MATH-6
Short Answer Expressing the answer in simplest form, solve [the absolute value of the quantity 2r minus 13 fourths is less than 5 halves].
3/8 < r < (ACCEPT: 3/8 < r < ) TOSS-UP
Short Answer A square has a side of 8 millimeters. Providing your answer in terms of ?? and in square millimeters, what is the difference between the areas of its circumscribed circle and its inscribed circle?
16??
Short Answer The volume of an open-ended circular cylinder is 32?? cubic centimeters, and its base has a radius of 4 meters. What is the surface area of the cylinder, in terms of ?? and in square meters?
16??
Short Answer What is the degree of the polynomial: (x ??? 3)3 (x ??? 7)4 [open parenthesis x minus 3 close parenthesis cubed times open parenthesis x minus 7 close parenthesis to the power of 4]?W) -13/12 X) -13/5 Y) 13/5 Z) 13/12TOSS-UP
7
Multiple Choice If the surface area of a cube is 96 square units, which of the following is the length of a diagonal of a face of the cube?W) 4X) 4???2 Y) 4???3 Z) 16???2
X) 4???2
Multiple Choice For all real numbers, the expressionof the quantity x squared minus 4 x plus 4] equals which of the following?W)x 2X)x 2x+2Y) |x 2| [the absolute value of the quantity x minus 2] Z) x + 2BONUS[the square root
Y) |x 2|
Short Answer In terms of x and in standard polynomial form, what is the volume of a right rectangular prism with dimensions (x + 4), (x + 1), and (x + 6)?
x3 + 11x2 + 34x + 24
Short Answer Evaluate the following:over t times e to the power of the natural log of t dt].[the integral from 0 to 2 of 1
2 ANSWER: Y) 2??
Short Answer If ln [natural log of the quantity x cubed equals 6], what is ln [the natural log of the quantity x squared]?
4
Short Answer If two 6-sided fair dice are rolled, providing your answer as a fraction in lowest te1rms, what is the probability that both numbers will be even?
4
Short Answer If the radius of a spherical balloon is expanding at the rate of 5 inches per second, assuming the initial volume is 0 and providing your answer as an improper fraction in lowest terms, what is its volume in inches cubed in terms of ?? after 2 seconds?
4000??/3
Multiple Choice Which of the following values for a and b provide a counterexample to the statement ???If 4 divides a + b, then 4 divides a or 4 divides b.???W) a = 5 and b = 7 X) a = 5 and b = 6 Y) a = 4 and b = 8 Z) a = 4 and b = 6
W) a = 5 AND b = 7
Multiple Choice Which of the following is an equivalent form of 2/(3 + i) [2 over thequantity 3 plus i]?W) (3 ??? i)/4 [open parenthesis 3 minus i,close parenthesis, over 4] X) (3 ??? i)/5 [open parenthesis 3 minus i,close parenthesis, over 5] Y) (4 ??? i)/4 [open parenthesis 4 minus i,close parenthesis, over 4] Z) (4 ??? i)/5 [open parenthesis 4 minus i,close parenthesis, over 5]
X) (3 ??? i)/5
Multiple Choice A jar contains 50 marbles. Exactly 10% are green, 20% are blue, 30% are yellow, and the rest are orange. Which of the following is the probability of randomly picking first a blue marble, replacing it, and then picking an orange marble?1 W) 252 X) 253 Y) 254 Z) 25 2
X) 25
Short Answer Express [the quantity 1 plus 2 i divided by the quantity 4minus 5 i] in standard a + bi form.
-6/41 + (13/41)i [DO NOT ACCEPT: (-6 +13i)/41]
Short Answer What is the sum of the infinite geometric series with a first term of 1/3 and a second term of 1/9?
1/2 (ACCEPT: 0.5)
Short Answer How many points of intersection exist for the graphs of y = 2 [y equals2tothepowerofx]andy=-x2 +2?
2
ShortAnswer Intermsofa,b,c,andd,whatistheslopeoftheline3 x+2by=cd?W) (-4, -1) X) (3, 1) Y) (0, -3) Z) (4, 3)
X) (3, 1)
Multiple Choice The equation -mx + 1 = 13 ??? 4(x + 3) [negative m x plus 1 equals 13 minus 4 times the quantity x plus 3] is an identity if m equals which of the following?W)-4 X) -1 Y) 1 Z) 4
Z) 4
Multiple Choice Given that a second degree polynomial function f(x) has a zero at x = 3 with multiplicity 2, which of the following is true?W) The graph of f(x) crosses the y-axis at 3X) As x approaches infinity, f(x) approaches infinityY) The graph of f(x) crosses the x-axis at 3Z) The graph of f(x) touches but does not cross the x-axis at 3
Z) THE GRAPH OF f(x) TOUCHES BUT DOES NOT CROSS THE x-AXIS AT 3 BONUS
Short Answer Given that x and y are real numbers, solve for x and y: 2y + ix = 4 + x ??? i.
x = -1; y = 3/2 Round 5
Short Answer What are the coordinates of the vertex of the graph of y = 2x2 + 8x ??? 3?
(-2, -11)
Short Answer An open box is to be made from a rectangular piece of material 8 inches by 6 inches by cutting equal squares of side x from the four corners and turning up the sides. In terms of x, give an expression for the volume of the box in cubic inches.
x(8- 2x)(6- 2x) (ACCEPT: 4x3 ??? 28x2 + 48x)
Short Answer Find an equation of the graph that results from reflecting the graph of y = over the y-axis, and then shifting the graph 3 units to the left.
y = (ACCEPT: y = )
Short Answer What is the limit of as x approaches 0?BONUSTOSS-UP
1
Short Answer A coin is tossed 10 times. Providing your answer as a fraction in lowest terms, what is the probability that there are 3 heads and 7 tails?
15/128
ShortAnswer Ifg(b)=6b3???4b2+b+4b-1 [gofbequals6bcubedminus4b squared plus b plus 4 b to the negative 1], what is g???(b) [g prime of b]?
18b2 ???8b+1???4b-2 (ACCEPT:18b2 ???8b+1??? )
Short Answer Providing your answer to one decimal place, find the value of the factorial].
10.5
Short Answer Providing your answers as improper fractions in lowest terms, solve[negative 7 plus the absolute value of the quantity 3 minus 2x equals15] for x.
-19/2 AND 25/2
ShortAnswer If-4x???9y???3z=-10and-5a???9b=-6,thenwhatis-9b???15z???45y???20x ??? 5a?
-56
Short Answer If a person walks 4 miles due north, 6 miles due east, then 4 miles due north, how far in miles is the person displaced from his or her original position?
10
Short Answer Providing your answer as an improper fraction in lowest terms, what is the area under the curve bounded by the x-axis, x = 4 and y = ?
16/3
Short Answer For what values of x is the function f(x)= [f of x equals the fraction with numerator x squared and denominator x squared minus 4 x plus 4] NOT defined?
2
ShortAnswer Solveforx:5+ quantity x plus 14 equals x plus 7].
2 (DO NOT ACCEPT: -5)
Short Answer What are the solutions to x ??? 5x + 6 = 0?BONUS
2 AND 3
Short Answer If each side of a rectangle is increased by 10%, by what percentage is its area increased?
21 (ACCEPT: 21%)
Short Answer In the three by three matrix, [such that row one contains negative 2, 2, and 0; row two contains 4, 1, and negative 5; row three contains 8,BONUS is the surface area in square units of the cube?
486 ANSWER: 5
Short Answer Mary travels for 110 miles averaging 55 miles per hour and for 150 miles averaging 50 miles per hour. What is Mary???s average speed in miles per hour for the trip?
52
Short Answer What is the radius of the circle with equation x2 + 6x + y2 8y 11= 0?
6
Short Answer How many real solutions does the following equation have: (x2 + 1)2 + 2(x2 + 1) - 3 = 0 [x squared plus 1 quantity squared plus 2 times open parenthesis x squared plus 1 close parenthesis minus 3 equals zero]?
ONE
Multiple Choice The lines y = (a ??? 5)x + 5 [ y equals open parentheses a minus 5 close parentheses x plus 5] and y = -2x + 7 are perpendicular if a equals which of the following?BONUS
f IS CONTINUOUS ON [-1, 3] (ACCEPT: F IS CONTINOUS ON THE INTERVAL)
Short Answer Solve
i
ShortAnswer Thepolynomialp(x)=x4 +5x3 ???2x2 ???24xhasazeroatx=2.Factorp completely.
x(x ??? 2)(x + 3)(x + 4)
Short Answer Expressing your answer in simplest form, find the derivative with respect to x of y = [the fraction with numerator x cubed minus 8 and denominator x minus 2] for all values for which y is defined.
y???=2x+2 (ACCEPT:2x+2)
Short Answer Find a value for a such that the [limit as x approaches infinity of the fraction with numerator ax to the fifth minus x cubed plus x and denominator x minus x cubed plus 2 x to the fifth equals 3].
6
Multiple Choice Which of the following is [the limit as x approaches 0 of the absolute value of x over x]?W) -1X) 0Y) 1Z) The limit does not exist
Z) THE LIMIT DOES NOT EXIST
Short Answer Name all of the quadrants that contain solutions of the inequality 2x ??? y > 4 .
I, III, IV (ACCEPT: 1, 3, 4 or FIRST, THIRD, FOURTH)
Short Answer If the graph of the function f lies in quadrant IV, then in which quadrant does the graph of the inverse of f lie?
II (ACCEPT: 2 OR SECOND)
Multiple Choice If f(x) = -2x2 + 8x ??? 4, which of the following is true?W) f is not a one to one functionX) The graph of f opens upwardY) The graph of f has no x-intercept Z) The maximum value of f(x) is -4
W) f IS NOT A ONE TO ONE FUNCTION
Multiple Choice Which of the following is an identity?W) cos(2x) = 2 cos(x)[cosine of 2x equals 2 cosine of x]X) sin(2x) = 2 sin(x) cos(x) [sine of 2 x equals 2 sine of x cosine of x]
X) sin(2x) = 2 sin(x) cos(x)
Multiple Choice Which of the following numbers is NOT prime?W) 107 X) 109 Y) 111 Z) 113
Y) 111
Multiple Choice Which of the following is NOT an even function?W) cosx X) cos(x2) Y) sinxZ) sin(x2)
Y) sinx
Short Answer What is the period of the function f(x) = sin((??/6) x + ??/4) [f of x equals the sine of the quantity pi over 6 times x plus pi over 4]?
12
Short Answer For Valentine???s Day, Adam bought several dozen roses and several dozen carnations. The roses cost $15 per dozen, and the carnations cost $8 per dozen. Adam bought a total of 17 dozen flowers and paid a total of $192. How many dozen roses did he buy?
8
Multiple Choice Which of the following statements is NOT true?W) cos(-x) = cos(x) [cosine of negative x equals cosine of x]X) tan(-x) = tan(x) [tangent of negative x equals tangent of x]Y) The amplitude of y = -2 cos(t) is equal to 2Z) The range of y = -5 sin(t) is [-5 , 5] [the closed interval from negative 5 to 5]
X) tan(-x) = tan(x) Round 1
Multiple Choice Bacteria in a culture are growing exponentially, such that on day 0, there are 100 bacteria, on day 1, there are 200 bacteria, and on day 2, there are 400 bacteria. Which of the following equations expresses the number of bacteria, y, present at any time t?W) y = 100 + 2t [y equals 100 plus 2 to the power of t]X) y = 100(2t) [y equals 100 times the quantity 2 to the power of t] Y) y = 2t [y equals 2 to the power of t]Z) y = 200(2t) [y equals 200 times the quantity 2 to the power of t]
X) y = 100(2t)
Multiple Choice Which of the following is the volume of the solid created by revolving the area bounded by semicircle [y equals the square root ofopen bracket 16 minus open parenthesis x minus 4 close parenthesis squared close brackets] and the x-axis around the x-axis?W) 16?? X) 64??/3 Y) 64??Z) 256??/3
Z) 256??/3 ROUND 14
Short Answer The midpoint of segment AB is (1.5, -3). The coordinates of point A are (7, -5); what are the coordinates of point B?
(-4, -1)
Short Answer If the height of a cone is equal to the diameter of its base, express the volume of the cone in terms of its radius r and as a fraction in terms of pi.
(2/3) ??r3 (ALSO ACCEPT:: 2??r3/3) BONUS
Short Answer Differentiate sin(cosx) [sine of cosine of x].BONUS
-cos(cos x)sinx [ACCEPT: cos (cos x)(-sin x) or ???sinx cos(cos(x)); DO NOT ACCEPT: -cos2x sinx]
Short Answer A fair standard six-sided die is rolled two times. What is the probability that the sum of the numbers on the two rolls will be greater than 9?
1/6 Round 6
Short Answer If the exterior angle of a base angle of an isosceles [eye-SOS-uh- lees] triangle measures 141o, what is the measure of the vertex angle?
102??
Short Answer W is one of the vertices of a polygon. If there are 8 diagonals of the polygon that contain W, how many sides does the polygon have?
11
Short Answer In a standard deck of cards with no jokers, providing your answer as a fraction in lowest terms, what is the probability of picking a card that is black or a number less than 10 (which includes aces)?
11/13
Short Answer A national achievement test is administered. The test has a mean score of 100 and a standard deviation of 15. If Vince???s z-score is 1.20, what is his score on the test?
118
Short Answer Providing your answer as an improper fraction in lowest terms, solve the following equation for x over the real numbers: [9 to the power of 2x equals 27 to the power of the quantity 3x minus 4].
12/5
Short Answer After 40 times at bat, BJ has 9 hits. What is the least number of hits he would need in his next 30 times at bat so that he has hits in at least 31% of his total at-bats?
13
Short Answer Providing your answer as a fraction in lowest terms, if a family has exactly four children, what is the probability of having three girls and one boy?
1???4
Multiple Choice The lines defined by y = 2x and 2y = -x are which of the following?W) ParallelX) Perpendicular Y) HorizontalZ) Vertical intercepts of the graph of y = 12x2 ??? 5x ??? 2?
2/3 AND -1/4 ANSWER: X) PERPENDICULAR
Short Answer How many terms does the binomial expansion of (x2 + 2y3)20 [open parenthesis x squared plus 2 y cubed close parenthesis to the power of 20] contain?
21
Short Answer If the length, width, and height of a right rectangular prism are in the ratio of 3:4:12 [3 to 4 to 12], find the height in meters of the solid if the diagonal of the solid is 26 meters long.
24
Short Answer Todd the Tortoise is 268 years old, while Sammy the Snail is 32 years old. How many years will it take for Todd???s age to be exactly 5 times Sammy???s age?
27
Multiple Choice Which of the following points lies in the solution set for the system of two inequalities: 2y ??? x ??? -6 and 2y ??? 3x < -6?
3 /2b
Short Answer Expressing your answer in simplest form, if y = (x6) ln(x) [y equals x to the sixth power times the natural log of x], what is the derivative of y with respect to x?
6x5 ln(x) + x5
Short Answer Given that g(????) ??? f (????) ??? h(????) for all x, the lim???????a ????(????) = M [limit as x approaches a of g of x is M], and the lim???????a h(????) = M [limit as x approaches a of h of x is M], what is the lim???????a ????(????) [limit as x approaches a of f of x]?W) Ionosphere [eye-ON-uh-sfeer] X) StratosphereY) ThermosphereZ) Troposphere
W) IONOSPHERE
Multiple Choice Which of the following functions has an oblique asymptote?W) f(x) = (x5 + 1)/(x4 + 3x2 + 2) [f of x equals open parenthesis x to the fifth plus 1 close parenthesis over open parenthesis x to the fourth plus 3 x squared plus 2 close parenthesis]X) f(x) = (x2 + 1)/(x3 - x2 - 1) [f of x equals open parenthesis x squared plus 1 close parenthesis over open parenthesis x cubed minus x squared minus 1 close parenthesis]Y) f(x) = (4x2 + x + 1)/x2 [f of x equals open parenthesis 4 x squared plus x plus 1 close parenthesis over x squared]Z) f(x) = x5/(x2 - 1) [f of x equals x to the fifth over open parenthesis x squared minus 1 close parenthesis]
W) f(x) = (x5 + 1)/(x4 + 3x2 + 2) TOSS-UP
Multiple Choice A certain radioactive element decays over time according to the equation [y equals R times one half to the power of the quantity x over300], where R equals the number of grams that were present initially and x equals time in years. If 1000 grams were present initially, how many grams will remain after 900 years?W) 62.5 X) 125 Y) 250 Z) 500
X) 125
Multiple Choice The hyperbola with equation = 1 possesses which of the following characteristics?W) It opens left and right and has asymptotes y = x and y = x X)Itopensupanddownandhasasymptotesy= xandy= x Y) It opens left and right and has asymptotes y = x and y = x Z) It opens up and down and has asymptotes y = x and y = x
X) IT OPENS UP AND DOWN AND HAS ASYMPTOTES y = x AND y = x
Multiple Choice The variables x and y vary directly. Which of the following equations could represent the relationship between x and y?W) (1/5)x = 1/y [one fifth x equals 1 over y] X) x/y = 1/5 [x over y equals one fifth]Y) xy = 1/5 [x y equals one fifth]Z) xy = 5
X) x/y = 1/5
Short Answer Determine the largest possible real domain of y = ??????????1 [y equalsBONUS???????2??? 1the fraction with numerator the square root of the quantity x minus 1 and denominator the square root of the quantity x squared minus 1 ].
x > 1
Multiple Choice Which of the following is equivalent to sin24ocos17o + cos24osin17o [sine of 24 degrees times cosine of 17 degrees plus cosine of 24 degrees times sine of 17 degrees]?W) Sine of 7oX) Cosine of 41o Y) Sine of 41oZ) Tangent of 41o
Y) SINE OF 41o
Multiple Choice Which of the following inequalities has NO solutions?W) 7x + 4 > 3X) |x ??? 1| > -10 [the absolute value of the quantity x minus 1 is greater than negative 10] Y) |x + 3| < -2 [the absolute value of the quantity x plus 3 is less than negative 2]Z) -100x + 5 ??? 8
Y) |x + 3| < -2
Short Answer If g(u) = [g of u equals the integral from 0 to u of secant squared of t dt], find g???(u) [g prime of u].
sec2u
Short Answer Find the remainder when f(x) = x6 + 5x5 ??? x3 + x ??? 6 is divided by (x + 1).
-10
Short Answer If f(x) = -2x - ex [f of x equals negative 2x minus e to the x], what isthe range of f??? [the derivative of f]?
(-???, -2) (ACCEPT: x < -2 or THE OPEN INTERVAL FROM NEGATIVE INFINITY TO
Short Answer What is the determinant of the 2 by 2 matrix [such that row one includes 2 and negative 3, and row 2 includes negative 8 and negative 4]?
-32
Short Answer Given f(x) = x + 1 and g(x) = 3x, what is f(g(x)) [f of g of x]?BONUS
3x + 1
Short Answer Find the measure in degrees of the largest angle of a triangle with sides of 24 centimeters, 7 centimeters, and 25 centimeters.
90??
Short Answer What is the solution to the following system of three equations: equation one: 2x ??? y + 3z = 8; equation two: x ??? 6y ??? z = 0; and equation three: -6x + 3y ??? 9z = 24?
NO SOLUTION
Short Answer What are the radius and the coordinates of the center of the circle with equation x2 + 6x + y2 + 8y = 0?
RADIUS = 5; CENTER = (-3, -4)
Short Answer What is the multiplicity of the zero 1 in the polynomial p(x)=x4 +x3 9x2 +11x 4?
3
Short Answer Convert 420 degrees to radians as an improper fraction in terms of pi.
7 /3
Short Answer The perimeters of two similar figures have a ratio of 5:7. What is the ratio of their areas?
25:49 (ACCEPT: 25/49)
Short Answer If the graph of y = (x ??? 2) ??? 3 [y equals open parenthesis x minus 2 close parenthesis squared minus three] is translated 5 units up and 2 units to the right, what is the vertex of the new parabola obtained?
(4, 2)
Multiple Choice Which of the following points is on the graph of the inverse of theW) (100, 0) X) (0, 100) Y) (10, 0) Z) (0, 10)[f of x equals 10 to the power of the quantity x plus 2]?
W) (100, 0) Round 1
Multiple Choice If x is an angle such that tan(x) = 5/12 and ?? < x < 3??/2, then sec(x)[secant of x] is equal to which of the following?
W) -13/12
Multiple Choice The equation -3 + |-2x - 5| = k [negative 3 plus the absolute value of the quantity negative 2x minus 5 equals k] has no solution if k equals which of the following?W) -5 X) -3 Y)0 Z) 7
W) -5
Multiple Choice Given triangle ABC with right angle A, angle B with a measure of 30o, and AC equal to , which of the following is the length of side AB?W)9 X) 6 Y)9 Z) 12
W) 9
Short Answer What is the largest possible real domain of f(x) = ln(3x ??? 1) [f of xequals the natural log of the quantity 3x minus 1]?
x > 1/3 (ACCEPT: THE OPEN INTERVAL FROM 1/3 TO (POSITIVE) INFINITY)
