MATH-4

Short Answer Find the polynomial with real coefficients, leading coefficient 1, and least degree that has 2 + 3i as a zero.

x2 ??? 4x +13

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 ANSWER: X) NEAP TIDES ANSWER: W) CRETACEOUS PERIOD

Short Answer Express (read as: the summation of x equals 1 to n of log of x) with a factorial.

log n!

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

Short Answer Solve for x in simplest form for 3x2 + 2x = 2.

x = ???1?? 7 (ACCEPT: -1/3 ?? /3) 3

Short Answer Simplify the following expression: x 2 x 59

x10 (ACCEPT: 10 x9 )

Short Answer The point (1, 2) is reflected across the x axis. What are the coordinates of its image?

(1, -2)

Short Answer What is the point of intersection of these two lines: y = -2x + 3 and y = 3x - 7?

(2, -1)

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

(2, 8) ANSWER: X) OLIVINE ANSWER: ANDESITIC (ACCEPT: ANDESITE) (Solution: 3 basic types: basaltic, andesitic, rhyolitic)

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

Short Answer What is the fifth number in the geometric sequence that begins: 27, 9, 3, 1?

1/3

Short Answer Factor the following expression completely over the integers: .

(a + 2)

Short Answer If the determinant of a 2 by 2 matrix, denoted A, is equal to -2, what is the determinant of 2 times A?

- 8

Short Answer Evaluate y = 5x2 + 4x3 + 12 (read as: 5x squared plus 4 x cubed plus 12) when x = -2.

0

Short Answer A spherical balloon is being inflated at a constant rate of ?? cubic inches per second. In inches per second, how fast is the radius increasing when the radius is 3 inches?

1/36

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 ANSWER: 90 ANSWER: W) CONTINENTAL TROPICAL

Short Answer A number is obtained by tripling an original value, then tripling that result. If the final resulting value obtained by applying the process previously described is 1, what was the original number?

1/9

Short Answer A triangle has sides of length 5, 7, and 8 meters. In simplest form and in meters squared, what is the area of the triangle?

10

Short Answer If the mean of a certain sample is 8 and the standard deviation is 0.25, what value has a z-score of 12?

11

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

2,5,7,???3 414141 41 ANSWER: X) 6.0 TO 7.0 ANSWER: Y) ALUMINUM TOXICITY TO THEIR ROOTS

Short Answer If N represents the number of sides for a regular polygon that tessellates the plane, how many different values of N are there?

3

Short Answer How many different letter arrangements can be formed using the six letters in the word ???energy????

360

Short Answer Find the derivative of 12x3 - 6x2 + ??? 25 (read as: 12 x cubed minus 6 x squared plus 3 over x to the fifth minus 25)

36x2 ???12x -

Short Answer An ichthyologist wants to know the fish population of a pond. She catches 60 fish, tags them, and releases them. Two weeks later, she catches 50 fish and 7 of them have tags. Based on the data, what is the best estimate of the fish population of the pond? Round your answer to the nearest hundred.

400

Short Answer How many terms are there in the arithmetic sequence with first term 10, second term 15, third term 20, and final term 250?

49

Short Answer If someone has 1 red shirt, 2 blue shirts, 4 red pants, and 3 green pants from which to choose, what is the probability that a randomly selected shirt and pant combination has at least one red item? Provide your answer as a fraction in simplest form.

5/7

Short Answer Find the limit as x approaches -2 of (x3 + 8)/(2x + 4) (read as: the quantity x cubed plus 8 divided by the quantity 2x plus 4).

6

Short Answer A particle???s displacement in meters can be described by the function f(x) = 2x3 + 3x2 - 10x + 30. At x = 5 seconds, what is the acceleration in meters per second squared? Provide your answer to the nearest integer.

66

Short Answer Determine the slope of the line that has the equation: y ??? 14 = 7 (x + 2) - 5.

7

Short Answer How many solutions are there for the equation, cosine 4x = 12 , for the interval 0 ??? x < 2???

8

Short Answer Simplify the following rational expression: 5y ??? 3x2 9y2 +5x

CANNOTBEFURTHERSIMPLIFIED (ACCEPT: 5y???3x2 orTHESAME) 9y2 +5x

Short Answer Identify the type of conic section represented by the equation, x2 + y2 + 10y + 16 = 0:

CIRCLE (Solution: x2 + (y + 5)2 = 9)

Short Answer What type of growth does y = 36 7x (read as: y equals 36 times 7 to the power of x) represent?

EXPONENTIAL

Short Answer What adjective is used to describe a set that can be placed in one-to- one correspondence with a subset of itself?

INFINITE

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)

Short Answer If the distribution graph of a set of data has a positive skew, then which tail of the graph is longer?

RIGHT

Short Answer Consider the polynomial 5x2 + 13x + 10. How many and what kind of roots does it have?

TWO COMPLEX ROOTS

Short Answer What do we call a mathematical object that possesses both magnitude and direction?

VECTOR

Multiple Choice If a train???s wheels have a diameter of 4 feet and turn at rate of ?? radians per second, how fast is the train moving in feet per second?W) 2 X) 4 Y) 2?? Z) 4??

Y) 2??

Multiple Choice If x = 4 and y = 2, which of the following expressions is undefined? W) 3x +X) 2y + 4x Y) xy ??? x2Z) x +

W) 3x +

Multiple Choice Which of the following has the largest amplitude?W) 9sin(x) - 2 X) 2cos(6x) + 5 Y) cos(2x)Z) 4sin(10x)

W) 9 sin(x) - 2

Multiple Choice In the use of a statistical test, which of the following constitutes a Type I (read as: type one) error?W) rejecting a true null hypothesisX) accepting a false null hypothesisY) using a sample size that is too small for the test Z) comparing samples that differ too much in size

W) REJECTING A TRUE NULL HYPOTHESIS

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

Multiple Choice Which of the following is congruent to (n + 1) modulus n?W) 0X) 1Y) (n ??? 1) Z) (n ??? 2)

X) 1

Short Answer Evaluate log (read as: log of the quantity 10 to the x times 100 over 10 thousand)W) 2 - x X) x - 2 Y) x + 3 Z) 10x

X)x???2

Multiple Choice Evaluate the following expression: (read as: the summation from -1 to 4 of 3 k squared).W) 31 X) 87 Y) 93 Z) 243

Y) 93

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 primeZ) their quotient is the golden ratio

Y) THEY ARE RELATIVELY PRIME

Multiple Choice Which of the following functions is one-to-one?W) f(x) = |x| + 3 (read as: f of x equals the absolute value of x plus 3)X) f(x) = x2 ??? 6x + 11 (read as: f of x equals x squared minus 6 x plus 11) Y)f(x)=5x3 +9(readas:fofxequals5xcubedplus9) Z) f(x) = (read as: f of x equals 1 over x squared)

Y) f(x) = 5x3 + 9

Multiple Choice In a parallelogram ABCD, the sides AB and DC can be represented by:W) Opposite vectorsX) Two different vectors with the same direction Y) Two different vectors with the same magnitude Z) The same vector

Z) THE SAME VECTOR

Short Answer Give the numerical value for the number of different orders in which 7 people can line up at a cash register?

5,040

Short Answer The area of a square is 36 square centimeters. What is the length of its diagonal in centimeters in simplest radical form?

6

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 ANSWER: W) THEY BEGIN TO DISSOLVE ANSWER: W) PASSIVE MARGINS

Short Answer The first row in a theatre contains 8 seats. Every other row contains 2 seats more than the one in front of it. How many people can sit in the first 6 rows?

78 ANSWER:

Short Answer The lengths of two sides of a triangle are 4 and 9. If the triangle is isosceles, what is the length of the third side?

9

Short Answer If the volume of a cube is 64 cubic centimeters, then what is the surface area of the cube in square centimeters?

96

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

???65 ANSWER: Z) SLEET ANSWER: MARBLE = METAMORPHIC; PUMICE = IGNEOUS; CONGLOMERATE = SEDIMENTARY

Multiple Choice Which of the following functions is continuous at x = -1? W)X) Y) Z)

Y)

Multiple Choice Which of the following intervals contains both solutions of x2 - 3x = 0?W) 0 less than x less than 2X) 0 less than x less than 4Y) 0 less than or equal to x less than 4 Z) -3 less than x less than or equal to 2

Y) 0 less than or equal to x less than 4 BONUS

Short Answer A viper had a length of 30 centimeters at 6 months of age and a length of 1.3 meters at 15 years old. Assuming that its growth was linear, which of the following is closest to its length in meters at 10 years old?W) 0.6 X) 0.8 Y) 1 Z) 1.2

Y) 1

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

Multiple Choice A math teacher is trying to describe her favorite triangle. The lengths of two sides are 4 centimeters and 6 centimeters. The angle opposite the 4 centimeter side is 12??. How many non-congruent triangles fit this description?W) 0X) 1Y) 2Z) An infinite number

Y) 2

Multiple Choice Find the derivative of 2xex (read as: 2x e to the x). W) 2ex +2xX) 2xex + ex Y) 2xex + 2ex Z) 2xex

Y) 2xex + 2ex

Multiple Choice Which of the following numbers is relatively prime with 15?W) 348 X) 350 Y) 352 Z) 354

Y) 352

Multiple Choice What are the solutions for x in the following equation: x2 ??? 2x = 8?W) 0X) 0 and 2 Y) 4 and -2 Z) -4 and 2

Y) 4 AND -2

Multiple Choice Which of the following numbers is not a Mersenne prime?W) 7 X) 31 Y) 61 Z) 127

Y) 61

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-axisX) 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

Multiple Choice If b is a negative vector of a given vector a, then how do b and a compare?W) a has a smaller magnitude than bX) b has a smaller magnitude than aY) b has the same magnitude as a, applied in the opposite direction Z) b has a larger magnitude than a, applied in the opposite direction

Y) B HAS THE SAME MAGNITUDE AS A, APPLIED IN THE OPPOSITE DIRECTION

Multiple Choice A student at your school conducts a survey about hair products. He determines the hair color of 50 of his classmates, and then randomly selects 5 redheads and 5 brunettes to participate in his survey. What type of sampling did he use?W) Simple random X) Stratified random Y) ClusterZ) Systematic

Y) CLUSTER

Short Answer Giving your answer as a fraction reduced to lowest terms, solve the following equation for x: 2 x ??? 1 = 10 x + 13462 A N S W E R : ??? 43TOSS-UP12) EARTH SCIENCE Multiple Choice Which of the following is best used to date the age of the Earth to about 4.5 billion years old:W) uranium-235 X) uranium-238 Y) potassium-40 Z) carbon-14

X) URANIUM-238 ANSWER: Y) ZIRCON

Short Answer The lengths of two sides of a triangle are 30 centimeters and 35 centimeters, respectively. Between what values, in centimeters, must the length of the third side lie?

BETWEEN 5 AND 65

Short Answer What is the slope of a vector in standard position with an angle of 45?? below the positive x axis?

-1

Short Answer If x is negative, simplify (read as: 7 times the square root of 5x times the square root of, open parenthesis, 180x to the fifth, close parenthesis)

-210x3

Short Answer What is the derivative of cos ( + w) (read as: cosine of open parenthesis pi over 2 plus w close parenthesis) with respect to w, in terms of cos(w)?

-cos(w) (DO NOT ACCEPT: OTHER ANSWERS)

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 AND 4

Short Answer What is the smallest integer greater than 1 that is relatively prime with 210?

11

Short Answer If Jill takes three blouses, two pairs of pants, and two pairs of shoes for a weekend trip, how many different complete outfit combinations can she put together?

12

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

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

120 ANSWER: ARGON ANSWER: X) OUTGOING INFRARED SOLAR RADIATION IS TRAPPED BY THE LOWER ATMOSPHERE

Short Answer How far apart, in degrees, are the asymptotes of the graph of 2tan(3x/2) (read as: 2 times the tangent of 3x over 2)?

120??

Short Answer If a random number R is a real number from the closed interval [0,1], then how many possible integer values could be generated by the expression 12R + 7?

13

Short Answer A man who is 6 feet tall spots a bird at the top of a 14-foot telephone pole. If the angle of elevation from his eyes to the top of the pole is 30 degrees, then to the nearest foot, how far away is he standing from the base of the pole?

14

Short Answer If all of the interior angles of a polygon sum to 3060 degrees, how many sides does the polygon have?

19

Short Answer If y = p(x) and y = q(x) are two cubic polynomial functions that have the same leading coefficient, what is the maximum possible number of intersections of their graphs?

2

Short Answer When the discriminant of a quadratic function ax2 + bx + c = 0 is greater than 0, how many x intercepts does the graph have?

2

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 ANSWER: RADIATION FOG (ACCEPT: RADIATION or RADIATIONAL) (Solution: brought about by radiational cooling) ANSWER: NIGHT

Short Answer Bethany and Charlene are 7 years apart in age. In two years, Charlene will be twice Bethany???s age. What is Bethany???s current age?

5

Short Answer If four numbers have an arithmetic mean of 20, and three of the numbers are 17, 18, and 19, what is the fourth number?

26

Short Answer Rebekah wants to fill a spherical pin??ata with candy. If the radius of her pin??ata is 6 inches, what is the volume in cubic inches of her pin??ata in terms of pi?

288??

Short Answer What is the perimeter of a sector of angle ??/3 radians in a circle with circumference 2??2? Provide your answer in simplest form in terms of ??.

2??+ ??2/3 (ACCEPT: )

Short Answer One side of an equilateral triangle is 6. In simplest form, what is the altitude?

3

Short Answer Giving your answer in simplest radical form, rationalize the denominatorof the following expression: ??? 3 2( 3??? 5)

3 6+3 10 (ACCEPT: 3( 6+ 10)) 22 ANSWER: W) BIOTITE ANSWER: Z) THEY ARE BOTH INTRUSIVE IGNEOUS ROCKS (Solution: basalt = extrusive; gabbro = intrusive)

Short Answer Find the measure of angle C in degrees in triangle ABC with sides equal to the following: AB = 15 centimeters, AC = 15 centimeters, and BC = 30 centimeters.

30

Short Answer Two triangles are similar. If the smaller one has a perimeter of 18 and the ratio between them is 5:3 (read as: 5 to 3), what is the perimeter of the larger triangle?

30

Short Answer Solve the following equation for x: log2 x = 5 (read as: log base 2 of x equals 5).

32

Short Answer If you roll a standard 6-sided die 2 times, how many different outcomes are possible?

36

Short Answer Evaluate the following expression when a = 13 , b = 4, c = ???1, and d=???5: 2[3a???(b+c)???4d]

36 ANSWER: W) 20,000 FEET AND ABOVE ANSWER: Y) SUBDUCTION ZONES

Short Answer AB and CD are parallel line segments intersected by the line segment EF. Endpoint E lies on AB, and endpoint F lies on CD. If angle CEF is 18 ?? and angle CFE is 125 ??, what is the measure of angle AEC?

37??

Short Answer What is 224% of 17? Provide your answer as a decimal to the nearest integer.

38

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

Short Answer The diagonals of a rhombus are 12 centimeters and 16 centimeters long. What is the perimeter of the rhombus in centimeters?

40

Short Answer Find the length and width in meters of a rectangle with perimeter of 200 meters and maximum possible area.

LENGTH AND WIDTH = 50

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)

Multiple Choice Which of the following radical expressions is in simplest form?W) X) -5Y) 6 Z) ???(read as: the square root of 31 over 3)(read as: negative 5 times the square root of 175)(read as: 6 times the square root of the quantity x squared over 4) (read as: the negative square root of 153 x)

W)

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

W) 500o

Multiple Choice Which of the following categories of statistical plots displays the first, second, and third quartiles for the data that it represents?W) Box plot X) Scatter plot Y) HistogramZ) Pie chart

W) BOX PLOT

Multiple Choice Which of the following matrices does not have the same determinant as the 2 by 2 matrix with row 1: 0, -1; and row 2: 1, 0?W) the 2 by 2 matrix row 1: 0, -1; row 2: -1, 0 X) the2by2matrixrow1:1,0;row2:0,1 Y) the2by2matrixrow1:1,-1;row2:0,1 Z) the2by2matrixrow1:0,1;row2:-1,0

W)THE2BY2MATRIXROW1:0,-1;ROW2:-1,0

Multiple Choice Which of the following numbers is not prime?W) 137 X) 143 Y) 167 Z) 229

X) 143

Multiple Choice The length of a rectangle is 5 inches less than twice the width. What is the width in inches if the perimeter is 38 inches?W) 5 X) 8 Y) 11 Z) 14

X) 8

Multiple choice Psoriasis, a chronic skin disorder caused by the immune system, affects 1% to 2% of Caucasians. If there are 16,098,000 Caucasians in New York State, about how many would be expected to have psoriasis?W) Between 16,000 and 32,000X) Between 160,000 and 325,000Y) Between 1,600,000 and 3,220,000 Z) 241,470

X) BETWEEN 160,000 AND 325,000

Multiple Choice In a plane, the set of points equidistant from a point and a line form a:W) EllipseX) ParabolaY) TriangleZ) Tip of a cone

X) PARABOLA

Multiple Choice The graph of the relation y = ???W) circleX) semi-circle Y) parabolaZ) straight line(25 ??? x2 ) is a:

X) SEMI-CIRCLE

Multiple Choice If f(x) (read as: f of x) represents the function whose graph is the standard normal distribution curve, then how do the inflection points on the curve for 2f(x) (read as: 2 f of x) compare to those of f(x)?W) Both curves have the same inflection pointsX) The 2f(x) inflection points are twice as far apart but the same heightY) The 2f(x) inflection points are twice as high but the same distance apart Z) The 2f(x) inflection points are both twice as far apart and twice as high

Y) THE 2F(X) INFLECTION POINTS ARE TWICE AS HIGH BUT THE SAME DISTANCE APART

Multiple Choice Solve the quadratic equation 3x2 + 2x ??? 8 = 0 .W) x = 2 or ??? 4 X) x=8or???12 Y) x = ???2 or 4/3 Z) x = 8 or ??? 4/3

Y)x=-2OR4/3

Multiple Choice Line 1 and line 2 are parallel. If line 1 contains the points (6, 13) and (4, 11) and line 2 contains the point (8, 20), determine which of the following points lies on line 2.W) (12, 15) X) (18, 10) Y) (10, -12) Z) (14, 26)

Z) (14, 26)

Multiple Choice If the sine of an angle is 0.3, which of the following is a possible cosine of that angle?W) .09 X) .7

Z) .91

Multiple Choice The radius of a bicycle tire is 10 inches. How far does the wheel travel in inches in 6 revolutions?W) 45 ?? X) 60 ?? Y) 90 ?? Z) 120 ??

Z) 120 ??

Multiple Choice A cylinder and a cone share the same radius and height. What is the ratio of the cylinder???s volume to the cone???s volume?W) 1:1 (read as: 1 to 1)X) 1.5:1 (read as: 1.5 to 1) Y) 2:1 (read as: 2 to 1)Z) 3:1 (read as: 3 to 1)

Z) 3:1

Multiple Choice Given two parallel lines in a plane, the set of points that lie in that plane and are equidistant from the given lines forms a:W) PointX) Segment perpendicular to the lines Y) CircleZ) Line

Z) LINE

Multiple Choice Which of the following equations does not have real solutions?W) -3x2 + 3 = 0X)x2 ???5x+2=0 Y)4x2 ???3x???0.25=0 Z)x2 ???x+1=0

Z)x2 ???x+1=0