Math Questions - Science Bowl

BONUS 11) Math SA Expand the following expression, giving your answer in standard form: (2x2 + 4)3

8x6 + 48x4 + 32x2 + 64

BONUS 46) Math SA Calculate the volume of a regular tetrahedron with a side length of 6.

18sqrt2

TOSSUP 3) Math SA A rectangle has side lengths of 7 and 7√3. What is the distance between the midpoint of this rectangle and any of its vertices?

7

TOSSUP 31) Math SA A regular hexagon has a perimeter of 84 units. What is the length of its apothem?

7√3

BONUS 2) Math SA Giving your answer in simplest form, find the standard deviation of the following set of 5 numbers: 9, 3, 7, 2, 4

√(170)/5

TOSSUP 140) Math SA Calculate the area of a square whose circumcircle has a radius of 8.

128

BONUS 139) Math SA In a universe with strange and unforeseen geometric relationships, the area of a circle is given by (1+r)2/pi, with pi=2. In the universe described, what is the radius of a circle with an area of 98?

13

TOSSUP 158) Math SA Evaluate 210 mod 16.

2

TOSSUP 53) Math SA Calculate the dot product between the vectors <7, 3> and <2, -4>.

2

BONUS 179) Math SA Multiply the following two octal numbers: 5-7 and 3-3

2-3-6-5

TOSSUP 99) Math SA What is the probability of drawing a queen or a king from a standard deck of cards?

2/13

BONUS 109) Math SA A particle's position is represented by the function x(t) = -t2+4t+14. Calculate the total distance traveled by the particle on the interval from [0, 6].

20

TOSSUP 139) Math SA You have some number of marbles of several different sizes and colors. For any set of 6 marbles, at least two of them will be the same size and at least three of them will be the same color. What is the maximum possible number of size-color combinations?

20

TOSSUP 183) Math SA Calculate the area of a square whose circumcircle has a radius of 10.

200

BONUS 32) Math SA Find the lateral area of a hexagonal prism with a height of 4 and base side lengths 8, 12, 14, 11, 5, and 2.

208cm

BONUS 153) Math SA An unfair coin that lands heads 60% of the time is flipped 5 times. What is the probability that the coin lands exactly 3 heads?

216/625

BONUS 20) Math SA Calculate the area of a regular hexagon whose circumcircle has a radius of 4.

24√3

TOSSUP 103) Math SA 70% of Mr. Martinez's students passed the AP chemistry exam. Of those students, 5/7 earned a 3. If Mr. Martinez taught 50 students, how many earned a 3?

25

BONUS 126) Math SA The tangent line to the graph y=-x2+3x+1 at the point (2, 3) intersects both coordinate axes. What is the area of the triangle formed by this tangent line and the coordinate axes?

25/2 (ACCEPT: 12.5)

BONUS 14) Math SA A rectangle has a diagonal length of 10cm and has a width of 5cm. What is the area of this rectangle?

25√3

TOSSUP 57) Math SA A convex polyhedron with 50 edges and 25 faces has how many vertices?

27

BONUS 112) Math SA Giving your answer as an improper fraction in terms of pi, find the volume of a solid generated when the area bounded by the graph of y=x3 and the x-axis from x=0 to x=1 is revolved around the line y=8.

27pi/7 (ALSO ACCEPT: 3 6/7)

TOSSUP 164) Math SA Find the indefinite integral of 1/sqrt(5x) dx

2sqrt(5x)/5 + C

TOSSUP 21) Math SA Find the altitude of a 30-60-90 triangle with a hypotenuse of length 8.

2√3

BONUS 144) Math SA A particle moves along a curve with equations x=5sin(t), y=2cos(t), and z=4t. What is the speed of the particle at time t=pi/2?

2√5

BONUS 62) Math SA Calculate the sum of the infinite geometric series with third term 4/9 and fourth term 8/27

3

BONUS 172) Math SA How many unique combinations can be made from the letters in the word "parallel?"

3360

TOSSUP 96) Math SA Find the length of the minor axis of the ellipse with equation y2/289 + x2/500 = 1

34

TOSSUP 42) Math SA Multiply the following complex numbers: (7+2i) and (4-3i).

34-13i

BONUS 100) Math SA A fair coin is flipped 8 times. What is the probability of landing exactly 4 heads?

35/128

BONUS 165) Math SA A fair coin is flipped 7 times. What is the probability of landing exactly 3 heads?

35/128 Week of 1/30

BONUS 75) Math SA If secθ - tanθ =¼, what is the value of secθ+tanθ?

4

TOSSUP 12) Math SA What is the integer part of log5 800?

4

BONUS 53) Math SA Multiply the following matrices: 2x3 matrix with top row -1, 3, 2 and bottom row 6, 5, -2 and 3x2 matrix with top row 4, -5, second row 2, -3, and bottom row 1, 1.

4 -2 32 -47

BONUS 17) Math SA 28 is the geometric mean between 196 and what other number?

4 (accept: 5488)

TOSSUP 71) Math SA Find the dot product of the vectors 4i -3j and 2i +j.

5

BONUS 49) Math SA Consider the functions f(x) = 4cscx and g(x) = 5/x. Calculate g(f(pi/6))

5 /8

TOSSUP 176) Math SA A bag contains 19 white marbles, 3 red marbles, 15 black marbles, 6 yellow marbles, and 8 orange marbles. What is the probability of drawing a black marble?

5/17

BONUS 85) Math SA Giving your answer in standard radical form,, what is the tan(75)?

5/3 + √3

BONUS 8) Math SA Find the derivative with respect to x of the following expression: 6x * ln(7x2)

6ln(7x2) + 6

BONUS 1) Math SA Determine the length of a pi/4 radian arc on a circle with a diameter of 7 meters.

7/8 meters

TOSSUP 67) Math SA A wheel completes 6 revolutions to roll down a 48m long path. In terms of pi, what is the diameter of the wheel?

8/pi

BONUS 10) Math SA A circle has two secant lines AB and CD that intersect at a point N within the circle. If arc AC is 127 degrees and arc BD is 35 degrees, what is the value angle ANC?

81 degrees

TOSSUP 137) Math SA Evaluate the limit as x approaches infinity of sinh-1(x)

infinity

TOSSUP 51) Math SA Simplify the following log expression: ⅓ log 8 + 3 log 2 - log 4

log 4

BONUS 156) Math SA A dying businessman divides his wealth among his four sons. Timmy will receive half the estate, less 7000; John will receive one third, less 4000, Harrison will receive exactly one quarter; and Bobby will receive one sixth, plus 4000. How much money did the businessman possess?

$28,000

BONUS 68) Math SA Find the center and radius of a circle with equation x2+22x+y2+6y=-124.

(-11, -6) and 6

TOSSUP 29) Math SA The point (7, -4) is reflected across the origin, translated up 5 units, and translated left 6 units. What are the coordinates of the new point?

(-13, 9)

BONUS 83) Math SA Find sin(225) - cot(270) + cos(330)

(-√2 + √3)/2

BONUS 42) Math SA Calculate the centroid of a triangle with points at (6,2), (-7,4), (4, -3) if it is reflected across the line y=x and translated 4 units down.

(1, -3)

TOSSUP 151) Math SA Find the common ratio of a geometric sequence with first term 3 and third term 432.

12

TOSSUP 157) Math SA Find 2 mean proportionals between 3 and 192.

12 and 48

BONUS 72) Math SA Find the limit as x approaches pi/2 of the fraction with numerator 4-x2 and denominator cos(x).

pi

BONUS 148) Math SA What are the mean and median, respectively, of the prime numbers less than 30? 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Mean - 129/10, Median - 12

TOSSUP 156) Math MC The series from n = 1 to infinity of an diverges when an is equal to which of the following? W. 1/n3 X. 1/2n Y. (1- 1/n)n Z. 1/n4/3

Y

TOSSUP 177) Math MC The series from n=0 to infinity of the fraction with numerator xn and denominator n! is equal to which of the following? W. sin(x) X. cos(x) Y. ex Z. arctan(x)

Y

TOSSUP 28) Math MC Which of the following numbers is divisible by 8? W. 562 X. 204 Y. 376 Z. 663

Y

TOSSUP 4) Math MC Which of the following sets of numbers are possible side lengths of a 30-60-90 triangle? W. 40, 20, 20 X. 25, 26, 50 Y. 14, 28, 14√3 Z. 5, 12, 13

Y

TOSSUP 14) Math MC Which of the following is equal to the expression 2 log(3x) + 3 log(5x2) W. log(125x2) + log(9x6) X. log(1125x3) Y. 2 log(5x2) + 3 log(3x) Z. log(9x2) + log(125x6)

Z

TOSSUP 7) Math MC Which of the following numbers is divisible by 7? W. 949 X. 262 Y. 562 Z. 812

Z

TOSSUP 70) Math SA What conic section is represented by the equation x2 +4xy + y2 +7x -8y -13 = 0? W. Circle X. Ellipse Y. Parabola Z. Hyperbola

Z

TOSSUP 97) Math SA Which of the following equations corresponds to a conic section with eccentricity greater than 1? W. 12x2+12y2=16 X. 13x2+2y2=11 Y. -4x2=12 Z. y=2x

Z

TOSSUP 2) Math MC One side of a 30-60-90 triangle is of length 8. Which of the following is not a possible length for one of the other two sides? W. 4 X. 4√3 Y. 16 Z. 24

Z.

TOSSUP 5) Math MC Which of the following is equivalent to the expression (5 times the log of the quantity x2) W. 10 log x2 X. 5 log x Y. 5x Z. 10 log x

Z.

TOSSUP 84) Math MC Which of the following is equivalent to the fraction with numerator 1-tan2θ and denominator 2tanθ? W. tanθ/2 X. tan2θ Y. cotθ/2 Z. cot2θ

Z.

TOSSUP 119) Math SA Evaluate the limit as x approaches 2 of x raised to the fraction with numerator 2 and denominator x-2.

e

BONUS 41) Math SA Factor the following polynomial: x3-7x-6:

(x+1)(x-3)(x+2)

BONUS 142) Math SA Differentiate sinh(x)/x2 with respect to x.

(x*cosh(x) - 2sinh(x)) / x3

TOSSUP 56) Math SA If vector a = 5i + 2j and vector b = 1i +3j, calculate the magnitude of a cross b.

13

TOSSUP 175) Math SA What is 135 squared?

18225

BONUS 173) Math SA In 1992, February 20th fell on a Thursday. What day of the week was February 20th in the year 2000?

Sunday

BONUS 55) Math SA Find the inverse of the following 2x2 matrix: Top row: 3, 2 Bottom row: -3, -4

Top row: ⅔, ⅓ Bottom row: -½ , -½

BONUS 113) Math SA Solve the differential equation for V in terms of t: dV/dt = 0.5V, assuming V=600 at t=0.

V=600e0.5t

BONUS 101) Math SA A certain test for the bacteria A. baumanii is 50% accurate. Another test for the same bacteria is 75% accurate. Given that both tests give positive results, what is the probability that the patient is not infected with the bacteria?

¼

BONUS 44) Math SA Jared takes out a 30,000 dollar loan at a 7% interest rate. If interest is compounded annually, and he pays none of it off, how much money will he owe after one year?

$32,100

TOSSUP 13) Math SA The point (-7, 4) is translated up 7 units and reflected across the line y=x. What are the coordinates of the new point?

(11, -7)

TOSSUP 32) Math SA A triangle has vertices at (19, 22), (21, -3), and (-7, -1). Find the coordinates of the centroid of this triangle.

(11, 6)

TOSSUP 43) Math SA Convert the polar coordinates (8, 405) to cartesian form.

(4√2, 4√2)

TOSSUP 32) Math SA The point (4, -6) is reflected across the y-axis and rotated about the origin 90 degrees counterclockwise. What are the coordinates of the new point?

(6, -4)

BONUS 37) Math SA Consider the function f(x) = 4√(3x+2). Giving your answer in simplest form, evaluate 1/f(-3x) at x = -2

(√5) / 40

BONUS 48) Math SA Calculate the determinant of the following matrix operation: -6 1 2 3 Times -4 -2 3 -5

-520

TOSSUP 16) Math SA Convert -13/4 pi radians to degrees.

-585 degrees

BONUS 47) Math SA Multiply the following 2x2 matrices: 5 -4 2 1 1 -2 3 3

-7 -22 5 -1

TOSSUP 36) Math SA Evaluated the limit as x approaches infinity of (2-3x) / (3x + 5x2)

0

TOSSUP 44) Math SA Solve for x in the following equation: |x-4| = 3x

1 (DO NOT ACCEPT: -2)

BONUS 27) Math SA Order the following three triangles from closest to farthest based on the distance of their centroids to the origin: I. Vertices at (1, 6), (1, 3), (4, 3) II. Vertices at (11, 1), (5, 7), (2, 4) III. Vertices at (9, 5), (3, 2), (2, 5)

1, 3, 2

TOSSUP 39) Math SA Giving your answer in simplest form, find the derivative with respect to x of the following expression: 4x^(2)√x

10x5/2 ACCEPT: 10x√x

BONUS 15) Math SA A 30-60-90 triangle has a hypotenuse of length 8 and a longer leg of length 2√x. Find the value of x.

12

BONUS 24) Math SA The sum of interior angles of a regular polygon is 3,420 degrees. Calculate the measure of one exterior angle of this polygon.

120/7

BONUS 4) Math SA One side of a 30-60-90 triangle is of length 24. List all of the possible lengths for the longer leg of this triangle.

12√3, 24√3, 48√3

BONUS 50) Math SA Find 2 mean proportionals between 2 and 686.

14 and 98

BONUS 23) Math SA A heptacontadigon has 72 sides. Calculate the measure of one interior angle of a regular heptacontadigon.

175 degrees

BONUS 18) Math SA Find three mean proportionals between 6 and 486.

18, 54, 162

BONUS 30) Math SA The point (-3, 14) is rotated 180 degrees about the origin, then reflected across the x-axis, then translated right 7 units, and translated down 4 units. What is the distance between the two points?

25

BONUS 9) Math SA Multiply the following binomials and give your answer in standard form: (7x^(7) + 5x^(6))(4x^(4) - 2x)

28x^(11) + 20x^(10) - 14x^(8) - 10x^(7)

TOSSUP 20) Math SA Find the area of a regular hexagon with a perimeter of 72?

3/4

BONUS 12) Math SA A circle with a center point Q has two secant lines EF and GH, which intersect at a point X outside the circle. If angle EQG is 30 degrees and FQH is 170 degrees, what is the value of angle EXF?

70 degrees

BONUS 39) Math SA Giving your answer in standard radical form, find the surface area of a regular hexagonal prism with a base side length of 4 and a height of 3.

72+96√3

TOSSUP 24) Math SA What is the exterior angle measure, in radians, of a regular dodecagon?

pi/6 radians

TOSSUP 9) Math SA In terms of pi, what is the length, in cm, of an arc with an angle of pi/6 radians if its circle has a diameter of 8cm?

⅔ pi

BONUS 166) Math SA After a 40% increase, the new price of an item is $168. What was the original price of the item?

$120

BONUS 40) Math SA Convert the following rectangular coordinates to polar coordinates: (15, 5√3)

(10√3, pi/6) ACCEPT: (10√3, 30 degrees)

BONUS 28) Math SA The point (2, 5) is reflected across the line y=x-3. Find the coordinates of the new point.

(8, -1)

TOSSUP 27) Math SA Find the coordinates of the centroid of a triangle whose vertices lie at (7,1), (16, 5), and (4, 9).

(9, 5)

BONUS 96) Math SA Find the equation of the ellipse with a center located at (-7, 8), a vertical major axis of length 36 and minor axis of length 28.

(y-8)2/324 + (x+7)2/196 = 1

BONUS 34) Math SA Giving your answer in simplest form, find the standard deviation of the following set of 4 numbers: 14, 7, 9, 6.

(√38)/2

TOSSUP 22) Math SA Evaluate i3,258

-1

TOSSUP 58) Math SA Find the dot product of the vectors 6i-3j+5k and 2i +j -2k.

-1

TOSSUP 83) Math SA Find cos(-180) +sec(135)

-1-√2

TOSSUP 160) Math SA For the function f(x) = 3/x, what is f'(6)?

-1/12

TOSSUP 159) Math SA Evaluate sin(5pi/6) - tan(4pi/3) + sec(pi)

-1/2 - sqrt(3)

TOSSUP 126) Math SA What is the slope of a vector in standard position with an angle of 30 degrees below the positive x-axis?

-rad(3)/3

BONUS 89) Math SA Consider the parametric function with equations x=cos(t) and y=sin(t). In terms of x and y, find dy/dx.

-x/y

TOSSUP 173) Math SA Perform the following operations in base 7: 5-2-2 minus 3-4-4

1-4-5

TOSSUP 98) Math SA What is the probability of drawing a red 5 or a black 6 out of a standard deck of cards?

1/13

BONUS 136) Math SA Y is implicitly defined as a function of x in the following equation: y2+2xy=5x2-16. Find dy/dx at the point (1,4)

1/5

TOSSUP 64) Math SA Find the 10th term of the geometric sequence with first term 1 and second term ½

1/512

BONUS 84) Math SA If cscx - cotx = 6, what is cscx + cotx?

1/6

TOSSUP 182) Math SA How many solutions exist for the equation sin(8x)=½ on the interval 0 <= x <= pi?

16

TOSSUP 115) Math SA Take the partial derivative with respect to z of 16x2y3z

16x2y3

BONUS 158) Math SA The point (-1, 4) is rotated clockwise about the origin 90 degrees, translated right 3 units and up 10 units, and finally reflected across the x-axis. What is the distance between the point and its initial position?

17

BONUS 147) Math SA What is the units digit of 8 to the 71st power?

2

BONUS 171) Math SA Find the exact value of cos(150 degrees) + csc(30 degrees) + cot(90 degrees)

2.5 Week of 2/2

TOSSUP 172) Math SA Find the partial fraction decomposition of the following: 4/(x^2 - 1).

2/(x-1) - 2/(x+1)

BONUS 178) Math SA 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 6 less than that of the original cube, what was the volume of the original cube?

216

TOSSUP 78) Math SA Find the area of a hexagon with a perimeter of 72.

216√3

BONUS 145) Math SA What is the area of a triangle whose sides are of length 12, 14, and 16?

21√15

BONUS 176) Math SA Find the derivative of arcsin(x^2) with respect to x.

2x/sqrt(1-x^4)

BONUS 60) Math SA Multiply the following matrices: 2x2 Top row: 3, -7 Bottom row: -9, -11 2x2 Top row: 6, 1 Bottom row: -5, 4

2x2 Top row: 53, -25 Bottom row: 1, -53

TOSSUP 155) Math SA Mario and Christian are 12 years apart in age. In three years, Christian will be three times Mario's age. What is Mario's current age?

3

TOSSUP 52) Math SA Consider the functions f(x)=3√x and g(x) = 4cos2x. Calculate f(g(pi/3)).

3

TOSSUP 6) Math SA What is the integer part of log7 500

3

BONUS 162) Math SA Perform the following operation in base 6: 5-2-4 minus 1-3-3

3-5-1

BONUS 152) Math SA Find the volume when rotating the area bounded by the function sqrt(9-(x-3)2) and the x-axis about the x-axis.

36pi

BONUS 87) Math SA Find the derivative with respect to x of sin^(3)xcosx.

3sin2xcos2x - sin4x

BONUS 131) Math SA Consider a single elimination quiz bowl competition in which 100 teams enter. In the first round, 24 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 2 rounds?

69

TOSSUP 94) Math SA What is the distance between the vertices of the hyperbola with equation x2/18 - y2/9 = 1?

6√2

BONUS 63) Math SA Find the sum of the first 6 terms geometric sequence with first term 2 and second term 6.

728

TOSSUP 109) Math SA Find the slope of the line tangent to the graph f(x)=2x4 - 5x3+3x2 + 9x - 4 at x=1.

8

TOSSUP 47) Math SA Calculate the determinant of the 2x2 matrix: [2 -4] [3 -2] 2 -4 3 -2

8

TOSSUP 88) Math SA What is the maximum value of the function f(x)=5sin(4pix)+3

8

TOSSUP 145) Math SA What base-10 numeral is represented by the Roman numeral DCCCXXXIV?

834

BONUS 36) Math SA A 30-60-90 triangle has legs of length 4 and 4/√x. Giving your answer in simplest form, find the length of the hypotenuse.

8√3 / 3

TOSSUP 181) Math SA Calculate the volume of a regular tetrahedron of side length 3.

9/4 * sqrt(2)

TOSSUP 26) Math SA A polyhedron with 32 faces and 60 vertices has how many edges?

90

BONUS 80) Math SA Evaluate the integral from 0 to 2 of the fraction with numerator 1 and denominator open parenthesis x2+1 close parenthesis to the 3/2 power.

ANSWER: 2√5/5

BONUS 96) Math SA Consider the ellipse with equation (x+5)2/36+ (y-12)2/49 = 1. Identify all of the following three statements that are true concerning this ellipse: I. The length of the major axis is 14 II. The eccentricity is √13/7 III. The center is located at (-5, 12)

All

BONUS 92) Math SA Find the amplitude, period, and horizontal shift of the function f(x)=6tan(4pi x -3pi/2) +4

Amplitude: 6, period: ¼, horizontal shift: 3/8

TOSSUP 25) Math SA The set of all integers is closed under all except which one of the four basic operations?

Division

BONUS 26) Math SA Find the number of faces, vertices, and edges on an octagonal prism.

Faces = 10, vertices = 16, edges = 24

TOSSUP 144) Math SA Secant is positive and tangent is negative in which quadrant?

Fourth

TOSSUP 54) Math SA What is the limit as x approaches infinity of (4x) / (12x2 -5)

Infinity

TOSSUP 130) Math SA Express the base-8 number three-six in base 16.

One-"E"

BONUS 31) Math SA A triangle has angles A, B, and C, where C is the largest angle and A is the smallest. It has side lengths P, Q, and R, where P is the largest side and Q is the smallest. Which of the following expressions is equivalent to the length of side R? W. P sinB/sinC X. P sinC/sinB Y. Q sin B/sinC Z. Q sinA/sinB

W

TOSSUP 122) Math MC Which of the following quadratic expressions has a root with a multiplicity of 2? W. 5x2-25x+125 X. x2-x-56 Y. x2+12x+32 Z. 16x2-25

W

TOSSUP 143) Math MC Which of the following is equivalent to (a-1 + b-1)-1? W. ab/(a+b) X. a+b Y.a2b2 Z. ab

W

TOSSUP 8) Math SA Which of the following numbers is divisible by 15? W. 48,555 X. 955 Y. 8,260 Z. 2,935

W.

TOSSUP 91) Math MC The function y = sinx is stretched horizontally by a factor of 2pi and stretched vertically by a factor of 8. What is the equation of the new function? W. y=8sin(x/2pi) X. y=2pi sin(x/8) Y. y=8sin(2pi*x) Z. y=1/2pi*sin(8x)

W.

BONUS 118) Math SA In 1999, New Year's Day fell on a Friday. What day of the week did New Year's Day fall on this year (2020)?

Wednesday

BONUS 77) Math MC If A does not equal B, which of the following expressions is equal to sin(A+B)? W. sinAsinB +cosAcosB X. sinAcosB + sinBcosA Y. sinAsinB - cosAcosB Z. sinAcosB - sinBcosA

X

TOSSUP 178) Math MC What the degree measure, to the nearest integer, of the angle of the polar form of the cartesian coordinates (-11, -12)? W. 222 X. 227 Y. 132 Z. 137

X

TOSSUP 41) Math MC A population of 2000 bacteria doubles every 14 minutes. What is the approximate population after one hour? W. 8,000 X. 16,000 Y. 32,000 Z. 64,000

X

TOSSUP 48) Math MC Which of the following sets of matrices cannot be multiplied? W. 3x2 and 2x5 X. 3x4 and 5x2 Y. 6x11 and 11x1 Z. 4x1 and 1x5

X

TOSSUP 1) Math MC Which of the following is not an example of a pythagorean triple? W. 14, 48, 50 X. 8, 15, 16 Y. 21, 28, 35 Z. 13, 5, 12

X.

TOSSUP 180) Math MC 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

X???

TOSSUP 110) Math SA Find the 64th derivative of sin(-x)

sin(-x)

TOSSUP 80) Math SA Express the following expression as a single trigonometric function: sin(2x)/2cos(x)

sin(x)

BONUS 78) Math SA Evaluate the definite integral, from 0 to pi, of the fraction with numerator 1 and denominator square root of open quantity 64-x2 close quantity dx.

sin-1 pi/8

BONUS 114) Math SA Evaluate the indefinite integral of cos5x dx

sin5(x)/5 - ⅔ sin3(x) + sin(x)+C

BONUS 33) Math SA A triangle has angles A, B, and C and sides a, b, and c. Each side's opposite angle has the same letter name. If the measure of angle A=60 degrees, side b = 5 units, and side c = 3 units, what is the length of side a?

√19

TOSSUP 81) Math SA Simplify the fraction with number csc(pi/2) and denominator (sin(pi/4)).

√2

BONUS 86) Math SA A triangle has two sides of length 5 and 6 with an angle of 60 degrees between them. What is the length of the third side?

√31

BONUS 74) Math SA Giving your answer in simplest form, find the standard deviation of the following set of four numbers: 7, 2, 11, 4

√46/2

TOSSUP 68) Math SA Giving your answer in simplest form, calculate the radius of the circle with equation x2+y2 = 1/5.

√5 /5

TOSSUP 38) Math SA Consider the function f(x) = 4√3x. Giving your answer in simplest form, find f'(2).

√6

BONUS 81) Math SA Giving your answer in simplest form, find csc(15°).

√6+√2

BONUS 45) Math SA Find the absolute value of the midpoint between the complex coordinates (5+6i) and (13-2i).

√85

TOSSUP 40) Math SA Find the distance between the complex numbers (6+7i) and (4-2i)

√85

BONUS 71) Math SA A triangle with vertices at (2, 4), (-6, -2) and (1, 1) is reflected across the x-axis and translated 4 units left. What are coordinates of the centroid of the transformed triangle?

(-5, -1)

BONUS 150) Math SA Find the coordinates of the centroid of the four-sided figure with vertices located at (1, -2, 5), (19, -8, -1), (-14, 10, 3), and (-2, 0, 1).

(1, 0, 2)

TOSSUP 66) Math MC What type of conic section is represented by the equation 4x2 - 5y2 +7x -7y = 0? W. Circle X. Ellipse Y. Parabola Z. Hyperbola

Z

TOSSUP 168) Math SA Reduce the following radical expression to its simplest radical form: 4throot(cuberoot(81)).

cuberoot(3)

BONUS 105) Math SA Consider the set of all perfect squares on the interval from 1 to 600 inclusive. What is the probability that a number randomly selected from this set is divisible by 4?

½

BONUS 3) Math SA Expand the following log statement: Log of the fraction with numerator square root of x times the cube-root of y squared and denominator z to the fourth power.

½ log x + ⅔ log y - 4 log z

BONUS 91) Math SA Find the indefinite integral of cos2xdx.

½ x + ¼ sin(2x) +C

BONUS 29) Math SA Triangle ABC lies in the first quadrant, with point A at (2, 7), point B at (5, 3), and point C at (2, 2). The triangle is then reflected across the X-axis, and translated left 3 units. Find the coordinates of the centroid of the new triangle.

(0, -4)

BONUS 21) Math SA Calculate the side length of an equilateral triangle whose circumcircle has a radius of 8.

(16√3)/3

BONUS 65) Math SA Find the vertex and radius of the circle with the equation x2-4x+y2-2y=4.

(2, 1) and 3

TOSSUP 35) Math SA Consider the function f(x) = 3(x-2)2 -4. The function is scaled by a factor of 3 and reflected across the x-axis. What are the coordinates of the vertex of the new function?

(2, 4)

TOSSUP 30) Math SA The point (-6, -2) is reflected across the y-axis and rotated 90 degrees counterclockwise about the origin. What are the coordinates of the new point?

(2, 6)

TOSSUP 63) Math SA Calculate the sum of the first 8 terms of the arithmetic sequence with first term 5, second term 3, and third term 1.

-16

BONUS 82) Math SA Giving your answer in standard radical form, find csc(210) + cot(90) + sec(210).

-2- 2√3/3

BONUS 107) Physics SA An object undergoes simple harmonic oscillation and its potential energy graphed against its position is represented by the equation U = 7x2-5x+12. Find the force exerted on the object at x=2.

-23

TOSSUP 76) Math SA What is sec(210)?

-2√3/3

TOSSUP 82) Math SA Find csc(5pi/3)

-2√3/3

BONUS 54) Math SA Calculate the determinant of the following 3x3 matrix: Top row 2, -7, 4 Middle row: -3, 5, -3 Bottom row: 3, 1, 0

-3

TOSSUP 128) Math SA Set W contains all negative integers that are the differences of the squares of two positive integers. What is the greatest element of W?

-3

TOSSUP 112) Math SA Evaluate the definite integral from negative pi to pi of x3sinx dx.

0

TOSSUP 118) Math SA Differentiate the following expression with respect to x, provided x is not 0: x/|x|.

0

TOSSUP 34) Math SA Consider the following polynomial: 36x5 + x4 - 2x3 + 3x2 -2x + 1. Based on the signs of each coefficient, what are the possible amounts of real roots of this polynomial?

0, 2, 4

BONUS 52) Math SA Find the zeros of the following equation on the closed interval [0, pi]: 2cos2x - cos x = 1

0, 2pi/3

BONUS 120) Math SA How many positive integers a exist such that log base a of 729 is a positive integer?

4

BONUS 93) Math SA Consider the ellipse with equation x2/16 + y2/25 = 1. Identify all of the following three equations that are true about this ellipse. I. The major axis is horizontal II. The each focus is 3 units away from the center III. The length of the minor axis is 8 units.

II and III only

BONUS 123) Math SA If all A are B and some C are A, identify all of the following three conclusions that necessarily follow: I. all A are C II. Some B are C III. Some A are not C

II only

BONUS 7) Math MC Identify all of the following 3 numbers that are divisible by 8. I. 4485 II. 22,256 III. 5766

II only

BONUS 163) Math SA Simplify the following: (x^5 + 3x^3 + 7x^2 - 4x - 18) / (x+2)

x^4 - 2x^3 + 7x^2 - 7x + 19

BONUS 108) Math SA Consider the function f(x) = -3x3+2x+8. Find the slope-intercept equation of a line parallel to the normal of the curve at x=1 and passing through the point (4, 2).

y = -7x+30

BONUS 95) Math SA Find the slope-intercept equations of the asymptotes of the hyperbola with equation (y+4)2/64 - (x-2)2/16 = 1

y = 2x-8 and y=-2x

BONUS 66) Math SA Find the equation of a parabola, in general form, with a focus located at (4, -1) and a directrix with equation x=-8.

y2-24x+2y-47=0

TOSSUP 136) Math SA What are the asymptotes and foci of the hyperbola x2/64 - y2/225 = 1?

y= (15/8)x, y=(-15/8)x, (17,0), (-17,0)

BONUS 43) Math SA Calculate the equation of the perpendicular bisector of the line segment formed between the points (3, 7) and (-1, -5)

y= -1/3x + 4/3

TOSSUP 116) Math SA Solve the following differential equation for y: dy/dx = 6/y, assuming y=5 when x=2

y= sqrt(12x+1)

BONUS 70) Math SA Find the equation of a parabola in standard form with a focus at (2, 2) and directrix with equation y=-2.

y= ⅛ x2-½ x + ½

BONUS 97) Math SA Find the equation of the line tangent to the circle with equation x2-12x+y2+14y=15 at the point (0, -15).

y=-¾ x-15

BONUS 149) Math SA Find the slope-intercept equations of the asymptotes of the hyperbola represented by the equation (x+4)2/4 - (y-4)2/36 = 1.

y=3x+16, y=-3x-8

TOSSUP 163) Math SA Find the equation of the directrix of the parabola with equation (x+7)^(2) = -24(y+2).

y=4

TOSSUP 142) Math SA The line with equation y=-4x+16 is reflected across the x-axis. What is the slope-intercept equation of its image?

y=4x-16

TOSSUP 37) Math SA Find the oblique asymptote of the following function: f(x) = (5x2- 3x+1) / (x-4)

y=5x+7

BONUS 137) Math SA Evaluate the indefinite integral of the fraction with numerator x2 and denominator 1+x6dx.

⅓ tan-1(x3)+C

BONUS (probably not reasonable) 115) Math SA Calculate the volume of the solid formed by revolving the area bounded by the function y=ex and the line y=2 about the x-axis.

ln16 - 3.5

BONUS 181) Math SA A circle has two secant lines AB and CD that intersect at a point outside the circle. If arc AC is 131 degrees and arc BD is 22 degrees, what is the value of angle N?

109

TOSSUP 113) Math SA Take the partial derivative with respect to y of 5x3y2

10x3y

BONUS 103) Math SA A bag contains one fair coin, and a biased coin that flips heads 55% of the time. Jared picks a coin out of the bag at random and flips it. Given that the coin lands heads, what is the probability that Jared picked the unfair coin?

11/21

BONUS 121) Math SA If the average of a set of 6 numbers is 31 and the average of another set of 19 numbers is 6, what is the average of all 25 numbers?

12

BONUS 130) Math SA A set of three positive consecutive integers has a product 40 times their sum. What is the largest element in this set?

12

TOSSUP 179) Math SA Using the point names A, B, C, D, E, and F, how many different names are there for hexagon ABCDEF?

12

BONUS 135) Math SA Providing your answer in terms of pi, what is the volume of the solid generated when the area bounded by y=5x2, x=3, and the x-axis is revolved around the x-axis?

1215pi

TOSSUP 92) Math SA Find the limit as x approaches 7pi/2 of 17sin(x)-4

13

TOSSUP 93) Math SA Points A and B are the foci of an ellipse. Points C and D are located on the ellipse. If line AC = 18 units, line BC = 6 units, and line AD = 11 units, what is the length of line BD?

13

TOSSUP 95) Math SA What is the eccentricity of the hyperbola with equation (x+5)2/25 - (y-2)2/144 = 1

13/5

BONUS 168) Math SA Find the perimeter of a rhombus with diagonals of length 32 and 60.

136

BONUS 124) Math SA A bag contains 22 socks: 4 are blue, 8 are red, and 10 are black. How many socks must you take out to be certain that you will have at least one pair of black socks?

14

BONUS 64) Math SA Find the volume of a prism with a hexagonal base of side length 4 and lateral height of 6.

144√3

TOSSUP 153) Math SA Points A and B are the foci of an ellipse. Points C and D are located on the ellipse. If line AC = 10 units, line BC = 22 units, and line AD = 17 units, what is the length of line BD?

15

TOSSUP 124) Math SA If you roll 2 six-sided dice, what is the probability that the product of the two numbers is composite?

5/6

TOSSUP 61) Math SA Calculate the 11th term of the arithmetic sequence with first term 1, second term 6, and third term 11.

51

BONUS 51) Math SA Each side of a cube has a diagonal length of 6 units. Giving your answer in simplest form, calculate the volume of the cube.

54√2

BONUS 98) Math SA Carlos flips a coin 6 times. What is the probability that he lands heads at least twice?

57/64

BONUS 151) Math SA How many positive integers a exist such that log base a of 4096 is a positive integer?

6

TOSSUP 17) Math SA Find 2 mean proportionals between the numbers 2 and 54.

6 and 18

TOSSUP 72) Math SA Find two mean proportionals between 2 and 54.

6, 18

BONUS 138) Math SA Set A consists of only positive integers less than or equal to 100, where no two elements of the set sum to 179. What is the maximum possible number of elements in set A?

89

TOSSUP 86) Math SA A polyhedron with 32 faces and 60 vertices has how many edges?

90

TOSSUP (more like a bonus) 141) Math SA What is the greatest common divisor of 360 and 6930?

90

BONUS 180) Math SA A wire that is 48 centimeters long is bent into the shape of a regular hexagon. What is the area of the hexagon in square centimeters?

96sqrt(3)

TOSSUP 174) Math SA Calculate the volume of a regular octahedron with side length 3.

9sqrt(2)

TOSSUP 101) Math SA Out of a pool of 200 hundred college students, 120 play sports, 50 students are freshman, and 20 freshman play sports. What is the probability that a student plays sports or is a freshman?

3/4

BONUS 99) Math SA A bag contains 5 red marbles and 7 black marbles. What is the probability of drawing 2 of the same color in a row?

31/66

BONUS 117) Math SA Find the volume of a solid formed when revolving the area bounded by y=sqrt(x) and y=2 and the y-axis about the y-axis.

32pi/5

BONUS 160) Math SA Calculate the perimeter of a regular hexagon with an area of 108sqrt(3)

36

TOSSUP 11) Math SA How many terms are in the expansion of the expression (13x17 + 5x3)37?

36

BONUS 154) Math MC A prism has a base in the shape of a regular hexagon with side length x. The height of the prism is x. Give the volume of the prism in terms of x.

3x3 sqrt(2)/2

BONUS 104) Math SA A bag contains 6 blue marbles, 10 red marbles, 11 white marbles, and 2 black marbles. What is the maximum number of marbles that can be removed from the bag, without replacement, before a duplicate color is drawn?

4

BONUS 116) Math SA What is the area in the first quadrant bounded by the graphs of y=4x and y=x3?

4

BONUS 16) Math SA Order the following 4 angles from least to greatest. I. 12/5 pi radians II. 275 degrees III. ⅞ pi radians IV. 135 degrees

4, 3, 2, 1

TOSSUP 152) Math SA The bob on a pendulum swings through an arc 8 feet long when the string swings through an angle of 0.2 radians. What is the length of the pendulum in feet?

40

BONUS 129) Math SA How many positive integer divisors does 3600 have?

45

BONUS 106) Math SA Six students, Abby, Sarah, Jackson, Mike, Laurel, and Peter are being seated on a bench at a party. Sarah will only sit on the far left side, and Jackson and Mike must sit together. Following these conditions, how many different ways can these students be arranged?

48

TOSSUP 150) Math SA Calculate the surface area of a cube if each side has a diagonal length of 4 units.

48

BONUS 134) Math SA AB and CD are parallel line segments intersected by line segment EF. Endpoint E lies on AB, and endpoint F lies on CD. If angle CEF is 24 degrees and angle CFE is 107 degrees, what is the measure of angle AEC?

49

BONUS 58) Math SA Find the equation of the oblique asymptote of the following rational function: f(x) = 4x3 + 6x2 - x + 7 / x + 2

4x2 - 2x + 3

TOSSUP 102) Math SA What is the distance between the vertices of the hyperbola with equation x2/24 - y2/9 = 1?

4√6

TOSSUP 10) Math SA A triangle has one side of length 7 and another side of length 11. What is the smallest integer value possible for the third side of the triangle?

5

BONUS 161) Math SA Differentiate the following with respect to x: arctan(x^(3)).

(3x2)/(1+x6)

BONUS 56) Math SA Vector a = 2i + j - 3k and vector b = -4i +5j - 2k. Calculate a cross b:

13i + 16j + 14k

BONUS 59) Math SA Find the 18th term in the arithmetic sequence with first term -3 and third term 25

235

BONUS 141) Math SA What is the largest prime factor of the quantity 43013+43014+43015?

7

TOSSUP 23) Math SA A polygon's interior angles sum to 5pi radians How many sides does it have?

7

BONUS 167) Math SA If $20,000 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?

$22,050

TOSSUP 104) Biology SA In a population of frogs, the probability of a frog having poisonous skin is 0.4. The probability of a frog having extra long legs is 0.7. The probability of a frog having poisonous skin AND extra long legs is 0.2. Given that a frog has poisonous skin, what is the probability that the frog also has long legs?

½

BONUS 159) Math SA Consider the set of all perfect squares on the closed interval from 1 to 400. What is the probability that a number randomly selected from this set is divisible by 4?

½ Week of 1/20

BONUS 76) Math SA Giving an exact answer, what is cos(15 degrees).

(√2+√6)/4

BONUS 157) Math SA Find the 13th derivative with respect to x of cos(2x).

-8192sin(2x)

TOSSUP 73) Math SA Evaluate i67

-i

TOSSUP 148) Math SA Evaluate sin(tan-1(-√3)).

-√3/2

TOSSUP 77) Math SA What is sin(300)?

-√3/2

BONUS 79) Math SA Evaluate the limit as x approaches pi of the fraction with numerator secx+1 and denominator x-pi.

0

TOSSUP 146) Math SA Evaluate 578 mod 17.

0

TOSSUP 154) Math SA In a group of 17 students, 10 take history and 6 take chemistry. One student takes neither history nor chemistry. How many students take both?

0

BONUS 125) Math SA What is the sum from n = 0 to 4893 of cosine (pi * n/2)?

1

TOSSUP 121) Math SA Evaluate the definite integral from 0 to pi/4 of sec2x dx

1

TOSSUP 162) Math SA Find the dot product of the following vectors: x+4y+z and 3x-y+2z

1

TOSSUP 59) Math SA Find the first term in the geometric sequence with 3rd term 1/9, fourth term 1/27, and fifth term 1/81

1

TOSSUP 75) Math SA What is the value of csc -3pi/2

1

BONUS 140) Math SA The graph of the polar equation r=5+5sin(theta) is a cardioid. In which two quadrants is most of the area of this cardioid?

1 and 2

BONUS 128) Math SA The three sides of a triangle of lengths 5 centimeters, 8 centimeters, and 9 centimeters. What is the cosine of the largest angle?

1/10

TOSSUP 100) Math SA What is the probability of landing heads on a fair coin flip 10 times in a row?

1/1024

BONUS 133) Math SA Assuming 2y2 + 4x2y = 5x2 + 30x implicitly defines y as a function of x, find dy/dx at the point (2, 3)

1/14

TOSSUP 133) Math SA There is a well-shuffled deck of 52 cards containing 13 cards each of spades, clubs, diamonds, and hearts. You draw 2 cards without replacement. What is the probability that both cards are spades?

1/17

TOSSUP 108) Physics SA Find the derivative of ln(√x).

1/2x

BONUS 102) Math SA there are 10 students in a class, 6 boys and 4 girls. If 3 students are chosen at random, what is the probability that all three are girls?

1/30

BONUS 90) Math SA Find the indefinite integral of sec5x * tan3x dx.

1/7 sec7x - 1/5 sec5x +C

BONUS 177) Math SA Xander has two coins, one is fair and the other lands heads 45% of the time. He puts both coins into a bag and picks one at random. If he lands heads, what is the probability that he picked the fair coin?

10/19 Week of 2/9

BONUS 61) Math SA Calculate the sum of the first 21 terms of the arithmetic sequence with first term -7, and second term -1.

1060

TOSSUP 171) Math SA How far apart, in degrees, are the asymptotes of the graph of 4tan(5x/3)?

108

TOSSUP 46) Math SA Calculate the radial coordinate of the polar form of the following cartesian coordinates: (15, -8)

17

TOSSUP 132) Math SA Assume A and B are the subsets of the universal set that contains 200 elements. If the number of elements in set A is 48 and the number of elements in set B is 152, and the number of elements in the intersection set of A and B equals 26, then how many elements are in the union of A and B?

174

TOSSUP 111) Math SA Find the second derivative with respect to x of tan(3x).

18sec2(3x)tan(3x)

BONUS 132) Math SA What is the remainder when 2x7+x5-3x4+4x2+x-3 is divided by x-1?

2

TOSSUP 161) Math SA Give the radial coordinate of the polar form of the cartesian coordinates (-20, 21).

29

BONUS 175) Math SA Find the 18th term of the arithmetic sequence with first term 4 and third term 30.

225

TOSSUP 117) Math SA What is the length of the minor axis of an ellipse with equation x2/144 + y2/169 = 1

24

TOSSUP 131) Math SA An arc of length 4pi is cut off by a central angle of pi/6 radians. What is the radius of the circle?

24

BONUS 155) Math SA How many sides does a regular polygon have if each interior angle measures 174 degrees?

60

TOSSUP 106) Math SA How many unique ways can the letters of the word "SORRY" be arranged?

60

TOSSUP 120) Math SA How many permutations consisting of four letters each, starting with the letter E, can be formed from the letters of in the word energy?

60

BONUS 174) Math SA Giving your answer in terms of pi, calculate the lateral surface area of a cone with height 7 and base diameter 48.

600 pi

BONUS 164) Math SA A cone is stacked on a cylinder, which is stacked on a cube. The cone and cylinder have the base, and the cube's length is equal to the cylinder's diameter. All three shapes have the same height. If the cube has a surface area of 96 units, calculate the sum of the volumes of the cone and the cylinder, in terms of pi.

64pi/3

BONUS 119) Math SA If y varies directly with x and z, and y=14 when x=4 and z=7, find y when x=10 and z=15.

75

TOSSUP 19) Math SA What test can be visually performed on a function to determine if it is a one-to-one function?

Horizontal line test

BONUS 67) Math SA Identify all of the following 3 statements that are true concerning the ellipse with equation 1/16(x-7)2 + 1/25(y+7)2 = 1 I. The major axis is vertical II. The distance between the center and either focus is 3 III. The center is located at (-7, 7)

I & II only

BONUS 94) Math SA Consider the hyperbola with equation (y-4)2/16 - (x+5)2/9 = 1. Identify all of the following three statements that are true concerning this hyperbola: I. The transverse axis is vertical. II. One focus is located at (-5, 9) III. The vertices are 4 units apart.

I & II only.

TOSSUP 135) Math SA The Seven Bridges of Konigsberg was a historically notable problem in graph theory and topology that was resolved by what mathematician?

Leonhard Euler

BONUS 127) Math SA In a particular year, if May 4th is on a Tuesday, what day of the week is November 8th?

Monday

BONUS 6) Math SA Identify all of the following 3 sets of numbers that are not pythagorean triples. I. 24, 45, 54 II. 24, 10, 26 III. 75, 72, 21

None

BONUS 143) Math MC 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

W

BONUS 146) Math MC Which of the following is a solution of x to the following equation: 2x-3 = pix W. log(8) / (log(2)-log(pi)) X. (log(2) - log(pi))/ log(8) Y. log(2) / (log(8)-log(pi)) Z. (log(8) - log(pi)) / log(2)

W

BONUS 22) Math MC Which of the following equations is correct? W. i63 = i3223 X. i722 = i223 Y. i8968 = i690 Z. i885 = i812

W

TOSSUP 15) Math MC A cone and a cylinder have the same radius and height. What is the ratio of their volumes? W. 1:3 X. 1:1 Y. 3:1 Z. 1:2

W

TOSSUP 85) Math MC Which of the following is equal to 2sin16cos14 W. sin30 +sin2 X. sin30 - sin 2 Y. cos30 + cos2 Z. cos30 - cos2

W

TOSSUP 87) Math MC What is the limit as x approaches infinity of the inverse tangent of x? W. pi/2 X. pi Y. 2pi Z. infinity

W

TOSSUP 105) Math MC If f(x) is a polynomial and f'''(x) [f triple prime of x] is a constant, what is the maximum possible multiplicity of f(x)? W. 2 X. 3 Y. 4 Z. 5

X

TOSSUP 149) Math MC Which of the following is equal to tan(75)? W. (tan(45) + tan(30)) / (1 + tan(45)tan(30)) X. (tan(45) + tan(30)) / (1 - tan(45)tan(30)) Y. (tan(45) - tan(30)) / (1 + tan(45)tan(30)) Z. (tan(45) - tan(30)) / (1 - tan(45)tan(30))

X

TOSSUP 170) Math MC Which of the following is congruent to (n+1) modulus n? W. 0 X. 1 Y. (n-1) Z. (n-2)

X

TOSSUP 55) Math MC Which of the following 2x2 matrices has a multiplicative inverse? W. Top row: 5, 5 Bottom row: -5, -5 X. top row: -5, 5 Bottom row: 5, 5 Y. Top row: -5, -5 Bottom row: 5, 5 Z. Top row: 5, 0 Bottom row: 5, 0

X

BONUS 111) Math MC Find the derivative with respect to x of the function f(x)= x/sinx. W. (cosx - xsinx)/sin2x X. (sinx - xcosx)/cos2x Y. csc(x) - x*csc(x)*cot(x) Z.sec(x) - x*sec(x)*tan(x)

Y

BONUS 169) Math MC Which of the following is not an antiderivative for sin(x)cos(x)? W. sin^2(x)/2 X. -(cos^2(x))/2 Y. sin(2x)/4 Z. -(cos(2x))/4

Y

TOSSUP 123) Math MC Which of the following best converts the rectangular coordinates (5, 12) to polar coordinates? W. (13, 23 degrees) X. (23 degrees, 13) Y. (13, 67 degrees) Z. (67 degrees, 13

Y

TOSSUP 125) Math MC For a population of 100 individuals with a normal distribution, how many individuals will be found to fall within one standard deviation above the mean? W. 68 X. 95 Y. 34 Z. 32

Y

TOSSUP 129) Math MC A regular nonagon is inscribed in a circle with radius 5. Which of the following is the length of one of its sides? W. 5 sin 40° X. 5 cos 40° Y. 10 sin 20° Z. 10 cos 20°

Y

TOSSUP 138) Math MC Cos(A-B) is equal to which of the following? W. cosAsinB+sinAcosB X. cosAsinB-sinAcosB Y. cosAcosB+sinAsinB Z. cosAcosB-sinAsinB

Y

TOSSUP 147) Math MC Which of the following is TRUE about any two successive terms in the Fibonnaci 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

TOSSUP 60) Math MC Which of the following does not appear in the infinite arithmetic sequence with first term 1/2 and third term 1/8 W. 1/64 X. 1/256 Y. 1/1048 Z. 1/4096

Y

TOSSUP 69) Math MC In what direction does the parabola with equation (y-7)2 = -8(x+6) open? W. Up X. Down Y. Left Z. Right

Y

TOSSUP 96) Math MC What conic section is represented by the equation 12x2+89y2 +4x-2y+4 = 0? W. Hyperbola X. Circle Y. Ellipse Z. Parabola

Y

TOSSUP 62) Math MC The length of one side of a 30-60-90 triangle is 16 units. Which of the following is not a possible value for the length of the shortest side? W. 16 X. 16/√3 Y. 8 Z. 8/√3

Z

TOSSUP 89) Math MC Which of the following trigonometric functions has the greatest frequency? W. sin(4x - 6) +3 X. cos(1/4x - 10)+17 Y. sin(16x-14)-2 Z. cos(1/8x + 12)

Y.

TOSSUP 90) Math MC Which of the following values is outside the range of the function f(x)=csc(x)+4 W. 2 X. 3 Y. 4 Z. 5

Y.

BONUS 110) Math MC The radius of a sphere is increasing at a constant rate of 6cm/s. At what rate, in cubic centimeters per second, is the volume of the sphere increasing when the radius is 10cm? W. 160 X. 2400 Y. 160pi Z. 2400pi

Z

BONUS 170) Math MC The series with nth term (-1)^n/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

Z

TOSSUP 127) Math MC 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

Z

TOSSUP 165) Math MC For a population of 50 individuals with a normal distribution, how many individuals will be found to fall within one standard deviation below the mean? W. 46 X. 23 Y. 34 Z. 17

Z

TOSSUP 166) Math MC Given that the function f of x has a zero at x = 6, at what value must 2 + f of x have a zero? W. 3 X. 4 Y. 8 Z. It need not have a zero

Z

TOSSUP 169) Math MC Which of the following angles lies in the third quadrant? W. 17pi/4 X. 15 pi/6 Y. 11pi/5 Z. 9pi/8

Z

TOSSUP 107) Math SA Find the derivative with respect to x of the function f(x)= excotx

excotx - excsc2x

TOSSUP 114) Math SA Giving your answer in simplest form, evaluate the definite integral from 2 to 4 of 1/x dx.

ln 2

TOSSUP 134) Math SA What is the magnitude of the phase shift of the function y=sinx to y=5sin(13x+pi) - 12?

pi/13

BONUS 183) Math SA Calculate the volume of the solid formed when the area bounded by the graph y=e^x, x=1, the y-axis, and the x-axis, is revolved around the x-axis.

pi/2*e^2 - pi/2

BONUS 122) Math SA If x is measured in radians, find all values of x between zero and 2pi that satisfy the equation sin2x=2cos4x.

pi/4, 3pi/4, 5pi/4, 7pi/4

TOSSUP 167) Math SA What is the polar form of the equation y= x*sqrt(3)?

theta=60 degrees or theta=pi/3

TOSSUP 79) Math SA Find the derivative with respect to x of x*tanx.

x*sec2x + tanx

BONUS 69) Math SA Find the equation of a circle, in general form, with a center located at (3, -2) and a radius of 5.

x2+y2-6x+4y-12 = 0

BONUS 88) Math SA Find the indefinite integral of x3*sinx dx.

x3cosx + 3x2sinx - 6xcosx -6sinx + C

BONUS 182) Math SA Find the equation of a parabola in vertex form with a focus located at (1, 2) and directrix with equation x=9.

x=1/16 (y-1)^2 -2

TOSSUP 65) Math SA Find the equation of the directrix of the parabola with equation (y-4)^(2)/(x+6) = -32

x=2

BONUS 38) Math SA Find the coordinates of the removable discontinuity of the following function: f(x) = x2-2x-8 / x2-16

(4, ¾)

BONUS 25) Math MC A sphere has a radius that is equal to the radius of the base of a cone. The sphere's diameter is equal to the height of the cone. What is the ratio of the sphere's volume to the cone's volume? W. 1:1 X. 2:1 Y. 4:3 Z. 3:2

X

BONUS 13) Math MC The centers of four coplanar circles of radius r form a square with a side length 2r. What is the sum of the lengths of the circular arcs not contained within the square? W. 2πr X. 4πr Y. 6πr Z. 8πr

Y

BONUS 35) Math MC Consider the function f(x) = 2x2 + 4x. Which of the following points does not lie on f(x-3)? W. (1,0) X. (2, -2) Y. (4,6) Z. (5, 0)

Z

TOSSUP 18) Math MC Which of the following is not a valid set of mean proportionals between 2 and 128? W. 16 X. 4, 8, 16, 32, 64 Y. 8, 32 Z. 32, 64

Z

TOSSUP 45) Math MC Which of the following increases on the interval from -pi/2 to 0 and decreases from 0 to pi/2? W. sin x X. tan x Y. csc x Z. cos x

Z

BONUS 5) Math SA Evaluate the following expression for x = 64: log8 (x1/2) + log2(1/x)

-4

BONUS 19) Math SA Solve the following equation for x: |7x+2|+3x = 7-2x

x=5/12, x= -9/2