SB: Math 2
What is the sum of the largest prime number less than 50 and the largest prime number less than 100?
144
How many points of intersection are there for the graphs of y= 3x and y= -x²+ 5?
2
MATH Short Answer Providing your answer in simplest form, what is sec(11π/6) [secant of 11 pi over 6]?
2√3/3
MATH Short Answer Linear correlation coefficients must lie between what two values?
ANSWER: -1 AND 1
Math - Short Answer What is the log base 3 of 729?
ANSWER: 6
BONUS 8) COMPUTER SCIENCE Short Answer Data travels on a 100MHz, 64-bit bus at how many megabytes per second?
ANSWER: 800
If n is an odd integer, how many lines of symmetry does a regular n-gon have?
n
What is the product of the complex numbers 3 + i and 2 + 3i?
3+11i
BONUS MATH Short Answer Each exterior angle of a regular polygon has a measure of 10°. What is the sum, in degrees, of the measures of the interior angles of the polygon?
6120°
TOSS-UP 8) COMPUTER SCIENCE Short Answer How fast data flows on a given transmission path and the width of the range of frequencies that a signal occupies on a given transmission medium is generally known as:
ANSWER: BANDWIDTH
TOSS-UP 21) MATH Short Answer What is the longest chord of a circle also known as?
ANSWER: DIAMETER OF THE CIRCLE (ACCEPT: DIAMETER
MATH Multiple Choice Which of the following series converges? W) ∑1/n^0.5 X) ∑1/n+1 Y) ∑n/e^n Z) ∑e^n/n
ANSWER: Y) ∑n/e^n
Bonus: What is the image of the point (0, 0) when it is reflected across the line y= x -1?
(1, -1)
Bonus: Solve the following equation for x over the real numbers: 8 to the power open parenthesis 2x close parenthesis equals 4 to the power open parenthesis 2x minus 1 close parenthesis.
-1
Bonus: What is the remainder when 3x³+ 6x²-7x+ 2 is divided by the binomial x+ 4?
-66
MATH Short Answer If y = -x², what is the slope of the tangent line to the graph at x = 4?
-8
BONUS MATH Short Answer Find the x-coordinates of every point on the graph of f(x) = x³ + 3x² - 9x + 3 where the tangent line is horizontal.
1 AND -3
Identify all of the four quadrants in which cosecant is positive.
1 and 2 (ACCEPT: FIRST and SECOND)
BONUS MATH Short Answer Evaluate ∑ 30, 𝑘=1 (3𝑘 + 2) [the summation from k equals 1 to 30 of the quantity 3 k plus 2].
1,455
What is the 4th term of the geometric series with first term 400 and second term 120?
10.8 (ACCEPT: 10 4/5, 54/5)
Bonus: Simplify the following expression involving the complex number i: i+ 2i²+ 3i³+ 4i⁴
2 -2i
A special coin has a 1/3 probability of landing on heads, and a 2/3 probability of landing on tails. In a series of three coin flips, what is the probability of the outcome sequence heads, heads, tails?
2/27
BONUS MATH Short Answer A regular decagon with a perimeter of 40 units has an area of 40k square units. Find its apothem.
2k
Bonus: What is the average value of the function f(x) = x² over the interval -2 to 2?
4/3
MATH Short Answer No three points of a particular set of 4 points are collinear. How many lines are determined by pairs of those points?
6
What is the area, in square centimeters, of an equilateral triangle whose circumcircle has a radius of 10 centimeters?
75√3
MATH Short Answer An acute angle has a measure of 2a + 2b. What is the difference between the degree measures of the supplement and complement of that angle?
90
MATH Short Answer What is the maximum number of spheres with a radius of 1 that can fit inside a cube with edge lengths of 6?
ANSWER: 27
TOSS-UP 20) MATH Short Answer In statistics, what is the square root of the variance most commonly known as?
ANSWER: STANDARD DEVIATION
BONUS 1. MATH Short Answer Find the largest possible real range of the function 𝑦𝑦 = 1 − 2𝑒𝑒 𝑥𝑥 2 −3 [y equals 1 minus 2 times e to the power of the quantity x over 2 minus 3].
ANSWER: y < 1 (ACCEPT: ALL REAL NUMBERS LESS THAN 1; THE OPEN INTERVAL FROM MINUS INFINITY TO 1)
BONUS MATH Short Answer If 8^(x+y) = 16 [8 to the power of the quantity x plus y equals 16], determine the slope-intercept form of the equation satisfied by points with coordinates (x, y).
ANSWER: y = -x + 4/3
MATH Short Answer Suppose that 𝜃𝜃 = sin⁻¹( 3/5 ) [theta equals the inverse sine of three fifths]. Find the exact value of tan(𝜃)[tangent of theta].
ANSWER: ¾
Bonus: What are themean and the median, respectively, of the prime numbers less than 25?
MEAN 100/9 (ACCEPT: 11 1/9), MEDIAN 11
BONUS MATH Multiple Choice Which of the following represents a simplified form of: sin x + cos²/sinx [sine of x plus the fraction with numerator cosine squared of x and denominator sine of x]? W) csc x [cosecant of x] X) sec x [secant of x] Y) cos²𝑥 [cosine squared of x] Z) 1
W) csc x
MATH Multiple Choice If |x|>-5 [the absolute value of x greater than negative 5] is graphed on a number line, which of the following could describe its graph? W) Segment X) Ray Y) Line Z) Two opposite rays, not sharing a common endpoint
Y) LINE
Which of the following is equivalent to cosine56°cosine23° -sine23°sine56°? W) sine 33° X) cosine 33° Y) sine 79° Z) cosine 79°
Z) COSINE 79°
MATH Short Answer Express the following in simplest form, with variables raised only to positive powers: (4𝑥⁵𝑦⁻³)⁻² [open parenthesis 4x to the fifth y to the power of negative 3 close parenthesis to the power of negative 2]
y⁶/16x¹⁰
BONUS MATH Short Answer If sin θ + cos θ = 1/3 [sine of theta plus cosine of theta equals one third], find sin 2θ
− 8/9
MATH Short Answer Providing your answer in simplest form, what is the cotangent of x, if cos(x) < 0, sin(x) > 0, and x has reference angle pi/6?
− √3
Bonus: One dimension of a cube is increased by 1, another is decreased by 1, and the other is left unchanged. If the new solid has a volume 5 less than that of the original cube, what was the volume of the original cube?
125
BONUS MATH Short Answer What is the sum of the first 50 terms of the arithmetic sequence with second term 35 and fourth term 55?
13,500
BONUS 13) MATH Short Answer Find the solution set of the following equation: (4 1) 2 (2 3) 2 + = x − x
ANSWER: -2
BONUS 21) MATH Short Answer Find the following number: When the number, one-half of the number, and one-quarter of the number are added, and then 8 is subtracted, the result is 2 less than twice the number:
ANSWER: -24 (Solution: n + 1/2n + 1/4n - 8 = 2n -2)
BONUS 13) MATH Short Answer Subtract the following 2 polynomials: (-4x3 y + 2x3 y 2 + 2x2 y 3 + 2y) - (4x3 y - 7x3 y 2 + x2 y 3 - y)
ANSWER: -8x3 y + 9x3 y 2 + x2 y 3 + 3y
MATH Short Answer Express i⁴⁴³ in simplest form.
ANSWER: -i
MATH Short Answer If x² + y² = 5² , find dy dx in terms of x and y in simplest form.
ANSWER: -x/y
BONUS MATH Short Answer Assuming that the probability of A is 0.3, the probability of B is 0.3, and the probability of A union B is 0.5, providing your answers as decimals to the nearest tenth, what are the probabilities, respectively, of A intersection B and the complement of the quantity A union B?
ANSWER: 0.1 AND 0.5
BONUS 16) COMPUTER SCIENCE Short Answer What is the three-bit natural binary code equivalent of the decimal value 5/ 8 ?
ANSWER: 0.101
BONUS 13. MATH Short Answer Evaluate lim(𝑥 →∞) 𝑥(−1 + (𝑒^1⁄𝑥)) [the limit as x approaches infinity of x times the quantity negative 1 plus e to the 1 over x].
ANSWER: 1
BONUS 21) MATH Short Answer What is the limit of x^x as x approaches 0 from the positive side?
ANSWER: 1
MATH Short Answer Find the exact value of the expression: sin ( 5𝜋/4 )/cos( 5π/4 ) [the fraction with numerator, sine of, 5 pi over 4, and denominator, cosine of, 5 pi over 4].
ANSWER: 1
MATH Short Answer Evaluate limx→π/3 sinx 3 2 x π !!3 (read as: the limit as x approaches pi over three of open parenthesis sine of x [pause] minus the square root of 3 over 2 close parenthesis over open parenthesis x minus pi over 3 close parenthesis).
ANSWER: 1/2
BONUS MATH Short Answer What is the value of the infinite sum: 1 2! - 1 3! + 1 4! - 1 5! +... (read as: 1 over 2 factorial minus 1 over 3 factorial plus 1 over 4 factorial minus 1 over 5 factorial and so on)?
ANSWER: 1/e
Short Answer What is the value of the infinite sum: 1 2! - 1 3! + 1 4! - 1 5! +... (read as: 1 over 2 factorial minus 1 over 3 factorial plus 1 over 4 factorial minus 1 over 5 factorial and so on)?
ANSWER: 1/e
BONUS Math - Short Answer A restaurant's 4 dollar box allows you to pick any 2 of 4 possible entrees (including 2 of the same), one of 2 sides, one of 2 desserts, and one of 3 drinks. How many different orders are possible?
ANSWER: 120
BONUS MATH Short Answer Water flows at 10 cubic feet per minute into a cylinder with a radius of 5 feet and height of 12 feet. Providing your answer as a fraction in simplest form in terms of π, how fast is the water rising in feet per minute when the height is 4 feet?
ANSWER: 2/(5π)
BONUS Math - Short Answer A square has sides of length 10 centimeters. In square centimeters, what is the difference between the areas of its circumscribing circle and its inscribed circle?
ANSWER: 25π
BONUS MATH Short Answer A rectangular box has the dimensions 6 inches by 10 inches by 12 inches. What is the length of the space diagonal in inches, in simplest radical form?
ANSWER: 2√70
BONUS 20) MATH Short Answer To the nearest cubic inch, find the volume of a sphere whose diameter is 4 inches:
ANSWER: 33 (ACCEPT: 32 - 34) (Solution: V = 4/3 πr 3 ; = 4/3 (3.14)(8); = 33.49)
MATH Short Answer Consider the polar equation r = sin(2θ) (read as: r equals the sine of 2 theta). Its graph looks like a rose. How many petals would there be on the "rose" in this graph?
ANSWER: 4
MATH Short Answer What is the minimum possible value of 2x + 2y (read as: 2 to the power of x plus 2 to the power of y) if x + y = 2?
ANSWER: 4
Short Answer What is the minimum possible value of 2x + 2y (read as: 2 to the power of x plus 2 to the power of y) if x + y = 2?
ANSWER: 4
MATH Short Answer Providing your answer as a fraction in simplest form, what is the probability of drawing a heart or a king from a standard playing deck of cards?
ANSWER: 4/13
BONUS MATH Short Answer A series is defined recursively. If 𝑎₁ = −2 and 𝑎ₙ = 3 + (aₙ−₁)ⁿ⁻¹ [a sub n equals 3 plus open parenthesis a sub the quantity n minus 1 close parenthesis to the power of the quantity n minus 1], determine the value of 𝑎₄.
ANSWER: 67
MATH Short Answer Pablo walks 4 miles north, 6 miles east, and then 2 miles north again. In simplest form, how many miles is he from his starting point?
ANSWER: 6√2
TOSS-UP 13) MATH Short Answer What is the sum of the interior angles of a 6-sided polygon?
ANSWER: 720°
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)
MATH Multiple Choice You are conducting an experiment. In a large elementary school, you select two age-matched groups of students. Group 1 follows a normal schedule. Group 2 spends 30 minutes a day in art class in addition to their other classes. You want to test whether learning art makes a student less likely to get in trouble. You consider a student in trouble if he or she was sent to the principal's office at any time during the year. The data you collect would BEST be analyzed by which of the following? W) Two populations, difference in means, paired data X) Two populations, difference in means, unpaired data Y) Two populations, difference in proportions Z) Two populations, contingency table
ANSWER: Y) TWO POPULATIONS, DIFFERENCE IN PROPORTIONS
BONUS MATH Multiple Choice The sum of the squares of reciprocals of all positive integers equals which of the following? W) π X) π/3 Y) π²/6 Z) π³/12
ANSWER: Y) π²/6
BONUS 8) COMPUTER SCIENCE Multiple Choice In Windows 98, long file names can be up to how many characters long: W) 35 X) 75 Y) 100 Z) 255
ANSWER: Z) 255TOSS-UP 13)
Math - Multiple Choice Given two sets A and B with A union B containing exactly 3 elements, which of the following must be true about sets A and B? W) Each set contains at least 2 elements X) Each set contains at most 2 elements Y) Each set contains at least 3 elements Z) Each set contains at most 3 elements
ANSWER: Z) EACH SET CONTAINS AT MOST 3 ELEMENTS
BONUS 1. MATH Short Answer Providing your answer in simplest form, what is the volume generated by rotating the region bounded by y = x² and y = x about the line x = 2?
ANSWER: π/2
MATH Short Answer Solve the following equation for x on the interval 0 ≤ 𝑥 < 2𝜋: 4cos²𝑥 − 1 = 0
ANSWER: π/3, 2π/3, 4π/3, 5π/3
MATH Short Answer Solve the following equation over the complex numbers: (x + 3)² + 16 =0.
ANSWER: −3 ± 4i
In the conversion of the rectangular coordinates (-8, 6) into polar coordinates, to the nearest whole number, what is the degree measure of the angle? W) 127 X) 143 Y) 307 Z) 323
X) 143
Bonus: If the third derivative of a position function can be described by the function 4t, what is the coefficient on the highest order term in the position function?
1/6
Bonus: The bob on a pendulum swings through an arc 6 feet long when the string swings through an angle of 0.5 radians. What is the length of the pendulum in feet?
12
If an exterior angle adjacent to a base angle of an isosceles [eye-SOSS-uh-lees] triangle measures 132º, what is the degree measure of the vertex angle?
84
BONUS MATH Short Answer Solve the system of equations: x + y = 1, and x² + 3y² = 21.
ANSWER: (-3/2, 5/2), (3, -2)
BONUS MATH Short Answer In simplest radical form, what is the radius of the circle tangent to the sides of an equilateral triangle with a side length of 2?
ANSWER: (3)^(1/2)/3
BONUS MATH Short Answer Each of the following equations represents a plane: x - y = 6; 2x - 3z = 16; 2y + z = 4. At which point (x, y, z), will they intersect?
ANSWER: (8, 2, 0)
BONUS 19. MATH Short Answer Expressing your answer in simplest form, find all values of x for which the determinant of the following matrix is 3: [the 2 by 2 matrix with row 1: the quantity x minus 3, 6 and row 2: 1, the quantity 2x plus 1].
ANSWER: -1.5 AND 4 (ACCEPT: -3/2 AND 4)
BONUS 10) MATH Short Answer Find the second derivative of the function f(x) = (3 + 2x)e^-3x .
ANSWER: 3(6x + 5)e^-3x [ACCEPT: (18x + 15)e^-3x ]
BONUS 16) MATH Short Answer A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 200 square feet. What is the rate of change of the width of the rectangle in feet per second when the height is 5 feet, if the height is decreasing at that moment at the rate of 0.5 feet per second?
ANSWER: 4
MATH Short Answer What is the name of the point at which the three angle bisectors of a triangle intersect?
ANSWER: INCENTER
BONUS 8) COMPUTER SCIENCE Short Answer What is the term for half a byte, or four bits?
ANSWER: NIBBLE (ACCEPT: NYBBLE)
BONUS 7. MATH Short Answer Identify, in the context of regression analysis, all of the following three statements that are ALWAYS true: 1) When the data set includes an influential point, the data set is nonlinear; 2) Influential points reduce the coefficient of determination, 3) All outliers are influential data points.
ANSWER: NONE
TOSS-UP 5) MATH Short Answer In algebra, what is a second degree polynomial equation most commonly called?
ANSWER: QUADRATIC (ACCEPT: QUADRATIC EQUATION)
BONUS MATH Short Answer Find all points of inflection and extrema, including type, of the function f(x) = (e^x+ e^x)/2 . NOTE: question is probably incorrect
ANSWER: RELATIVE MINIMUM (ACCEPT: MINIMUM) AT (0, 1) [DO NOT ACCEPT: (0, 1) ALONE
MATH Multiple Choice A long-play record rotates at 33 1 3 revolutions per minute. Which of the following represents this in radians per minute? W) 66 2/3 𝜋 X) 33 1/33 𝜋 Y) 16 2/3 𝜋 Z) 6𝜋
ANSWER: W) 66 2/3 𝜋
Math - Multiple Choice Let f(x) be a polynomial function with real coefficients and at least one real root. Which of the following must be true? W) f(x) has an even number of non-real complex roots X) f(x) is of odd degree Y) f(x) is an even function Z) The graph of f(x) has a horizontal asymptote
ANSWER: W) f(x) HAS AN EVEN NUMBER OF NON-REAL COMPLEX ROOTS
MATH Multiple Choice The last two digits, in order, of a positive integer n are 1 and 8. Which of the following statements about n can be TRUE? W) n is divisible by 7 X) n is divisible by 5 Y) n is divisible by 4 Z) n is a perfect square
ANSWER: W) n IS DIVISIBLE BY 7
MATH Multiple Choice Which of the following values represents the slope of the tangent line at x = 0 to the curve y = (e^-x) [y equals e to the negative x]? W) -e X) -1 Y) 0 Z) 1
ANSWER: X) -1
MATH Multiple Choice Which of the following represents the number of inches a rolling wheel with a radius of 4 inches travels on level ground in 6 revolutions? W) 24 𝜋 X) 48 𝜋 Y) 96 𝜋 Z) 144 𝜋
ANSWER: X) 48 𝜋
MATH Multiple Choice Which of the following is NOT true? W) A rational function's graph may intersect its horizontal asymptote X) A rational function's graph may intersect one of its vertical asymptotes Y) The function f(x) = -1/x is its own inverse Z) The function f(x) = -x is its own inverse
ANSWER: X) A RATIONAL FUNCTION'S GRAPH MAY INTERSECT ONE OF ITS VERTICAL ASYMPTOTES
Math - Multiple Choice Which of the following equations does NOT include the half-line y = x, where x and y are positive, in its solution set? W) x^y = y^x X) cosine of the product xy equals sine of the product xy Y) x natural log of y = y natural log of x Z) 2^x + 3^y = 2^y + 3^x
ANSWER: X) COSINE OF THE PRODUCT xy EQUALS SINE OF THE PRODUCT xy
TOSS-UP 13) MATH Multiple Choice A parallelogram whose adjacent sides are unequal is called a: W) rhombus X) rhomboid Y) deltoid Z) rectangle
ANSWER: X) RHOMBOID
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)
MATH Multiple Choice Which of the following is equivalent to ln(1/8) [the natural log of one eighth]? W) 3ln2 [3 natural log of 2] X) -ln3 [negative natural log of 3] Y) -3ln2 [negative 3 natural log of 2] Z) log₂3 [log base 2 of 3]
ANSWER: Y) -3ln2
BONUS 16) COMPUTER SCIENCE Multiple choice A logic chip that is just 20 nanometers wide would be about how many times wider than a single silicon atom? W) 5 X) 50 Y) 200 Z) 500
ANSWER: Y) 200
MATH Multiple Choice Populations P1 and P2 are normally distributed and have identical means; however, the standard deviation of P1 is twice the standard deviation of P2. Which of the following is TRUE about the percentage of observations falling within two standard deviations of the mean for each population? ' W) The percentage for P1 is twice the percentage for P2 X) The percentage for P1 is greater, but not twice as great, as the percentage for P2 Y) The percentage for P2 is twice the percentage for P1 Z) The percentages are identical
ANSWER: Z) THE PERCENTAGES ARE IDENTICAL
Which of the following best describes the type of conic section represented by the equation x²+ 10x+ y²+ 16 equals zero? W) Circle X) Ellipse Y) Hyperbola Z) Parabola
W) CIRCLE
Bonus: According to the rational root theorem, which of the following is NOT a possible solution to the equation x³-2x²+ x-2 = 0? W) -1 X) ½ Y) 1 Z) 2
X) ½
Bonus: Which of the following is nearest to 1,000,000? W) 5 to the 6thpower X) 10 to the 7thpower Y) 2 to the 20thpower Z) 400 squared
Y) 2 TO THE 20TH POWER
MATH Multiple Choice Which of the following represents an equivalent value for log₁₀ √1000 [log base 10 of the square root of 1000]? W) 10³/² [10 to the power of three halves] X) 10²/³ [10 to the power of two thirds] Y) 3/2 Z) 2/3
Y) 3/2
BONUS MATH Multiple Choice Which of the following represents the solution in degrees of the equation 4sin² x = 1 in the open interval from 0° to 180°? W) 30o X) 30o, 60o Y) 30o, 150° Z) 60o, 120o
Y) 30o, 150°
Let f(x) be a continuous and differentiable function on the closed interval [3,6]. Which of the following could be the x-value guaranteed by the Mean Value Theorem for this situation? W) 2 X) 3 Y) 5 Z) 7
Y) 5
BONUS MATH Short Answer Giving your answer with r positive and theta in radians, what are the equivalent polar coordinates to the rectangular coordinates (-3√3, −3)?
ANSWER: (6, 7π/6)
MATH Short Answer Expressing your answer in interval notation, what is the largest possible real domain of the function: 𝑓(𝑥) = √(𝑥²−16)/|𝑥+9| [f of x equals the fraction with numerator, the square root of the quantity x squared minus 16, and denominator the absolute value of the quantity x plus 9]?
ANSWER: (−∞, −9) ∪ (−9, −4] ∪ [4, ∞) [NOTE: NEED NOT USE UNIONS, BUT MUST CLEARLY INDICATE THAT -9 IS NOT INCLUDED, WHILE ± 4 ARE]
BONUS 12. MATH Short Answer Find dy/dx at the point with coordinates (1, 2) if y is implicitly defined by the equation x³y + xy² = 6.
ANSWER: -2
BONUS MATH Short Answer If the recursive sequence tₙ is defined by t₁ = 3 and tₙ = -5 + 3tₙ-₁ , what is the value of t₆?
ANSWER: 124
BONUS 14. MATH Short Answer Express the following complex number in simplest a + bi form: 5i¹³ + 6i¹² - 7i¹⁰ + 3i.
ANSWER: 13 + 8i
BONUS Math - Short Answer What is the area between the curves y = x + 3 and y = x 3 between x = 0 and x = 1?
ANSWER: 13/4 (ACCEPT: 3.25, 3 ¼)
BONUS MATH Short Answer In square centimeters and in terms of pi, find the area of a circle with an inscribed triangle with side lengths of 10 centimeters, 24 centimeters, and 26 centimeters.
ANSWER: 169π
BONUS 23. MATH Short Answer A spherical balloon initially contains no air and is inflated in such a way that its radius increases at a rate of 2 centimeters per second. Providing your answer in terms of pi, how fast is the volume increasing in cubic centimeters per second 3 seconds after inflation starts?
ANSWER: 288π
MATH Short Answer Factor the following polynomial completely over the real numbers: 2x⁵ - 32x.
ANSWER: 2x(x2 + 4)(x + 2)(x - 2)
MATH Short Answer What is the limit as x approaches 0 of sin(3𝑥)/𝑥 [the fraction with numerator sine of 3x and denominator x]?
ANSWER: 3
TOSS-UP 13) MATH Short Answer What is the formula for the volume of a sphere?
ANSWER: 3 4 πr 3 (read as: four third pi radius cubed)
BONUS MATH Short Answer Determine the value of the following: [the summation as n goes from 1 to 17 of the quantity 3n minus 5 ].
ANSWER: 374
TOSS-UP 5) MATH Short Answer Convert 135° into radians:
ANSWER: 3π /4
TOSS UP 1. MATH Short Answer Find the number of degrees in the angle of elevation of the Sun when a 10-foot vertical flag pole casts a 10-foot shadow on level ground.
ANSWER: 45°
BONUS MATH Short Answer If the volume of oil leaked into the ocean from a damaged drilling platform is given by the equation 2 V = 0.05πr , where r is the radius of the spill, use differentials to estimate the error in cubic meters of the volume if there is a possible error of 0.5 meters in the radius measurement of a spill of radius 100/π meters.
ANSWER: 5
BONUS 17. MATH Short Answer Two objects move along a number line. At t seconds, their positions are given as s₁ = 2t - t² and s₂ = 2t² - 3t. Providing your answers as fractions in simplest form, give all times in seconds when the two objects have the same speed.
ANSWER: 5/6 AND 1/2
TOSS-UP 21) MATH Short Answer Convert 300° into radians:
ANSWER: 5π /3
5) MATH Short Answer In a triangle ABC, angle A = 55° and angle B = 70°. If line segment AB = 3x - 2 and line segment BC = x + 10, what is the value of x?
ANSWER: 6 (Solution: Isosceles, thus: AB = BC; 3x - 2 = x + 10; x = 6
TOSS-UP 8) COMPUTER SCIENCE Short Answer In most computer systems, a byte is a unit of data that is how many binary digits long?
ANSWER: 8
BONUS Math - Short Answer A national achievement test is administered. The test has a mean score of 100 and a standard deviation of 10. If Ann's Z-score is -1.3, what is her score on the test?
ANSWER: 87
BONUS 5) MATH Short Answer What is the area of an equilateral triangle whose side is 6?
ANSWER: 9 3 (ACCEPT: 15 - 16) (Solution: A = 9 3 4 3 2 = s )
TOSS-UP 5) MATH Short Answer What German mathematician in 1865 cut a long rectangular strip of paper, gave the paper a half-twist, and pasted the ends together, to show that a sheet can have only one side?
ANSWER: AUGUSTUS MOBIUS (ACCEPT: MOBIUS)
TOSS-UP 16) COMPUTER SCIENCE Short Answer In word processing, a collection of letters and associated characters in the same typeface, style and point size is called:
ANSWER: FONT
BONUS 16) COMPUTER SCIENCE Short Answer What does the acronym for the JPEG graphics file format stand for?
ANSWER: JOINT PHOTOGRAPHIC EXPERTS GROUP
MATH Multiple Choice Solve the following equation for x: (𝑥 − 9)^(2/3) = 16 [the quantity x minus 9 to the power of two thirds equals 16]. W) 73 X) ± 73 Y) 73 and -55 Z) − 64/9
ANSWER: Y) 73 AND -55
TOSS-UP 16) COMPUTER SCIENCE Multiple Choice Software for which the source code is furnished and users agree NOT to limit the distribution of improvements is called: W) public-domain X) freeware Y) open-source Z) shareware
ANSWER: Y) OPEN-SOURCE
TOSS-UP 16) COMPUTER SCIENCE Multiple Choice Resetting a computer that is already turned on to its initial state whereby any data or programs in main memory are erased is called a: W) clean boot X) cold boot Y) warm boot Z) hot boot
ANSWER: Y) WARM BOOT
TOSS-UP 8) COMPUTER SCIENCE Multiple Choice The allowing of long file names was a primary difference between: W) DOS and Windows 3.11 X) Windows 3.11 and Windows for Workgroups Y) Windows 3.11 and Windows 95 Z) Windows 95 and Windows 98
ANSWER: Y) WINDOWS 3.11 AND WINDOWS 95
MATH Short Answer Find the values of a and b so that the given function f(x) is continuous everywhere: f(x) is a three part function: For x less than or equal to 1, f(x) = x + 3, for x between 1 and 4, f(x) = ax + b; and for x greater than or equal to 4, f(x) = 2x - 10.
ANSWER: a = -2, b = 6
BONUS 21) MATH Short Answer Solve the following equation for b: d c d b (a b) ( + ) = +
ANSWER: b = c ad
BONUS 13) MATH Short Answer Use the Binomial Theorem to expand and simplify the following equation: (x - 1)4
ANSWER: x 4 - 4x 3 + 6x 2 - 4x +1
BONUS 5) MATH Short Answer Solve the following inequality: 3 - 6x > 15
ANSWER: x < -2
MATH Short Answer Solve the following expression when x = 4: ( 𝑥³/9 )^(-1/2) [open parenthesis, x cubed over 9, close parenthesis, to the negative ½ power].
ANSWER: x = 3/8
