MATH Short Answer What is the smaller of two integers whose sum is 19 and whose product is 48?

ANSWER: 3 (Solution: 16 + 3 = 19; 16 × 3 = 48)

Short Answer Given that tangent θ = -(3/4) , find the possible values of sine θ:

ANSWER: 3/5 AND -3/5

BONUS MATH Short Answer Expressing the answer in simplest form, solve |2r-13/4|<5/2[the absolute value of the quantity 2r minus 13 fourths is less than 5 halves].

ANSWER: 3/8 < r <2 (7/8) (ACCEPT: 3/8 < r < 23/8)

BONUS MATH Short Answer Evaluate the following expression when a = 3 1 , b = 4, c = -1, and d = -5: 2[3a - (b + c) - 4d]

ANSWER: 36

BONUS MATH Short Answer: Consider triangle ABC, where the measure of angle A = 20º, B =117º, and C = 43º. Arrange the 3 sides in order of increasing length:

BC; AB; AC

Short Answer A circle has a radius of 8 centimeters. Find the central angle, in degrees, of a sector of a circle if its arc length is 2π centimeters:

ANSWER: 45 (Solution: arc/circumference = n/360; n = 45º)

Bonus: Which of the following points lies in the solution set for the following system of two inequalities in two unknowns: 3y-x≥ -9 and 3y-2x< -9? W) (3, 1) X) (4, -4) Y) (8, -2) Z) (8, 2)

Z) (8, 2)

BONUS12) Math - Short Answer Evaluate the following definite integral: the integral from x = -3 to 0 of the square root of open parenthesis 9 - x² close parenthesis dx.

ANSWER: (9π)/4 (ACCEPT: 2.25π)

MATH Short Answer Simplify the following expression: x^(1/2)*x^(2/5)

ANSWER: x^(9/10)

BONUS MATH Short Answer Find tan(arccos (2x)) [the tangent of the arc-cosine of 2x] in terms of x.

ANSWER: √(1 − 4𝑥^2)/(2x)

If f(x)=7x+19 for what values of x is f(x) [f of x] greater than 33? W) x is greater than 2 X) x is less than 2 Y) x is between 2 and -2 Z) All real numbers

W) X IS GREATER THAN 2

If ݂݂ f(x)=7x+19 [f of x equals seven x plus nineteen], for what values of x is f(x) [f of x] greater than 33? W) x is greater than 2 X) x is less than 2 Y) x is between 2 and -2 Z) All real numbers

W) X IS GREATER THAN 2

Bonus: What is the probability that the bottom card in a deck of cards is a queen and the top card is a king?W) 1/169X) 4/663Y) 5/663 Z) 1/2702

X) 4/663

Matrices with which of the following pairs of dimensions cannot be multiplied together? W) 3 rows, 2 columns times 2 rows, 3 columns X) 6 rows, 5 columns times 6 rows, 5 columns Y) 1 row, 2 columns times 2 rows, 2 columns Z) 1,000 rows, 2,000 columns times 2,000 rows, 4,000 columns

X) 6 ROWS, 5 COLUMNS TIMES 6 ROWS, 5 COLUMNS

Bonus: Give the Cartesian coordinates of the point described by the cylindrical coordinates (r, theta, h) = (8, π/3, 24).

(4, 4√3, 24)

BONUS MATH Short Answer: A flagpole casts a 100-foot long shadow. If a 6-foot tall person standing at the base of the pole casts an 8-foot shadow, how many feet tall is the flagpole?

75

[bonus] Short Answer If $1000 is placed in a savings account that pays 6% annual interest compounded semiannually, what is the total amount of money in the account at the end of 1 year, to the nearest dollar?

ANSWER: $1061.00 (Solution: A = P[1 + (r/n)]ⁿt; = $1,000[1 + (0.06/2)](²x¹) = $1060.90)

BONUS MATH Short Answer What are the coordinates of the vertex in the graph of the following equation: y = 4x² + 8x - 5

ANSWER: (-1, -9) (Solution: x = -b/2a = -8/2(4) = -1; y = 4(-1)² +8(-1) - 5 = -9)

MATH Short Answer Simplify the following without the use of negative exponents: (-24x³y⁵)/(10y⁶z²)

ANSWER: (-12x³)/(5yz²)

BONUS MATH Short Answer The midpoint of segment AB is (1.5, -3). The coordinates of point A are (7, -5); what are the coordinates of point B?

ANSWER: (-4, -1)

BONUS 10) MATH Short Answer If f(x) = -2x - e^x [f of x equals negative 2x minus e to the x], what is the range of f' [the derivative of f]?

ANSWER: (-∞, -2) (ACCEPT: x < -2 or THE OPEN INTERVAL FROM NEGATIVE INFINITY TO -2)

BONUS MATH Short Answer Giving your answer in simplest radical form, rationalize the denominator of the following expression: (-3√2)/(√3-√5)

ANSWER: (3√6+3√10)/2 (ACCEPT: (3/2)(√6+√10)

TOSS-UP6) Math - Short Answer For a normal distribution with mean of 94 and standard deviation of 4, for a score of 88, what is the corresponding Z-score?

ANSWER: -1.5 (ACCEPT -3/2 or -1½)

BONUS MATH Short Answer Suppose that g is the inverse function of f, f(-1) = 2 (read as: f of negative 1 equals 2), and f'(-1) = -2 (read as: f prime of negative 1 equals negative 2). Find g'(2) (read as: g prime of 2).

ANSWER: -1/2

BONUS Math - Short Answer If air leaves a spherical balloon at a rate of 1 cubic centimeter per second, at what rate in centimeters per second is the radius changing when the radius is 1/2 centimeter?

ANSWER: -1/pi (ACCEPT: DECREASING BY 1/pi; DO NOT ACCEPT: 1/pi)

BONUS 14) MATH Short Answer Find the remainder when f(x) = x⁶ + 5x⁵ - x³ + x - 6 is divided by (x + 1).

ANSWER: -10

BONUS 19) MATH Short Answer Providing your answers as improper fractions in lowest terms, solve -7+|3-2x|=15[negative 7 plus the absolute value of the quantity 3 minus 2x equals 15] for x.

ANSWER: -19/2 AND 25/2

BONUS20) Math - Short Answer Let f(x) = x^2 + e^x and g(x) = 1/(x^2). Determine g prime of f prime of zero.

ANSWER: -2

BONUS MATH Short Answer Giving your answer as a fraction reduced to lowest terms, solve the following equation for x: 2x/3 - 1/4 = 10x/6 + 1/2

ANSWER: -3/4

MATH Short Answer In terms of a, b, c, and d, what is the slope of the line 3 ax + 2by = cd?

ANSWER: -3a/2b

MATH Short Answer If the graph of the complex number z = 3 + 4i is rotated 90° counterclockwise, what complex number is represented by the result?

ANSWER: -4 + 3i

BONUS MATH Short Answer For the implicit function xy^2 + x^3y = 2, what is the slope of its tangent line at the point (1, 1)?

ANSWER: -4/3

BONUS 5) MATH Short Answer Solve for x: 2^(x+1) = 4^(x+3)[2 raised to the quantity x+1 equals 4 raised to the quantity x+3].

ANSWER: -5

BONUS Math - Short Answer Express the fraction with numerator 3 - 2i and denominator 1 + 4i in standard a + bi form.

ANSWER: -5/17 - (14/17)i

BONUS MATH Short Answer If -4x - 9y - 3z = -10 and -5a - 9b = -6, then what is -9b - 15z - 45y - 20x - 5a?

ANSWER: -56

BONUS MATH Short Answer Let f(x) be a function with antiderivative g(x) satisfying g(1) = 2 and g(3) = 4. Calculate 2f x dx - 5f x dx 3 1 3 1 (read as: the integral from 1 to 3 of 2 f of x dx minus the integral from 1 to 3 of 5 f of x dx).

ANSWER: -6

BONUS2) Math - Short Answer Given the three vectors, a = 2i + j, b = -i + 3j + 4k, and c = -2j + k, find a dot open parenthesis 2b + 4c close parenthesis.

ANSWER: -6

BONUS 10) MATH Short Answer Express (1+2i)/(4-5i) [the quantity 1 plus 2 i divided by the quantity 4 minus 5 i] in standard a + bi form.

ANSWER: -6/41 + (13/41)i [DO NOT ACCEPT: (-6 +13i)/41]

BONUS MATH Short Answer What is the slope of a line perpendicular to the line given by the graph of the equation, -5x = -6y + 4

ANSWER: -6/5

BONUS MATH Short Answer Find (1 + i) 12 (read as the quantity 1 plus i to the twelfth).

ANSWER: -64

BONUS Math - Short Answer What is the cross product of the vectors i + j + k and j?

ANSWER: -i + k (ACCEPT: -1i + 0j + 1k, -1i + 1k )

BONUS MATH Short Answer The probability that a doctor is correct when making a diagnosis is 0.8. If the doctor makes an incorrect diagnosis, the probability that a patient sues is 0.3. What is the probability that the doctor makes an incorrect diagnosis and the patient sues?

ANSWER: 0.06 (ACCEPT: 3/50 or 6%)

MATH Short Answer Solve the following equation for x over the real numbers: 27(3^x ) = 81 [27 times 3 to the power of x equals 81].

ANSWER: 1

TOSS-UP14) Math - Short AnswerThe inverse of the function f(x) = x⁴ + x³ + x² + x + 1 is not itself a function, but how many distinct zeroes does the inverse have?

ANSWER: 1

BONUS MATH Short Answer Solve the following base-10 logarithmic equation for x: log(x^2 + 3x) + log(5x) = 1 + log(2x) [log base 10 of open parenthesis x squared plus 3x close parenthesis plus log base 10 of 5x equals 1 plus log base 10 of 2x].

ANSWER: 1 (DO NOT ACCEPT: -4)

BONUS MATH Short Answer Find the product of complex numbers (1 - i) × (2 - i) [open parenthesis 1 minus i close parenthesis times the quantity 2 minus i].

ANSWER: 1 - 3i

BONUS14) Math - Short Answer Identify all of the following three numbers that are evenly divisible by eight: 1) 1,256,424; 2) 1,216; 3) 662,322.

ANSWER: 1, 2

[bonus] Short Answer Find the product of the following, giving your answer without negative exponents: (x⁻² +y)(x²-y⁻²)

ANSWER: 1-(1/(x²y²))+x²y-(1/y) (Note: the terms can be given in any order)

Short Answer: Simplify the following, giving your answer in proper scientific notation: (2.0 × 10-6 ) 4

ANSWER: 1.6 × 10-23

MATH Short Answer Given 𝑔(𝑥) = (1−cos(𝑥))/(𝑥^2) [g of x equals the fraction with numerator 1 minus cosine of x and denominator x squared], find lim𝑥→0 𝑔(𝑥) [the limit as x approaches 0 of g of x].

ANSWER: 1/2

Short Answer: What is the 5th term in the geometric progression whose first three terms are: 64, 16, 4

ANSWER: 1/4 (ACCEPT: 0.25)

TOSS UP #4) What is the 5th term in the geometric progression whose first three terms are: 64, 16, 4?

ANSWER: 1/4 (ACCEPT: 0.25)

BONUS 10) MATH Short Answer A fair standard six-sided die is rolled two times. What is the probability that the sum of the numbers on the two rolls will be greater than 9?+

ANSWER: 1/6

TOSS-UP14) Math - Short Answer If you roll 2 six-sided dice, what is the probability that the product of the two numbers is prime?

ANSWER: 1/6

BONUS MATH Short Answer Find the slope of the line tangent to the parametric curve at the given point: x = et , and y = lnt (read as: y equals the natural log of t) at t = 1.

ANSWER: 1/e

MATH Short Answer If a person walks 4 miles due north, 6 miles due east, then 4 miles due north, how far in miles is the person displaced from his or her original position?

ANSWER: 10

Short Answer If you roll 2 fair dice simultaneously, what is the probability, given as a fraction, that you will roll the number 6 on AT LEAST one die?

ANSWER: 11/36

BONUS 1) MATH Short Answer A national achievement test is administered. The test has a mean score of 100 and a standard deviation of 15. If Vince's z-score is 1.20, what is his score on the test?

ANSWER: 118

BONUS23) Math - Short Answer What is the greatest common divisor of 132 and 6432?

ANSWER: 12

BONUS MATH Short Answer Factor the following expression completely: 12x² + 24x - 36

ANSWER: 12(x + 3)(x - 1) (ACCEPT: 12(x - 1)(x + 3))

BONUS 14) MATH Short Answer Providing your answer as an improper fraction in lowest terms, solve the following equation for x over the real numbers: 9^2x=27^(3x-4)[9 to the power of 2x equals 27 to the power of the quantity 3x minus 4].

ANSWER: 12/5

TOSS-UP2) Math - Short Answer In a triple-elimination tournament with 512 contestants, what is the maximum numbers of games played if there are no ties?

ANSWER: 1535

[Bonus] Short Answer: Reduce the following radical expression to its simplest radical form: ((225)^(1/3))^(1/2) (read as: the square root of the cube root of 225)

ANSWER: 15^(1/3)

TOSS-UP20) Math - Short Answer You have some number of marbles of several different sizes and colors. For any set of 5 marbles, at least two of them will be the same size and at least two of them will be the same color. What is the maximum possible number of size-color combinations?

ANSWER: 16

[bonus] Short Answer Giving your answer in standard form, what is the fourth term in the binomial expansion of the following: (4x + y)⁴

ANSWER: 16xy³ (ACCEPT: 16y³x)

BONUS 11) MATH Short Answer A square has a side of 8 millimeters. Providing your answer in terms of π and in square millimeters, what is the difference between the areas of its circumscribed circle and its inscribed circle?

ANSWER: 16π

BONUS 22) MATH Short Answer The volume of an open-ended circular cylinder is 32π cubic centimeters, and its base has a radius of 4 meters. What is the surface area of the cylinder, in terms of π and in square meters?

ANSWER: 16π

BONUS MATH Short Answer Let a = 0.845454545... be an infinite repeating decimal with the digits 4 and 5 repeating. If a is written as a fraction in lowest terms, by how much does the denominator exceed the numerator?

ANSWER: 17

BONUS MATH Short Answer Considering the function f x = 3x2- 4x + 1, what is the average rate of change from x = 2 to x = 5?

ANSWER: 17

BONUS 16) COMPUTER SCIENCE Short Answer The decimal number 15 is equivalent to what octal number?

ANSWER: 17

BONUS MATH Short Answer Find the sum of all interior angles, in degrees, in a regular polygon having 100 sides:

ANSWER: 17,640 (Solution: (100 - 2)(180) = 17,640º)

BONUS16) Math - Short Answer If A is an acute angle and sin A times cos A = 60/169, find the numerical value of sin A + cos A.

ANSWER: 17/13

BONUS16) Math - Short Answer In a collection of red, blue, and green marbles, there are 25% more red marbles than blue marbles, and there are 60% more green marbles than red marbles. Suppose that there are 50 red marbles. What is the total number of marbles in the collection?

ANSWER: 170

BONUS MATH Short Answer Convert the angle, 18º18'36" (read as: 18 degrees, 18 minutes, 36 seconds) to degrees, to the second decimal place:

ANSWER: 18.31 (Solution: 18 + 18/60 + 36/3600 = 18.31)

BONUS 13) MATH Short Answer If g(b) = 6b³ - 4b² + b + 4b ⁻¹ [g of b equals 6 b cubed minus 4 b squared plus b plus 4 b to the negative 1], what is g'(b) [g prime of b]?

ANSWER: 18b² - 8b + 1 - 4b⁻² (ACCEPT: 18b² - 8b + 1 - 4/b²)

BONUS- Short Answer The average of -40, 36, 5, 0, 10 and x is 5. What is the value of x?

ANSWER: 19

Short Answer Solve the following equation for x: x² - 20x + 19 = 0

ANSWER: 19 AND 1

MATH Short Answer The IQ of a Martian varies directly with the square of the number of tentacles it has. If a Martian with 5 tentacles has an IQ of 75, what is the IQ of a Martian having 8 tentacles?

ANSWER: 192

BONUS20) Math - Short Answer Determine all values in the closed interval from zero to 2 times the square root of 3 that are prescribed by Rolle's [Rolls] Theorem for f(x) = x³ - 12x.

ANSWER: 2

BONUS8) Math - Short Answer If all A are B and some C are A, identify all of the following three conclusions that necessarily follow: 1) All A are C; 2) Some B are C; 3) Some A are not C.

ANSWER: 2

MATH Short Answer Find the sum of the two solutions for the quadratic equation: 2x^2 - 4x + 8 = 0.

ANSWER: 2

Short Answer: Boolean algebra involves ideas or subjects that have how many possible states?

ANSWER: 2

MATH Short Answer How many terms does the binomial expansion of (x² + 2y³)²⁰ [open parenthesis x squared plus 2 y cubed close parenthesis to the power of 20] contain?

ANSWER: 21

MATH Short Answer If each side of a rectangle is increased by 10%, by what percentage is its area increased?

ANSWER: 21 (ACCEPT: 21%)

BONUS MATH Short Answer Multiply the following complex numbers, giving your answer in standard a + bi form: (6 + 3i)(4 + i)

ANSWER: 21 + 18i

BONUS MATH Short Answer A triangle has two sides with lengths of 4 feet and 5 feet, and a 60- degree included angle. What is the length, in feet and in simplest form, of the third side of the triangle?

ANSWER: 21^(1/2)

MATH Short Answer A cube painted red on all sides has an edge length of 4 inches. If the cube is then cut into 64 cubes of edge length 1 inch, how many of the 1 inch cubes have exactly one face painted red?

ANSWER: 24

MATH Short Answer What is the area of a rhombus with diagonals of lengths 6 and 8?

ANSWER: 24

BONUS21) Math - Short Answer How many positive integral factors exist for 1800?

ANSWER: 36

BONUS MATH Short Answer Giving your answer in meters squared, find the total surface area of a right prism whose base is a right triangle with legs of length 3 meters and 4 meters and whose altitude is 2 meters:

ANSWER: 36 (Solution: 3:4:5; P(base) = 3+4+5 = 12m; A = ½bh = 6 m² ; TA = LA + 2B = (12)(2) + 2(6) = 36 m² )

Short Answer Expand the following expression, giving your answer in standard binomial form: (6x+3y)²

ANSWER: 36x² + 36xy + 9y²

BONUS MATH Short Answer The sides of a right triangle have lengths m, m + n, and m + 2n. If n is positive, what is the ratio of m to n?

ANSWER: 3:1 (ACCEPT: 3)

BONUS MATH Short Answer Solve the following equation for x: -2|3 + (x/2)| = -10 (read as: negative 2 times the absolute value of 3 plus, open parenthesis, x divided by 2, close parenthesis, close absolute value, equals negative 10)

ANSWER: 4 AND -16

BONUS MATH Short Answer Solve the following equation for x: 2⁷ * 2^(x²-2) = 2²¹

ANSWER: 4 OR -4 (ACCEPT: X = ±4) (Solution: 7 + x² = 21; x = 4 and -4)

BONUS Math - Short Answer What is the sum of the first 6 terms in the geometric sequence with first term 3 and second term 12?

ANSWER: 4095

[bonus] Short Answer Giving your answer in centimeters to the nearest whole number, what is the perimeter of a closed quarter-circle whose radius is 12 centimeters?

ANSWER: 43 (Solution: curve of circle = ¼ πd = 6π = 18.84; sides = 12 + 12 = 24; 24 + 18.84 = 42.8cm)

TOSS-UP6) Math - Short Answer How many sides does a regular polygon have if each interior angle equals 172 degrees?

ANSWER: 45

MATH Multiple Choice The line with equation y = −3x - 5 contains points in each quadrant EXCEPT which of the following? W) I X) II Y) III Z) IV

ANSWER: W) I

BONUS 11) MATH Multiple Choice Which of the following functions has an oblique asymptote? W) f(x) = (x⁵ + 1)/(x⁴ + 3x² + 2) [f of x equals open parenthesis x to the fifth plus 1 close parenthesis over open parenthesis x to the fourth plus 3 x squared plus 2 close parenthesis] X) f(x) = (x² + 1)/(x³ - x² - 1) [f of x equals open parenthesis x squared plus 1 close parenthesis over open parenthesis x cubed minus x squared minus 1 close parenthesis] Y) f(x) = (4x² + x + 1)/x² [f of x equals open parenthesis 4 x squared plus x plus 1 close parenthesis over x squared] Z) f(x) = x⁵/(x² - 1) [f of x equals x to the fifth over open parenthesis x squared minus 1 close parenthesis]

ANSWER: W) f(x) = (x⁵ + 1)/(x⁴ + 3x² + 2)

MATH Multiple Choice If the derivative of f(x) is positive on the closed interval [a, b], then which of the following statements is TRUE? W) f(x) is increasing on [a, b] X) f(x) has critical points at a and b Y) f(x) is constant on [a, b] Z) f(x) cannot have an inflection point on [a, b]

ANSWER: W) f(x) IS INCREASING ON [a, b]

[bonus] Multiple Choice Which of the following is closest to the radius of a sphere, in meters, given that its volume is 400 cubic meters: W) 2.15 X) 4.57 Y) 6.28 Z) 9.76

ANSWER: X) 4.57 (Solution: V = 4/3πr³; 400 = 4/3(3.14)(r)³ ; r = (95.5)^(1/3)= 4.57)

MATH Multiple Choice In the graph of the function f(x) = (3/2)sin (x/2 ) [f of x equals three halves the sine of the quantity x over 2], at which of the following x coordinates would f(x) = 0? W) π/2 X) π Y) 2π Z) 3π/2

ANSWER: Y) 2π

Math - Multiple Choice Consider a restaurant menu with nine meals. A table at the restaurant has n diners, all of whom order different meals. For which of the following values of n could the table add a diner without changing the number of combinations of meals the table can order? W) 1 X) 2 Y) 4 Z) 8

ANSWER: Y) 4

TOSS-UP10) Math - Multiple Choice Set q contains all irrational numbers r such that 0 < r < 1. Which of the following is true about q? W) It is an empty set X) It has a countably infinite number of elements Y) It has an uncountably infinite number of elements Z) It has a nonzero finite number of elements

ANSWER: Y) IT HAS AN UNCOUNTABLY INFINITE NUMBER OF ELEMENTS

MATH Multiple Choice Which of the following is NOT true about the function y = |x| (read as: y equals the absolute value of x)? W) It is symmetric around the y-axis X) The derivative of the function does not exist at x = 0 Y) It is monotonic Z) The integral of the function over the real line is unbounded

ANSWER: Y) IT IS MONOTONIC

BONUS Math - Multiple Choice If x + y = 1 and x minus y equals the product of the square root of 2 and the sine of theta, what is x times y? W) Cosine of 2 theta X) Sine of 2 theta Y) One-fourth the cosine of 2 theta Z) One-fourth the sine of 2 theta

ANSWER: Y) ONE-FOURTH THE COSINE OF 2 THETA

BONUS1) Math - Multiple Choice If x + y = 1 and x minus y equals the product of the square root of 2 and the sine of theta, what is xtimes y? W) Cosine of 2 theta X) Sine of 2 theta Y) One-fourth the cosine of 2 theta Z) One-fourth the sine of 2 theta

ANSWER: Y) ONE-FOURTH THE COSINE OF 2 THETA

TOSS-UP12) Math - Multiple Choice Divide a unit segment into 3 congruent segments and remove the middle segment. Do this process a second time on each of the remaining two segments. If this process is carried out a total of n times, what is the sum of the lengths of the remaining segments? W) One-third to the nth power X) One minus one-third to the nth power Y) Two-thirds to the nth power Z) One minus two-thirds to the nth power

ANSWER: Y) TWO-THIRDS TO THE nth POWER

TOSS-UP10) Math - Multiple Choice If star is a binary operation on a subset of the real numbers, for which of the following definitions is star commutative? W) a star b = a - b X) a star b = a/b Y) a star b = the fraction with numerator a + b and denominator a times b Z) a star b = a^2 - b^2

ANSWER: Y) a star b = THE FRACTION WITH NUMERATOR a + b AND DENOMINATOR a TIMES b

BONUS MATH Multiple Choice A point has rectangular coordinates (3, 3). What are its equivalent polar coordinates? W) (3, 𝜋/6) X) (3, 𝜋/4) Y) (3√2, 𝜋/6) Z) (3√2, 𝜋/4)

ANSWER: Z) (3√2, 𝜋/4)

MATH Multiple Choice The lines y = (a - 5)x + 5 [ y equals open parentheses a minus 5 close parentheses x plus 5] and y = -2x + 7 are perpendicular if a equals which of the following? W) -2/9 X) 9/2 Y) 5 Z) 11/2

ANSWER: Z) 11/2

MATH Multiple Choice The equation -mx + 1 = 13 - 4(x + 3) [negative m x plus 1 equals 13 minus 4 times the quantity x plus 3] is an identity if m equals which of the following? W) -4 X) -1 Y) 1 Z) 4

ANSWER: Z) 4

MATH Multiple Choice The graph of r = 3 secant (θ) (read as: r = 3 secant theta) is a: W) parabola X) circle Y) hyperbola Z) line

ANSWER: Z) LINE

MATH Multiple Choice Which of the following is NOT a property of the normal p.d.f.? W) The p.d.f. is symmetric X) The p.d.f. has two inflection points Y) The variance has to be positive Z) The domain of the p.d.f. is non-negative real numbers

ANSWER: Z) THE DOMAIN OF THE P.D.F. IS NON-NEGATIVE REAL NUMBERS

MATH Multiple Choice Given that a second degree polynomial function f(x) has a zero at x = 3 with multiplicity 2, which of the following is true? W) The graph of f(x) crosses the y-axis at 3 X) As x approaches infinity, f(x) approaches infinity Y) The graph of f(x) crosses the x-axis at 3 Z) The graph of f(x) touches but does not cross the x-axis at 3

ANSWER: Z) THE GRAPH OF f(x) TOUCHES BUT DOES NOT CROSS THE x-AXIS AT 3

BONUS20) Math - Short Answer Evaluate the limit as x approaches 1 of x raised to the fraction with numerator 1and denominator x - 1.

ANSWER: e

BONUS 7) MATH Short Answer What is the largest possible real domain of f(x) = ln(3x - 1) [f of x equals the natural log of the quantity 3x minus 1]?

ANSWER: x > 1/3 (ACCEPT: THE OPEN INTERVAL FROM 1/3 TO (POSITIVE) INFINITY)

[bonus] Short Answer Solve the following quadratic inequality for x: x² + 5x + 4 ≥ 0

ANSWER: x ≥ -1 OR x ≤ -4 (must give both answers)

BONUS MATH Short Answer An open box is to be made from a rectangular piece of material 8 inches by 6 inches by cutting equal squares of side x from the four corners and turning up the sides. In terms of x, give an expression for the volume of the box in cubic inches.

ANSWER: x(8- 2x)(6- 2x) (ACCEPT: 4x^3 - 28x^2 + 48x)

MATH Short Answer If f(x) = x^2 - 1 and g(x) = x - 1, what is the composite function f(g(x)) [f of g of x]?

ANSWER: x^2 - 2x

MATH Short Answer What is the derivative of the integral of x4 with respect to x?

ANSWER: x^4 )

[bonus] Short Answer Divide and simplify the following 2 polynomials, combining like terms:(x³-8)/(x-2)

ANSWER: x² + 2x + 4

BONUS MATH Short Answer Given f(x) = x² + 2x + 3, express ƒ(x + 1) in standard polynomial form:

ANSWER: x² + 4x + 6

MATH Short Answer Giving your answer in standard form, give the equation of the circle with center at (0, 0) and diameter of 6:

ANSWER: x² + y²= 9

BONUS MATH Short Answer In terms of x and in standard polynomial form, what is the volume of a right rectangular prism with dimensions (x + 4), (x + 1), and (x + 6)?

ANSWER: x³ + 11x² + 34x + 24

BONUS 23) MATH Short Answer Providing your answer in slope intercept form, what is the equation of the normal line to the function f(x) = x^3 + 2x^2 + 5x - 2 at the point where x = 0?

ANSWER: y = (-1/5)x - 2

[Bonus] Short Answer What is the slope-intercept equation of the line that passes through the point (4, -1) and is parallel to the line with equation 2x - 3y = 9?

ANSWER: y = (2/3)x-(11/3)

MATH Short Answer What is the slope-intercept form of the equation of the line that is tangent to the circle with equation x^2 + y^2 = 25 at the point (-3, 4)?

ANSWER: y = (¾)x + 25/4

BONUS MATH Short Answer What is the equation, in slope-intercept form, of the perpendicular bisector of the line segment with endpoints (4, 10) and (-6, 8)?

ANSWER: y = -5x + 4

Math - Short Answer If y varies jointly with x and z, and y = 12 when x = 4 and z = 5, find y when x = 20 and z = 4.

ANSWER: y = 48

TOSS-UP8) Math - Short Answer What is the equation of the plane, parallel to one of the coordinate planes, that passes through the two points (4,7,-2) and (3,7,12)?

ANSWER: y = 7

BONUS MATH Short Answer Providing your answer in slope intercept form, what is the equation of the line tangent to the graph of 𝑦 = (𝑒^(2𝑥))/(𝑥^2) [y equals the fraction with numerator e to the power of 2x and denominator x squared] where x = 1?

ANSWER: y = e2 (ACCEPT: y = 0x + e2)

BONUS MATH Short Answer Find an equation of the graph that results from reflecting the graph of y = √x over the y-axis, and then shifting the graph 3 units to the left.

ANSWER: y=√(-(x+3)) (ACCEPT: y = √(-x-3))

MATH Short Answer Giving your answer in standard form, what is the last term in the binomial expansion of the following: (x + y)^6

ANSWER: y^6

MATH Short Answer Of the following 5 functions identify all that are NOT differentiable for all real numbers: |x| (read as: absolute value of x); cosine(x); tangent(x); e x ; the greatest integer function

ANSWER: |x|; TAN(x); THE GREATEST INTEGER FUNCTION

[bonus] Short Answer Solve the following equation for x, expressing your answer in simplest radical form over the real numbers: x⁴-9x²+8=0

ANSWER: ± 2 √2 AND ±1 (ACCEPT ALL: + 2√2 , − 2√2 , +1, -1)

BONUS MATH Short Answer Arrange the following 4 radicals in order of increasing value: ⁶√12; ⁶√63; ³√2; ⁴√8

ANSWER: ³√2; ⁶√12; ⁴√8; ⁶√63

MATH Short Answer Providing your answer as a fraction in lowest terms, if a family has exactly four children, what is the probability of having three girls and one boy?

ANSWER: ¼

TOSS-UP1) Math - Short Answer If the radius of a right circular cylinder is doubled, by what factor must the height be multiplied in order to keep the volume the same?

ANSWER: ¼

MATH Short Answer If a family has four children, what is the probability of having exactly 3 girls?

ANSWER: ¼ (ACCEPT: 0.25 OR 25%)

BONUS1) Math - Short Answer Find an antiderivative with respect to x for the fraction with numerator e²ⁿ and denominator 1 + e⁴ⁿ.

ANSWER: ½ arctan e²ⁿ (ACCEPT: ½ arctan e²ⁿ + C for any constant C)

MATH Short Answer Simplify the following rational expression: (5y-3x²)/(9y²+5x)

CANNOT BE FURTHER SIMPLIFIED (ACCEPT: (5y-3x²)/(9y²+5x) or THE SAME)

Bonus: Identify the center and radius of the sphere with equation 36 = open parenthesis x-2 close parenthesis squared+ open parenthesisy -7 close parenthesis squared+ open parenthesisz + 1 close parenthesis squared.

CENTER (2, 7, -1); RADIUS 6

MATH Short Answer Identify the type of conic section represented by the equation, x² - 16y² = 64:

HYPERBOLA

MATH Short Answer Giving your answer as up, down, left, or right, the graph of the equation x = 5y - 8y² - 1 opens in what direction?

LEFT

Short Answer Which two mathematicians are generally credited with the invention of calculus?

LEIBNIZ AND NEWTON

BONUS MATH Short Answer: The terminal side of angle θ (read as: theta) in standard position passes through the point (-5, 12). Find the sine, cosine and tangent, in fractional form:

SIN = 12/13 ; COS = -5/13 ; TAN = -12/5

Bonus: The terminal side of an angle in standard position passes through the point (8, -15). Find the sine and tangent, respectively, of the angle.

SINE = -15/17, TANGENT = -15/8 (ACCEPT: -1 7/8)

MATH Short Answer: What is the name for the test that can be used to visually determine whether or not a relation defined by a graph represents a function?

VERTICAL LINE TEST (ACCEPT: VERTICAL LINE)

MATH Multiple Choice A data set has a mean of 10 and variance of 10. If every set element is multiplied by 2, which of the following is TRUE of the new mean and variance: W) mean is 20, variance is 40 X) mean is 20, variance is 10 Y) mean is 20, variance is 20 Z) mean is 10, variance is 20

W) MEAN IS 20, VARIANCE IS 40

Bonus: If f(x) = the square root of open parenthesis x+ 3 close parenthesis and g(x) = the square root of open parenthesis x-3 close parenthesis, what is the domain of the function f(x) divided by g(x)? W) x > 3 X) x ≥ 3 Y) x ≥ -3 Z) -3 < x < 3

W) x > 3

MATH Multiple Choice Which of the following is the equation for the tangent line for y = x⁴ at the point (1, 1): W) y = 4x - 3 X) y = 4x - 1 Y) y = 4x + 1 Z) y = 4x + 3

W) y = 4x - 3

MATH Multiple Choice At x = -1/2 , the graph of y = x³ is: W) increasing and concave up X) increasing and concave down Y) decreasing and concave up Z) decreasing and concave down

X) INCREASING AND CONCAVE DOWN

What is the fourth term in the series given by the sum from n = 0 to infinity of the fraction with numerator 1 and denominator 2 to the nth power?

1/8

Short Answer Providing your answer as an improper fraction in simplest form in terms of π, what is the volume of the solid generated when the area bounded by y = x3 , x = 2, and the x axis is revolved around the x-axis?

128/7 π

The average of -40, 36, 5, 0, 10 and x is 5. What is the value of x?

19

Math - Short Answer Simplify i raised to the 22nd power.

ANSWER: -1

MATH Short Answer Solve for x: 14 − √(3 − 𝑥) = 9 [14 minus the square root of the quantity 3 minus x equals 9].

ANSWER: -22

TOSS-UP 21) MATH Short Answer Convert 5π /3 radians into degrees:

ANSWER: 300°

Short Answer: Evaluate the expression, x(y + z) 2 , when x = 2, y = -8; and z = 3:

ANSWER: 50

MATH Multiple Choice What is [the derivative with respect to x of the integral from 4 to x of t squared dt]? W) x^2 X) (1/3)x^3 Y) (64/3)x Z) 16x^2

ANSWER: W) x2

MATH Multiple Choice Which of the following is NOT a Pythagorean triple: W) 15, 20, 25 X) 10, 24, 26 Y) 16, 24, 30 Z) 33, 44, 55

ANSWER: Y) 16, 24, 30

Bonus: What mathematical rule can be appliedto give information about the number of positive or negative real roots of a polynomial based on the number of sign changes in the polynomial's coefficients?

DESCARTES' RULE OF SIGNS

Bonus: Which of the following points does the line 2x-3y = -12 NOT pass through? W) (-2, 8/3) X) (1, -14/3) Y)(3, 6) Z) (7, 26/3)

X) (1, -14/3)

BONUS MATH Multiple Choice: The equation x² + y² = 121 with x > 0 and y < 0 would result in the graph of: W) A semicircle below the x-axis X) A quarter circle in the 2nd quadrant Y) A quarter circle in the 4th quadrant Z) A complete circle with a radius of 11

Y) A QUARTER CIRCLE IN THE 4TH QUADRANT

Which of the following is true regarding the graph of y= -x3 at x= -2? W) increasing and concave up X) increasing and concave down Y) decreasing and concave up Z) decreasing and concave down

Y) DECREASING AND CONCAVE UP

Multiple Choice Suppose, in a certain part of the world, in any 50-year period, the probability of a major plague is 39%, the probability of a major famine is 52%, and the probability of both a plague and a famine is 15%. Given that there is a plague, which of the following is the probability of a famine? W) 0.240 X) 0.288 Y) 0.370 Z) 0.385

Z) 0.385

MATH Multiple Choice: One-fifth of 0.04% is equal to: W) 8 × 10⁻² X) 8 × 10⁻³ Y) 8 × 10⁻⁴ Z) 8 × 10⁻⁵

Z) 8 × 10⁻⁵

BONUS Short Answer Given f(x) = x² + 2x + 3, express f(x + 1) in standard polynomial form:

x² + 4x + 6

What are the prime factors of 105?

3, 5, and 7

BONUS MATH Short Answer: It takes 20 minutes for Janis to prepare lunch. When Kristen helps, it only takes 12 minutes. How many minutes would it take Kristen to prepare the same lunch if she worked alone?

30

Bonus: Maggie bakes 48 cookies and sells half of them that morning for $2.50 each. In the afternoon, she sells two-thirds of what she has left at half price. In the late afternoon, she sells the remaining cookies at a dollar each. If each cookie costs 75 cents for her to make, what was her profit, in dollars, for the day?

52

MATH Short Answer In a circle with diameter AB, if the radius is 6 centimeters, find the length in centimeters, giving your answer in terms of π, of the arc AB:

6π

MATH Short Answer In degrees, what is the smallest angle x > 0 such that sin(x) + cos(2x) = 1?

30°

Short Answer: Solve the following inequality for x: x 2 < 3x

ANSWER: 0 < x < 3

BONUS MATH Short Answer Let n be the number of faces of a regular polyhedron. What is the sum of all possible values of n?

ANSWER: 50

MATH Short Answer What is the angle formed, in degrees, between the hour and minute hand of an analog clock at 10:30 AM?

135

TOSS-UP7) Math - Short Answer How many different sequences of 26 coin tosses result in at least 25 'heads'?

ANSWER: 27

BONUS MATH Short Answer What is the area of a square inscribed in a circle of radius k?

ANSWER: 2k^2

BONUS MATH Short Answer Simplify: (x^(1/2))(x^(1/2) + x^(1/2)) [x to the power of one half times open parenthesis x to the power of one half plus x to the power of one half close parenthesis].

ANSWER: 2x

BONUS Math - Short Answer What is the distance between the two points with polar coordinates of r = 4 and theta = 60 degrees, and r = 6 and theta = 0 degrees?

ANSWER: 2√7

MATH Short Answer If f(x) = 2 - x [f of x equals 2 minus x], find f(f '(x)) [f of f prime of x].

ANSWER: 3

BONUS MATH Short Answer What is the inner product of the vectors -4i +3j +5k and 3i - 6j +7k?

ANSWER: 5

MATH Short Answer If a family has 5 children, what is the probability that there are 4 girls and 1 boy?

ANSWER: 5/32

MATH Short Answer What is the next number in the arithmetic sequence that has first three terms of 17, 31, and 45?

ANSWER: 59

BONUS3) Math - Short Answer Two integers between 1 and 10, inclusive, are selected at random, noting that the two numbers may be the same. What is the probability that both numbers selected are prime, and their product is odd?

ANSWER: 9/100 (ACCEPT: 0.09 OR 9%)

BONUS 10) MATH Short Answer Name all of the quadrants that contain solutions of the inequality 2x - y > 4 .

ANSWER: I, III, IV (ACCEPT: 1, 3, 4 or FIRST, THIRD, FOURTH)

BONUS MATH Multiple Choice Which of the following points is on the graph of the inverse of the function f(x) = 10x + 2 [f of x equals 10 to the power of the quantity x plus 2]? W) (100, 0) X) (0, 100) Y) (10, 0) Z) (0, 10)

ANSWER: W) (100, 0)

BONUS MATH Short Answer Give the median for the following data set: 1, 2, 7, 7, 8, 9, 10, 11.

7.5

BONUS MATH Multiple Choice The line determined by points (0, 2b) and (2a, 0) intersects the line determined by points (0, b) and (a, b). What represents the x-value of the point where the two lines intersect? W) a X) 2a Y) a + b Z) b/a

ANSWER: W) a

[BONUS] Short Answer: Find the positive geometric mean between the numbers 1 and 10,000:

ANSWER: 100 (Solution: n^th = a(r)^n-1 ; 10,000 = 1r^(3-1) = 100; 100 × 100 = 10,000)

MATH Short Answer W is one of the vertices of a polygon. If there are 8 diagonals of the polygon that contain W, how many sides does the polygon have?

ANSWER: 11

BONUS12) Math - Short Answer If x/2 = y^2 and x/4 = 4y, what is the largest possible value of x?

ANSWER: 128

[BONUS] Giving your answer in centimeters to the first decimal place, if one leg of an isosceles right triangle is 100 centimeters long, how long is the hypotenuse?

ANSWER: 141.4

TOSS-UP17) Math - Short Answer If the difference between two prime numbers is 11, what is their sum?

ANSWER: 15

MATH Multiple Choice The graph of the relation y = -√(25-x²) is a: W) circle X) semi-circle Y) parabola Z) straight line

X) SEMI-CIRCLE

Each day, Adam eats 20% of the cookies left in a jar. At the end of the 2nd day, there are 32 cookies left in the jar. How many cookies were in the jar originally? W) 40 X) 48 Y) 50 Z) 60

Y) 50

BONUS MATH Multiple Choice: Which of the following numbers is evenly divisible by both 11 and 3: W) 7791 X) 7553 Y) 5181 Z) 8769

Y) 5181

MATH Multiple Choice: What is the product of the following 2 values: (1) the greatest common divisor of 7 and 14; and (2) the least common multiple of 7 and 14: W) 21 X) 49 Y) 98 Z) 196

Y) 98

MATH Short Answer Add the following rational expressions and give your answer in fully factored form: x/(x+2)+4x/(x-6)

x(5x+2)/(x-6)(x+2) (ACCEPT: x(5x+2)/(x+2)(x-6)

Bonus: Solve the following equation for y: 3y minus open parenthesis 2 minus 2y close parenthesis plus5 = 15 minus y.

2

BONUS MATH Short Answer: Find the area, in centimeters squared and in simplest radical form, of a regular or equilateral triangle whose circumcircle has a radius of 8 centimeters:

48√3

Evaluate the following expression: log base 3 of 27 + log base 5 of 25.

5

MATH Short Answer Find the center of the circle given by the following equation: x² + y² + 4x + 16y + 3 = 0

ANSWER: (-2, -8)

Short Answer: Evaluate the following radical expression: 5 (3)^(1/2) − (75)^(1/2)

ANSWER: 0

MATH Short Answer What is the value of i⁴ ?

ANSWER: 1

MATH Short Answer What are the solutions to x² - 5x + 6 = 0?

ANSWER: 2 AND 3

BONUS Math - Short Answer Find the derivative with respect to x of the product of the two binomials 4x³ - 12 and 8x⁴ + 7.

ANSWER: 224x⁶ - 384x³ + 84x²

BONUS MATH Short Answer Solve the following equation for all real values of x: (x²/8)-(x/4)-1=0

ANSWER: 4 OR -2

MATH Short Answer How many distinct diagonals does a pentagon have?

ANSWER: 5

[BONUS] Short Answer: How many different letter arrangements are possible with the six letters in the word 'SECOND'?

ANSWER: 720 (Solution: 6! = 720)

MATH Multiple Choice A data set has a mean of 10 and variance of 10. If every set element is multiplied by 2, which of the following is TRUE of the new mean and variance: W) mean is 20, variance is 40 X) mean is 20, variance is 10 Y) mean is 20, variance is 20 Z) mean is 10, variance is 20

ANSWER: W) MEAN IS 20, VARIANCE IS 40

15) GENERAL SCIENCE Multiple Choice One knot is approximately equal to how many kilometers per hour? W) 0.6 X) 1.9 Y) 1.65 Z) 1.0

ANSWER: X) 1.9

BONUS MATH Multiple Choice Given the two sequences s1 with nth term 2/(𝑛+6) and s2 with nth term 𝑛/(5+𝑛) , which of the following statements is correct? W) s1 and s2 are both increasing X) s1 is increasing and s2 is decreasing Y) s1 is decreasing and s2 is increasing Z) s1 and s2 are both decreasing

ANSWER: Y) s1 IS DECREASING AND s2 IS INCREASING

MATH Multiple Choice Which of the following is NOT an even function? W) cosx X) cos(x²) Y) sinx Z) sin(x²)

ANSWER: Y) sinx

MATH Multiple Choice For all real numbers, the expression [the square root of the quantity x squared minus 4 x plus 4] equals which of the following? W) x - 2 X) x - 2x + 2 Y) |x - 2| [the absolute value of the quantity x minus 2] Z) x + 2

ANSWER: Y) |x - 2|

MATH Multiple Choice A hypersphere is described by a set of points such that w^2 + x^2 + y^2 + z^2 = 36. Which of the following statements is NOT true? W) (1, 2, 3, 1) lies inside the hypersphere X) (1, 5, 5, 1) lies outside the hypersphere Y) (3, 3, 3, 3) lies on the hypersphere Z) (1, 2, 5, 1) lies outside the hypersphere

ANSWER: Z) (1, 2, 5, 1) LIES OUTSIDE THE HYPERSPHERE

BONUS MATH Multiple Choice The series with n th term (-1^n)/n [negative 1 to the nth power, divided by n] is which of the following? W) Divergent and unbounded X) Divergent and bounded from above only Y) Divergent and bounded Z) Convergent and bounded

ANSWER: Z) CONVERGENT AND BOUNDED

TOSS-UP 16) COMPUTER SCIENCE Multiple Choice The file extension .MID (read as: dot, M, I, D) usually means that the file can be opened by what type of program: W) text editor X) graphics Y) database Z) music

ANSWER: Z) MUSIC

Multiple Choice Which of the following is NOT a regular polyhedron: W) regular tetrahedron X) cube Y) regular icosahedron Z) regular hexadecagon

ANSWER: Z) REGULAR HEXADECAGON

BONUS MATH Short Answer Given 𝑓(𝑥) = √(2 − 𝑥) [f of x equals the square root of the quantity 2 minus x], for what value or values of x does f(x+2) = 1 [f of the quantity x plus 2 equals 1]?

ANSWER: x = -1

BONUS MATH Short Answer Given that x and y are real numbers, solve for x and y: 2y + ix = 4 + x - i.

ANSWER: x = -1; y = 3/2

BONUS 12) MATH Short Answer Expressing your answer in simplest form, find the derivative with respect to x of y =(x³-8)/(x-2) [the fraction with numerator x cubed minus 8 and denominator x minus 2] for all values for which y is defined.

ANSWER: y' = 2x + 2 (ACCEPT: 2x + 2)

BONUS17) Math - Short Answer Determine the limit as x approaches negative π of the fraction with numerator cos of the fraction x/2 and denominator π plus x.

ANSWER: ½

TOSS-UP23) Math - Short Answer Evaluate the following definite integral: the integral from 0 to π/2 of sinx cosx dx.

ANSWER: ½ (ACCEPT: 0.5)

BONUS7) Math - Short Answer If x is measured in radians, find all values of x between zero and 2π that satisfy the equation sin²x = 2 cos⁴x.

ANSWER: π/4, 3π/4, 5π/4, 7π/4

If n is an integer, and x^n is positive for all nonzero real numbers x, which of the following must be true about n? W) n is greater than zero X) n does not equal zero Y) n is even Z) n is odd

Y) n IS EVEN

MATH Multiple Choice Which of the following relations does NOT represent a function? W) {(2, 3), (-4, 3), (7, 3)} X) {(0, 0), (-1, -1), (2, 2)} Y) {(2, 3), (-5, 3), (2, 7)} Z) {(-1, 3), (-5, 3), (-9, 0)}

Y) {(2, 3), (-5, 3), (2, 7)}

BONUS MATH Short Answer Arrange the following 4 radicals in order of increasing value: ⁶√12; ⁶√63; ³√2; ⁴√8

³√2; ⁶√12; ⁴√8; ⁶√63

Short Answer What is magnitude of the phase shift of the function y = sinx to y = 2sin(3x - π) - 4 (read as: 2 sine of open parenthesis 3x minus pi close parenthesis minus 4)?

π/3

Short Answer Factor the following expression: 49x² - 169y⁴

ANSWER: (7x+13y²)(7x-13y²)

MATH Short Answer Solve the following equation for x over the integers: x² = 3x

0; 3

Short Answer If f(x) = x^2 - 3 and g(x) = 6 − x, what is the value of f(g(16)) (read as: f of g of 16)?

1

How many points of intersection do the graphs of the functions f(x)= -x^2 and g(x) = 2 raised to the x power have?

0(ACCEPT: NONE)

BONUS MATH Short Answer What are the coordinates of the vertex in the graph of the following equation: y = 4x² + 8x - 5

(-1, -9)

MATH Short Answer Find the center of the circle given by the following equation: x² + y² + 4x + 16y + 3 = 0

(-2, -8)

Bonus: What are the coordinates of the vertex of the graph of y= -2x^2 - 8x + 7?

(-2,15)

MATH Short Answer What are the coordinates of the hole in the graph of the function, g(x) =(2x²-8)/(x-2)?

(2,8)

One endpoint of a diameter of a sphere centered at (4, 2, -9) is (5, -6, 2). What are the coordinates of the other endpoint of that diameter?

(3, 10, -20)

BONUS MATH Short Answer Factor the following expression completely over the integers: x⁴ - 16

(x - 2)(x + 2)(x² + 4)

BONUS MATH Short Answer Simplify the following rational expression by combining like terms, assuming x is not equal to 4: (x²-16)/(4x-x²)

-(x+4/x) (ACCEPT: (x+4/-x) or (-(x+4)/x) or (-x-4/x)

MATH Short Answer For the function f(x) = 1/x, what is f '(5)(read as: f prime of 5)?

-1/25

MATH Short Answer: What is the determinant of a 2-by-2 square matrix whose rows are 4, 2 and -3, -4?

-10

MATH Short Answer: Simplify the following without the use of negative exponents: -24x³y⁵/10y⁶z²

-12x³/5yz²

What is the discriminant of the quadratic function y = (x^2)-4x+ 10?

-24

What is the slope of the line with equation 5x+ 3y = 8?

-5/3 (ACCEPT: -1 2/3)

BONUS MATH Short Answer: What is the slope of a line perpendicular to the line given by the graph of the equation, -5x = -6y + 4

-6/5

Bonus: What number must be ADDED to both the numerator and denominator of 3/4 to get 4/3?

-7

Bonus: Perform the following complex number subtraction: -4 -25i subtracted from -11 -7i.

-7 + 18i

Bonus: Solve the following equation for x: negative 8 plus the absolute value of open parenthesis 4 minus 3x close parenthesis equals 20.

-8, 32/3 (ACCEPT: 10 2/3 for 32/3)

BONUS MATH Short Answer: Given the function y = 4x - x², what are the two values of x for which the corresponding value for y is 0?

0 & 4

Short Answer What is the multiplicative identity of the complex numbers in standard a + bi form?

1 + 0i (ACCEPT: 1)

BONUS MATH Short Answer Solve the following equation for all real values of x: (x + 3)² = 16

1 AND -7

MATH Short Answer In the algebra of real-valued functions, give the name or number of all of the following 3 choices that the implied domain usually excludes: 1) numbers causing division by zero 2) numbers causing imaginary numbers in the range 3) numbers causing irrational numbers in the range

1 AND 2

BONUS MATH Short Answer: Multiply the following complex numbers, giving your answer in standard a + bi form: (6 + 3i)(4 + i)

21 + 18i

Short Answer An isosceles triangle has a base of 30 feet and height of 15 feet. In feet, how far apart are the legs 10 feet above the base?

10

Short Answer If the median of the five numbers 1, 7, 14, 28, and x is 10, what is x?

10

What is the value of 60 factorial divided by open parenthesis 59 factorial times 3 factorial close parenthesis?

10

Short Answer To what value does the geometric series that starts 1/3 + 1/9 + 1/27 + ... converge?

1/2

MATH Short Answer: As a fraction in lowest terms, what is the probability of rolling 1 or 3 on a standard 6-sided die?

1/3

What are the critical numbers for the function y = 3t^3 - t?

1/3, -1/3 (ACCEPT: ±1/3)

What is the limit as x approaches 3 of the function with numerator x -3 and denominator (x^2)-9?

1/6

MATH Short Answer What is the circumference of the circle with equation (x + 3)2 + (y − 5)2 = 25 ?

10π

MATH Short Answer Express 600º in radians as a reduced fraction in terms of π:

10π/3

MATH Short Answer Find the inverse of the 2-by-2 matrix whose rows are 3, 5 and 7, -2. Give your answer in rows.

2/41, 5/41, 7/41, -3/41

BONUS MATH Short Answer: What is the degree measure of the angle formed by 2 secants intersecting outside a circle if the measures of the intercepted arcs are 80º and 34º?

23

Bonus: The three sides of a triangle have lengths4 centimeters, 6 centimeters, and 7 centimeters. What is the cosine of the smallest angle?

23/28

BONUS MATH Short Answer: Find the area, in square centimeters, of a rhombus with a diagonal of 6 centimeters and a side of 5 centimeters:

24

[BONUS] Short Answer How many distinct signals can be made using four flags of different colors on a vertical flagpole?

24

What is the perimeter of a right triangle whose leg lengths are 6 and 8 and whose hypotenuse is 10?

24 (Solution: perimeter = 6+8+10=24)

BONUS MATH Short Answer: Factor the following expression completely: 100x² - 25y²

25(2x + y)(2x - y)

MATH Short Answer Solve the following equation for all real values of x: 1/8x²-1/4x-1=0

4 OR -2

BONUS MATH Short Answer Divide the following and give your answer in scientific notation: (8*10^7)/[(4*10^4)^(1/2)]

4*10^5

The ratio of the measures of the three angles in a triangle is 2:3:4. What are the degree measures of the three angles?

40, 60, 80

Bonus: The perimeters of two squares differ by 16 inches and their areas differ by 96 square inches. What is the perimeter, in inches, of the larger square?

56

MATH Short Answer: Find 2 mean proportionals between the numbers 3 and 24:

6 AND 12

Bonus: What is the sum from n= 1 to 4 of 2n²?

60

If the radius of a sphere is doubled, by what percent does the volume increase?

700 % (DO NOT ACCEPT: 800%)

Bonus: What is the least common multiple of the first four composite numbers?

72

What is the integral from -6 to 6 of 6 dx?

72

How many exterior angles does a parallelogram have?

8

What is the degree of the polynomial x²+ 3x⁸+ 7x?

8

Bonus: Two circles with radii of 3 inches and 1 inch have the same center. What is the ratio of the area of the annulus between the inner circle and the outer circle to the area of the inner circle?

8 (ACCEPT: 8 TO 1)

MATH Short Answer How many solutions are there for the equation, cosine 4x = 1/2 , for the interval 0 ≤ x < 2π?

8 (Solution: 4 cycles, 2 solutions per cycle)

What is binary one-zero-zero-one in decimal form?

9

BONUS MATH Short Answer The curve defined by the equation, Ax² + Bx + Cy² + Dy + E =0, can be an ellipse if which of the constants are positive?

A AND C

MATH Short Answer By words or number, name all of the following 3 statements that are TRUE for the function, f(x) = -3x² - 2x - 2 = 0: 1) there are no real zeros 2) the graph is a parabola opening downward 3) the graph has no x-intercepts

ALL

Short Answer For which real values of x does the following the series converge: xn n! ∞ n=0 (read as the summation from n equals 0 to infinity of [pause] x to the power of n over n factorial)?

ALL REAL NUMBERS

MATH Short Answer If the graph of y = (x - 2)² - 3 [y equals open parenthesis x minus 2 close parenthesis squared minus three] is translated 5 units up and 2 units to the right, what is the vertex of the new parabola obtained?

ANSWER: (4, 2)

MATH Multiple Choice What is the value of (i)^21? W) -i X) i Y) -1 Z) 1

ANSWER: X) i

TOSS-UP9) Math - Multiple Choice What type of conic section is represented by the following equation: 0 = (x^2) + 2x - (y^2) + 6y - 14? W) ellipse X) circle Y) hyperbola Z) parabola

Answer: Y) HYPERBOLA

Math Multiple Choice Consider the graph of the function 4x^2 - 4y^2 = 0. Which of the following shapes most resembles the graph of this function? W) Circle X) Hyperbola Y) Pair of intersecting straight lines Z) Ellipse

Answer: Y) PAIR OF INTERSECTING STRAIGHT LINES

TOSS-UP6) Math - Short AnswerWhat is the 10th term of the arithmetic sequence with first 3 terms -8, 8, 24?

Answer: 136

TOSS-UP7) Math - Short Answer Identify all of the following four operations that are NOT closed over the set of all positive real numbers: 1) addition; 2) subtraction; 3) multiplication; 4) division.

Answer: 2

TOSS-UP16) Math - Short Answer Determine all of the prime factors of 111

Answer: 3 and 37

TOSS-UP16) Math - Short Answer If x is a positive number such that 6 is the geometric mean between x + 3 and x - 3, what is the value of x?

Answer: 3 times the square root of 5

TOSS-UP23) Math - Short Answer If tangent theta = ¾, what is cosecant theta?

Answer: 5/3

BONUS2) Math - Short Answer A wire, 36 centimeters long, is bent into the shape of a regular hexagon. What is the area of the hexagon in square centimeters?

Answer: 54 times the square root of 3

TOSS-UP 3) Math - Short Answer Where is the derivative of the function f(x) = 2x^2 + 5x - 3 equal to zero?

Answer: AT x = -5/4 (ALSO ACCEPT x = -1.25 OR -1¼)

What are the radius and the coordinates of the center, respectively, of the circle with equation x²+ 8x+y²-6y = 0?

RADIUS 5; CENTER (-4, 3)

MATH Short Answer: If the distribution graph of a set of data has a positive skew, then which tail of the graph is longer?

RIGHT

MATH Short Answer Given the equation 2x - y + 5 = 0, find the slope and y-intercept of the line it represents.

SLOPE = 2; Y-INTERCEPT = 5 OR (0, 5)

If the radius of a right circular cylinder is tripled, by what factor must the height be multiplied in order to keep the volume the same?

1/9

Short Answer What is the exponent of 5 in the prime factorization of 325?

2

There are 8 siblings in a family, and when ranked from youngest to oldest, all differ from the next oldest in age by the same number of years. If the youngest is 8 and the oldest is 29, what is the common difference in their ages?

3

Short Answer What is the measure in radians of an interior angle of a regular pentagon?

3π/5

BONUS MATH Short Answer What are the coordinates of the points of intersection of the graphs of y = 2x^2 - x and y = 2x + 35?

ANSWER: (-7/2, 28) AND (5, 45) (ACCEPT: (-3.5, 28) AND (5, 45))

MATH Short Answer A graph has symmetry with respect to the origin and passes through the point (-2, 3). What other point must be on this graph?

ANSWER: (2, -3)

MATH Short Answer What are the coordinates of the point where the graph of x^(2)y + 3x - 4y - 24 = 0 [x squared y plus 3 x minus 4 y minus 24 equals zero] crosses the x-axis?

ANSWER: (8, 0) (DO NOT ACCEPT: 8 ALONE, X = 8)

MATH Multiple Choice What is the derivative of y = (3x + 1)^2 [y equals 3x plus 1 quantity squared]? W) 18x + 6 X) 18x Y) 6x + 1 Z) 6x + 2

ANSWER: W) 18x + 6

Math - Short Answer If you roll 2 six-sided dice, what is the probability that the product of the two numbers is prime?

ANSWER: 1/6

BONUS MATH Short Answer Given (2^x )(3^y )(5^z ) = 2700 [2 to the power of x times 3 to the power of y times 5 to the power of z equals 2700], find the product xyz.

ANSWER: 12

BONUS 21) MATH Short Answer A different universe has nine spatial dimensions. If an object travels four meters in all nine dimensions, then what is the object's displacement in meters in this universe?

ANSWER: 12

BONUS MATH Short Answer What is the period of the function f(x) = sin((π/6) x + π/4) [f of x equals the sine of the quantity pi over 6 times x plus pi over 4]?

ANSWER: 12

MATH Short Answer Giving your answer in centimeters, what is the length of a side of a square whose diagonal measures 12(sqrt2) centimeters?

ANSWER: 12

TOSS-UP23) Math - Short Answer Assemblies coming from a plant are inspected for defects. Historical records indicate that 8% have defects in shafts, 6% have defects in bushings, and 2% have defects in both shafts and bushings. One of the assemblies is selected at random. What is the probability, in percentage form, that the assembly has a shaft or bushing defect?

ANSWER: 12

MATH Short Answer If the shortest leg of a 30-60-90 right triangle is 6 inches, what is the measure, in inches, of the other 2 sides?

ANSWER: 12 AND 6sqrt3

BONUS MATH Short Answer What are the coordinates of the vertex of the graph of y = 2x² + 8x - 3?

ANSWER: (-2, -11)

BONUS MATH Short Answer What is the largest possible real domain for the function 𝑓(𝑥) = (4𝑥^2)/√(4 − 𝑥^2) [f of x equals the fraction with numerator 4 x squared and denominator the square root of the quantity 4 minus x squared]?

ANSWER: (-2, 2) (ACCEPT: -2 < x < 2)

MATH Short Answer Evaluate: [the integral from 0 to 4 of 4 dx].

ANSWER: 16

BONUS MATH Short Answer Find the prime factorization of 240:

ANSWER: 2 × 2 × 2 × 2 × 3 × 5 (ACCEPT: 2^4 × 3 × 5)

Short Answer What is the domain and range for the function defined by the following set of three ordered pairs: {(-2, 6), (0, 9), (3, 7)}

ANSWER: DOMAIN = -2, 0, 3; RANGE = 6, 9,

MATH Multiple Choice At x = -1/2, the graph of y = x³ is: W) increasing and concave up X) increasing and concave down Y) decreasing and concave up Z) decreasing and concave down

ANSWER: X) INCREASING AND CONCAVE DOWN (Solution: at the indicated value the 1st derivative is positive (implying increasing) and the 2nd derivative is negative (implying concave down))

MATH Short Answer A point rotates around a circle at the rate of 40° per second. Convert this to revolutions per minute.

ANSWER: 20/3 (ACCEPT: 6 2/3)

[Bonus] Short Answer: What is the greatest common factor for the numbers 63 and 273?

ANSWER: 21

MATH Short Answer Simplify the following rational expression: (5y-3x²)/(9y²+5x)

ANSWER: CANNOT BE FURTHER SIMPLIFIED

MATH Short Answer If g(u) =∫0,u (sec²(t)) dt [g of u equals the integral from 0 to u of secant squared of t dt], find g'(u) [g prime of u].

ANSWER: sec²(u)

MATH Short Answer Given that t ≠ 0, find 𝑓( 1/𝑡 ) if 𝑓(t) =1/𝑡

ANSWER: t

BONUS 10) Math - Short Answer A particle's position is defined by the equation x(t) = 2t 3 - 15t 2 + 24t - 60. At what times t is the particle at rest?

ANSWER: t = 1 AND 4

MATH Short Answer: Giving your answer in standard form, give the equation of the circle with center at (0, 0) and diameter of 6:

x² + y² = 9

Giving your answer in standard form, what is the equation of the circle with center at (0, 0) and diameter 10?

x²+y²= 25

MATH Short Answer Giving your answer in standard form, what is the last term in the binomial expansion of the following: (x + y) ⁶

y⁶

What is the determinant of the 2 by 2 matrix with first row -2, -3 and second row 8, -4?

32

BONUS MATH Short Answer Factor the following expression completely over the integers: x⁴ - 16

ANSWER: (x - 2)(x + 2)(x² + 4)

BONUS MATH Short Answer Add the following rational expressions and give your answer in fully factored form: (x / (x+2)) + (4x / (x-6))

ANSWER: (x(5x+2)) / ((x-6)(x+2))

TOSS-UP14) Math - Short Answer If 1/x - 1/y = 1/z, what does z equal in terms of x and y?

ANSWER: (xy)/(y - x) ( ACCEPT: (-yx)/(x - y) )

Short Answer Remove all negative exponents and simplify the following expression for all non-zero values of x, y, and z: (2x²y⁻¹z³)⁰/(2x⁻³y⁻⁴z⁻⁵)

ANSWER: (x³y⁴z⁵)/2 (ACCEPT: (1/2)x³y⁴z⁵)

Math - Short Answer What is the smallest positive angle, in degree measure, between the vectors i + 2j + 3k and 2i - 3j - k?

ANSWER: 120

MATH Short Answer What is the determinant of the 2 by 2 matrix [such that row one includes 2 and negative 3, and row 2 includes negative 8 and negative 4]?

ANSWER: -32

MATH Short Answer If f(x) = 4x³ - 4x² + 10, then what is f(-2) [f of negative 2]?

ANSWER: -38

MATH Short Answer Considering the function f x = 2x3 + 5x2+ 4, what is the instantaneous rate of change at the point (-1, 7)?

ANSWER: -4

BONUS12) Math - Short Answer The product of three positive consecutive odd integers is 7 times their sum. Find the smallest of the three integers.

ANSWER: 3

MATH Short Answer How many points of intersection do the graphs of the functions f(x) = x² and g(x) = 2^x have?

ANSWER: 3

[Bonus] Short Answer Express the following radical in its simplest radical form: -2(80a²b⁴c³)^(1/2)

ANSWER: 8ab²c√5c

MATH Short Answer Identify the type of conic section represented by the equation, x² + y² + 10y + 16 = 0:

ANSWER: CIRCLE (Solution: x² + (y + 5)² = 9)

BONUS 15) GENERAL SCIENCE Short Answer What term describes the ability of a microscope to remain very nearly in focus when switching from one objective lens to another:

ANSWER: PARFOCAL (ACCEPT: PARFOCALITY)

BONUS 22) MATH Short Answer What are the radius and the coordinates of the center of the circle with equation x² + 6x + y² + 8y = 0?

ANSWER: RADIUS = 5; CENTER = (-3, -4)

Short Answer: In a Venn diagram, what is the most appropriate name of the rectangle that contains the circles that represent the subsets?

ANSWER: UNIVERSAL SET

MATH Short Answer What is the name for the test that can be used to visually determine whether or not a relation defined by a graph represents a function?

ANSWER: VERTICAL LINE TEST (ACCEPT: VERTICAL LINE)

If the graph ofyequals open parenthesis xminus twoclose parenthesis squared minus threeis translated 6 units up and 3 units to the right, what are the coordinates of the vertex of the image?

(5,3)

BONUS MATH Short Answer Giving your answer in simplest radical form, rationalize the denominator of the following expression: (-3√2)/(√3-√5)

(5√6)+(3√10)/2 (ACCEPT: 3/2(√6+√10)

Evaluate the following expression: open parenthesis negative cosine 360 degrees + sine 270 degrees close parenthesis times open parenthesis cosine 0 degrees + sine 0 degrees close parenthesis squared.

-2

BONUS MATH Short Answer: Solve the following inequality for x: |3 - 2x| ≤ 7 (read as: the absolute value of, 3 minus 2x, close absolute value, is less than or equal to 7)

-2 ≤ x ≤ 5 (ACCEPT: 5 ≥ x ≥ -2)

Bonus: What is the slope of the tangent line to the function F(x) = 1000-200x-5(x^2) at x= 4?

-240

BONUS MATH Short Answer: Giving your answer as a fraction reduced to lowest terms, solve the following equation for x: 2/3x-1/4=10/6x+1/2

-3/4

BONUS MATH Short Answer Give the resulting vector for the cross product of vector 1,0,0 with vector 0,0,1 :

0,−1,0

Subtracting a certain positive number from its square gives 110. Find the number

11

MATH Short Answer Giving your answer in centimeters, what is the length of a side of a square whose diagonal measures 12√2 centimeters?

12

Short Answer If a = cos(x), what is cos(2x) in terms of a?

2a^2 - 1

BONUS MATH Short Answer Giving your answer in meters squared, find the total surface area of a right prism whose base is a right triangle with legs of length 3 meters and 4 meters and whose altitude is 2 meters:

36

BONUS MATH Short Answer: If you roll a standard 6-sided die 2 times, how many different outcomes are possible?

36

MATH Short Answer Giving your answer as a proper fraction, what is the cube root of 125/343?

5/7

MATH Short Answer: A circle has a diameter of 32 meters. Find the degree measure of the central angle of a sector of the circle if its arc length measures 8π meters:

90

BONUS MATH Short Answer Giving your answers in terms of π and in inches squared, find the total surface area of a closed right circular cone whose altitude is 8 inches and radius is 6 inches:

96π

TOSS UP- Short Answer: What is the perimeter of a right triangle whose leg lengths are 6 and 8 and whose hypotenuse is 10?

ANSWER: 24 (Solution: perimeter = 6+8+10=24)

BONUS6) Math - Short Answer Simplify the fraction with numerator 3 raised to the 2k + 1 power and denominator 243 raised to the negative k power.

ANSWER: 3 raised to the (7k + 1) power

BONUS MATH Multiple Choice What is dy/dx for x^2 + y^2 = 2 at the point with coordinates (1, 1)? W) -1 X) -1/2 Y) 0 Z) 3/2

ANSWER: W) -1

MATH Short Answer Simplify the following expression, where a is not equal to zero if b = 0 or if b = -1: (a^(b^2))(a^b)

ANSWER: a^((b^2)+b)

BONUS MATH Short Answer Solve the following equation for x over the interval 0 ≤ x < 2π: 2sin^2 x − sin x - 1 = 0 [2 sine squared of x minus sine of x minus 1 equals 0].

ANSWER: π/2 , 7π/6, AND 11π/6

BONUS MATH Short Answer The graph of the polar equation, r = 5 - 5 cosine θ, is a cardioid. In which two quadrants is most of the area of this cardioid?

II AND III (ACCEPT: 2 AND 3 or SECOND AND THIRD)

MATH Short Answer: What is the specific name for a common tangent that intersects the segment joining the centers of 2 circles?

INTERNAL COMMON TANGENT (ACCEPT: INTERNAL or INTERNAL TANGENT)

Bonus: Which of the following base 2 sums is the largest? W) 1 + 1111[one plus one one one one] X) 100 + 1001[one zero zero plus one zero zero one] Y) 110 + 1000[one one zero plus one zero zero zero] Z) 111 + 111[one one one plus one one one]

W) 1 + 1111

MATH Multiple Choice Which of the following is a quadratic equation with a root of multiplicity of 2: W) 9x² - 30x 2 + 25 = 0 X) x² + 2x - 15 = 0 Y) 6x² - 11x - 2 = 0 Z) 4x² - 1 = 0

W) 9x² - 30x² + 25 = 0

MATH Multiple Choice: If triangle ABD is congruent with triangle EFG, which of the following MUST be true: W) side AB is congruent to side EF X) side AD is congruent to side FG Y) measure of angle B = measure of angle G Z) measure of angle A = measure of angle G

W) SIDE AB IS CONGRUENT TO SIDE EF

For a twice-differentiable function f(x), f(3) is 4, f prime of 3 is 0 and f double prime of 3 is 5. Which of the following is true of the graph of y= f(x) at the point (3, 4)? W) There is a local minimum X) There is a local maximum Y) There is an inflection point Z) The graph is concave down

W) THERE IS A LOCAL MINIMUM

Multiple Choice Which of the following 2 by 2 matrices is equivalent to a clockwise rotation of 90 degrees? W) 0 −1 1 0 (read as: row 1: 0, -1; row 2: 1, 0) X) 0 1 −1 0 (read as: row 1: 1, 1; row 2: -1, 0) Y) 0 −1 −1 0 (read as: row 1: 0, -1; row 2: -1, 0) Z) 0 1 1 0 (read as: row 1: 0, 1; row 2: 1, 0)

X) 0 1 −1 0

How many faces does a cuboctahedron [kyoo-bok-tuh-HEE-druhn] have? W) 8 X) 14 Y) 24 Z) 48

X) 14

Given sets A and B with A intersect B=the set containing the element 5, which of the following must be true? W) Set A may be the empty set X) Set A contains at least one element Y) Set B contains at most one element Z) Sets A and B have the same number of elements

X) SET A CONTAINS AT LEAST ONE ELEMENT

BONUS MATH Multiple Choice Which of the following is the sum of the first three nonzero terms of the Taylor series of sin(x) around 0? W) x + x3 /3! + x5 /5! (read as: x plus x cubed over 3 factorial plus x to the fifth over 5 factorial) X) x − x3 /3! + x5 /5! Y) 1 − x2 /2! + x4 /4! Z) 1 + x2 /2! + x4 /4!

X) x − x3 /3! + x5 /5!

BONUS MATH Multiple Choice: Which of the following points is closest to the point (1, -2): W) (3, -5) X) (0, 3) Y) (3, 0) Z) (-5, -5)

Y) (3, 0)

BONUS MATH Short Answer: At what value of x is there a minimum for the function f(x)= x² - 6x (read as: f of x equals x squared minus 6x)?

x = 3

BONUS MATH Short Answer: Giving your answer in millimeters squared, find the lateral surface area of a right pentagonal prism whose altitude is 12 millimeters and base has sides of length 8, 10, 12, 14, and 16 millimeters, respectively:

720

What is the sum of the two vectors 7i+ 3j and 2i-5j?

9i-2j

BONUS 13) MATH Short Answer Find the prime factorization of 1050:

ANSWER: 2×3×5×5×7 (ACCEPT: 2×3×52 ×7)

The complex number -4 lies on the boundary between what two quadrants in the complex plane?

2 AND 3 (ACCEPT: SECOND AND THIRD)

BONUS MATH Short Answer: Find the prime factorization of 240:

2 × 2 × 2 × 2 × 3 × 5 (ACCEPT: 24 × 3 × 5)

[BONUS] Short Answer :The Adams family bought a home entertainment system for $10,000.00. They paid $4,000.00 down and must pay off the balance in 12 equal payments. If the simple interest on the balance is 10% of the amount borrowed, how much is each monthly installment?

ANSWER: $550.00 (Solution: 10,000 - 4000 = 6000 bal; 6000 × 0.1 = 600; 6,600 ÷ 12 months = $550.00)

Short Answer: Simplify the following, giving your answer in simplest radical form: ((x)^6)^(1/9) (read as: the ninth root of x to the sixth power)

ANSWER: ((x)^2)^(1/3)

TOSS-UP15) Math - Short Answer Consider two lists of numbers, A and B, each with mean 10, that have a correlation coefficient r equal to 0.5. If all members of A are multiplied by 4 and all members of B are reduced by 7, what is the value of r for the two new lists?

ANSWER: 0.5 (ACCEPT: IT STAYS THE SAME)

MATH Short Answer Assuming that the natural log of 5 = 1.6, find, to the first decimal place, the natural log of 5^(1/3):

ANSWER: 0.5 (Solution: (1/3)(ln 5) = 1.6/3 = 0.53)

TOSS-UP15) Math - Short Answer At his latest basketball game, LeBron attempted only 3-pointers and 2-pointers. He was successful on 20% of his 3 pointers and 30% of his 2-pointers. If LeBron attempted 30 shots, how many points did he score?

ANSWER: 18

BONUS 5) MATH Short Answer How old is Michelle if 4 years ago she was one-half the age she will be 10 years from now?

ANSWER: 18 (Solution: x - 4 = ½(x + 10))

BONUS3) Math - Short Answer A band produces an album with 14 songs. The band picks one of these songs to be released in April, a different one to be released in May, and a different one to be released in June. In how many different ways can this be done?

ANSWER: 2184

BONUS MATH Short Answer Factor the following expression completely: 100x² - 25y²

ANSWER: 25(2x + y)(2x - y)

BONUS15) Math - Short Answer What is the value of the infinite expression 2 times the square root of 2 times the fourth root of 2 times the eighth root of 2 times the sixteenth root of 2, and so on, where the index of each root is doubled to obtain the next one?

ANSWER: 4

MATH Short Answer There are 10 people on a bus who, when ranked from youngest to oldest, all differ from those on the bus closest in age to them by the same number of years. If the youngest is 6 and the oldest is 51, what is the common difference in their age?

ANSWER: 5 (Solution: 6-11-16-21-26-31-36-41-46-51)

Short Answer: Solve the following equation for x: - 3|x| = -15 (read as: minus 3 times the absolute value of x equals minus 15)

ANSWER: 5 AND -5

[bonus] Multiple Choice Which of the following is a prime polynomial over the integers: W) 5x ² - 8x + 2 X) 4x ² - 4x - 8 Y) 3x ² - 4x - 4 Z) 3x² - 10x² + 3x

ANSWER: W) 5x² - 8x + 2 (Solution: it cannot be factored)

TOSS-UP11 ) Math - Multiple Choice How many values of x satisfy the equation x - 2 equals the fraction with numerator 2x² - 8x and denominator x² - 4x? W) Zero X) One Y) Two Z) Three

ANSWER: W) ZERO

MATH Multiple Choice Which of the following values for a and b provide a counterexample to the statement "If 4 divides a + b, then 4 divides a or 4 divides b." W) a = 5 and b = 7 X) a = 5 and b = 6 Y) a = 4 and b = 8 Z) a = 4 and b = 6

ANSWER: W) a = 5 AND b = 7

BONUS6) Math - Multiple Choice For the arithmetic series with first three terms 3, 5, and 7, what is the sum of the first 10 terms of the series? W) 100 X) 120 Y) 140 Z) 160

ANSWER: X) 120

MATH Multiple Choice A certain radioactive element decays over time according to the equation y=R(1/2)^(x/300)[y equals R times one half to the power of the quantity x over 300], where R equals the number of grams that were present initially and x equals time in years. If 1000 grams were present initially, how many grams will remain after 900 years? W) 62.5 X) 125 Y) 250 Z) 500

ANSWER: X) 125

BONUS10) Math - Multiple Choice If you flip a coin five times, what is the probability that you will get at least two heads? W) 31/32 X) 13/16 Y) 25/32 Z) 9/16

ANSWER: X) 13/16

MATH Multiple Choice How many two digit positive integers have at least one 6 as a digit? W) 17 X) 18 Y) 19 Z) 20

ANSWER: X) 18

Multiple Choice: Which of the following numbers is evenly divisible by 4: W) 1,722 X) 2,636 Y) 4,114 Z) 6,126

ANSWER: X) 2,636 (Solution: 36, the last 2 digits, is a multiple of 4)

BONUS 7) Math - Multiple Choice It takes 3 painters 4 hours to paint one house. How many hours does it take one painter to paint two houses of the same size? W) 12 X) 24 Y) 36 Z) 48

ANSWER: X) 24

BONUS MATH Multiple Choice Which of the following points is closest to the point (1, -2): W) (3, -5) X) (0, 3) Y) (3, 0) Z) (-5, -5)

ANSWER: Y) (3, 0) (Solution: d = √(x₁-x₂)²+(y₂-y₁)²; √(3-1)²+(0-(-2))² = √8)

BONUS MATH Multiple Choice Which of the following inequalities has NO solutions? W) 7x + 4 > 3 X) |x - 1| > -10 [the absolute value of the quantity x minus 1 is greater than negative 10] Y) |x + 3| < -2 [the absolute value of the quantity x plus 3 is less than negative 2] Z) -100x + 5 ≥ 8

ANSWER: Y) |x + 3| < -2

BONUS MATH Short Answer Find h(t) if 2h'(t) - h(t) = 0 [2h prime of t minus h of t equals zero] and h(0) = 10.

ANSWER: h(t) = 10e^((1/2)t) (ACCEPT: 10e^((1/2)t) )

MATH Short Answer Simplify i 17 completely.

ANSWER: i

BONUS1) Math - Multiple Choice What is the inverse function of y = 1 over open parenthesis x + 3 close parenthesis? W) y = open parenthesis 1 - 3x close parenthesis divided by x X) y = x - 3 Y) y = 3 - 1/x Z) y = 3x - 1

Answer: W) y = OPEN PARENTHESIS 1 - 3x CLOSE PARENTHESIS DIVIDED BY x

With respect to x, which of the following has -3x2 as an antiderivative? W) -6x X) 6x Y) -x³ Z) x³

W) -6x

If a number eight times as large as x is increased by two, then one fourth of the result equals W) 2x + 1/2 [2x plus half] X) x + 1/2 [x plus half] Y) 2x + 2 [2x plus 2] Z) 2x + 4 [2x plus 4]

W) 2x + 1/2

MATH Multiple Choice: Which of the following is a second quadrant angle in standard position: W) 500º X) -180º Y) -680º Z) 930

W) 500º

BONUS16) Math - Multiple Choice The values of y that will satisfy the system of equations 2x² + 6x + 5y + 1 = 0 and 2x + y + 3 = 0 can be found by solving which of the following equations? W) y² + 14y - 7 = 0 X) y² + 10y - 7 = 0 Y) y² + 8y + 1 = 0 Z) y² + y - 12 = 0

X) y² + 10y - 7 = 0

TOSS-UP16) Math - Multiple Choice Which of the following functions will have its nth derivative equal to 0 over its entire domain for sufficiently large values of n? W) f(x) = x¹⁰⁰ + sin x X) f(x) = x - x-1 Y) f(x) = x¹⁰⁰¹ + x¹⁰⁰⁰ + ... + x² + x Z) f(x) = ln x - x²

Y) f(x) = x¹⁰⁰¹ + x¹⁰⁰⁰ + ... + x² + x

Which of the following equations is that of a line perpendicular to the line with equation 4x-5y = 10? W) 4x-5y= 12 X) 4x+ 5y= 12 Y) 5x-4y= 10 Z) 5x+ 4y= 10

Z) 5x+ 4y= 10

TOSS-UP12) Math - Short Answer For what integer value of k is 2015 cubed closest to 10k?

ANSWER: 10

MATH Short Answer How many points of intersection exist for the graphs of y = 2^x [y equals 2 to the power of x] and y = -x² + 2?

ANSWER: 2

BONUS MATH Short Answer An object is launched straight up from the ground with an initial velocity of 176 feet per second. What is the height of the object above the ground, in feet, 2 seconds into the flight?

ANSWER: 288 (Solution: P(t) = -16t² + 176t; P(2) = -16(4) + 352 = 288 ft)

TOSS-UP 5) MATH Short Answer The number 22.5 is 5 percent of what number?

ANSWER: 450

BONUS12) Math - Short Answer If a₁ = 4 and aₙ = 2aₙ-₁ + 5, what is the value of a₄?

ANSWER: 67

Short Answer: What are the lengths, in centimeters, of the hypotenuse and the longer leg, respectively, of a 30-60-90 degree right triangle if the shorter leg is 12 centimeters long?

ANSWER: HYPOTENUSE = 24; LONGER LEG = 12*3^(1/2)(ACCEPT: LONGER LEG = 20 - 21)

BONUS MATH Multiple Choice Which of the following is a solution for x of the equation 2𝑥−2 = 𝜋𝑥 [2 to the quantity x minus 2 equals pi to the x]? W) (log(4))/(log(2)−log(𝜋)) [the fraction with numerator log of 4 and denominator log of 2 minus log of pi] X) (log(4))/(log(𝜋)−log(2)) [the fraction with numerator log of 4 and denominator log of pi minus log of 2] Y) (log(𝜋)−log(2))/(log(4)) [the fraction with numerator log of pi minus log of 2 and denominator log of 4] Z) (log(2)−log(𝜋))/(log(4)) [the fraction with numerator log of 2 minus log of pi and denominator log of 4]

ANSWER: W) (log(4))/(log(2)−log(𝜋))

MATH Multiple Choice What is lim𝑥→𝜋 (sin 𝑥)/(𝑥 − 𝜋) [the limit as x approaches pi of the fraction with numerator sine of x and denominator x minus pi]? W) -1 X) 0 Y) 1 Z) Undefined

ANSWER: W) -1

BONUS MATH Multiple Choice If x is an angle such that tan(x) = 5/12 and π < x < 3π/2, then sec(x) [secant of x] is equal to which of the following? W) -13/12 X) -13/5 Y) 13/5 Z) 13/12

ANSWER: W) -13/12

BONUS MATH Multiple Choice If y = 2(cos x)^2 [y equals 2 cosine squared of x], what is dy/dx at x = 𝜋/4? W) -2 X) -1 Y) 1 Z) 2

ANSWER: W) -2

MATH Multiple Choice The equation -3 + |-2x - 5| = k [negative 3 plus the absolute value of the quantity negative 2x minus 5 equals k] has no solution if k equals which of the following? W) -5 X) -3 Y) 0 Z) 7

ANSWER: W) -5

TOSS-UP20) Math - Short Answer If f(x) equals the fraction with numerator 1 and denominator open parenthesis 2x- 1 close parenthesis cubed, which of the following is the numerator in the expression for the derivative of fwith respect to x: W) -6 X) -3 Y) 1 Z) 2

ANSWER: W) -6

MATH Multiple Choice If f(x) = (sinx)^2 + (cosx)^2 [f of x equals sine squared of x plus cosine squared of x], what is f '(x) [f prime of x]? W) 0 X) 1 Y) 2sinxcosx [2 sine of x cosine of x] Z) sin(2x) [sine of 2x]

ANSWER: W) 0

TOSS-UP 13) MATH Multiple Choice Which of the following is a rational number: W) 1+ 4 X) 2+ 5 Y) 6 Z) π

ANSWER: W) 1+ √4

TOSS-UP3) Math - Multiple Choice Molly picks 4 coins out of her purse. Which of the following cannot be the total value, in cents, of the four coins? W) 15 X) 16 Y) 25 Z) 45

ANSWER: W) 15

BONUS8) Math - Multiple Choice Consider a basketball tournament in which 100 teams enter. In the first round, 28 teams are given a bye and the remaining teams are paired off to play. After each round, the remaining teams are paired off in the next round. How many matches are played in the first 3 rounds? W) 84 X) 88 Y) 92 Z) 99

ANSWER: W) 84

MATH Multiple Choice Given triangle ABC with right angle A, angle B with a measure of 30⁰ , and AC equal to 3√3, which of the following is the length of side AB? W) 9 X) 6√3 Y) 9√3 Z) 12√3

ANSWER: W) 9

MATH Multiple Choice Which of the following is a quadratic equation with a root of multiplicity of 2: W) 9x² - 30x² + 25 = 0 X) x² + 2x - 15 = 0 Y) 6x² - 11x - 2 = 0 Z) 4x² - 1 = 0

ANSWER: W) 9x² - 30x² + 25 = 0 (Solution: x = 5/3)

MATH Multiple Choice Which of the following can be constructed using only a compass and a straightedge? W) A line segment with one-third the length of a given line segment X) A cube with twice the volume of a given cube Y) An angle with one-third the measure of a given angle Z) A square with the same area as that of a given circle

ANSWER: W) A LINE SEGMENT WITH ONE-THIRD THE LENGTH OF A GIVEN LINE SEGMENT

MATH Multiple Choice If X and Y are bounded sets, then which of the following is true? W) Both the union and the intersection of sets X and Y are bounded X) Both the union and the intersection of sets X and Y are unbounded Y) The union of sets X and Y is bounded and the intersection of sets X and Y is unbounded Z) The union of sets X and Y is unbounded and the intersection of sets X and Y is bounded

ANSWER: W) BOTH THE UNION AND THE INTERSECTION OF SETS X AND Y ARE BOUNDED

MATH Multiple Choice If triangle ABD is congruent with triangle EFG, which of the following MUST be true: W) side AB is congruent to side EF X) side AD is congruent to side FG Y) measure of angle B = measure of angle G Z) measure of angle A = measure of angle G

ANSWER: W) SIDE AB IS CONGRUENT TO SIDE EF

BONUS10) Math - Multiple Choice Consider a criminal trial in which the defendant is innocent until proven guilty. If the jury accepts the null hypothesis when the defendant is innocent, which of the following has occurred? W) The jury made the right decision X) The jury committed a type I error Y) The jury committed a type II error Z) The jury committed a type III error

ANSWER: W) THE JURY MADE THE RIGHT DECISION

TOSS-UP 8) COMPUTER SCIENCE Multiple Choice Which of the following would offer the most protection against power-failure data loss: W) UPS X) surge protector Y) data backup Z) line conditioner

ANSWER: W) UPS

BONUS 4) MATH Multiple Choice If f(x) = -2x² + 8x - 4, which of the following is true? W) f is not a one to one function X) The graph of f opens upward Y) The graph of f has no x-intercept Z) The maximum value of f(x) is -4

ANSWER: W) f IS NOT A ONE TO ONE FUNCTION

BONUS 9) MATH Multiple Choice Which of the following is equivalent to (a^(-1) + b^(-1))^(-1) [open parenthesis a to the power of negative 1 plus b to the power of negative 1 close parenthesis to the power of negative 1]? W) 𝑎b/(𝑎+𝑏) [the fraction with numerator ab and denominator a plus b X) a + b Y) (a^2)(b^2) Z) ab

ANSWER: W) 𝑎b/(𝑎+𝑏)

MATH Multiple Choice Which of the following is an equivalent form of 2/(3 + i) [2 over the quantity 3 plus i]? W) (3 - i)/4 [open parenthesis 3 minus i,close parenthesis, over 4] X) (3 - i)/5 [open parenthesis 3 minus i,close parenthesis, over 5] Y) (4 - i)/4 [open parenthesis 4 minus i,close parenthesis, over 4] Z) (4 - i)/5 [open parenthesis 4 minus i,close parenthesis, over 5]

ANSWER: X) (3 - i)/5

BONUS 20) MATH Multiple Choice Which of the following points lies in the solution set for the system of two inequalities: 2y - x ≥ -6 and 2y - 3x < -6? W) (-4, -1) X) (3, 1) Y) (0, -3) Z) (4, 3)

ANSWER: X) (3, 1)

MATH Multiple Choice The points on a scatter plot are extremely close to their least-squares regression line, which is expressed by the equation y = -2x + 3. The correlation coefficient r between x and y is closest to which of the following? W) -2 X) -1 Y) 1/2 Z) 1

ANSWER: X) -1

BONUS MATH Multiple Choice A curve is given by the equation: x3 + 3y2 = 4. What is the slope of the tangent line at the point with coordinates (1, 1)? W) -2 X) -1/2 Y) 1/2 Z) 2

ANSWER: X) -1/2

BONUS MATH Multiple Choice What is the exact value of tan(120) + cot(30) [tangent of 120 degrees plus cotangent of 30 degrees]? W) −2√3 X) 0 Y) 2√(3)/3 [2 times the square root of 3 over 3] Z) 2√3

ANSWER: X) 0

BONUS MATH Multiple Choice A balloon is being filled with water. Its volume in gallons is given by the function V(r) = r^(3/10) [V of r equals r cubed over 10], where r is the radius of the balloon in inches. What is the average rate of change in gallons per inch of the volume of the balloon as the radius is increased from 1 to 2 inches? W) 0.3 X) 0.7 Y) 0.8 Z) 1.2

ANSWER: X) 0.7

MATH Multiple Choice A positive three digit integer n is chosen at random, with each three digit number having an equal chance of being chosen. What is the probability that log2n [log base 2 of n] is an integer? W) 3/899 X) 1/300 Y) 1/222 Z) 1/150

ANSWER: X) 1/300

MATH Multiple Choice A jar contains 500 jellybeans, 100 each of red, white, blue, orange, and green. If you reach in without looking, how many jellybeans must you grab to be certain that at least five are of the same color? W) 6 X) 21 Y) 25 Z) 26

ANSWER: X) 21

MATH Multiple Choice The price of an item is discounted by 10% and then the new price is further discounted by 20%. What single discount is equivalent to this double discount? W) 15% X) 28% Y) 30% Z) 72%

ANSWER: X) 28%

BONUS15) Math - Multiple Choice The two legs of a right triangle have lengths of 6 and 2 times the square root of 3. How long is the altitude to the hypotenuse? W) 2 X) 3 Y) 4 Z) 5

ANSWER: X) 3

BONUS MATH Multiple Choice Which of the following represents a simplification of: (𝐴^(1/2) + 𝐴^(1/2))^2 [open parenthesis a to the power of one half plus a to the power of one half close parenthesis squared]? W) A2 X) 4A Y) 2A Z) √𝐴

ANSWER: X) 4A

MATH Multiple Choice If the surface area of a cube is 96 square units, which of the following is the length of a diagonal of a face of the cube? W) 4 X) 4√2 Y) 4√3 Z) 16√2

ANSWER: X) 4√2

MATH Multiple Choice Which of the following equations is that of a line perpendicular to 3x - 7y = 5? W) 3x + 7y = 10 X) 7x + 3y = 10 Y) 7x - 3y = 10 Z) 3x - 7y = 10

ANSWER: X) 7x + 3y = 10

MATH Multiple Choice A student must enroll in 5 classes. She must take English, either Sociology or Economics, and either Chemistry, Biology, or Geology. For the other two courses, six offerings are available. How many different schedule selections are possible? W) 36 X) 90 Y) 180 Z) 360

ANSWER: X) 90

MATH Multiple Choice If an arc of 60° on circle 1 has the same length as an arc of 45° on circle 2, what is the ratio of the area of circle 1 to the area of circle 2? W) 16:9 X) 9:16 Y) 4:3 Z) 3:4

ANSWER: X) 9:16

BONUS10) Math - Multiple Choice Consider the following two statements: 1) If A and B, then C; 2) Not C. Which of the following conclusions follows from these statements? W) Not A and not B X) Not A or not B Y) If A, then C Z) If not C, then not B

ANSWER: X) NOT A OR NOT B

MATH Multiple Choice The lines defined by y = 2x and 2y = -x are which of the following? W) Parallel X) Perpendicular Y) Horizontal Z) Vertical

ANSWER: X) PERPENDICULAR

MATH Multiple Choice The graph of the relation y = -√(25-x²) is a: W) circle X) semi-circle Y) parabola Z) straight line

ANSWER: X) SEMI-CIRCLE

MATH Multiple Choice The variables x and y vary directly. Which of the following equations could represent the relationship between x and y? W) (1/5)x = 1/y [one fifth x equals 1 over y] X) x/y = 1/5 [x over y equals one fifth] Y) xy = 1/5 [x y equals one fifth] Z) xy = 5

ANSWER: X) x/y = 1/5

MATH Multiple Choice Bacteria in a culture are growing exponentially, such that on day 0, there are 100 bacteria, on day 1, there are 200 bacteria, and on day 2, there are 400 bacteria. Which of the following equations expresses the number of bacteria, y, present at any time t? W) y = 100 + 2^t [y equals 100 plus 2 to the power of t] X) y = 100(2^t) [y equals 100 times the quantity 2 to the power of t] Y) y = 2^t [y equals 2 to the power of t] Z) y = 200(2^t) [y equals 200 times the quantity 2 to the power of t]

ANSWER: X) y = 100(2^t)

MATH Multiple Choice Which of the following best represents the conversion of the rectangular coordinates (3, 4) into polar coordinates? W) (5, 37o) X) (37o, 5) Y) (5, 53o) Z) (53o, 5)

ANSWER: Y) (5, 53o)

MATH Multiple Choice Which of the following represents the inverse function of f(x) = x³ + 5: W) (x - 5)³ X) x³ - 5 Y) (x − 5)^(1/3) Z) (1/x-5)³

ANSWER: Y) (x-5)^(1/3)

Math - Multiple Choice Which of the following describes the solutions for the equation x to the x power = x to the x + 1 power? W) -1 and 1 X) 0 Y) 1 Z) No solution exists

ANSWER: Y) 1

MATH Multiple Choice In the mid-state football conference, each team plays every other team exactly once during a calendar year. If a total of 45 conference games were played in 2012, how many teams were in the conference? W) 8 X) 9 Y) 10 Z) 11

ANSWER: Y) 10

MATH Multiple Choice Which of the following numbers is NOT prime? W) 107 X) 109 Y) 111 Z) 113

ANSWER: Y) 111

TOSS-UP18) Math - Multiple Choice The derivative of sine-cubed of 2 theta with respect to theta is equal to which of the following? W) Cosine-cubed of 2 theta X) 3 sine-squared of 2 theta Y) 6 sine-squared of 2 theta cosine of 2 theta Z) 6 cosine-cubed of 2 theta sine-squared of 2 theta

ANSWER: Y) 6 sine-squared of 2 theta cosine of 2 theta

Multiple Choice Which of the following is NOT a geometric sequence: W) 30, 6, 6/5 ... X) a² , a³ b, a⁴b² ... Y) 6, 13, 20... Z) 3/2, 3/4, 3/8...

ANSWER: Y) 6, 13, 20...

TOSS-UP18) Math - Multiple Choice Which of the following best describes the following system of two linear equations: y - 2x = - 2, y + x = 4? W) Consistent, Dependent X) Inconsistent, Independent Y) Consistent, Independent Z) Inconsistent, Dependent

ANSWER: Y) CONSISTENT, INDEPENDENT

BONUS3) Math - Multiple Choice What transformation occurs in going from the graph of f(x) = 0.5x² + x to the graph of g(x) = 0.5x² - x? W) Horizontal shift right by 1 unit X) Horizontal shift left by 1 unit Y) Horizontal shift right by 2 units Z) Horizontal shift left by 2 units

ANSWER: Y) HORIZONTAL SHIFT RIGHT BY 2 UNITS

MATH Multiple Choice A line with the equation y = cx + c, where c is a non-zero real number, must intersect which of the following? W) Positive x-axis X) Positive y-axis Y) Negative x-axis Z) Negative y-axis

ANSWER: Y) NEGATIVE x-AXIS

MATH Multiple Choice Which of the following is TRUE about any two successive terms in the Fibonacci sequence: W) their product is a Fibonacci number X) they are either both odd or both even Y) they are relatively prime Z) their quotient is the golden ratio

ANSWER: Y) THEY ARE RELATIVELY PRIME

MATH Short Answer: Simplify the following expression: x¹/²x²/⁵

x⁹/¹⁰ (ACCEPT: ¹⁰√x⁹)

Bonus: Solve the following system of two equations in two unknowns: (x^2) + (y^2) = 2 and x + y = 2.

(1, 1) (ACCEPT: x= 1 and y= 1)

What is the midpoint of the segment with endpoints (1, 6) and (5, -2)?

(3, 2)

MATH Short Answer Simplify the following without the use of negative exponents: (-24x³y⁵)/(10y⁶z²)

ANSWER: (-12x³

BONUS12) Math - Short Answer For real numbers a and b, define the binary operation "star" by a "star" b is equal to open parenthesis a + b close parenthesis times open parenthesis a - b close parenthesis. What is 3 "star" open parenthesis 4 "star" 5 close parenthesis?

ANSWER: -72

BONUS 6) MATH Short Answer Differentiate sin(cosx) [sine of cosine of x].

ANSWER: -cos(cos x)sinx [ACCEPT: cos (cos x)(-sin x) or -sinx cos(cos(x)); DO NOT ACCEPT: -cos² x sinx]

TOSS-UP23) Math - Short Answer Evaluate the limit, as n approaches infinity, of the sequence whose nth term is n²/3ⁿ.

ANSWER: 0

MATH Short Answer Solve the following equation for x over the integers: x² = 3x

ANSWER: 0; 3

BONUS MATH Short Answer Solve the following equation for all real values of x: (x + 3)² = 16

ANSWER: 1 AND -7

TOSS-UP17) Math - Short Answer Consider a bag of five marbles, 3 red and 2 white. You draw marbles from the bag until you draw the last white marble, at which point you stop. What is the probability you stop drawing after the 2nd marble is selected?

ANSWER: 1/10 (ACCEPT: 0.1 OR 10%)

MATH Short Answer Given 𝑓(𝑥) = 𝑙n√(𝑒^𝑥) [f of x equals the natural log of the square root of the quantity e to the x], find its first derivative with respect to x.

ANSWER: 1/2

MATH Short Answer If log(100)^(2𝑥)= 2 [log base 10 of 100 to the power of 2x equals 2], what is the value of x?

ANSWER: 1/2 (ACCEPT: 0.5)

MATH Short Answer What is the sum of the infinite geometric series with a first term of 1/3 and a second term of 1/9?

ANSWER: 1/2 (ACCEPT: 0.5)

Short Answer: Give the value of c that completes the square of the following expression: x² + (2/5)x + c

ANSWER: 1/25 (ACCEPT: 0.04 or 4/100 )

BONUS MATH Short Answer A card is drawn at random from a standard deck of 52 cards. Given that the card drawn is a face card, what is the probability that the drawn card is a Jack?

ANSWER: 1/3

MATH Short Answer Find the sum of the infinite geometric series with first three terms 1/4, 1/16, and 1/64.

ANSWER: 1/3

Math - Short Answer What is the sum of the infinite geometric series with first term 1/4 and second term 1/16?

ANSWER: 1/3

BONUS 1) Math - Short Answer Subtracting a certain positive number from its square gives 110. Find the number.

ANSWER: 11

Math - Short Answer What is the average of the integers from 1 to 21, inclusive?

ANSWER: 11

Short Answer: What is the side of a square, in centimeters to the nearest whole number, given that its diagonal is 16 centimeters?

ANSWER: 11 (Solution: s = 16/ (2)^(1/2) = 11.3 cm)

BONUS MATH Short Answer In a standard deck of cards with no jokers, providing your answer as a fraction in lowest terms, what is the probability of picking a card that is black or a number less than 10 (which includes aces)?

ANSWER: 11/13

MATH Short Answer How many edges does a hexagonal prism have?

ANSWER: 18

BONUS MATH Short Answer Find the area, in square centimeters, of a rhombus with a diagonal of 6 centimeters and a side of 5 centimeters:

ANSWER: 24 (Solution: A = ½ d₁d₂ = ½ (6)(8) = 24 cm² , (3:4:5 triangle))

BONUS 5) MATH Short Answer The three sides of a triangle are 5 centimeters, 6 centimeters, and 8 centimeters. What is the cosine of the smallest angle in reduced fractional form?

ANSWER: 25/32

BONUS MATH Short Answer Find the sum of the first 10 terms of the arithmetic sequence whose first three terms are 7, 11, and 15:

ANSWER: 250

BONUS MATH Short Answer Find the sum of the first 10 terms of the arithmetic sequence whose first three terms are 7, 11, and 15:

ANSWER: 250

BONUS23) Math - Short Answer The sums of three whole numbers taken in pairs are 11, 13, and 16. What is the product of these three numbers?

ANSWER: 252

TOSS-UP 10) Math - Short Answer If one side of a right triangle is 14 inches and its opposite angle is 30 degrees, what is the diameter of the circle circumscribed around this triangle?

ANSWER: 28

BONUS MATH Short Answer Find the following product, giving your answer in standard form: (4x^3 + x)(7x^3 + 4x^2 )

ANSWER: 28x^6 + 16x^5 + 7x^4 + 4x^3 (ACCEPT: x^3 (28x^3 + 16x^2 + 7x + 4)

Short Answer In degrees, what is the least positive angle that is coterminal with 650°?

ANSWER: 290° (Solution: 650° - 360° = 290°)

MATH Short Answer In what quadrant does θ (read as: theta) terminate if sine θ is positive and secant θ is negative?

ANSWER: 2nd (ACCEPT: 2)

BONUS Math - Short Answer In a circle with radius 4, what is the area of a circular segment defined by an arc of 45°?

ANSWER: 2pi - 4√2

MATH Short Answer By number, identify which one of the following statements is TRUE regarding the set of means of samples of size n from a given population: 1) the mean of the set of sample means varies inversely as the square root of n; 2) the variance of the set of sample means varies directly as n; or 3) the standard deviation of the set of sample means varies inversely as the square root of n.

ANSWER: 3

MATH Short Answer What is the multiplicity of the zero 1 in the polynomial p(x) = x⁴ + x³ - 9x² + 11x - 4?

ANSWER: 3

TOSS-UP23) Math - Short Answer Consider the set of all positive integers that are the differences of the squares of two positive integers. What is the least element of the set?

ANSWER: 3

TOSS-UP 21) MATH Short Answer The price of a postage stamp changes from 33 cents to 34 cents. What is the percent increase in price?

ANSWER: 3 (ACCEPT: 3.03)

[bonus] Short Answer Solve the following logarithmic equation in base 10 for x over the real numbers: log (2x - 1) = log (x + 2) + log (x - 2)

ANSWER: 3 (DO NOT ACCEPT 3 and -1) (Solution: 2x - 1 = (x + 2)(x - 2); (x - 3)(x + 1) = 0; x = 3, x ≠ -1 - the log(-1) does not exist in the real number system)

MATH Short Answer Given f(x) = x + 1 and g(x) = 3x, what is f(g(x)) [f of g of x]?

ANSWER: 3x + 1

BONUS 10) MATH Short Answer What is ∫ |𝑥| 2 −2 𝑑𝑑 [the integral from negative 2 to 2 of the absolute value of x dx]?

ANSWER: 4

BONUS MATH Short Answer A line in parametric mode is given by the equations: x = 1/2 t + 2 and y = 2t. What is the slope of this line?

ANSWER: 4

BONUS23) Math - Short Answer How many positive integers a exist such that log base a of 15,625 is a positive integer?

ANSWER: 4

MATH Short Answer If ln(x³) = 6 [natural log of the quantity x cubed equals 6], what is ln(x²) [the natural log of the quantity x squared]?

ANSWER: 4

TOSS-UP12) Math - Short Answer How many integers in the closed interval from 0 to 100 are the squares of perfect squares?

ANSWER: 4

TOSS-UP12) Math - Short AnswerWhat is the value of (log₂4)(log₄6)(log₆8)(log₈16)?

ANSWER: 4

BONUS MATH Short Answer Convert the complex number -2 - 2i 3 to trigonometric form.

ANSWER: 4 (cos 4π/3 + i sin 4π/3)

BONUS MATH Short Answer Find the area, in centimeters squared and in simplest radical form, of a regular or equilateral triangle whose circumcircle has a radius of 8 centimeters:

ANSWER: 48√3 (Solution: apothem = 4; perimeter = (8√3)(3); A = ½(4)(24√3) = 48√3 cm² )

BONUS17) Math - Short Answer Four coplanar circles of radius r have their centers arranged to form the vertices of a square of side length 2r. What is the area of the region enclosed in the square, but not enclosed in any of the four circles?

ANSWER: 4r^2 - πr^2 (ACCEPT: r^2 (4 - π))

BONUS Math - Short Answer What is the area of a triangle with sides of length 11, 8, and 5?

ANSWER: 4√21

BONUS MATH Short Answer A point moves on the curve 6x^2 - 3y^2 = 18 so that its y-coordinate increases at a constant rate of 12 meters per second. At what rate, in meters per second, is the x-coordinate changing when the point is at (3, 2√3 )?

ANSWER: 4√3

MATH Short Answer In the three by three matrix, [such that row one contains negative 2, 2, and 0; row two contains 4, 1, and negative 5; row three contains 8, 3, and 7], which is the x(2,3) [x sub 2, 3] element?

ANSWER: 5

TOSS-UP10) Math - Short Answer Find the modulus of the complex conjugate of 3 - 4i.

ANSWER: 5

[bonus] Short Answer Find the 101st term in the arithmetic sequence whose first three terms are 5, 11, and 17:

ANSWER: 605 (Solution: an = a1 + (n - 1)d; = 5 + (101 - 1)(6) = 605)

MATH Short Answer If logb(5) = c [log base b of 5 equals c], then what does (b^(4c)) [b to the power of 4 c] equal?

ANSWER: 625

Math - Short Answer What is the lateral surface area of a cone whose height is 12 cm and whose base diameter is 10 cm?

ANSWER: 65 pi

MATH Short Answer What is x equal to in the following expression: logx7 = 1 [log base x of 7 equals 1]?

ANSWER: 7

BONUS MATH Short Answer The linear function y = f(x) contains the two points (2, 1) and (5, 8). In simplest form, what is f(13)?

ANSWER: 80/3 (ACCEPT: 26 2/3)

BONUS23) Math - Short Answer What is the sum of the digits of the square of 111,111,111?

ANSWER: 81

[bonus] Short Answer Consider a blue circle inscribed in a white square. If the radius of the circle is 10 centimeters, what is the area of all visible white portions of the square, to the nearest whole number in centimeters squared?

ANSWER: 86 (Solution: A square = 20² = 400; A circle = πr² = 100π = 314; 400 - 314 = 86cm² )

MATH Short Answer Four consecutive odd integers are added. If the smallest integer is 2m - 1, then what is their sum in terms of m?

ANSWER: 8m + 8

TOSS-UP23) Math - Short Answer A circular cone-shaped reservoir holds 3 gallons of water. How many gallons does a circular cylindrical reservoir hold if it has the same base and height as the conical reservoir?

ANSWER: 9

TOSS-UP7) Math - Short Answer A Diophantine equation is a polynomial equation in two or more variables such that the solutions are what type of number?

ANSWER: INTEGERS

BONUS MATH Short Answer What are the vertical and horizontal asymptotes, respectively, of f(x) = (x^2 - √3)/(x^2 - 2x - 15) [f of x equals the fraction with numerator x squared minus the square root of 3 and denominator x squared minus 2x minus 15]?

ANSWER: VERTICAL: x = -3, x = 5; HORIZONTAL: y = 1

MATH Multiple Choice Which of the following is an identity? W) cos(2x) = 2 cos(x)[cosine of 2x equals 2 cosine of x] X) sin(2x) = 2 sin(x) cos(x) [sine of 2 x equals 2 sine of x cosine of x] Y) cos(x + y) = cos(x) + cos(y) [cosine of the quantity x plus y equals cosine of x plus cosine of y] Z) sin(x - y) = sin(x) - sin(y) [sine of the quantity x minus y equals sine of x minus sine of y]

ANSWER: X) sin(2x) = 2 sin(x) cos(x)

BONUS14) Math - Multiple Choice Consider a 2 by 2 matrix with first row 2, A and second row B, 3, where A and B are integers. How many different combinations exist of the values of A and B so that the matrix is singular? W) 4 X) 6 Y) 8 Z) 10

ANSWER: Y) 8

MATH Multiple Choice What is the product of the following 2 values: (1) the greatest common divisor of 7 and 14; and (2) the least common multiple of 7 and 14: W) 21 X) 49 Y) 98 Z) 196

ANSWER: Y) 98 (Solution: the product will be the same as the product of the two numbers, 7 and 14)

MATH Multiple Choice Which of the following statements is TRUE? W) A correlation of +0.8 is stronger than a correlation of -0.8 X) A correlation of +0.8 is weaker than a correlation of -0.8 Y) A correlation of +0.8 is just as strong as a correlation of -0.8 Z) It is impossible to tell which correlation is stronger

ANSWER: Y) A CORRELATION OF +0.8 IS JUST AS STRONG AS A CORRELATION OF -0.8

MATH Short Answer Identify the type of conic section represented by the equation, x² + y² + 10y + 16 = 0:

CIRCLE

MATH Short Answer: Find the cotangent and cosecant, respectively, of a 90º angle:

COTAN = 0; COSECANT = 1

MATH Multiple Choice The graph of r = 3 secant (θ) (read as: r = 3 secant theta) is a: W) parabola X) circle Y) hyperbola Z) line

Z) LINE

Following are four pairs of intersecting lines that are related to circles. For three of them, the measures of the angles formed can always be found by taking half of the difference of the angle measures of the intercepted arcs. For which does this calculation generally fail? W) Two tangents X) Two secants that intersect outside the circle Y) A tangent and a secant that intersect outside the circle Z) The lines containing two intersecting chords

Z) THE LINES CONTAINING TWO INTERSECTING CHORDS

BONUS MATH Short Answer The point (3, 2) is reflected across the graph of y = 6 and the resulting point is then reflected across the graph of y = x. What are the coordinates of the final point?

(10, 3)

MATH Short Answer If a point has polar coordinates (3, π), what are the rectangular coordinates?

(-3, 0)

BONUS MATH Short Answer: Giving your answer as an ordered pair, find the solution of the system of the following 2 equations: x=2/3y-2 and x=y-3

(0, 3)

Bonus: Evaluate 11²+ 21²+ 31².

1523

MATH Short Answer Of the following 5 functions identify all that are NOT differentiable for all real numbers: | x | (read as: absolute value of x); cosine(x); tangent(x); e^x ; the greatest integer function

| x |; TAN(x); THE GREATEST INTEGER FUNCTION