2025.11 International A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

If 9x+4=67,what is the value of 90x+40?

  1. A7
  2. B70
  3. C130
  4. D670
DAlgebra / Solve linear equation
image
2

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

  1. A36
  2. B72
  3. C180
  4. D252
BGeometry and Trigonometry / Angles and Arc length
3

A length of 450 meters is equal to how many decimeters? (1 meter = 10 decimeters)

4500Problem Solving and Data Analysis / Units
4

The equation 58=2x+2y gives the perimeter of a rectangular garden that has length x, in feet, and width y, in feet. The width of the garden is 14 feet. What is the length, in feet, of the garden?

15Algebra / Linear equation word problem
5

The relationship between the variables x and y is defined by an exponential equation. When x=0, the value of y is 40, and for every increase in the value of x by 1, the corresponding value of y increases by 50% of its previous value. Which equation represents this relationship?

  1. Ay=40(1.50)^x
  2. By=40(1.05)^x
  3. Cy=50(1.40)^x
  4. Dy=50(1.04)^x
AAdvanced Math / Exponential word problems
6

The function f is defined by f(x)=1/8x. What is the value of f(x) when x=9?

.0138,1/72Algebra / Linear functions word problem
7

The function f is defined by f(x)=3x-1/4 . What is the y-intercept of the graph of y=f(x) in the xy-plane?

  1. A(0,-1/4)
  2. B(0,-3)
  3. C(0,3)
  4. D(0,4)
AAlgebra / Graphing linear equations
8

x+6y=28
6y=14
The solution to the given system of equations is (x,y). What is the value of x?

14Algebra / Solving systems of linear equations
9

The length of a side of square X is 9 centimeters. The area of rectangle Y is 32 square centimeters. What is the total area, in square centimeters, of square X and rectangle Y?

  1. A145
  2. B113
  3. C82
  4. D81
BGeometry and Trigonometry / General polygons
10

During hibernation, American black bears do not eat or replenish calories. A certain black bear weighed 293 pounds when entering hibernation and lost weight at a mean rate of 0.9 pounds per day. At this rate, how many days after entering hibernation would the black bear weigh 230 pounds?

  1. A57
  2. B63
  3. C70
  4. D207
CAlgebra / Linear equation word problem
image
11

The complete graph of y=f(x) is shown. For how many values of x does f(x)=0?

  1. AOne
  2. BTwo
  3. CThree
  4. DFour
CAdvanced Math / Nonlinear equation graphs
12

b^2+4c=7d
The given equation relates the real numbers b, c, and d, where d>4/7c. Which equation correctly expresses b in terms of c and d ?

  1. Ab=(7d+4c)/2
  2. Bb=(7d-4c)/2
  3. Cb=±√7d+4c
  4. Db=±√7d-4c
DAdvanced Math / Isolating quantities
13

x^2-81/16=0
How many distinct real solutions does the given equation have?

  1. AZero
  2. BExactly one
  3. CExactly two
  4. DInfinitely many
CAdvanced Math / Solving quadratic equations
image
14

Triangles ABC and A′B′C′ are shown. Triangle ABC is dilated by a scale factor of 6 to form triangle A′B′C′ . If the length of AB is 18, what is the length of A′B′?

  1. A3
  2. B6
  3. C24
  4. D108
DGeometry and Trigonometry / Congruence and similarity
15

What is the radius of the circle in the xy-plane defined by (x+3)^2+(y+9)^2=361 ?

19Geometry and Trigonometry / Circle equation
16

In the xy-plane, which of the following does NOT contain any points that are part of the solution set to 5x-7y>35?

  1. AThe x-axis
  2. BThe region where x > 0 and y > 0
  3. CThe region where x < 0 and y < 0
  4. DThe region where x < 0 and y > 0
DAlgebra / Solve linear inequality

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

image
17

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. A0.24
  2. B0.32
  3. C0.50
  4. D0.92
BProblem Solving and Data Analysis / Ratios and proportion
18

Line h is defined by 1/2x+1/9y-54=0. Line j is perpendicular to line h in the xy-plane. What is the slope of line j?

  1. A-9/2
  2. B-2/9
  3. C2/9
  4. D9/2
CAlgebra / Graphing linear equations
19

a, 26, 29, b, 31, 47, c
For the given data set, the data values are listed in ascending order, where a, b, and c are constants. For this data set, the mean is 36, the median is 29, and the range is 72. What is the value of c?

  1. A54
  2. B72
  3. C81
  4. D98
CProblem Solving and Data Analysis / Mean, mode, median
image
20

In triangle QRS shown, QR<RS. Which expression represents the length of QS ?

  1. A37cosQ
  2. B37sinQ
  3. C37/(cos Q)
  4. D37/(sin Q)
DGeometry and Trigonometry / Trigonometric functions
21

y=9(a/7)^(x+c)-b
How many times does the graph of the given equation in the xy-plane cross the x-axis, where a, b, and c are positive constants such that a>7 and b>c?

  1. AZero
  2. BOne
  3. CTwo
  4. DThree
BAdvanced Math / Nonlinear equation graphs
22

A certain town has an area of 4.29 square miles. What is the area, in square yards, of this town? (1 mile = 1,760 yards)

  1. A410
  2. B7,550
  3. C722,051
  4. D13,288,704
DProblem Solving and Data Analysis / Units

Module 2 (Advanced)

1

Zuri has a goal to run at least 16 miles per week while training for a race. This week, she has run 4 miles. If x represents the additional number of miles Zuri needs to run this week to meet her goal, which inequality represents this situation?

  1. A4-x≤16
  2. B4+x≤16
  3. C4-x≥16
  4. D4+x≥16
DAlgebra / Linear inequality word problem
image
2

In the figure shown, line k intersects lines r and s. If w=147, which additional piece of information is sufficient to prove that lines r and s are parallel?

  1. Ax=33
  2. By=147
  3. Cw+y=180
  4. Dy+z=180
BGeometry and Trigonometry / Angles and Arc length
image
3

At a fundraiser, a family pays a fixed entrance fee. They then purchase food tickets, which each have the same cost. The table shows the relationship between the number of food tickets, x, that are purchased and the total amount paid y, in dollars, for both the entrance fee and the food tickets. Which equation represents the relationship between x and y?

  1. Ay=3/2x+29
  2. By=3/2x-56
  3. Cy=2/3x+112/3
  4. Dy=2/3x+58/3
AAlgebra / Linear functions word problem

A group of 10 gardeners recorded data on the germination rates of their tomato crop for one growing season. The scatterplot shows the relationship between the number of tomato seeds planted, x, and the number of tomato seeds that germinated, y, for each of the gardeners. A line of best fit is also shown.

image
4

Which of the following is the best interpretation of the slope of the line of best fit in this context?

  1. AThe number of tomato seeds planted is predicted to increase by 60 seeds every 100 days.
  2. BThe number of tomato seeds planted is predicted to increase by 300 seeds every 100 days.
  3. CThe number of tomato seeds that germinate is predicted to increase by 60 seeds for every additional 100 tomato seeds that are planted.
  4. DThe number of tomato seeds that germinate is predicted to increase by 300 seeds for every additional 100 tomato seeds that are planted.
CProblem Solving and Data Analysis / Scatter Plot
5

The graph of 2x+y=11 in the xy-plane is a line. What is the slope of the line?

-2Algebra / Graphing linear equations
6

f(x)=2x+3
g(x)=7x-2
h(x)=5x+6
The functions f, g , and h are defined as shown. If f(x)·g(x)-h(x)=ax^2+bx+c , where a, b , and c are constants, what is the value of b?

  1. A-5
  2. B12
  3. C20
  4. D22
BAdvanced Math / Operations of polynomials
7

The function f is defined by f(x)=(x+11)/5, and f(a)=-18, where a is a constant. What is the value of a?

  1. A-101
  2. B-79
  3. C-79/5
  4. D-5/7
AAlgebra / Linear functions word problem

The table shows values of x and their corresponding values of y for three points on line j in the xy-plane.

image
8

Line k also lies in the xy-plane and is defined by the equation y=4x. At what point (x,y) do lines j and k intersect?

  1. A(5,20)
  2. B(5,-44)
  3. C(6,24)
  4. D(6,26)
AAlgebra / Systems of linear equations word problem
9

h(t)=-16t^2+b
The function h estimates an object's height, in feet, above the ground t seconds after the object is dropped, where b is a constant. The function estimates that the object is 19.36 feet above the ground when it is dropped at t=0. How many seconds after being dropped does the function estimate the object will hit the ground?

1.1Advanced Math / Quadratic word problems
10

|4x-3|=-9
How many solutions does the given equation have?

  1. AZero
  2. BOne
  3. CTwo
  4. DInfinitely many
AAlgebra / Solve linear equation
11

The function h is defined by h(x)=a^x+b , where a and b are positive constants. The graph of y=h(x) in the xy-plane passes through the points (0, 10) and (2, 13). What is the value of ab?

  1. A13
  2. B18
  3. C20
  4. D26
BAdvanced Math / Exponential word problems
12

A circle has center P, and points A and B lie on the circle. The measure of arc AB is 45° and the length of arc AB is 4π units. What is the length, in units, of the radius of the circle?

16Geometry and Trigonometry / Angles and Arc length
13

The function f is defined by f(x)=56(0.19)^x. For any positive integer n, the value of f(n) is p% less than the value of f(n-1). What is the value of p?

  1. A19
  2. B44
  3. C56
  4. D81
DAdvanced Math / Exponential word problems
14

x^2+(√k-3)x+42=0
In the given equation, k is a constant. The equation has exactly one real solution. What is the value of k?

  1. A171
  2. B168
  3. C165
  4. D45
AAdvanced Math / Solving quadratic equations
15

x^2+y^2=36
y=mx+b/4
In the given system of equations, m and b are negative constants. In the xy-plane, the graphs of the equations in the given system intersect at the point (-5,y), where y<0. Which expression represents the value of b?

  1. A-5m/4+(√11)/4
  2. B5m/4-(√11)/4
  3. C-20m+4√11
  4. D20m-4√11
DAdvanced Math / Isolating quantities
16

A biologist mixed a solution that is 0.3% sodium chloride by mass with a solution that is 0.15% sodium chloride by mass to obtain a new solution, which has a mass of 80 grams and contains 0.21 grams of sodium chloride. How many grams of 0.3% sodium chloride solution did the biologist use?

  1. A0.14
  2. B20
  3. C60
  4. D79.86
CAlgebra / Linear equation word problem

For data set A, the table summarizes the distribution of the number of pieces of mail received by a business each day during a period of 11 days.

image
17

The data value 13 is removed from data set A to create data set B, which consists of the remaining 10 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 less than the median of data set A.
  2. BThe median of data set B is greater than the median of data set A.
  3. CThe median of data set B is equal to the median of data set A.
  4. DThere is not enough information to compare the medians of the two data sets.
CProblem Solving and Data Analysis / Mean, mode, median
18

x/5+y/9=47/45
An engineer connects resistors in series, where the resistors in the series have a total resistance of 47/45 ohms. In this series, there are x resistors of type A, which each have a resistance of a ohms, and y resistors of type B, which each have a resistance of b ohms. The given equation represents this situation. According to this equation, what is the positive difference between the value of a and the value of b?

  1. A47
  2. B4
  3. C47/45
  4. D4/45
DAlgebra / Interpreting linear equation
19

9x^2+8=nx
In the given equation, n is a constant. The equation has exactly one solution. What is the value of (n^2)/8?

36Advanced Math / Solving quadratic equations

The table gives the areas and perimeters of two similar rectangles, where n is a constant.

image
20

What is the value of n?

  1. A2,100
  2. B1,680
  3. C840
  4. D420
DGeometry and Trigonometry / Congruence and similarity
21

The mass of object A is 444% of the mass of object B, and the mass of object A is 0.740% of the mass of object C. If the mass of object C is p% of the mass of object B, what is the value of p?

60000Problem Solving and Data Analysis / Percents
22

Which expression is a factor of y^2(x-3)-25(x-3)^3 ?

  1. Ay(x-3)
  2. B(x-5)(x-3)
  3. Cy+x-3
  4. Dy+5x-15
DAdvanced Math / Operations of polynomials