2025.8 International A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

The length of each side of triangle A is 270 millimeters. The length of each side of triangle B is double the length of each side of triangle A. What is the length, in millimeters, of each side of triangle B?

  1. A270
  2. B272
  3. C540
  4. D1,080
CAlgebra / Linear functions word problem · Accuracy 99.05%
2

Carrie has c dollars and Marjani has m dollars. Carrie has 4 times as many dollars as Marjani, and together they have a total of $40.00. Which system of equations represents this situation?

  1. Ac=4m
    c+m=40
  2. Bm=4c
    c+m=40
  3. Cc=40m
    c+m=4
  4. Dm=40c
    c+m=4
AAlgebra / Systems of linear equations word problem · Accuracy 97.34%
3

Anton is selling toys from his toy collection. When he started selling the toys, there were 2,800 toys in the collection. At the end of each week for 3 weeks after Anton started selling the toys, the number of toys in the collection had decreased by 1/2 of the toys in the collection at the end of the previous week. Which equation gives the number of toys, c, in the collection w weeks after Anton started selling the toys, where 0≤w<3 ?

  1. Ac=w^(1/2)
  2. Bc=2,800^w
  3. Cc=1,400(1/2)^w
  4. Dc=2,800(1/2)^w
DAdvanced Math / Exponential word problems · Accuracy 98.14%
4

√w+22=28
What is the solution to the given equation?

  1. A2
  2. B3
  3. C12
  4. D36
DAdvanced Math / Radical and rational exponent problems · Accuracy 98.73%
5

The function f is defined by f(x)=7x^3+6. What is the value of f(2)?

62Advanced Math / Function notations and transforms · Accuracy 98.58%
6

The function f(x)=-30x+310 gives the predicted height above the ground f(x), in feet, of a model airplane x minutes after it begins to descend. What is the predicted height above the ground, in feet, of the model airplane 2 minutes after it begins to descend?

  1. A60
  2. B250
  3. C280
  4. D370
BAlgebra / Linear functions word problem · Accuracy 99.7%
7

2x=9+7y
-2x=3+7y
The solution to the given system of equations is (x,y) . What is the value of 4x?

6Algebra / Solving systems of linear equations · Accuracy 94.16%
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8

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?

15Problem Solving and Data Analysis / Key feature of graphs · Accuracy 95.35%
9

y=-12x+16
y=-20x+24
What is the solution (x,y) to the given system of equations?

  1. A(1,4)
  2. B(16,24)
  3. C(24,16)
  4. D(4,1)
AAlgebra / Solving systems of linear equations · Accuracy 99.47%
10

A rectangle has a length that is 73 times its width. The function y=(73w)(w) represents this situation, where y is the area, in square feet, of the rectangle and y>0. Which of the following is the best interpretation of 73w in this context?

  1. AThe length of the rectangle, in feet
  2. BThe area of the rectangle, in square feet
  3. CThe difference between the length and the width of the rectangle, in feet
  4. DThe width of the rectangle, in feet
AAlgebra / Interpreting linear equation · Accuracy 97.31%
11

An entomologist placed an initial population of 40 Tenebrio molitor, a type of beetle, into a habitat and monitored the population over time. When the number of Tenebrio molitor in the habitat reached 170% of the initial population, the entomologist moved 75% of the Tenebrio molitor to a second habitat. How many Tenebrio molitor did the entomologist move to the second habitat at this time?

51Problem Solving and Data Analysis / Percents · Accuracy 94.32%
12

For the polynomial function f, the graph of y=f(x) in the xy-plane passes through the points (-3,0), (1,0), and (4,0). Which of the following must be a factor of f(x)?

  1. Ax+1
  2. Bx+4
  3. Cx-1
  4. Dx-3
CAdvanced Math / Polynomial factors and graphs · Accuracy 97.89%
13

A circle has a circumference of 89π centimeters. What is the diameter, in centimeters, of the circle?

89Geometry and Trigonometry / Circle theorems · Accuracy 94.42%
14

If (x-17)/18=(x-17)/6, what is the value of x+17?

  1. A0
  2. B3
  3. C17
  4. D34
DAdvanced Math / Rational transformation · Accuracy 87.31%
15

For what value of a is a√r^42 equivalent to r^(6/7) , where r>1?

49Advanced Math / Radical and rational exponent problems · Accuracy 91.11%
16

In the xy-plane, line s passes through the point (0,0) and is parallel to the line represented by the equation y=36x+6. If line s also passes through the point (9,d), what is the value of d?

324Algebra / Graphing linear equations · Accuracy 91.98%
17

Circles A and B are graphed in the xy-plane. Circle A is represented by the equation (x+8)^2+(y-8)^2=64 and intersects the x-axis at the point (r, s). Circle B has its center at (r, s) and has a radius of the same length as circle A. Which equation represents circle B?

  1. Ax^2+(y+8)^2=64
  2. Bx^2+(y-8)^2=64
  3. C(x+8)^2+y^2=64
  4. D(x-8)^2+y^2=64
CGeometry and Trigonometry / Circle equation · Accuracy 84.81%

The dot plots represent the distributions of values in data sets A and B.

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18

Which of the following statements must be true?
I. The median of data set A is equal to the median of data set B.
II. The standard deviation of data set A is equal to the standard deviation of data set B.

  1. AI and II
  2. BI only
  3. CII only
  4. DNeither I nor II
  5. AI and II
  6. BI only
  7. CII only
  8. DNeither I nor II
BProblem Solving and Data Analysis / Spread of distribution · Accuracy 89.06%

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown.

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19

For how many of the 9 data points is the actual y-value greater than the y-value predicted by the line of best fit?

  1. A8
  2. B7
  3. C5
  4. D2
CProblem Solving and Data Analysis / Scatter Plot · Accuracy 95.92%
20

RS=504
ST=128
TR=520
The side lengths of right triangle RST are given. Triangle RST is similar to triangle UVW, where S corresponds to V and T corresponds to W. What is the value of tan W?

  1. A16/65
  2. B16/63
  3. C63/65
  4. D63/16
DGeometry and Trigonometry / Trigonometric functions · Accuracy 88.3%
21

f(x)=20(2)^x+6(2)^x
The function f is defined by the given equation. Which of the following equivalent forms of fdisplays, as a coefficient or a base, the y-coordinate of the y-intercept of the graph of y=f(x) in the xy-plane?

  1. Af(x)=80(2)^(x-2)+24(2)^(x-2)
  2. Bf(x)=2(10(2)^x+3(2)^x)
  3. Cf(x)=20(4)^(x/2)+6(4)^(x/2)
  4. Df(x)=26(2)^x
DAdvanced Math / Exponential word problems · Accuracy 83.42%
22

In a set of three consecutive integers, where the integers are ordered from least to greatest, the first integer is represented by x. The sum of 4 and the second integer is less than the product of 17 and the third integer. Which inequality represents this situation?

  1. A4+(x+1)>17(x+2)
  2. B4+(x+1)<17(x+2)
  3. C4+(x+2)>17(x+3)
  4. D4+(x+2)<17(x+3)
BAlgebra / Linear inequality word problem · Accuracy 92.63%

Module 2 (Advanced)

1

The function g is defined by g(x)=19-x. What is the value of g(4)?

  1. A4
  2. B15
  3. C19
  4. D23
BAlgebra / Linear functions word problem · Accuracy 99.57%
2

Micah deposited a total of $6,600 into two retirement accounts last year by depositing x dollars once each month into one account and y dollars twice each month into the other account. Which equation represents this situation?

  1. A6,600=12x+12y
  2. B6,600=12x+24y
  3. C6,600=24x+12y
  4. D6,600=24x+24y
BAlgebra / Linear equation word problem · Accuracy 96.98%
3

The measure of angle G is π/10radians. If the measure of angle G is 9n degrees, where n is a constant, what is the value of n?

  1. A2
  2. B9
  3. C10
  4. D18
AGeometry and Trigonometry / Angles and Arc length · Accuracy 95.77%
4

The ratio 6 to 3 is equivalent to the ratio 24 to 3k, where k is a constant. What is the value of k?

  1. A0.75
  2. B4
  3. C12
  4. D72
BProblem Solving and Data Analysis / Ratios and proportion · Accuracy 98.19%
5

Which expression is equivalent to (8nr^2+2nr)+(4n^2r+3nr) ?

  1. A12n^2r^2+5nr
  2. B12n^3r^3+5n^2r^2
  3. C32n^3r^3+6n^2r^2
  4. D8nr^2+4n^2r+5nr
DAdvanced Math / Operations of polynomials · Accuracy 96.9%
6

R=0.43l/A
The given equation relates the resistance R, in ohms, of a wire to its length l , in meters, and its cross-sectional area A, in square meters. Which equation correctly expresses the length, in meters, of the wire in terms of its resistance, in ohms, and its cross-sectional area, in square meters?

  1. Al=(R-A)/0.43
  2. Bl=(R+A)/0.43
  3. Cl=0.43R/A
  4. Dl=AR/0.43
DAdvanced Math / Isolating quantities · Accuracy 96.61%
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7

The graphs of y=-3x+7 and y=x-5 are shown. Point P (not shown) has coordinates (3,-5) and lies in the shaded region. The coordinates of P satisfy which of the following inequalities?
I. y<-3x+7
II. y>x-5

  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
AAlgebra / Solving systems of linear inequalities · Accuracy 88.94%
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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 that represents this relationship in the xy-plane?

24/5,4.8Problem Solving and Data Analysis / Linear growth · Accuracy 97.16%
9

If (1/2x-21/2)^2-81=0 , what is the value of (x-21)^2 ?

  1. A324
  2. B162
  3. C21
  4. D9
AAdvanced Math / Transform of quadratic expressions · Accuracy 94.94%
10

Rectangles ABCD and EFGH are similar. The length of each side of EFGH is 6 times the length of the corresponding side of ABCD. The area of ABCD is 90 square units. What is the area, in square units, of EFGH?

  1. A15
  2. B36
  3. C540
  4. D3,240
DGeometry and Trigonometry / Congruence and similarity · Accuracy 96.1%
11

On a plot of land, 48.0% of the square footage is farmland and the remaining square footage is pasture. There are buildings on exactly 23.5% of the square footage of the farmland, and there are buildings on exactly 16.0% of the square footage of the pasture. If there are buildings on exactly p% of the square footage of the plot of land, what is the value of p?

19.6Problem Solving and Data Analysis / Percents · Accuracy 81.47%

The scatterplot shows data set A, which consists of the weights y, in pounds, of a Labrador retriever puppy at various ages, x, in months. The equation of a line of best fit for the relationship in data set A can be written as y=-5.1+8.7x , where 2≤x≤6.

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12

The puppy was weighed again at 9 months old and weighed 52 pounds. Data set B consists of all the data points in data set A as well as the data point (9, 52). The equation of a line of best fit for data set B can be written as y=r+sx, where r and s are constants and 2≤x≤9. Assuming the equations of the lines of best fit are calculated in the same way, which of the following is the best estimate for the value of s?

  1. A5.9
  2. B8.7
  3. C13.8
  4. D17.7
AProblem Solving and Data Analysis / Scatter Plot · Accuracy 78.93%
13

If |16-2x|=58, which of the following is a value of 8-x ?

  1. A0
  2. B8
  3. C29
  4. D42
CAlgebra / Solve linear equation · Accuracy 99.06%
14

A book-of-the-month club charges $16 for the first book purchased during the month and an additional $11 for each book after the first. Which equation describes this situation, where y is the total cost, in dollars, for books purchased during a month, x is the number of books purchased during the month, and x>0?

  1. Ay=x+16
  2. By=11x+16
  3. Cy=11(x-1)+16
  4. Dy=(x-1)+16
CAlgebra / Linear functions word problem · Accuracy 95.64%
15

A company developed a plan to set the selling price of a product. The company determined that for a selling price of $120.00, zero products would be sold. For each $2.50 decrease in the selling price, the number of products sold would increase by one. For a revenue of exactly $1,437.50, which of the following could be the number of products sold? (revenue = price × number of products sold)

  1. A23
  2. B24
  3. C527
  4. D1,440
AAdvanced Math / Quadratic word problems · Accuracy 87.97%
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16

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

11Advanced Math / Nonlinear equation graphs · Accuracy 74.05%
17

y=7x^2-bx-6
Which of the following equations is equivalent to the given equation, where b is a positive constant?

  1. Ay=7(x-b/14)^2-6-(b^2)/28
  2. By=7(x-b/14)^2-6
  3. Cy=7(x+b/14)^2-6-(b^2)/28
  4. Dy=7(x+b/14)^2-6
AAdvanced Math / Transform of quadratic expressions · Accuracy 86.87%
18

The equation d=6t+210 gives the distance d, in feet, from a reference point on the surface of Mars to a Mars rover, where t is the number of minutes after the start of a period of observation. By how many feet does the Mars rover's distance from the reference point increase over a period of 20 minutes?

  1. A330
  2. B230
  3. C120
  4. D6
CAlgebra / Linear equation word problem · Accuracy 64.36%
19

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of the acute angles is (7x-410)°. The sum of the measures of one of the acute angles and three of the obtuse angles is (-14x+w)°. What is the value of w?

1360Geometry and Trigonometry / Angles and Arc length · Accuracy 78.65%

The table summarizes the distribution of age and assigned group for 90 participants in a study.

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20

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age?

  1. A1/6
  2. B1/4
  3. C11/30
  4. D1/2
BProblem Solving and Data Analysis / Ratios and proportion · Accuracy 67.37%
21

A circle in the xy-plane has its center at (2,9). Line t is tangent to this circle at the point (a,-4), where a is a constant. The slope of line t is 6/5. What is the value of a?

  1. A-68/5
  2. B-53/6
  3. C77/6
  4. D88/5
DGeometry and Trigonometry / Circle theorems · Accuracy 67.43%
22

-x^2+bx-49=0
In the given equation, b is an integer. The equation has no real solutions. What is the least possible value of b?

-13Advanced Math / Solving quadratic equations · Accuracy 64.43%