2025.12 International A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

The function f is defined by the equation f(x)=5x-6. What is the value of f(x) when x=10?

44Algebra / Linear functions word problem
2

On a certain day in June, the lowest recorded wind speed in a town was 5 miles per hour (mph) and the highest recorded wind speed was 14 mph. Which inequality is true for all values of w, where w represents any wind speed, in mph, recorded in the town on this day?

  1. Aw≤5
  2. Bw≤9
  3. Cw≥14
  4. D5≤w≤14
DAlgebra / Linear inequality word problem
3

What value of p is the solution to the equation 4p-5p=14?

  1. A-14
  2. B-1/14
  3. C1/14
  4. D14
AAlgebra / Solve linear equation
4

A polygon with 22 sides has a perimeter of 131 inches. The length of one side is 5 inches. The other 21 sides have equal lengths. What is the length, in inches, of one of the 21 sides with equal lengths?

6Geometry and Trigonometry / General polygons
5

To purchase a used car at a total price of 13,000 dollars, a onetime down payment is required, and then fixed monthly payments are made for the remaining amount owed for the car. The equation 13,000=2,600+260t represents this situation, where t is the number of fixed monthly payments that are made. Which of the following is the best interpretation of 260 in this context?

  1. AThe amount, in dollars, of the down payment
  2. BThe amount, in dollars, of each fixed monthly payment
  3. CThe total amount, in dollars, paid for the car after t fixed monthly payments
  4. DThe total number of fixed monthly payments
BAlgebra / Interpreting linear equation
6

If 3-2x=42, what is the value of 1/6(3-2x)?

  1. A6
  2. B7
  3. C42
  4. D252
BAlgebra / Solve linear equation
7

The ratio 72 to m is equivalent to the ratio 4 to 24. What is the value of m?

  1. A3
  2. B24
  3. C144
  4. D432
DProblem Solving and Data Analysis / Ratios and proportion
8

(z+4)(z-6)=0
What are all possible solutions to the given equation?

  1. A-4 and -6
  2. B-4 and 6
  3. C4 and -6
  4. D4 and 6
BAdvanced Math / Solving quadratic equations
9

7x-8y=x^2
7x-8y=36
A solution to the given system of equations is (x,y), where x is positive. What is the value of x?

6Advanced Math / linear and quadratic systems
image
10

The table shows four values of x and their corresponding values of y. There is a linear relationship between x and y. Which of the following equations represents this relationship?

  1. A9x+3y=90
  2. B9x+3y=3
  3. C3x+9y=90
  4. D3x+9y=3
AAlgebra / Linear equation word problem
image
11

For a rational function f, the table shows three values of x and their corresponding values of f(x). Which of the following could be the graph of y=f(x)?

  1. A
    image
  2. B
    image
  3. C
    image
  4. D
    image
AAdvanced Math / Nonlinear equation graphs
12

A real estate company offers a series of three webinars. 3,125 people attended the first webinar. 56% of the people who attended the first webinar attended the second webinar, and 26% of the people who attended the first and second webinars attended the third webinar. How many people attended all three webinars?

455Problem Solving and Data Analysis / Percents
image
13

The scatterplot has 9 data points.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
image
14

What is the value of tan X in the triangle shown?

  1. A24/25
  2. B7/25
  3. C24/7
  4. D7/24
DGeometry and Trigonometry / Trigonometric functions
15

The expression 15x(x^2+9) is equivalent to ax^b+cx , where a, b, and c are constants. What is the value of abc?

6075Advanced Math / Operations of polynomials
16

In the xy-plane, an equation of circle R is (x+8)^2+(y+19)^2=100. Circle S is obtained by shifting circle R to the right 3 units. An equation defining circle S is (x+h)^2+(y+k)^2=100, where h and k are constants. What is the value of h?

5Geometry and Trigonometry / Circle equation
17

On January 1, there were 237 views of a video posted on a social media site. Every 2 days after January 1, the number of views of the video had increased by 70% of the number of views 2 days earlier. The function j gives the predicted number of views x days after January 1. Which equation defines j?

  1. Af(x)=237(0.70)^(x/2)
  2. Bf(x)=237(0.70)^2x
  3. Cf(x)=237(1.70)^(x/2)
  4. Df(x)=237(1.70)^2x
CAdvanced Math / Exponential word problems
image
18

Triangle TUV is dilated by a scale factor of 1/2 to obtain triangle T'U'V' (not shown), where T corresponds to T' and U corresponds to U'. What is the measure, in degrees, of angle V'?

  1. A68
  2. B24
  3. C34
  4. D48
BGeometry and Trigonometry / Congruence and similarity
19

f(x)=4x^2+16x+22
The function f is defined by the given equation. The function h is defined by h(x)=f(x)+9. What is the minimum value of h(x)?

  1. A31
  2. B15
  3. C7
  4. D6
BAdvanced Math / Transform of quadratic expressions
20

7(5x)+9(8y)=189
7(5x)-9(8y)=-819
The solution to the given system of equations is (x,y). What is the value of5x+8y?

  1. A-101
  2. B45
  3. C11
  4. D56
CAlgebra / Solving systems of linear equations
21

For the polynomial function f(x) , when f(x) is divided by x-8, the remainder is 9. Which of the following must be true about the graph of y=f(x) in the xy-plane?

  1. AIt passes through the point (9, -8).
  2. BIt passes through the point (-8, 9).
  3. CIt passes through the point (9, 8).
  4. DIt passes through the point (8, 9).
DAdvanced Math / Polynomial factors and graphs
image
22

The line segment shown in the xy-plane represents side JK of isosceles triangle JKL, where side JL is congruent to side KL. The perimeter of this triangle is 13√17units. What is the length, in units, of side JL of this triangle?

  1. A√17
  2. B3√17
  3. C5√17
  4. D10√17
CGeometry and Trigonometry / General triangle

Module 2 (Advanced)

1

In triangle JKL, the measures of ∠K and ∠L are each 51. What is the measure of ∠J , in degrees? (Disregard the degree symbol when entering your answer.)

78Geometry and Trigonometry / General triangle
image
2

The table shows three values of x and their corresponding values of y for the equation y=7(2)^x+8. In the table, a is a constant. What is the value of a?

  1. A120
  2. B64
  3. C56
  4. D50
BAdvanced Math / Exponential word problems
image
3

The figure shows the xy-plane with the quadrants labeled. The graph of a linear function h (not shown), where y=h(x), is a line completely contained in only quadrants Ⅰ and Ⅱ of the xy-plane. Which of the following could define the function h?

  1. Ah(x)=16x+16
  2. Bh(x)=16x
  3. Ch(x)=16
  4. Dh(x)=16x-16
CAlgebra / Graphing linear equations

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

image
4

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

  1. Ay=-0.007(x-50)^2+34
  2. By=-0.007(x-34)^2+50
  3. Cy=-0.007(x+34)^2+50
  4. Dy=-0.007(x+50)^2+34
AProblem Solving and Data Analysis / Scatter Plot
5

A researcher is designing a study to investigate the average number of hours students at a high school spend reading per day. The researcher will report an estimated average number of hours students at the high school spend reading per day with an associated margin of error. The researcher is considering using a random sample of either 90 or 180 students from the high school. Which of the following would be the most likely effect of using the larger random sample compared to the smaller random sample?

  1. AThe reported margin of error would be lower
  2. BThe reported margin of error would be higher
  3. CThe reported average number of hours would be lower.
  4. DThe reported average number of hours would be higher.
AProblem Solving and Data Analysis / Spread of distribution
6

4x^2+x-7=0
What is the greatest solution to the given equation?

  1. A-1/8-(√113)/8
  2. B-1/8+(√113)/8
  3. C-1/4-(√113)/4
  4. D-1/4+(√113)/4
BAdvanced Math / Solving quadratic equations
7

If 16+1/4(7x-6)=3/4(7x-6) , what is the value of 7x-6?

32Algebra / Solve linear equation
8

8x-7y=5
4x+y=8
The solution to the given system of equations is (x,y). What is the value of x+y?

35/12,2.917,2.916Algebra / Solving systems of linear equations
9

H=2.419L+22.83
A group of biology students conducted an experiment to study the relationship between a person's femur length and the person's height. The given equation describes the relationship between the length L, in inches, of a student's femur and the student's estimated height H, in inches, for the students in the group. Which of the following is the best interpretation of 2.419 in this context?

  1. AThe increase in a student's estimated height, in inches, for each increase of 1 inch in the student's femur length
  2. BThe increase in a student's femur length, in inches, for each increase of 1 inch in the student's estimated height
  3. CThe increase in a student's femur length, in inches, for each increase of 22.83 inches in the student's estimated height
  4. DThe estimated height, in inches, of a student whose femur has a length of L inches
AAlgebra / Interpreting linear equation
10

0.10x+0.20y=0.17(x+y)
The equation gives a volume x, in gallons, of a 10% saltwater solution that could be mixed with a volume y, in gallons, of a 20% saltwater solution to produce a 17% saltwater solution. According to this equation, what volume, in gallons, of the 20% saltwater solution could be mixed with 75.0 gallons of the 10% saltwater solution to produce a 17% saltwater solution? (Assume that the volume of the mixture is the sum of the volumes of the two solutions before they were mixed.)

175Algebra / Linear equation word problem
11

y<15x+13
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?

  1. A
    image
  2. B
    image
  3. C
    image
  4. D
    image
BAlgebra / Linear inequality word problem
12

In the xy-plane, line h passes through the point (0, 0) and is perpendicular to the line represented by the equation -3x+y=20. If line h also passes through the point (18, t), what is the value of t?

  1. A-54
  2. B-6
  3. C6
  4. D54
BAlgebra / Graphing linear equations
13

Which system of linear equations has no solution?

  1. A-3x+9y=-2
    3x-9y=2
  2. B3x-9y=2
    4x+10y=3
  3. C3x-9y=2
    -9x+27y=-6
  4. D-3x+9y=2
    6x-18y=4
DAlgebra / Solving systems of linear equations
14

f(x)=6,000(1.003)^2x
The given function f models the balance of a bank account, in dollars, x years after it is opened. Which statement is the best interpretation of (1.003)^2x ?

  1. AEvery 6 months, the balance increases by about $3.
  2. BEvery 2 years, the balance increases by about $3.
  3. CAt the end of every 6-month interval, the balance increases by about 0.3% of the balance at the beginning of the 6-month interval.
  4. DAt the end of every 2-year interval, the balance increases by about 0.3% of the balance at the beginning of the 2-year interval
CAdvanced Math / Exponential word problems
15

Which of the following is a factor of the expression 2x^2+(18r+5)x+45r , where r is a nonzero constant?
I. x+9r
II. 2x+5r

  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
AAdvanced Math / Transform of quadratic expressions
16

The equation 5|x-8|=k , where k is a constant, has exactly one solution. Which of the following could be the value of k/5?

  1. A-8 or 8
  2. B-8 only
  3. C0 only
  4. D8 only
CAlgebra / Solve linear equation
17

Which expression represents 1% of 31x ,where x>0 ?

  1. A101(31x)
  2. B100(31x)
  3. C0.01(31x)
  4. D1.01(31x)
CProblem Solving and Data Analysis / Percents
18

The quadratic function a models the depth, in meters, below the surface of the water of a Weddell seal t minutes after the seal entered the water during a dive. The function estimates that the seal reached its maximum depth of 382.2 meters 7 minutes after it entered the water and then reached the surface of the water 14 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 10 minutes after it entered the water?

312Advanced Math / Quadratic word problems
19

f(x)=11x^10+3x^8
g(x)=-17x^7+9x^5
The polynomial p(x) is defined as the product of the given polynomials, f(x) and g(x). What is the coefficient of x^15 in p(x)?

  1. A15
  2. B48
  3. C99
  4. D150
BAdvanced Math / Operations of polynomials
20

A scientist studied the effects of mixing two chemicals, chemical A and chemical B, by gradually adding more of each chemical to a mixture of the two chemicals. At the start of the study, the mass of chemical A in the mixture was equal to the mass of chemical B in the mixture. From the start of the study to the end of the study, the mass of chemical A in the mixture increased by 2,600% and the mass of chemical B in the mixture increased by 380%. At the end of the study, approximately how many times greater was the mass of chemical A in the mixture than the mass of chemical B in the mixture?

  1. A29.80
  2. B22.20
  3. C4.63
  4. D5.63
DProblem Solving and Data Analysis / Percents
21

r^2+qr=8r-87
In the given equation, q is an integer constant. The given equation has no real solutions. What is the largest possible value of q?

26Advanced Math / Solving quadratic equations
22

An isosceles right triangle has a perimeter of 34+34√2 inches. What is the length, in inches, of one leg of this triangle?

  1. A17
  2. B17√2
  3. C34
  4. D34√2
BGeometry and Trigonometry / Right triangle