2024.5 US B

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

A total of 50 people attended a conference and were offered 4 types of entrees. The table shows the number of people who chose each type of entree.

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1

If one of these people is selected at random, what is the probability of selecting a person who chose a vegetarian entree?

  1. A9/100
  2. B9/50
  3. C1/4
  4. D9/10
BProblem Solving and Data Analysis / Ratios and proportion · Accuracy 97.66%
2

If 7x+2=58, what is the value of 70x+20?

  1. A580
  2. B90
  3. C80
  4. D8
AAlgebra / Solve linear equation · Accuracy 99.5%

A certain gas is placed inside a container and kept at a constant pressure. The graph showsthe estimated volume y, in liters, of the gas when its temperature is x kelvins.

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3

What is the estimated volume, in liters, of the gas when its temperature is 200 kelvins?

  1. A200/7
  2. B7
  3. C7/200
  4. D0
BProblem Solving and Data Analysis / Key feature of graphs · Accuracy 98.9%
4

The function f is defined by f(x)=4x^3+7 . What is the value of f (2)?

39Advanced Math / Manipulation of other expressions · Accuracy 98.65%
5

A number x is less than 2 more than 1/7 times the value of a number y. If y is an integer and x = 9, what is the least possible value of y?

50Algebra / Linear inequality word problem · Accuracy 63.46%
6

During a trip, Bill drove his car for 16.0 miles and then began driving at a constant speed of 60.0 miles per hour. After 2 hours of driving at this speed, what is the total distance, in miles, Bill has traveled during this trip?

136Algebra / Linear functions word problem · Accuracy 96.86%
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7

The table shows three values of x and their corresponding values of y. There is a linear relationship between x and y. What is the y-coordinate of the y-intercept of the line in the xy-plane that represents this relationship?

17Algebra / Graphing linear equations · Accuracy 96.68%
8

The functionf(x)=180(x-2) gives the sum of the interior angles, in degrees, for a polygon with x sides. What is the sum of the interior angles, in degrees, for a polygon with 14 sides?

2160Algebra / Linear functions word problem · Accuracy 98.22%
9

y=7,400(0.87)^x
The given equation estimates the value, in dollars, of a certain car x years after it was purchased. According to the given equation, what was the estimated value, in dollars, of the car at the time it was purchased?

  1. A740
  2. B6,438
  3. C7,400
  4. D8,700
CAdvanced Math / Exponential word problems · Accuracy 97.11%
10

At how many points do the graphs of the equations y=x+11 and y=10x intersect in the xy-plane?

  1. A0
  2. B1
  3. C2
  4. D10
BAlgebra / Solving systems of linear equations · Accuracy 98.46%
11

A space probe uses a square-shaped solar sail to move through space. The side length of the solar sail is 8.83w meters, where w is the width, in meters, of the space probe.Which equation gives the area A, in square meters, of the solar sail?

  1. AA = (w + 8.83)(w + 8.83)
  2. BA = (4)(8.83w)
  3. CA = (8.83w)( 8.83w)
  4. DA=(8.83/w)(8.83/w)
  5. BA = (4)(8.83w)
  6. CA = (8.83w)( 8.83w)
  7. DA=(8.83/w)(8.83/w)
  8. CA = (8.83w)( 8.83w)
  9. DA=(8.83/w)(8.83/w)
  10. DA=(8.83/w)(8.83/w)
CGeometry and Trigonometry / General polygons · Accuracy 95.75%
12

The length of a rectangle is 20 inches and the width is x inches. The perimeter is at most 100 inches. Which inequality represents this situation?

  1. A2x+20≤100
  2. B2x+20≥100
  3. C2x+40≤100
  4. D2x+40≥100
CAlgebra / Linear inequality word problem · Accuracy 97.8%
13

A circle has a circumference of 48π centimeters. What is the diameter in centimeters, of the circle?

48Geometry and Trigonometry / Circle theorems · Accuracy 94.57%
14

2y=8x+19
-2y=9x-28
The solution to the given system of equations is (x , y). What is the value of 68x?

  1. A-36
  2. B-9
  3. C9
  4. D36
DAlgebra / Solving systems of linear equations · Accuracy 96.57%
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15

△QPR is similar to △overlineSTSTR . The lengths represented by ST , QP , overlinePRPR , and overlineoverlineQRQR in the figure are 5, 7, 24, and 25, respectively. What is the length of SR ?

  1. A125/7
  2. B125/24
  3. C35/24
  4. D35/25
AGeometry and Trigonometry / Congruence and similarity · Accuracy 97.62%
16

f(x)=(x-65)(x-67)
The function f is defined by the given equation. For what value of x does f (x) reach its minimum?

  1. A-1
  2. B65
  3. C66
  4. D67
CAdvanced Math / Transform of quadratic expressions · Accuracy 87.37%
17

h = (w^2(x-y))/4.7
A contractor installs a square window in a home. The given equation relates this window's hourly heat loss h, in British thermal units per hour, to this window's width w, in feet; the temperature inside the home x, in degrees Fahrenheit; and the temperature outside the home y, in degrees Fahrenheit. Which equation correctly expresses y in terms of h, w, and x?

  1. Ay=4.7h/(w^2)-x
  2. By=x-4.7h/(w^2)
  3. Cy=(hx^2)/4.7-x
  4. Dy=x-(hx^2)/4.7
BAdvanced Math / Isolating quantities · Accuracy 94.98%
18

9x+y=15
90x+10y=150
How many solutions does the given system of equations have?

  1. AExactly one
  2. BExactly two
  3. CInfinitely many
  4. DZero
CAlgebra / Solving systems of linear equations · Accuracy 94.71%
19

A scientist studying the life cycle of butterflies counted the number of butterflies in a certain habitat each day for 46 days. On June 15, there were 152 butterflies in the habitat. The percent increase in the number of butterflies in the habitat from May 1 to June 15 was 18.75%. How many butterflies were in the habitat on May 1?

  1. A8
  2. B29
  3. C124
  4. D128
DProblem Solving and Data Analysis / Percents · Accuracy 92.5%
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20

Right triangle ABC is shown. What is the value of tan A?

  1. A(√3)/22
  2. B1/(√3)
  3. C√3
  4. D11√3
CGeometry and Trigonometry / Trigonometric functions · Accuracy 86.59%
21

f(x)=(x-a)(x-b)
The function f is defined by the given equation, where a and b are integer constants. If f (18)>0 , f (21)<0 , and f (24)>0 , which of the following could be the value of a+b?

  1. A21
  2. B23
  3. C39
  4. D41
  5. A21
  6. B23
  7. C39
  8. D41
DAdvanced Math / Polynomial factors and graphs · Accuracy 83.57%
22

x^2+9x+y^2-5y+17=0
In the xy-plane, the graph of the given equation is a circle. What is the radius of the circle?

  1. A(√38)/2
  2. B(√178)/2
  3. C√17
  4. D17
AGeometry and Trigonometry / Circle equation · Accuracy 86.68%

Module 2 (Advanced)

1

A barrel contains 32 liters of a chemical solution. 50% of this chemical solution, by volume, is water. How much of this chemical solution, in liters, is water?

  1. A0
  2. B16
  3. C32
  4. D50
BProblem Solving and Data Analysis / Percents · Accuracy 99.53%
2

Which expression is equivalent to (5x^6)(x^3) ?

  1. A5x^9
  2. B5x^18
  3. C6x^9
  4. D6x^18
AAdvanced Math / Radical and rational exponent problems · Accuracy 97.74%
3

y=(x-7)(x+9)
Which table gives four values of x and the corresponding values of y for the given quadratic equation?

  1. A
    x | -1 | 0 | 1 | 2
    y | -70 | -63 | -56 | -49
  2. B
    x | -1 | 0 | 1 | 2
    y | 17 | 9 | 7 | -1
  3. C
    x | -1 | 0 | 1 | 2
    y | -64 | -63 | -60 | -55
  4. D
    x | -1 | 0 | 1 | 2
    y | 9 | 16 | 23 | 30
CAdvanced Math / Transform of quadratic expressions · Accuracy 98.98%
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4

The roofs on the buildings of a public garden are designed to allow water to drain into the garden. The table shows the relationship between the area x, in square feet, of a roof and the amount of water f (x), in gallons, drained from the roof into the garden over a certain period of time. Which equation could define f

  1. Af (x) = 0.6x
  2. Bf (x) = 1.8x
  3. Cf (x) = 2,052.0x
  4. Df (x) = 4,104.0x
BAlgebra / Linear functions word problem · Accuracy 98.04%
5

20x+19y=c
19x-20y=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?

  1. A(10, -10/39)
  2. B(10, 390)
  3. C(c,c/39)
  4. D（c, 0)
AAlgebra / Solving systems of linear equations · Accuracy 73.81%

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

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6

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

  1. Ay=0.06-1.03x
  2. By=1.03-0.06x
  3. Cy=-0.06+1.03x
  4. Dy=-1.03+0.06x
CProblem Solving and Data Analysis / Scatter Plot · Accuracy 94.46%
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7

In the figure shown, line r is parallel to line s, and both lines are intersected by line t. If x=2w+24 , y=5w+28 , and 7w=a , where a is a constant, what is the value of a?

128Geometry and Trigonometry / Angles and Arc length · Accuracy 89.05%
8

A total of 3 squares each have side length r. A total of 6 equilateral triangles each have side length t. None of these squares and triangles shares a side. The sum of the perimeters of all these squares and triangles is 60. Which equation represents this situation?

  1. A12r+18t=60
  2. B3r+6t=60
  3. C9r+24t=60
  4. D6r+3t=60
AAlgebra / Linear equation word problem · Accuracy 96.38%
9

A right triangle has sides of length 4√2 ,10√2 , and√232units. What is the area of the triangle, in square units?

  1. A14√2 +√232
  2. B80√232
  3. C80
  4. D40
DGeometry and Trigonometry / Right triangle · Accuracy 89.06%
10

(x-3)(x-6)/(x-2)=0
What is the sum of the solutions to the given equation?

  1. A2
  2. B6
  3. C9
  4. D11
CAdvanced Math / Rational transformation · Accuracy 92.72%
11

How many solutions does the equation 13(x+17)+4x=17(x+13) have?

  1. AExactly one
  2. BExactly two
  3. CInfinitely many
  4. DZero
CAlgebra / Solve linear equation · Accuracy 84.19%
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12

The table shows the frequencies of the values in a data set. Which of the following frequency tables represents a data set with the same mean as this data set?

  1. A
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  2. B
    image
  3. C
    image
  4. D
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AProblem Solving and Data Analysis / Mean, mode, median · Accuracy 82.96%
13

2x^2+10x+15=0
How many distinct real solutions does the given equation have?

  1. AExactly one
  2. BExactly two
  3. CInfinitely many
  4. DZero
DAdvanced Math / Solving quadratic equations · Accuracy 93.37%
14

During a specific 2-hour period of the day, the mean photosynthetic rate, P(x), of a plant species increases at a constant rate in terms of the photochemical energy available, x. During this period, P(300) = 9.5, and the mean photosynthetic rate increases by 0.125 micromoles per meter squared per second (μ mol • m^-2m^(-2)s^(-1) ) when the photochemical energy available increases by 5μ mol • m^-2m^(-2)s^(-1). Which equation gives the mean photosynthetic rate, in μ mol • m^-2m^(-2)s^(-1), in terms of the photochemical energy available, in μ mol • m^-2m^(-2)s^(-1), during this period?

  1. AP(x)=0.025x+9.5
  2. BP(x)=0.025x+2
  3. CP(x)=9.5x+0.025
  4. DP(x)=9.5x-2,840.5
BAlgebra / Linear functions word problem · Accuracy 78.99%
15

The solutions to x^2 - 3x - 5 = 0 are(3-√p)/2 and(3+√p)/2 . If the solutions to x^2 - 11x + c = 0, where c is a constant ,are (11-√p)/2 and (11+√p)/2 , what is the value of c?

23Advanced Math / Solving quadratic equations · Accuracy 84.45%

For an exercise physiology study, 75 participants were assigned to an activity, and their average heart rate while engaged in the activity was recorded. The table summarizes the results of this study.

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16

One of these participants will be selected at random. What is the probability of selecting a participant who was assigned to the swimming activity given that the participant had an average heart rate of less than 130 beats per minute while engaged in an activity? (Express your answer as a decimal or fraction, not as a percent.)

5/19,0.263,.263,0.2632,.2632Problem Solving and Data Analysis / Ratios and proportion · Accuracy 73.34%
17

In the xy-plane, lines k and j are perpendicular and intersect at the point (5,28). Line j passes through the origin, and line k passes through the point (p, 0), where p is a constant. What is the value of p?

  1. A-151.8
  2. B-151.4
  3. C161.4
  4. D161.8
DAlgebra / Graphing linear equations · Accuracy 83.33%
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18

The graph of y = f (x)+ 3 is shown. Which equation defines function f ?

  1. Af(x)=-2^x+2
  2. Bf(x)=-2^x+5
  3. Cf(x)=-2^x+7
  4. Df(x)=-2^x+8
BAdvanced Math / Nonlinear equation graphs · Accuracy 68.46%
19

A certain park has an area of 4,860,000 square meters. What is the area, in square kilometers, of this park ? (1 kilometer = 1,000 meters)

4.86,4.860Problem Solving and Data Analysis / Units · Accuracy 92.19%
20

Which of the following expressions has a factor of x + 2b, where b is a positive integer constant?

  1. A3x^2+9x+18b
  2. B3x^2+36x+18b
  3. C3x^2+54x+18b
  4. D3x^2+63x+18b
DAdvanced Math / Transform of quadratic expressions · Accuracy 70.34%
21

The function f is defined by f (x) = ab^(x/n) , where a, b, and n are constants, and b and n are integers. If f (2) = 6 and f (4) = 150, what is the value of f (5)?

750Advanced Math / Radical and rational exponent problems · Accuracy 74.8%
22

(x-k)^2=(k-4a)(x-k)
In the given equation, a and k are constants, where k > 4a. The sum of the solutions to the equation is 3k + 31. What is the value of a?

-31/4,-7.75Advanced Math / Solving quadratic equations · Accuracy 68.21%