2024.12 B

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

image
1

In the figure, two lines intersect at a point. If w = 128, what is the value of z?

  1. A28
  2. B52
  3. C64
  4. D128
DGeometry and Trigonometry / Angles and Arc length
2

Sabrina has a goal to save at least $240. Sabrina has already saved $180. If x represents the additional amount of money, in dollars, Sabrina needs to save to meet her goal, which inequality represents this situation?

  1. Ax/180≥240
  2. B180x≥240
  3. C180+x≥240
  4. D180-x≥240
CAlgebra / Linear inequality word problem
3

The function f is defined by f(x)=12x+18. What is the y-coordinate of the y-intercept of the graph ofy=f(x) in the xy-plane?

18Algebra / Linear functions word problem
4

A certain pigeon species can fly at an average speed of 16 meters per second when in continuous flight. At this rate, how many meters would this pigeon species fly in 4 seconds?

  1. A64
  2. B20
  3. C16
  4. D12
AAlgebra / Linear functions word problem

In the given scatterplot, a line of best fit for the data is shown.

image
5

Which of the following equations best represents this line of best fit?

  1. Ay=1.1x
  2. By=-1.1x
  3. Cy=5.2
  4. Dy=-5.2
AProblem Solving and Data Analysis / Scatter Plot
6

The function d is defined by d(x)=200-6^x. What is the value of d(0)?

  1. A140
  2. B194
  3. C199
  4. D200
CAdvanced Math / Exponential word problems
7

A rectangular region of land is divided into 40 square lots of equal area sqrt(R)R , in square units. The length of the region is 1.6 times the width of the region. If the width of the region is x√R units, what is the value of x ?

5Advanced Math / Quadratic word problems
8

Line k is defined by y=7x+2. Line j is parallel to line k in the xy-plane and passes through the point (0, 3). Which equation defines line j?

  1. Ay=7x+3
  2. By=-3x+3
  3. Cy=-7x+3
  4. Dy=3x+3
AAlgebra / Graphing linear equations
9

If x+4y=41 and 7x-20y=-97, what is the value of y?

8Algebra / Solving systems of linear equations
10

For the linear function f, the graph of y=f(x) in the xy-plane has a slope of 28 and passes through the point (0, 0). The function f is defined by f(x)=ax, where a is a constant. What is the value of a?

28Algebra / Graphing linear equations
image
11

The graph models the number of active projects a company was working on x months after the end of November 2011, where 0≤x≤6. According to the model, what is the predicted number of active projects the company was working on at the end of November 2011?

  1. A0
  2. B8
  3. C11
  4. D12
BProblem Solving and Data Analysis / Key feature of graphs
12

The list gives the number of individuals in each of 6 groups of ring-tailed lemurs.
17, 4, 20, 17, 18, 6
What is the range of the numbers of individuals for the 6 groups of ring-tailed lemurs?

16Problem Solving and Data Analysis / Spread of distribution
13

d=15t
The given equation relates the distance d, in inches, of an object from its starting position to the time t, in seconds, since the object started moving. What is the rate of change of the object's distance from its starting position over time?

  1. A15t inches per second
  2. B15 inches per second
  3. C1/15 inches per second
  4. D1/15t inches per second
BAlgebra / Interpreting linear equation
14

What is the slope of the graph of y=1/2(15x+12)+3x in the xy-plane?

21/2,10.5Algebra / Graphing linear equations
image
15

The table shows three values of x and their corresponding values of f(x), where f(x)=(kx+45)/(x+2) and k is a constant. What is the value of k?

5Advanced Math / Rational transformation
16

The function f is defined by f(x)=(x+11)/3,and f(a)=16, where a is a constant. What is the value of a?

  1. A9
  2. B16
  3. C37
  4. D59
CAlgebra / Linear functions word problem
17

Jasmin grows bean pods in her garden. This year, she harvested 330 bean pods and saved 10% of them to plant next year. How many of the harvested bean pods did Jasmin save to plant next year?

  1. A23
  2. B33
  3. C41
  4. D43
BProblem Solving and Data Analysis / Percents
18

A sphere has a radius of 8/3 feet. What is the volume, in cubic feet, of the sphere?

  1. A3/8π
  2. B32π/9
  3. C17π/3
  4. D(2,048π)/81
DGeometry and Trigonometry / Volume
19

A company that manufactures staplers calculates its monthly profit, in dollars, by subtracting its fixed monthly costs, in dollars, from its monthly sales revenue, in dollars. The equation 11,000=2.00x-6,500 represents this situation for a month where x staplers are manufactured and sold. Which statement is the best interpretation of 2.00x in this context?

  1. AThe monthly sales revenue, in dollars, from selling x staplers
  2. BThe monthly sales revenue, in dollars, from each stapler sold
  3. CThe monthly cost, in dollars, of manufacturing each stapler
  4. DThe monthly cost, in dollars, of manufacturing x staplers
AAlgebra / Interpreting linear equation
20

If (x-16)/27=(x-16)/9, what is the value of x+16?

  1. A0
  2. B3
  3. C16
  4. D32
DAlgebra / Solve linear equation
21

8|7-x|+1=81
What is the sum of the solutions to the given equation?

  1. A-14
  2. B-3
  3. C10
  4. D14
DAlgebra / Solve linear equation
image
22

The graph of line h is shown in the xy-plane. Line k (not shown) is defined by sx+40y=t, where s and t are constants. If line k is graphed in this xy-plane, the result is a graph of two linear equations. This system of two linear equations has no solution. Which of the following is NOT a possible value of t?

  1. A200
  2. B64
  3. C-8
  4. D-320
DAlgebra / Solving systems of linear equations

Module 2 (Advanced)

1

Levi and Marissa each have stamp collections. The number of stamps in Levi's collection is 200% of the number of stamps in Marissa's collection. If there are 460 stamps in Marissa's collection, how many stamps are in Levi's collection?

  1. A230
  2. B460
  3. C920
  4. D1,380
CProblem Solving and Data Analysis / Percents
image
2

The graph of a system of a linear equation and a quadratic equation is shown. Which of the following is a solution (x, y) to the system?

  1. A(-1,5)
  2. B(-1,1)
  3. C(0,0)
  4. D(-2,1)
AAdvanced Math / linear and quadratic systems
3

An object moves at a speed of 3/50 feet per second. What is this speed, in yards per second? (3 feet = 1 yard)

  1. A50
  2. B6
  3. C9/50
  4. D1/50
DProblem Solving and Data Analysis / Units
4

Which expression is equivalent to 158t^3-24t^2u ?

  1. A2t(79t^2-12u)
  2. B2t^2(79t-12u)
  3. C2tu(79t^2-12)
  4. D2t^2u(79t-12)
BAdvanced Math / Operations of polynomials
5

Circle K has a radius of 2 millimeters (mm). Circle L has an area of 144π mm². What is the total area, in mm², of circles K and L?

  1. A14π
  2. B28π
  3. C56π
  4. D148π
DGeometry and Trigonometry / Circle theorems
6

Which expression is equivalent to 2(x-3/2)(x+14) ?

  1. Ax^2+25x-21
  2. B2x^2+11x-21
  3. C2x^2+25x-42
  4. D2x^2-42
CAdvanced Math / Transform of quadratic expressions
7

The function f is defined by f(x)=(-7)(4)^x+31. What is the y-intercept of the graph of y=f(x) in the xy-plane?

  1. A(0,24)
  2. B(0,4)
  3. C(0,31)
  4. D(0,-7)
AAdvanced Math / Nonlinear equation graphs
8

In right triangle RST, the sum of the measures of angle R and angle S is 90 degrees. The value of sin(R) is (2√10)/7. What is the value of cos(S)?

  1. A(3√10)/20
  2. B(2√10)/7
  3. C(7√10)/20
  4. D(2√10)/3
BGeometry and Trigonometry / Trigonometric functions
9

y<42-7x
y/7>10
Which inequality represents the x values for all solutions (x, y) that satisfy the given system of inequalities in the xy-plane?

  1. Ax>6
  2. Bx<6
  3. Cx>-4
  4. Dx<-4
DAlgebra / Solving systems of linear inequalities
10

In the xy-plane, an equation of circle A is (x-2)^2+(y-3)^2=9. Circle B has the same center as circle A but has a radius that is twice the radius of circle A. Which equation represents circle B?

  1. A(x-2)^2+(y-3)^2=18
  2. B(x-2)^2+(y-3)^2=36
  3. C(x-2)^2+(y-3)^2=54
  4. D(x-2)^2+(y-3)^2=81
BGeometry and Trigonometry / Circle equation
image
11

A property owner wants to find the length x, in feet, across a pond as represented in the figure. PR intersects ST at point Q , and ∠PTQ is congruent to ∠RSQ. The lengths represented by PQ, TQ, QS, and RS were determined to be 4,200 feet, 8,400 feet, 1,400 feet, and 1,600 feet, respectively. What is the value of x?

9600Geometry and Trigonometry / Congruence and similarity
12

PC=N(44-C)
The given equation relates the variables P, N, and C. Which expression represents the value of C for distinct positive values of P and N?

  1. A(C(N+P))/N
  2. BPC/(44-C)
  3. C44N/(N+P)
  4. D44N/(P+1)
CAdvanced Math / Isolating quantities
image
13

In the figure shown, the measure of angle X is 52°. The length of XY is 24 units and the length of XZ is 17 units. What is the area, in square units, of triangle XYZ?

  1. A204
  2. B408
  3. C204sin52°
  4. D408sin52°
CGeometry and Trigonometry / Trigonometric functions
14

A partially filled container containing 24 milliliters of water is placed under a leaky faucet that produces one 0.03-milliliter drop of water every 3 seconds. Until the container is full, which of the following can be used to represent the volume v, in milliliters, of water in the container t seconds after it is placed under the faucet, where t is a multiple of 3?

  1. Av=0.01t+24
  2. Bv=0.03t+24
  3. Cv=0.09t+24
  4. Dv=3t
AAlgebra / Linear functions word problem
15

A research manager selected 2 random samples of ovens of a certain type to estimate the average amount of time this type of oven takes to preheat to 325 degrees Fahrenheit (°F). The research manager recorded the amount of time, in minutes, each oven takes to preheat to 325 °F. Based on the first sample, the research manager estimated that this type of oven takes an average of 15.2 minutes to preheat to 325 °F, with an associated margin of error of 1 minute. Based on the second sample, the research manager estimated that this type of oven takes an average of 15.4 minutes to preheat to 325 °F, with an associated margin of error of 2.2 minutes. Assuming the margins of error were calculated the same way, which of the following best explains why the first sample obtained a smaller margin of error than the second sample?

  1. AThe first sample contained more ovens than the second sample.
  2. BThe first sample contained fewer ovens than the second sample.
  3. CThe first sample took more time on average to preheat to 325 °F than the second sample.
  4. DThe first sample took less time on average to preheat to 325 °F than the second sample.
AProblem Solving and Data Analysis / Spread of distribution
16

-3/19rx+s/8=10-5/57x
In the given equation, r and s are constants. The equation has no solution. What is the value of r?

5/9,0.555,.555,.5556,.5555,.556,0.556Algebra / Solve linear equation
17

-8x(x+9)=40
One solution to the given equation can be written as x=-(s+√t)/2, where s and t are positive integers. What is the value of s/t?

  1. A9/101
  2. B9/76
  3. C9/61
  4. D18/61
CAdvanced Math / Solving quadratic equations
18

The equation N(m)=65(Q)^(m/4) gives the predicted population N(m), in thousands, of a certain bacteria colony m minutes after the initial measurement, where Q is a constant greater than 1. The predicted population increases by p% every 120 seconds. What is the value of p in terms of Q?

  1. A100(Q^(1/2)+1)
  2. B100(Q^30+1)
  3. C100(Q^(1/2)-1)
  4. D100(Q^30-1)
CAdvanced Math / Exponential word problems
19

A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object was launched. According to the model the object was launched from a height of 0 feet and reached its maximum height of 1,600 feet 10 seconds after it was launched. Based on the model, what was the height, in feet, of the object 7 seconds after it was launched?

1456Advanced Math / Quadratic word problems
20

The function p is defined by p(x)=a((x+5)^2-b)((x+5)^2-c), where a, b, and c are constants. In the xy-plane, the graph of y=p(x) passes through the points(-6,30) and (0,342). What is the value of p(-10)+p(-4)?

372Advanced Math / Transform of quadratic expressions
21

13(x-n)=13y+13n
One of the equations in a system of two linear equations is given, where n is a positive constant. The system has no solution. Which equation could be the second equation in this system?

  1. A2x-2y=4n
  2. B2x+2y=2n
  3. C2x+2y=4n
  4. D2x-2y=2n
DAlgebra / Solving systems of linear equations
22

(x-k)^2=(k-4a)(x-k)
In the given equation, a and k are constants, where k>4a. The sum of the solutions to the equation is 3k+35. What is the value of a?

-35/4,-8.75Advanced Math / Solving quadratic equations