2025.9 International A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

The number of muskrat in a 134-acre area is estimated to be 2,278. What is the estimated population density, in muskrat per acre, of this area?

  1. A17
  2. B134
  3. C151
  4. D2,295
AAlgebra / Linear functions word problem
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2

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 69 inches. Which equation represents this situation?

  1. Ax+y=69
  2. B2x+y=69
  3. Cx+2y=69
  4. D2x+2y=69
CGeometry and Trigonometry / General triangle
3

A jar has 330 buttons, and 20% of these buttons are green. How many buttons in the jar are green?

66Problem Solving and Data Analysis / Percents
4

In the ancient Roman measurement system, a leuga was a unit of length that was equal to 7,500 pedes. In this measurement system, how many pedes were equivalent to 3.8 leugas?

28500Problem Solving and Data Analysis / Units
5

There are a total of 1,200 milligrams of phosphorus in a sample of soil. Each kilogram of this sample contains 600 milligrams of phosphorus. Which equation represents this situation, where x is the mass, in kilograms, of the sample of soil?

  1. Ax+600=1,200
  2. B1,200x=600
  3. Cx+1,200=600
  4. D600x=1,200
DAlgebra / Linear equation word problem
6

The function f is defined by f(x)=1/2 (x+12). What is the value of f(6)?

  1. A36
  2. B24
  3. C18
  4. D9
DAlgebra / Linear functions word problem
7

If 9x+4=32, what is the value of 3(9x+4)?

  1. A84
  2. B96
  3. C108
  4. D128
BAlgebra / Solve linear equation
8

Triangles ABC and DEF are congruent, where A corresponds to D, and B and E are right angles. The measure of angle A is 64°. What is the measure, in degrees, of angle F?

26Geometry and Trigonometry / Congruence and similarity
9

A savings account is opened with an initial deposit of $7,000. The amount of money in the account t years after the initial deposit is given by the function f(t)=7,000(1.01)^2t. Which of the following is the best interpretation of the statement "f(3) is approximately equal to 7,430.64" in this context?

  1. A3 years after the initial deposit, the amount of money, in dollars, in the account is 7,430.64.
  2. BEvery 3 years, the amount of money, in dollars, in the account increases by 7,430.64.
  3. C3 years after the initial deposit, the amount of money, in dollars, in the account has increased by 7,430.64.
  4. DEvery 3 years, the amount of money, in dollars, in the account decreases by 7,430.64.
AAdvanced Math / Interpreting nonlinear expressions
10

y=(x-3)(x+10)
Which table gives four values of x and the corresponding values of y for the given quadratic equation?

  1. A
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  2. B
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  3. C
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  4. D
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CAdvanced Math / Quadratic word problems
11

In the linear function f, f(0)=3 and f(5)=3. Which equation defines f?

  1. Af(x)=0
  2. Bf(x)=5
  3. Cf(x)=3
  4. Df(x)=x+3
CAlgebra / Linear equation word problem
12

An arborist studying forestland in Illinois estimates that there are at least 50 and no more than 60 hickory trees per acre in a certain forest. Which of the following best represents the arborist's estimate of the number of hickory trees, x, that are in a 3-acre section of this forest?

  1. A180≤x≤360
  2. B150≤x≤180
  3. C53≤x≤63
  4. D50≤x≤60
BAlgebra / Linear inequality word problem
13

For the polynomial function p, the graph of y=p(x) in the xy-plane crosses through the points (-4,0), (0,9), (6,0), and (17,0). What is the value of p(0)?

9Advanced Math / Polynomial factors and graphs
14

The graph of -6x+4.4y=-660 in the xy-plane has intercepts at (a,0) and (0,b). What is the value of ab?

-16500Algebra / Graphing linear equations
15

x+24y=60
5x+3y=27
The solution to the given system of equations is (x,y). What is the value of y?

2.333,7/3Algebra / Solving systems of linear equations
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16

As part of a study on sedimentary habitats, the water temperature was recorded at different depths below the surface of the water in the northern Alboran Sea.
The data shown in the scatterplot give the recorded temperature, in degrees Celsius, for 7 depths, in meters, below the surface of the water.
Which of the following is closest to the slope of a line of best fit for the data shown?

  1. A-8.00
  2. B-6.00
  3. C-2.17
  4. D-0.17
DProblem Solving and Data Analysis / Scatter Plot
17

a=3/11b+6
The given equation relates the positive numbers a and b. Which equation correctly expresses b in terms of a?

  1. Ab=3/11a+6
  2. Bb=3/11a-22
  3. Cb=11/3a-6
  4. Db=11/3a-22
DAdvanced Math / Isolating quantities
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18

The shaded region shown represents the solutions to which inequality?

  1. Ay>3x+7
  2. By>3x-7
  3. Cy<3x+7
  4. Dy<3x-7
AAlgebra / Solve linear inequality
19

The measure of an angle, in radians, is (93)(2)π. What is the measure of the angle, in degrees?

  1. A(93/2)(360)
  2. B(93)(360)
  3. C(93)(2)(360)
  4. D(180)(93)(360)
BGeometry and Trigonometry / Angles and Arc length
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20

In triangles RST and XYZ shown, XY is parallel to TS and tanR=216/713. What is the value of sinX in triangle XYZ?

  1. A216/929
  2. B216/745
  3. C713/745
  4. D713/216
CGeometry and Trigonometry / Trigonometric functions
21

|x+4|+4=|2x-17|+4
What is the smallest solution to the given equation?

4.333,13/3Advanced Math / Solving quadratic equations
22

y=3x^2-24x+51
y+4=0
How many solutions are there to the given system of equations?

  1. AThere is exactly 1 solution.
  2. BThere are exactly 2 solutions.
  3. CThere are exactly 3 solutions.
  4. DThere are no solutions.
DAdvanced Math / linear and quadratic systems

Module 2 (Advanced)

1

In triangle EFG, the sum of the measures of angles E and F is 31°. What is the measure of angle G?

  1. A31°
  2. B59°
  3. C118°
  4. D149°
DGeometry and Trigonometry / General triangle
2

Which of the following lists represents a data set with the smallest standard deviation?

  1. A32, 33, 35, 37, 38
  2. B33, 33, 35, 37, 37
  3. C33, 34, 35, 36, 37
  4. D34, 35, 35, 35, 36
DProblem Solving and Data Analysis / Spread of distribution
3

In triangle RST, RS=ST and the length of RT' is 48 units. If tanR=7/24, what is the area, in square units, of triangle RST?

  1. A84
  2. B168
  3. C288
  4. D336
BGeometry and Trigonometry / General triangle
4

y=(x-21)(x-42)
y=0
The graphs of the equations in the given system of equations intersect at the point (x,y) in the xy-plane. What is a possible value of x?

  1. A0
  2. B2
  3. C42
  4. D63
CAdvanced Math / linear and quadratic systems

The cost to rent a kayak consists of a fixed fee for the first hour and an hourly fee for each additional hour. The table shows the rental cost for 4 hours and for 6 hours.

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5

Which function f gives the rental cost, in dollars, for x hours rental, where x≥1?

  1. Af(x)=30x
  2. Bf(x)=20x
  3. Cf(x)=20x+10
  4. Df(x)=20x+90
CAlgebra / Linear functions word problem
6

g(x)=(36-2x)(10+2x)
The function g is defined by the given equation. For what value of x does g(x) reach its maximum?

  1. A6.5
  2. B11.5
  3. C13
  4. D23
AAdvanced Math / Transform of quadratic expressions
7

Rectangle X has a length of 24 millimeters (mm) and a width of 17.5 mm. Right triangle Y has a base of 20 mm. The area of rectangle X is 3 times the area of right triangle Y. What is the height, in mm, of right triangle Y?

  1. A7
  2. B14
  3. C21
  4. D42
BGeometry and Trigonometry / General triangle
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8

There is a linear relationship between x and y. The table shows three values of x and their corresponding values of y in terms of a constant n. What is the slope of the line in the xy-plane that represents this relationship?

  1. A12
  2. B2
  3. C14/3
  4. D14
CAlgebra / Graphing linear equations
9

If a=3k+5r and b=9k-12r+6, which expression is equivalent to a-b?

  1. A-6k+17r-6
  2. B-6k+17r+6
  3. C-6k-7r+6
  4. D-6k-7r-6
AAdvanced Math / Operations of polynomials
10

An exponential function f is defined by f(x)=c^x, where c is a constant greater than 1. If f(8)=(49) • f(6), what is the value of c?

7Advanced Math / Exponential word problems
11

The equation h=(9(v-273.15))/5+32 gives the corresponding temperature h, in degrees Fahrenheit, of any substance that has a temperature of v kelvins, where v>0. If a substance has a temperature of 557.33 degrees Fahrenheit, what is the corresponding temperature, in kelvins, of this substance?

565Algebra / Linear equation word problem
12

81x^2+18/33x+p=0
In the given equation, p is a constant. The equation has exactly one real solution. What is the value of p?

  1. A33
  2. B2/33
  3. C33^2
  4. D33^(-2)
DAdvanced Math / Solving quadratic equations
13

f(x)=3,600(0.28)^(x/12)
The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p% of its value
the preceding year, what is the value of p?

  1. A2
  2. B10
  3. C28
  4. D72
DAdvanced Math / Exponential word problems
14

An equilateral triangle has a height of 49√3 units. What is the length, in units, of one side of this triangle?

  1. A98√3
  2. B98
  3. C49√3
  4. D49
BGeometry and Trigonometry / General triangle
15

Which expression is NOT a factor of 7,290x^4-1,440?

  1. A9x^2+4
  2. B3x^2-2
  3. C3x+2
  4. D90
BAdvanced Math / Operations of polynomials
16

2,590x=5,180x
How many solutions does the given equation have?

  1. AZero
  2. BExactly one
  3. CExactly two
  4. DInfinitely many
BAlgebra / Solve linear equation
17

In the xy-plane, line r passes through the points (2,16) and (7, 17). Line s passes through the point (1, 2) and is perpendicular to line r. An equation of line s is ax+7y=c, where a and c are constants. What is the value of c?

49Algebra / Graphing linear equations
18

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

  1. A3
  2. B7
  3. C9
  4. D18
CAlgebra / Solve linear equation

For 100 neurons, the table summarizes the distribution of classification and cell body diameter.

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19

One of these neurons will be selected at random. What is the probability of selecting a neuron with a cell body diameter that is less than or equal to 30 micrometers, given that it is not classified as a motor neuron? (Express your answer as a decimal or fraction, not as a percent.)

61/64,0.953,.9531Problem Solving and Data Analysis / Ratios and proportion
20

The value of a toy increased by 193% from the end of 2016 to the end of 2017 and then decreased by 31% from the end of 2017 to the end of 2018. What was the net percentage increase in the value of the toy from the end of 2016 to the end of 2018?

  1. A102.17%
  2. B133.17%
  3. C162.00%
  4. D283.83%
AProblem Solving and Data Analysis / Percents
21

5x+3y=6
The given equation is one equation in a system of two linear equations. If the system of equations has at least one solution, which of the following equations could be the other equation in the system?
I. 7.5x+4.5y=9
II. 7.5x-4.5y=9

  1. AI only
  2. BII only
  3. CI and II
  4. DNeither I nor II
CAlgebra / Solving systems of linear equations
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22

In the figure shown, points A, B, C, and E lie on the circle, and AB<BC. Segment AC is perpendicular to segment BE at point D, and BD=DE=√398. The diameter of the circle is 201. If CD/AD=r what is the value of r?

199/2,99.5Geometry and Trigonometry / Circle theorems