1
The function f is defined by f(x)=2/(11-x). What is the value of f(x) when x=9?
1
2025.12 International B
Math · 44 questions Go to Reading and Writing
Module 1 (Medium)
2
On a certain day in June, the lowest recorded wind speed in a town was 9 miles per hour (mph) and the highest recorded wind speed was 20 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?
- Aw≤9
- Bw≤11
- Cw≥20
- D9≤w≤20
D
3
A triangle has a base length of 80 centimeters and a height of 40 centimeters. What is the area, in square centimeters, of the triangle?
1600
4
y=45
y=5x^2
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?
- A3
- B5
- C9
- D45
A
5
Which of the following equations is the most appropriate exponential model for the data shown in the scatterplot?
- Ay=34(1.04)^(-x)
- By=34(1.04)^x
- Cy=34(1.4)^(-x)
- Dy=34(1.4)^x
B
6
Hector receives a gift card worth $70.00 to pay for movies online. He uses his gift card to buy 2 movies for $6.50 each. He will spend the rest of his gift card on renting movies for $1.50 each. How many movies can Hector rent?
38
7
In △JKL, the measures of both ∠J and ∠K are equal and the measure of ∠L is 138^(∘) . What is the measure of ∠J ?
- A90°
- B69°
- C42°
- D21°
D
8
50x+49y=c
49x-50y=c
In the given system of equations, c is a positive constant. Which of the following could be the point where the graphs of the equations in this system intersect in the xy-plane?
- A(10,-10/99)
- B(10,990)
- C(c,c/99)
- D(c,0)
A
9
For the linear function f, the graph of y=f(x) in the xy-plane has a slope of 25 and passes through the point (0, 0). Which equation defines f?
- Af(x)=-1/25x
- Bf(x)=-25x
- Cf(x)=1/25x
- Df(x)=25x
D
10
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 0.16. How many visitors are located in room C?
- A29
- B36
- C120
- D135
D
11
4, 4, 12, 25, 25
What is the range of the data set shown?
- A12
- B14
- C21
- D70
C
12
The table below shows three values of x and their corresponding values of y for the equation y=6(2)^x+4. In the table, a is a constant. What is the value of a?
- A40
- B48
- C52
- D100
C
13
If 7(x-3)^2=252, what is the value of x^2-6x?
- A18
- B27
- C36
- D45
B
14
x^2-5x+2=0
What is one of the solutions to the equation?
- A(5±√17)/2
- B(5±√33)/2
- C(-5±√17)/2
- D(-5±√13)/2
A
15
A circle in the xy-plane has its center at (-7,2), and the point (1,-2) lies on the circle. Which equation represents this circle?
- A(x+7)^2+(y-2)^2=80
- B(x+7)^2+(y-2)^2=36
- C(x+7)^2+(y+2)^2=80
- D(x+7)^2+(y+2)^2=36
A
16
A dance studio charges an introductory fee for the first 3 lessons and then charges a fixed fee for each additional lesson. One student took 4 lessons and was charged $60. Another student took 16 lessons and was charged $300. Which function f gives the total charge, in dollars, for any student who took x lessons, where x>2?
- Af(x)=15x
- Bf(x)=15x+60
- Cf(x)=20x
- Df(x)=20x-20
D
17
A car dealership has only sedans, SUVs, and minivans for sale. On Monday, 30% of the vehicles for sale were sedans and 50% were SUVs. If there were 57 sedans for sale at the dealership on Monday, how many minivans were for sale?
38
18
On January 1, there were 236 views of a video posted on a social media site. Every 3 days after January 1, the number of views of the video had increased by 60% of the number of views 3 days earlier. The function f gives the predicted number of views x days after January 1. Which equation defines f?
- Af(x)=236(0.60)^(x/3)
- Bf(x)=236(0.60)^3x
- Cf(x)=236(1.60)^(x/3)
- Df(x)=236(1.60)^3x
C
19
0.10x+0.20y=0.18(x+y)
This equation represents mixing a volume x, in gallons of a 10% saltwater solution with a volume y , in gallons of a 20% saltwater solution to produce an 18% saltwater solution. According to this equation, what volume, in gallons, of the 20% saltwater solution could be mixed with 45.0 gallons of the 10% saltwater solution to produce an 18% saltwater solution? (Assume that the volume of the mixture is the sum of the volumes of the two solutions before they were mixed.)
180
20
f(x)=x+3
g(x)=7x^2-rx+63
The function f and g are given. In function g, r is a constant. If f(x)·g(x)=7x^3+189, what is the value of r?
21
21
y<14x+12
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
- A
- B
- C
- D
B
22
(-22x-29+m)/2=k(x+5)
In the equation, k and m are constants. The equation has infinitely many solutions. What is the value of m?
- A39
- B-11
- C-26
- D-81
D
Module 2 (Advanced)
1
Two participants solved a puzzle cube during timed competitions. The lists give the times, to the nearest second, that participant A and participant B took to solve the cube at various competitions.
Participant A: 23, 23, 25, 27
Participant B: 23, 23, 25, 27, 38
Which statement correctly compares the mean solve times, to the nearest second, of participant A and participant B at these competitions?
- AThe mean solve time of participant A is greater than the mean solve time of participant B.
- BThe mean solve time of participant A is less than the mean solve time of participant B.
- CThe mean solve time of participant A is equal to the mean solve time of participant B.
- DThere is not enough information to compare the mean solve times of participant A and participant B.
B
2
Line j is defined by y=4x+9. Line k is parallel to line j in the xy-plane. What is the slope of line k ?
4
3
For a linear function f, the table below shows three values of x and their corresponding values of f(x). Which of the following could define f?
- Af(x)=3x+2
- Bf(x)=2x+3
- Cf(x)=x+3
- Df(x)=2x
B
4
The height of a right circular cylinder is 36 inches, and the circumference of its base is 360 inches. Which expression represents the total surface area, in square inches, of the cylinder?
- A(36)(360)+2π(180/π)^2
- B(36)(360)+π(180/π)^2
- Cπ(180/π)^2(36)
- D(36)(360)
A
5
A bookstore is giving away free books every day. The equation f(x)=162-9x gives the number of free books, f(x), that remain to be given away after x days. Which of the following is the best interpretation of f(18)=0 in this context?
- AThe bookstore has 18 free books to give away.
- BThe bookstore will give away 18 free books in 9 days.
- CIt will take 18 days to give away all the free books.
- DIt will take 162 days to give away 18 free books.
C
6
2x+5y=260
-2x+3y=260
The solution to the system is (x,y). What is the value of 8y?
- A0
- B65
- C260
- D520
D
7
If 9x/2-11=45/2-11, what is the value of 9x?
- A5
- B10
- C45
- D54
C
8
A right circular cylinder has a volume of 35,152π cubic inches. The height of the cylinder is 2 times its radius. What is the radius, in inches, of the cylinder?
- A26
- B52
- C676
- D1,352
A
9
2x^2=k
In the given the equation, k is a constant. The equation has no real solution. Which of the following could be the value of k ?
- A-92
- B0
- C46
- D55
A
10
Which expression is equivalent to (7x(x-9)-2(x-9))/(3x-27), where x>9?
- A(x-9)/3
- B(7x-2)/3
- C(7x^2-2x-18)/(3x-27)
- D(7x^2-7x-81)/(3x-27)
B
11
0.1242 is 0.09% of the number b. The number b is 25% of the number c. What is the value of c ?
552
12
The function f is defined by the equation f(x)=20^x+b, where b is a constant. In the xy-plane, the graph of y=f(x) contains the points (0,36) and (2,p+19), where p is a constant. What is the value of p?
416
13
A figure has an area of 3,744 square inches. What is the area, in square feet, of this figure? (1 foot = 12 inches)
- A26
- B61.2
- C312
- D734.3
A
14
f(x)=(x-a)(x-b)
The function f is defined by the given equation, where a and b are integer constants. If f(39)>0, f(42)<0, and f(45)>0, which of the following could be the value of a+b?
- A42
- B44
- C81
- D83
D
15
One of the factors of 8x^4+50x^2+63 is ax^2+b, where a and b are positive constants. Which of the following is a possible value of ab?
- A7
- B14
- C18
- D36
C
16
N(t)=1,000(3/2)^(t/3)
The function N gives the estimated number of bacteria in a growth medium t hours after a study began. According to the function, the number of bacteria is estimated to increase by 50% every k minutes. What is the value of k?
- A40
- B50
- C180
- D90
C
17
The equation5|x-6|=k , where k is a constant, has exactly one solution. Which of the following could be the value of k/5?
- A-6 or 6
- B-6 only
- C0 only
- D6 only
C
18
The quadratic function g 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 396.8 meters 8 minutes after it entered the water and then reached the surface of the water 16 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 11 minutes after it entered the water?
341
19
In triangle XYZ, the measure of angle X is 90^(∘). Point W lies on segment YZ, and segment WX is perpendicular to segment YZ. The length of segment WY is 668, and the length of segment WX is 501. What is the value of tan Z?
- A3/5
- B3/4
- C4/5
- D4/3
D
20
x^2+y^2-6x-10y-4n=0
The given equation represents circle A in the xy-plane, where n is a constant. Point (5, 7) lies on circle B, which has the same center but twice the diameter as circle A. What is the value of n?
-8
21
39(x-n)=39y+39n
One of the equations in a system of two linear equations is given, where n is a positive constant. The system has no solution. Which equation could be the second equation in this system?
- A4x-4y=8n
- B4x+4y=4n
- C4x+4y=8n
- D4x-4y=4n
D
22
In triangle ABC, the measure of angle B is 90^(∘) and BD is an altitude of the triangle. The length of AB is 13 and the length of AC is 19 greater than the length of AB. What is the value of BC/BD?
- A13/32
- B13/19
- C19/13
- D32/13
D