2025.9 US A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

Which expression is equivalent to v^4-590v^3 ?

  1. Av^3(v+590)
  2. B(v^2+59)(v^2-10)
  3. C(v^2-59)(v^2-10)
  4. Dv^3(v-590)
DAdvanced Math / Operations of polynomials
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2

In the figure shown, line r is parallel to line s, and line t intersects both lines. What is the value of x ?

  1. A90
  2. B180
  3. C17
  4. D107
DGeometry and Trigonometry / Angles and Arc length
3

The width of a rectangle is 9 centimeters. The length of the rectangle is 50 centimeters longer than the width. What is the area, in square centimeters, of this rectangle?

  1. A18
  2. B531
  3. C9
  4. D68
BGeometry and Trigonometry / General polygons

For the first 10 hours of an experiment, the scatterplot shows the temperature y, in degrees Fahrenheit (°F), of an object at various times x, in hours, since the start of the experiment. A line of best fit is also shown.

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4

Which of the following is the best interpretation of the slope of the line of best fit?

  1. AThe predicted temperature increases at a constant rate of approximately 170°F per hour over the 10-hour period.
  2. BThe predicted temperature decreases at a constant rate of approximately 170°F per hour over the 10-hour period.
  3. CThe predicted temperature increases at a constant rate of approximately 40°F per hour over the10-hour period.
  4. DThe predicted temperature decreases at a constant rate of approximately 40°F per hour over the 10-hour period.
CProblem Solving and Data Analysis / Scatter Plot
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5

A bank account was opened with an initial deposit. Over the next several months, regular deposits were made into this account, and there were no withdrawals made during this time. The graph of the function f shown, where y=f(x) , estimates the account balance, in dollars, in this bank account x months since the initial deposit. To the nearest whole dollar, what is the amount of the initial deposit estimated by the graph?

30Problem Solving and Data Analysis / Linear growth
6

y=-10x+13
y=-12x+15
What is the solution (x, y) to the given system of equations?

  1. A(13,15)
  2. B(15,13)
  3. C(3,1)
  4. D(1,3)
DAlgebra / Solving systems of linear equations
7

f(x)=-16x^2+76
The function f gives the estimated height, in feet, of an acorn x seconds after the acorn fell from a tree. Based on the function, what is the estimated height, in feet, of the acorn before it fell from the tree?

76Advanced Math / Quadratic word problems
8

During hibernation, American black bears do not eat or replenish calories. A certain black bear weighed 515 pounds when entering hibernation and lost weight at a rate of 0.5 pound per day. At this rate, how many days after entering hibernation did the black bear weigh 490 pounds?

50Algebra / Linear functions word problem
9

If x+1=3, what is the value of 2(x+1) ?

6Algebra / Solve linear equation
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10

The graph of the polynomial function f is shown, where y=f(x). What is the value of f(5)?

  1. A2
  2. B5
  3. C-3
  4. D0
DAdvanced Math / Nonlinear equation graphs
11

A freight elevator can hold a maximum weight of 5,450 pounds during one trip. A 190-pound person needs to deliver several boxes using the freight elevator. Some of these boxes weigh 23 pounds each and the others weigh 60 pounds each. Which inequality represents the possible combinations of the number of 23-pound boxes, x, and the number of 60-pound boxes, y, the person can deliver during one trip if only the person and the boxes are on the freight elevator?

  1. A60x+23y≥5,450
  2. B23x+60y≥5,260
  3. C60x+23y≤5,450
  4. D23x+60y≤5,260
DAlgebra / Linear inequality word problem
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12

In trangle JKL, cos y°=58/59 . What is the length of KL ?

58Geometry and Trigonometry / Trigonometric functions
13

b-19=x/y
The given equation relates the positive numbers b, x, and y. Which equation correctly expresses x in terms of b and y?

  1. Ax=(b-19)/y
  2. Bx=by-19y
  3. Cx=(by-19)/y
  4. Dx=by-19
BAdvanced Math / Isolating quantities
14

In the xy-plane, the graph of the linear function h contains the points(0, 0) and (1, 10). Which equation defines h, where y=h(x)?

  1. Ah(x)=10x
  2. Bh(x)=10x+10
  3. Ch(x)=1/10x+10
  4. Dh(x)=x+10
AAlgebra / Graphing linear equations
15

3x+y=21
9x-y=3
How many solutions does the given system of equations have?

  1. AInfinitely many
  2. BZero
  3. CExactly two
  4. DExactly one
DAlgebra / Solving systems of linear equations
16

The length of a rectangle is 35 centimeters greater than its width. Which equation gives the area A, in square centimeters, of the rectangle in terms of the width w, in centimeters, of the rectangle?

  1. AA=(w)(w+35)
  2. BA=(w)(35w)
  3. CA=(w)(w/35)
  4. DA=(w)(w-35)
AAdvanced Math / Quadratic word problems
17

The measure of angle K is π/(2(12))radians. The measure of angle L is 12 times the measure of angle K. What is the measure, in degrees, of angle L?

  1. A102
  2. B12
  3. C78
  4. D90
DGeometry and Trigonometry / Angles and Arc length
18

(x-7)(x-8)/(x-3)=0
What is the sum of the solu(x-7)(x-8)/(x-3)=0tions to the given equation?

  1. A8
  2. B18
  3. C15
  4. D3
CAdvanced Math / Rational transformation
19

What is the y-intercept of the graph of y=6^x+12 in the xy-plane?

  1. A(0,6)
  2. B(0,12)
  3. C(0,18)
  4. D(0,13)
DAdvanced Math / Nonlinear equation graphs
20

-6x+42px=84
In the given equation, p is a constant. The equation has no solution. What is the value of p?

  1. A1/3
  2. B0
  3. C2
  4. D1/7
DAlgebra / Solve linear equation
21

The density of a certain type of marble stone is 2.6000 grams per cubic centimeter. If a sample of this type of stone is in the shape of a sphere with a diameter of 31.000 centimeters, what is the mass of this sample, in grams, to the nearest whole number? (Use 3.14159 for π .)

40556Geometry and Trigonometry / Volume
22

The function w is defined by w(r)=1/(r-8)-(r-5)/(-r+4.25). What is the greatest possible value of r such that w(r)=0 ?

13/2,6.5Advanced Math / Rational transformation

Module 2 (Advanced)

1

1.5c+3d=108
The given equation describes the relationship between the number of cats, c, and the number of dogs, d, that can be cared for at a pet care business during a week. If the business cares for 36 dogs during a week, how many cats can it care for during this week?

  1. A3
  2. B54
  3. C0
  4. D108
CAlgebra / Linear equation word problem
2

Stefan purchased 500 feet of fencing. He used 80% of this fencing to surround a vegetable garden. How many feet of fencing did Stefan use to surround the vegetable garden?

  1. A16
  2. B420
  3. C400
  4. D40
CProblem Solving and Data Analysis / Percents
3

x+5=14
y=3x^2+3
At what point (x, y)do the graphs of the equations in the given system intersect?

  1. A(9,243)
  2. B(14,591)
  3. C(9,246)
  4. D(14,3)
CAdvanced Math / linear and quadratic systems
4

If (x+2)^2=18, what is the value of x^2+4x ?

  1. A14
  2. B22
  3. C36
  4. D18
AAdvanced Math / Transform of quadratic expressions
5

6(t+7)-8(t+7)=38
What value of t is the solution to the given equation?

-26Algebra / Solve linear equation
6

Which expression represents the product of (x^(-9)y^6z^5) and(x^4z^5+y^8z^(-7)) ?

  1. Ax^(-5)y^6z^10+y^8z^(-7)
  2. Bx^(-5)y^6z^10+x^(-9)y^14z^(-2)
  3. Cx^(-5)z^10+x^(-9)z^(-2)
  4. Dx^(-5)z^10+x^14z^(-2)
BAdvanced Math / Operations of polynomials
7

On January 1,2000, the population of a town was 26,255 and on January 1,2010, the population was 26,950. The equation 10x+26,255=26,950 describes this situation. Which of the following is the best interpretation of x in this context?

  1. AThe total increase in population between 2000 and 2010
  2. BThe average increase per year of the population between 2000 and 2010
  3. CThe percentage by which the population of the town increased each year between 2000 and 2010
  4. DThe projected population of the town 10 years after 2010
BAlgebra / Interpreting linear equation
8

Cube B has a volume of 125 cubic inches. The length of each edge of cube A is k times the length of each edge of cube B. If cube A has a volume of 3,375 cubic inches, what is the value of k?

  1. A27
  2. B3
  3. C25
  4. D5
BGeometry and Trigonometry / Congruence and similarity
9

A right square pyramid has a height of 6 units and a volume of 128 cubic units. What is the length, in units, of one side of the base of the pyramid?

  1. A8
  2. B256
  3. C64/3
  4. D(8√3)/3
AGeometry and Trigonometry / Volume
10

A researcher observes a sample of a nuclide. An exponential model estimates that the mass, in grams, of the sample decreases by 27% every 14.07 minutes. Which of the following equations could represent this model, where M is the estimated mass, in grams, of the sample t minutes after the researcher began observing the sample?

  1. AM=100(0.27)^(t/14.07)
  2. BM=100(0.27)^(t+14.07)
  3. CM=100(0.73)^(t/14.07)
  4. DM=100(0.73)^(t+14.07)
CAdvanced Math / Exponential word problems

A department store sells pants in three lengths: short, regular, and long. The table summarizes the distribution of pant length, by color, for all the pants in the store.

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11

A pair of pants is selected at random. What is the probability of selecting a pair of pants that is brown, given that the pair of pants is regular length? (Express your answer as a decimal or fraction, not as a percent.)

1/4,0.25Problem Solving and Data Analysis / Ratios and proportion
12

An equation of the line in the xy-plane that contains the points (0, -8) and (-2, 0) is Ax+By=9, where A and B are constants. What is the value of B ?

  1. A-2/9
  2. B-9/8
  3. C-9/2
  4. D-8/9
BAlgebra / Graphing linear equations
13

(x+k)+9/2(y+t)+19=0
(x+k)-9/2(y+t)-19=0
In the given system of equations, k and t are constants. The solution to this system is (x,y). What is the value of 18(y+t) ?

  1. A-76
  2. B0
  3. C38
  4. D9
AAlgebra / Solving systems of linear equations
14

y>2x-72
y<-1/6x-9
For which of the following tables are all the values of x and their corresponding values of y solutions to the given system of inequalities?

  1. A
    image
  2. B
    image
  3. C
    image
  4. D
    image
BAlgebra / Solving systems of linear inequalities
15

g(x)=1/11(6(2)^x+7)
The function g is defined by the given equation. For all values of x, the value of g(x) is greater than k, where k is a constant. What is the greatest possible value of k ?

  1. A0
  2. B13/11
  3. C7/11
  4. D7
CAdvanced Math / Exponential word problems

At a nature preserve, a wildlife biologist counted ducks from an observation deck at the same time each day for 41 days. The table summarizes the resulting data set, data set A.

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16

The data value 13 was recorded in error and is removed from data set A to create data set B, which consists of the remaining 40 data values. Which statement best compares the median of data set A and the median of data set B?

  1. AThe median of data set B is greater than the median of data set A.
  2. BThere is not enough information to compare the medians of the two data sets.
  3. CThe median of data set B is equal to the median of data set A.
  4. DThe median of data set B is less than the median of data set A.
CProblem Solving and Data Analysis / Mean, mode, median
17

Each 3.0-ounce serving of cheddar cheese and each 1.2-ounce serving of tuna provides about 1 microgram of vitamin B12. If a total of 1.7 micrograms of vitamin B12 are consumed from eating x ounces of cheese and y ounces of tuna, which equation best represents this situation?

  1. A3.0x+1.2y=1.7
  2. B0.33x+0.83y=1.7
  3. C0.83x+0.33y=1.7
  4. D1.2x+3.0y=1.7
BAlgebra / Linear equation word problem
18

A certain town has an area of 12,669,184 square yards. What is the area, in square miles, of this town? (1 mile = 1,760 yards)

  1. A2.02
  2. B7,198.4
  3. C4.09
  4. D3,559.38
CProblem Solving and Data Analysis / Units
19

f(x)=3d(26x+27)+18
Which of the following represents the x-intercept of the graph of y=f(x)+6 in the xy-plane, where d is a constant?

  1. A(81d+24,0)
  2. B((-81d-24)/78d,0)
  3. C(6-(81d+18)/78d,0)
  4. D(-45/(78d+6),0)
BAlgebra / Graphing linear equations
20

In triangle ABC, the measure of angle A is 52° and AC = 40. In triangle PQR, the measure of angle P is 52° and PR = 120. Which additional piece of information is sufficient to prove that triangle ABC is similar to triangle PQR?

  1. AAB = 45 and PQ = 45.
  2. BAB = 45 and QR = 135.
  3. CThe measures of angle B and angle R are 40° and 88°, respectively.
  4. DThe measures of angle B and angle Q are 52° and 40°, respectively.
CGeometry and Trigonometry / Congruence and similarity
21

A quadratic function gives the estimated length of daylight d(t), in hours, in a certain city t months after March 1, where 0≤t≤7 . According to the function, the estimated length of daylight is 12.66 hours 6 months after March 1 and the maximum estimated length of daylight is 13.91 hours 3.5 months after March 1. Based on this function, what is the estimated length of daylight, in hours, on March 1?

11.46Advanced Math / Quadratic word problems
22

nx^2-16x=26x^2-8
In the given equation, n is an integer constant. If the equation has two distinct real solutions, what is the greatest possible value of n?

33Advanced Math / Solving quadratic equations