2025.5 International B

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

In triangle ABC, the measure of angle A is 34° and the measure of angle B is 90°. What is the measure, in degrees, of angle C?

  1. A34
  2. B56
  3. C90
  4. D180
BGeometry and Trigonometry / Right triangle
2

Which expression is equivalent to 3xy(2x^2+7y) ?

  1. A5x^3y+10xy^2
  2. B6x^2y+7y
  3. C6x^2y+21xy
  4. D6x^3y+21xy^2
DAdvanced Math / Operations of polynomials
3

Which expression is equivalent to 30x^2+6x+6 ？

  1. A5x^2(6x+6)
  2. B30x(x+1)
  3. C65x^2+x+16(5x^2+x+1) 65x^2+x+1
  4. D4(2x^2+x+1)
CAdvanced Math / Operations of polynomials
4

For a particular tree species, it is recommended to plant a maximum of 92 trees per acre. Based on this recommendation, what is the maximum number of trees of this species that can be planted on 2 acres?

  1. A276
  2. B184
  3. C94
  4. D90
BAlgebra / Linear functions word problem
5

A gym charges its members a onetime $34 enrollment fee and a membership fee of $16 per month. If there are no charges other than the enrollment fee and the membership fee, after how many months will a member have been charged a total of $178 at the gym?

9Algebra / Linear equation word problem
6

f(x)=7x+b
For the linear function f, b is a constant and f(8)=56 . What is the value of b?

  1. A0
  2. B1
  3. C7
  4. D8
AAlgebra / Linear functions word problem
7

The function f defined by f(t)=14t+9 gives the estimated length, in inches, of a pothos plant t months after Shruti purchased it. Which of the following is the best interpretation of 9 in this context?

  1. AShruti will keep the pothos plant for 9 months.
  2. BThe pothos plant is expected to grow 9 inches each month.
  3. CThe pothos plant is expected to grow to a maximum length of 9 inches.
  4. DThe estimated length of the pothos plant was 9 inches when Shruti purchased it.
DAlgebra / Interpreting linear equation
8

At a convention center, there are a total of 375 visitors. Each visitor is located in either room A, room B, or room C. If one of these visitors is selected at random, the probability of selecting a visitor who is located in room A is 0.48, and the probability of selecting a visitor who is located in room B is 0.24. How many visitors are located in room C?

  1. A28
  2. B43
  3. C90
  4. D105
DProblem Solving and Data Analysis / Ratios and proportion
9

x^2-28x=0
Which of the following is a solution to the given equation?

  1. A56
  2. B28
  3. C14
  4. D√28
BAdvanced Math / Solving quadratic equations
10

A right square pyramid has a height of 12 inches and a volume of 196 cubic inches. What is the perimeter, in inches, of the base of this pyramid?

28Geometry and Trigonometry / Volume
11

The value of a share of stock was $240 on the day it was purchased. Every year, the value of the share of stock increases by 1% of its value the previous year. Which function V gives the value, in dollars, of the share of stock t years after the day it was purchased?

  1. AV(t)=240(1.01t)
  2. BV(t)=240(1.1t)
  3. CV(t)=240(1.01)^t
  4. DV(t)=240(1.1)^t
CAdvanced Math / Exponential word problems
12

If f(x)=x+3 and g(x)=3x , what is the value of 6f(3)-g(3) ?

  1. A-3
  2. B12
  3. C18
  4. D27
DAlgebra / Linear functions word problem
13

3x+9y=10
rx+18y=20
In the given system of equations, r is a constant. The system has infinitely many solutions. What is the value of r?

  1. A2
  2. B3
  3. C6
  4. D9
CAlgebra / Solving systems of linear equations
14

A club plans to sell tote bags. The club members estimate they will sell 80 tote bags when the bags are priced at $9 each. For every price increase of $1, they estimate they will sell 8 fewer bags. What is the estimated revenue, in dollars, when the bags are priced at $12 each? (revenue = price × number sold)

672Advanced Math / Quadratic word problems
15

3x+6y=17
-3x-4y=5
The solution to the given system of equations is (x,y). What is the value of 2y ?

22Algebra / Solving systems of linear equations
16

What value of w is the solution to the equation 0.7w-0.57=7(w-0.001) ?

-0.089,-.0894,-.0893Algebra / Solve linear equation
17

Which quadratic equation has exactly one distinct real solution?

  1. Ax^2-16=0
  2. Bx^2+16=0
  3. Cx^2-16x+56=0
  4. Dx^2-16x+64=0
DAdvanced Math / Solving quadratic equations
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18

Quinidra drove her car on a straight road to a certain location. The graph models Quinidra's distance, in miles, from her home as a function of time, in hours. Which of the following could the model describe?

  1. AQuinidra drove away from her home at a constant speed for 1 hour, spent 4 hours at the location, then continued to drive away from her home at a constant speed for 1 hour.
  2. BQuinidra drove away from her home at a constant speed for 1 hour, spent 4 hours at the location, then drove back to her home at a constant speed for 1 hour.
  3. CQuinidra drove away from her home at an increasing speed for 1 hour, spent 4 hours at the location, then drove back to her home at a decreasing speed for 1 hour.
  4. DQuinidra drove away from her home at an increasing speed for 1 hour, drove at a constant speed for 4 hours, then drove back to her home at a decreasing speed for 1 hour.
BProblem Solving and Data Analysis / Key feature of graphs
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19

The frequency table summarizes the mass, in grams, of 35 objects. What is the mean mass, in grams, of these objects?

24Problem Solving and Data Analysis / Mean, mode, median
20

What is the y-intercept of y=-(4)^x-39 in the xy-plane?

  1. A(0,-40)
  2. B(0,-43)
  3. C(0,-39)
  4. D(0,-38)
AAdvanced Math / Nonlinear equation graphs
21

A rectangular poster has an area of 330 square inches. A copy of the poster is made in which the length and width of the original poster are each increased by 50%. What is the area of the copy, in square inches?

742.5Geometry and Trigonometry / Congruence and similarity
22

A circle in the xy-plane has center (28,5) and y-intercepts (0,-16) and (0,26). What is the radius of this circle?

  1. A35
  2. B26
  3. C21
  4. D16
AGeometry and Trigonometry / Circle equation

Module 2 (Advanced)

1

The total cost f(x) , in dollars, to lease a car for 24 months from a particular car dealership is given by f(x)=24x+1,000 , where x is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $300?

  1. A$6,200
  2. B$7,000
  3. C$8,200
  4. D$25,300
CAlgebra / Linear functions word problem
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2

In the figure shown, line l intersects lines j and k. Which additional piece of information is sufficient to prove that lines j and k are parallel?

  1. Aw=54
  2. Bx=126
  3. Cy=54
  4. Dz=126
AGeometry and Trigonometry / Angles and Arc length
3

5x+3=rx+7
In the given equation, r is a constant. The equation has no solution. What is the value of r?

  1. A21
  2. B8
  3. C7
  4. D5
DAlgebra / Solve linear equation
4

If 5(2x+9)=3(2x+9)+74 , what is the value of 2x+9 ?

  1. A74
  2. B37
  3. C28
  4. D14
BAlgebra / Solve linear equation
5

If 350% of n is 35, what is the value of n?

  1. A12,250
  2. B1,225
  3. C1,000
  4. D10
DProblem Solving and Data Analysis / Percents
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6

The table shows two values of x and their corresponding values of h(x) for the linear function h. Which equation defines h?

  1. Ah(x)=1/3x-5/3
  2. Bh(x)=3x+5
  3. Ch(x)=4x+17
  4. Dh(x)=6x+23
BAlgebra / Linear functions word problem
7

y=x^2+17x+4
y=x+4
The graphs of the equations in the given system intersect at the point (x,y) in the xy-plane. What is a possible value of x?

  1. A-16
  2. B-15
  3. C13
  4. D15
AAdvanced Math / linear and quadratic systems
8

A piece of string with a length of 108 inches is cut into two parts. One part has a length of x inches, and the other part has a length of y inches. The value of x is 8 more than 4 times the value of y. What is the value of x?

  1. A25
  2. B29
  3. C58
  4. D88
DAlgebra / Systems of linear equations word problem
9

A landscaper will plant two types of shrubs, hydrangeas and winter hazels, in a park. There will be no more than 244 total shrubs planted, and the number of hydrangeas planted will be at most three times the number of winter hazels planted. Which of the following systems of inequalities best represents this situation, where h is the number of hydrangeas that will be planted and w is the number of winter hazels that will be planted?

  1. Ah+w≤244
    h≤3w
  2. Bh+w≤244
    3h≥w
  3. Ch+w≥244
    h≤3w
  4. Dh+w≥244
    3h≥w
AAlgebra / System of linear inequalities word problem
10

y≤x+3
y≥-3x-7
Which point (x,y) is a solution to the given system of inequalities in the xy-plane?

  1. A(0,-14)
  2. B(0,14)
  3. C(-14,0)
  4. D(14,0)
DAlgebra / Solving systems of linear inequalities
11

3x^2-5x-5=0
What is the greatest solution to the given equation?

  1. A5/6-(√85)/6
  2. B5/6+(√85)/6
  3. C5/3-(√85)/3
  4. D5/3+(√85)/3
BAdvanced Math / Solving quadratic equations
12

f(x)=-0.0038400x^2+15.236x-15,103
The model shown gives the predicted average Arctic sea ice area f(x) , in millions of square kilometers, for September of each year x, where x represents a year and 1979≤x≤2012 . Based on the model, what is the positive difference, in millions of square kilometers, between the predicted average Arctic sea ice area for September of the year 1991 and the predicted average Arctic sea ice area for September of the year 1992? (Round your answer to the nearest thousandth.)

0.059,.059Advanced Math / Quadratic word problems
13

What is the y-intercept of the graph of y=(8/13)^(x+1) in the xy-plane?

  1. A(8,13)
  2. B(0,13)
  3. C(0,8)
  4. D(0,8/13)
DAdvanced Math / Nonlinear equation graphs
14

f(x)=x^2-4x-320
The function f is defined by the given equation. Which of the following equivalent forms of the equation displays the minimum value of the function as a constant or coefficient?

  1. Af(x)=x^2-4(x+80)
  2. Bf(x)=(x-2)^2+(-324)
  3. Cf(x)=x(x-4)+(-320)
  4. Df(x)=(x+16)(x-20)
BAdvanced Math / Transform of quadratic expressions
15

Line s in the xy-plane is defined by 6x+2y=0 . Line t is perpendicular to line s and passes through the points (7,0) and (k,4/3) . What is the value of k?

11Algebra / Graphing linear equations
16

g(x)=x^3+ax^2+bx+c
The function g is defined by the given equation, where a, b, and c are integer constants. The zeros of the function are -2 , -7 , and 6 . What is the value of a?

  1. A-84
  2. B-3
  3. C3
  4. D84
CAdvanced Math / Polynomial factors and graphs

The weight of each object in two groups, A and B, was recorded. The histograms represent the distributions of weight, in grams, for the objects in groups A and B.

image
17

The mean weight of the objects in group A is equal to 2.1, and the mean weight of the objects in group B is equal to 11.1. Which of the following statements about the standard deviations of weight for the objects in these two groups is true?

  1. AThe standard deviation of weight for the objects in group A is less than the standard deviation of weight for the objects in group B.
  2. BThe standard deviation of weight for the objects in group A is equal to the standard deviation of weight for the objects in group B.
  3. CThe standard deviation of weight for the objects in group A is greater than the standard deviation of weight for the objects in group B.
  4. DThere is not enough information to compare the standard deviations of weight for the objects in these two groups.
CProblem Solving and Data Analysis / Spread of distribution
18

A carpenter charges a flat rate of $216 for the first 3 hours of work and $60 for each additional hour of work. Which equation gives the total amount y, in dollars, that the carpenter charges for x hours of work, where x>3 ?

  1. Ay=60x+216
  2. By=216x+396
  3. Cy=60x+36
  4. Dy=216x+60
CAlgebra / Linear functions word problem
19

46/p=46/q-46/r-46/s
The given equation relates the positive variables p, q, r, and s. Which of the following is equivalent to q?

  1. Aprs/(pr+ps+rs)
  2. Bprs/(46p+46r+46s)
  3. Cp+r+s
  4. D46(p+r+s)
AAdvanced Math / Isolating quantities
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20

In the figure, AD and BC intersect at point D . The measure of ∠ABD is w° , the measure of ∠CAD is z° , and AD=178 . If cos w°=9/41 , what is the value of tan z° ?

40/9,4.444Geometry and Trigonometry / Trigonometric functions
21

A right square pyramid has a total surface area of 70,560 square inches, and the combined surface area of the four lateral faces of this pyramid is 38,160 square inches. What is the height, in inches, of this pyramid?

  1. A56
  2. B90
  3. C106
  4. D180
AGeometry and Trigonometry / Volume
22

1/cx=x/96+1/c
In the given equation, c is a constant. If the equation has exactly one solution, what is the value of c?

-24Advanced Math / Rational transformation