2025.6 International A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

The function f is defined by the equation f(x)=10x+4. What is the value of f(x) when x=7?

  1. A21
  2. B38
  3. C47
  4. D74
DAlgebra / Linear functions word problem
2

A remotely operated vehicle (ROV) is used for underwater ocean research. When the ROV is at a depth of 26 fathoms, what is the ROV's depth in feet? (1 fathom = 6 feet)

156Problem Solving and Data Analysis / Units
3

6x=30
6x-10y=80
What is the solution (x,y) to the given system of equations?

  1. A(5, -5)
  2. B(5, -11)
  3. C(30, 80)
  4. D(30, 50)
AAlgebra / Solving systems of linear equations
4

Which expression is equivalent to 41x^2+41?

  1. A41(x^2+1/41)
  2. B41(41x^2+1)
  3. C41(x^2+41)
  4. D41(x^2+1)
DAdvanced Math / Operations of polynomials
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5

Which equation gives the relationship between the side lengths of the triangle shown?

  1. A9+12=r
  2. B12-9=r
  3. C9^2+12^2=r^2
  4. D12^2-9^2=r^2
CGeometry and Trigonometry / Right triangle
6

An event planner is planning an ice-skating event. It costs $45 to rent the rink and $10.75 per attendee. The budget is $275. What is the greatest number of attendees possible without exceeding the budget?

21Algebra / Linear inequality word problem
7

The ratio of cups of flour to cups of butter in a pie dough recipe is 2.75:1, and in a biscuit recipe is 7:1. Each recipe uses 1 cup of butter. How many more cups of flour are in the biscuit recipe than in the pie dough recipe?

4.25Problem Solving and Data Analysis / Ratios and proportion
8

A cube has an edge length of 13 inches. What is its volume in cubic inches?

  1. A39
  2. B78
  3. C169
  4. D2,197
DGeometry and Trigonometry / Volume
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9

In the figure shown, lines l and k are parallel and line t intersects both lines. If x>145, which of the following must be true?

  1. Ay<35
  2. By>35
  3. Cx+y<180
  4. Dx+y>180 x+y<180
AGeometry and Trigonometry / Angles and Arc length
10

(2x-4)(x-8)(x-9)=0
What is the sum of the solutions to the equation?

  1. A-21
  2. B-19
  3. C19
  4. D21
CAdvanced Math / Polynomial factors and graphs
11

The function g is defined by g(x)=7x^(-1). What is the value of g(x)g(13)?

7/13,0.538,.5384,.5385Advanced Math / Function notations and transforms
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12

The shaded region shown represents the solutions to which inequality?

  1. Ay<1/3x+8
  2. By<3x+8
  3. Cy>1/3x+8
  4. Dy>3x+8
BAlgebra / Solve linear inequality
13

y=-8x+26
y=2x^2+16
The graphs of the equations in the given system of equations intersect at the point (a,b) in the xy-plane. What is a possible value of a?

  1. A-5
  2. B-1
  3. C2
  4. D5
AAdvanced Math / linear and quadratic systems

The scatterplot shows the relationship between two variables, x and y.

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14

Which of the following equations is the most appropriate linear model for the data shown?

  1. Ay=0.07-1.02x
  2. By=1.02-0.07x
  3. Cy=-0.07+1.02x
  4. Dy=-1.02+0.07x
CProblem Solving and Data Analysis / Scatter Plot
15

(x-3)=11+2(x-3)
If x is the solution to the given equation, what is the value of x-3?

-11Algebra / Solve linear equation
16

In 1980, the population density of Carroll County was 125 people per square mile. In 1990, the population density of Carroll County was 141 people per square mile. The population density of Carroll County in 1990 was p% of the population density of Carroll County in 1980. What is the value of p?

  1. A116.0
  2. B112.8
  3. C16.0
  4. D12.8
BProblem Solving and Data Analysis / Percents
17

Which expression is equivalent to (2x+9)^2-(x-7)?

  1. A4x^2+35x+74
  2. B4x^2+35x+88
  3. C4x^2-x+74
  4. D4x^2-x+88
BAdvanced Math / Operations of polynomials
18

A circle has center oO, and points R and S lie on the circle. In triangle ORS, the measure of ∠ROS is 116°. What is the measure of ∠RSO, in degrees? (Disregard the degree symbol when entering your answer.)

32Geometry and Trigonometry / Angles and Arc length
19

32 teams are competing in a baseball tournament. The tournament has 5 rounds. After each round, half the teams competing are eliminated from the tournament. lf r teams remain in the tournament after x rounds of play, which of the following gives r in terms of x?

  1. Ar=1/2(32^x)
  2. Br=1/2x^32
  3. Cr=32(1/2)^x
  4. Dr=32x^(1/2)
CAdvanced Math / Exponential word problems
20

A boat traveled a certain distance upriver and then traveled downriver 10 miles farther than it traveled upriver. The boat took x hours to travel upriver at a speed of 12 miles per hour. The boat then took y hours to travel downriver at a speed of 18 miles per hour faster than the speed at which the boat traveled upriver. Which of the following equations best represents this situation?

  1. A12x-30y=-10
  2. B12x+30y=-10
  3. C12x+30y=10
  4. D12x-30y=10
AAlgebra / Linear equation word problem
21

The function f is defined by f(x)=4(x-3)(x^2-k), where k is a constant. In the xy-plane, the graph of y=f(x) passes through the point (-8,0). What is the value of f(0)?

768Advanced Math / Function notations and transforms
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22

For the linear function g, the table shows three values of x and their corresponding values of g(x). Function g is defined by g(x)=ax+b, where a and b are constants. What is the value of a+b?

  1. A28/5
  2. B63/10
  3. C63/8
  4. D35/4
DAlgebra / Linear functions word problem

Module 2 (Advanced)

1

A business owner purchased an energy-efficient air conditioning system for a cost of $4,200, including installation. The business owner saves $940 per year to operate the new system compared to the operating cost of the old system. Including the cost of the new system, which function f gives the total amount, in dollars, the business owner has saved x years after purchasing the new system?

  1. Af(x)=-4,200x+940
  2. Bf(x)=-940x-4,200
  3. Cf(x)=940x-4,200
  4. Df(x)=4,200x-940
CAlgebra / Linear functions word problem
2

For the linear function g, the graph of y=g(x) in the xy-plane has a slope of 5 and passes through the point (2, 37). Which equation defines g?

  1. Ag(x)=27x
  2. Bg(x)=27x+5
  3. Cg(x)=5x
  4. Dg(x)=5x+27
DAlgebra / Graphing linear equations
3

Parallelogram PQRS is similar to parallelogram TUVW, such that P, Q, R,Rand S correspond to T, U, V, and W, respectively. If PQ=28TU, then which of the following must be true?

  1. APR=3QR
  2. BPR=3VW
  3. CQR=28TU
  4. DQR=28UV
DGeometry and Trigonometry / Congruence and similarity
4

At a convention center, there are a total of 250 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 0.72 and the probability of selecting a visitor who is located in room B is 0.24. How many visitors are located in room C?

10Problem Solving and Data Analysis / Ratios and proportion
5

Line k is defined by y=4x+1/2. Line j is perpendicular to line k in the xy-plane. What is the slope of line j?

  1. A-2
  2. B-1/4
  3. C1/2
  4. D4
BAlgebra / Graphing linear equations
6

The kinetic energy K, in joules, of an object is given by the formula K=1/2mv^2 where m is the mass of the object, in kilgrams, and v is the velocity of the object, in meters per second. If the Kineti nergy of a certain biect can be found by using the formula K=82v^2, what is the mass of the object, in kilograms?

  1. A6,724
  2. B164
  3. C82
  4. D41
BAdvanced Math / Quadratic word problems
7

What is the y-intercept of the graph of y=16^x in the xy-plane?

  1. A(0, 1)
  2. B(0, 16)
  3. C(0, 0)
  4. D(0, 15)
AAdvanced Math / Nonlinear equation graphs
8

Which expression is equivalent to ((7√3)t)^(7/8) Where t>0?

  1. A7√3t^8
  2. B7√3^8t
  3. C8√3t^7
  4. D8√3^7t
CAdvanced Math / Radical and rational exponent problems
9

m(t)=-0.0274(t/7)^2+7.3873(t/7)+75.032
The function m gives the predicted body mass m(t) in kilograms (kg), of a male giraffe t days after it was born in a wildlife reserve, where t≤390. Which of the following is the best interpretation of the statement "m(370) is approximately equal to 389"in this context?

  1. AThe predicted body mass of a male giraffe was approximately 370 kg 389 days afterit was born.
  2. BThe predicted body mass of a male giraffe was approximately 389 kg 370 days after it was born.
  3. CThe predicted body mass of a male giraffe was approximately 389kg 370/7 days afterit was born.
  4. DThe predicted body mass of a male giraffe was approximately 370/7kg 389 days afterit was born.
BAdvanced Math / Interpreting nonlinear expressions
10

5/9(x-k)=k(x-9/5)
In the given equation, k is a constant. The equation has no solution. What is the value of k?

  1. A-5/9
  2. B-9/5
  3. C9/5
  4. D5/9
DAlgebra / Solve linear equation
11

f(x)=-3x^2+30x-48
The function f is defined by the given equation. Which of the following equivalent forms of the equation displays the maximum value of the function as a constant or coefficient?

  1. Af(x)=-3x^2+24x+6x-48
  2. Bf(x)=-3x(x-8)+6(x-8)
  3. Cf(x)=-3(x-5)^2+27
  4. Df(x)=-3(x-8)(x-2)
CAdvanced Math / Transform of quadratic expressions
12

An object's speed, in meters per hour, is increasing at a rate of 1,530 meters per hour per second. Which of the following is closest to this rate in feet per second squared? (Use 1 meter =3.28 feet.)

  1. A0.13
  2. B1.39
  3. C7.77
  4. D83.6
BProblem Solving and Data Analysis / Units
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13

The table shows four values of x and their corresponding values of y. The linear relationship between x and y can be represented by the equation 2x+By=C, where B and C are constants. What is the value of C?

-54Algebra / Systems of linear equations word problem
14

2x+5y=9
12x+30y=54
For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?

  1. A(r,-2r/5+9/5)
  2. B(-2r/5+9/5,r)
  3. C(-2r/5+9,2r/5+54)
  4. D(r/6+9,-r/6+54)
AAlgebra / Solving systems of linear equations
15

9x^2+30x+q=43
In the given equation, q is a constant. One solution to the given equation is (-5+√14)/3. What is the value of q?

  1. A54
  2. B43
  3. C11
  4. D5
AAdvanced Math / Solving quadratic equations
16

At a hotel, guests used the pool for a total of t hours in March. At the same hotel, guests used the pool for 3.61t hours in April. What is the percent increase in the number of hours guests used the pool from March to April?

  1. A2.61%
  2. B3.61%
  3. C261%
  4. D361%
CProblem Solving and Data Analysis / Percents
17

In the xy-plane, the point (6,7) is a solution to which of the following systems of inequalities?

  1. Ax<3
    y>5
  2. Bx<3
    y<5
  3. Cx>3
    y<5
  4. Dx>3
    y>5
DAlgebra / Solving systems of linear inequalities
18

At different times on a certain day, a manager at a theme park recorded the number of visitors. An exponential model gives the estimated number of visitors, V, at the theme park t hours after the theme park opened, where t≤3. Based on the model, 80 visitors were estimated to be at the theme park when it opened, and every 30 minutes the estimated number of visitors increased by 150% of the estimated number of visitors 30 minutes earlier. Which of the following equations best represents this model?

  1. AV=80(2.50)^2t
  2. BV=80(2.50)^(t/30)
  3. CV=80(1.50)^2t
  4. DV=80(1.50)^(t/30)
AAdvanced Math / Exponential word problems

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.

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19

The data value 17 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
20

Triangle ABC is similar to triangle DEF, where A corresponds to D and C corresponds to F. Angles C and F are right angles. If tan(A)=√3 and DF=53, what is the length of DE?

  1. A53(√3)/3
  2. B53(√3)/2
  3. C53√3
  4. D106
DGeometry and Trigonometry / Trigonometric functions
21

A right triangular pyramid has exactly six edges. Each of these edges is 96 centimeters long. If the surface area of the pyramid is k√3 square centimeters, what is the value of k?

9216Geometry and Trigonometry / Volume
22

x(kx-96)=-8
In the given equation, k is an integer constant. If the equation has two distinct real solutions, what is the greatest possible value of k?

287Advanced Math / Solving quadratic equations