2025.3 US A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

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1

The triangle shown has one side with a length of x inches and two sides each with a length of y inches. The perimeter of the triangle is 47 inches. Which equation represents this situation?

  1. Ax+y=47
  2. Bx+2y=47
  3. C2x+y=47
  4. D2x+2y=47
BAlgebra / Linear equation word problem
2

If 7+x=4 , what is the value of 42+6x ?

24Algebra / Solve linear equation
3

A batch of smoothies consists of 4 cups of milk and 2 bananas and has 1,228 milligrams (mg) of calcium. There is 304 mg of calcium in 1 cup of milk. How much calcium, in mg, is in 1 banana?

  1. A1,216
  2. B462
  3. C12
  4. D6
DAlgebra / Linear equation word problem
4

A furniture company is selling all tables with a 20% discount off their original price for the month of October. What is the discount, in dollars, on a table with an original price of $130?

  1. A110
  2. B90
  3. C52
  4. D26
DProblem Solving and Data Analysis / Percents
5

A sleep study consisted of 66 participants, of which 59 participants each had an average of more than 120 minutes of rapid eye movement (REM) sleep per night. If a participant from this sleep study is selected at random, what is the probability of selecting a participant that had an average of more than 120 minutes of REM sleep per night?

  1. A66/120
  2. B59/120
  3. C59/66
  4. D59/100
C
6

4x=16
-3x+y=-5
The solution to the given system of equations is (x,y) . What is the value of x+y?

  1. A-21
  2. B-11
  3. C11
  4. D21
CAlgebra / Solving systems of linear equations
7

A shopper is purchasing oranges that cost $0.67 each. If the shopper has a coupon for $2 off the entire purchase and there is no sales tax. Which inequality represents the number of oranges, x, that the shopper can purchase for no more than $12?

  1. A0.67x+2≤12
  2. B0.67x+2≥12
  3. C0.67x-2≤12
  4. D0.67x-2≥12
CAlgebra / Linear inequality word problem
8

Circle T has a radius of 35 millimeters (mm). What is the area of circle T, in mm²?

  1. A35π
  2. B70π
  3. C140π
  4. D1,225π
DGeometry and Trigonometry / Circle theorems
9

In the xy-plane, circle F is defined by the equation (x+7)^2+(y+7)^2=36 . Circle G has the same center as circle F, and the radius of circle G is 2 units greater than the radius of circle F. Circle G is defined by the equation (x+7)^2+(y+7)^2=p, where p is a constant. What is the value of p?

64Geometry and Trigonometry / Circle equation
10

Which expression is equivalent to 4yz^3+5yz+3yz^3 ?

  1. A7yz^3+5yz
  2. B7yz^6+5yz
  3. C12yz^6
  4. D12yz^7
AAdvanced Math / Operations of polynomials
11

If x/y=76 and cx/4y=76, what is the value of c?

4Advanced Math / Rational transformation
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12

In the figure shown, triangle CAE is similar to triangle CBD. The measure of angle CBD is 57°, and AE=21(BD).What is the measure of angle CAE?

  1. A(21•57)^(°)
  2. B(21+57)^(°)
  3. C57°
  4. D21°
CGeometry and Trigonometry / Congruence and similarity
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13

The graph shows the estimated boiling point y, in degrees Celsius, of a straight-chain alkane with a molecular weight of x grams per mole, where 1≤x≤280 .Which statement is the best interpretation of the point (141.32, 172.26)?

  1. AA straight-chain alkane with a molecular weight of 172.26 grams per mole has an estimated boiling point of 141.32 degrees Celsius.
  2. BA straight-chain alkane with a molecular weight of 141.32 grams per mole has an estimated boiling point of 172.26 degrees Celsius.
  3. CThe minimum estimated boiling point for straight-chain alkanes corresponds to an alkane with a molecular weight of 141.32 grams per mole and an estimated boiling point of 172.26 degrees Celsius.
  4. DThe maximum estimated boiling point for straight-chain alkanes corresponds to an alkane with a molecular weight of 141.32 grams per mole and an estimated boiling point of 172.26 degrees Celsius.
BAdvanced Math / Nonlinear equation graphs
14

y=x^2-24x+36
The given equation relates the variables x and y. For what value of x does the value of y reach its minimum?

  1. A-24
  2. B24
  3. C12
  4. D48
CAdvanced Math / Transform of quadratic expressions
15

If 72/x=6x, what is the value of 6x^2 ?

  1. A432
  2. B72
  3. C12
  4. D6
BAdvanced Math / Rational transformation
16

y≤5x-21
Which point (x,y) is a solution to the given inequality in the xy-plane?

  1. A(-5,-21)
  2. B(0,21)
  3. C(5,-21)
  4. D(6,21)
CAlgebra / Linear inequality word problem
17

(x-8)(x-16)/(x-7)=0
What is the sum of the solutions to the given equation?

  1. A8
  2. B24
  3. C31
  4. D7
BAdvanced Math / Rational transformation
18

f=((10x)^2)/7g
The given equation relates the positive numbers f, x , and g . Which equation correctly expresses x in terms of f and g?

  1. Ax=(√7fg)/10
  2. Bx=10√7fg
  3. Cx=√7fg/10
  4. Dx=√7fg-10
AAdvanced Math / Isolating quantities
19

In the xy-plane, line l passes through the point (0,0) and is parallel to the line represented by the equation y=8x+4. If line l also passes through the point (6,d) .What is the value of d?

48Algebra / Graphing linear equations
20

A circle in the xy-plane has its center at (14, 19) and has a radius of 7k. Which equation represents this circle?

  1. A(x-14)^2+(y-19)^2=49k
  2. B(x-14)^2+(y-19)^2=49k^2
  3. C(x-14)^2+(y-19)^2=7k
  4. D(x-14)^2+(y-19)^2=7k^2
BGeometry and Trigonometry / Circle equation
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21

According to a US law, ramps for use by the general public must form an angle with level ground such that tanθ≤1/12. If the ramp in the figure conforms to this law and has a height of 29.1 inches. What is the least possible value of x, in inches?

349.2Geometry and Trigonometry / Trigonometric functions
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22

The equation of the graph shown is y=a^x+b , where a and b are constants. What is the value of a-b ?

9Advanced Math / Exponential word problems

Module 2 (Advanced)

1

f(x)=(x+9)/3
For the function f defined by the equation shown, what is the value of f(-6)?

  1. A-3
  2. B-1
  3. C1
  4. D3
CAlgebra / Linear functions word problem
2

28, 28, 29, 30, 32, 33, 37
What is the mean of the data set shown?

  1. A28
  2. B30
  3. C31
  4. D37
CProblem Solving and Data Analysis / Mean, mode, median
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3

The potential difference across a capacitor in an electric circuit is initially 16 volts and decreases with time, as shown in the graph. Which of the following is closest to the time, in seconds, from the initial measurement at which the potential difference across the capacitor is 15% of its initial value?

  1. A0.43
  2. B0.85
  3. C1.71
  4. D3.41
CAdvanced Math / Nonlinear equation graphs
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4

The scatterplot shows the relationship between two variables, x and y, for data set A. A line of best fit for the data is also shown. Data set B is created by subtracting 9 units from the value of y for each data point from data set A. Which of the following is closest to the y-coordinate of the y-intercept of the line of best fit for data set B?

  1. A45.57
  2. B53
  3. C59.62
  4. D62.75
AProblem Solving and Data Analysis / Scatter Plot
5

In the linear function f, f(0)=5 and f(7)=5. Which equation defines f ?

  1. Af(x)=0
  2. Bf(x)=7
  3. Cf(x)=5
  4. Df(x)=x+5
CAlgebra / Graphing linear equations
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6

For the linear function f, the table shows three values of x and their corresponding values of f(x). Which equation defines f ?

  1. Af(x)=-5(5x-3) f(x)=-5(5x-3)
  2. Bf(x)=-5(5x-4) f(x)=-5(5x-3)
  3. Cf(x)=-5(x+3)
  4. Df(x)=-5(x-4)
CAlgebra / Linear functions word problem
7

A sample of a certain isotope takes 29 years to decay to half its original mass. The function s(t)=128(0.5)^(t/29) gives the approximate mass of this isotope, in grams, that remains t years after a 128-gram sample starts to decay. Which statement is the best interpretation of s(58)=32 in this context?

  1. AApproximately 32 grams of the sample remains 58 years after the sample starts to decay.
  2. BThe mass of the sample has decreased by approximately 32 grams 58 years after the sample starts to decay.
  3. CThe mass of the sample has decreased by approximately 58 grams 32 years after the sample starts to decay.
  4. DApproximately 58 grams of the sample remains 32 years after the sample starts to decay.
AAdvanced Math / Exponential word problems

The table shows the distribution of people in a certain city by age group.

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8

If a person in this city is selected at random, which of the following is closest to the probability of selecting a person who is greater than 65 years old, given that the person is at least 18 years old?

  1. A0.21
  2. B0.32
  3. C0.45
  4. D0.62
BProblem Solving and Data Analysis / Ratios and proportion
9

A right circular cone has a base diameter of 28 inches and a height of 6 inches. The volume of this cone is kπ cubic inches. What is the value of k?

392Geometry and Trigonometry / Volume
10

In triangle ABC, point D is the midpoint of segment AB and point E is the midpoint of segment BC. If BD=8 and DE=14. What is the length of segment AC ?

  1. A28
  2. B26
  3. C22
  4. D16
AGeometry and Trigonometry / Congruence and similarity
11

x(r-7)+3=19x+25
In the given equation, r is a positive integer. If the given equation has exactly one solution, what CANNOT be the value of r?

  1. A3
  2. B7
  3. C22
  4. D26
DAlgebra / Solve linear equation
12

In a collection of items, 10% are red, 25% are green, 35% are blue, and 30% are yellow. If there are 40 green items. How many blue items are in the collection?

  1. A14
  2. B16
  3. C48
  4. D56
DProblem Solving and Data Analysis / Percents
13

x(13x+27)+c=5
In the given equation, c is a constant. A solution to the equation is (-27+√261)/26. What is the value of c?

  1. A14
  2. B9
  3. C5
  4. D4
AAdvanced Math / Solving quadratic equations
14

One of the factors of 2x^3+44x^2+234x is x+b, where b is a positive constant. What is the smallest possible value of b?

9Advanced Math / Polynomial factors and graphs
15

A model estimates that at the end of each year from 2015 to 2020, the number of rabbits in a population was 170% more than the number of rabbits in the population at the end of the previous year. The model estimates that at the end of 2016, there were 216 rabbits in the population. Which of the following equations represents this model, where n is the estimated number of rabbits in the population t years after the end of 2015 and t≤5 ?

  1. An=80(1.7)^t
  2. Bn=80(2.7)^t
  3. Cn=216(1.7)^t
  4. Dn=216(2.7)^t
BAdvanced Math / Exponential word problems
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16

The figure shows a rectangular pool surrounded by a concrete path that is x feet (ft) wide on all sides. The pool is 21 ft long and 13 ft wide. The area of the concrete path is 240 ft^2t2 . What is the value of x?

  1. A3
  2. B6
  3. C20
  4. D40
AAdvanced Math / Quadratic word problems
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17

The table shows three values of x and their corresponding values of y, where s is a constant. There is a linear relationship between x and y. Which of the following equations represents this relationship?

  1. Asx+3y=11s
  2. B3x+sy=11s
  3. C3x+sy=11
  4. Dsx+3y=11
BAlgebra / Linear equation word problem
18

In a set of four consecutive odd integers, where the integers are ordered from least to greatest, the first integer is represented by x. The product of 28 and the third odd integer in the set is at most the value of 50 less than the sum of the first and fourth odd integers in the set. What is the greatest possible value of x?

-7Algebra / Linear inequality word problem
19

A square map has a side length of 30 inches, and 1 inch on the map represents an actual distance of 17 miles. A smaller version of the same map is printed as a square with the side length 65% shorter than the side length of the previous map. On the smaller map, which of the following is closest to the actual distance, in miles, represented by 1 inch?

  1. A5.95
  2. B10.30
  3. C19.50
  4. D48.57
DProblem Solving and Data Analysis / Ratios and proportion
20

The functions f and g are defined by the equations shown, where a and b are integer constants, a<0a<b andb<0 . If y-f(x)y=f(x) and y=g(x) are graphed in the xy-plane, which of the following equations displays, as a constant or coefficient, the y-coordinate of the y-intercept of the graph of the corresponding function?
Ⅰ.f(x)=a(2.1)^(x+b)
Ⅱ.f(x)=a(2.1)^x+bg(x)=a(2.1)^x+b

  1. AⅠ only
  2. BⅡ only
  3. CⅠ and Ⅱ
  4. DNeither Ⅰ nor Ⅱ
  5. AⅠ only
  6. BⅡ only
  7. CⅠ and Ⅱ
  8. DNeither Ⅰ nor Ⅱ
DAdvanced Math / Exponential word problems
21

The function h is defined by h(x)=-√x^2+bx+c where b and c are constants. In the xy-plane, the graph of y=h(x)contains the points (2,0) and (0,-√358). If h(m)=0,what is the greatest possible value of m?

179Advanced Math / Transform of quadratic expressions
22

The function f is defined by f(x)=(∣x∣)/a-14, wherea<0 . What is the product of f(15a) and f(8a)?

638Advanced Math / Function notations and transforms