2024.12 US A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

Julia purchased 400 feet of fencing. She used 90% of this fencing to surround a vegetable garden. How many feet of fencing did Julia use to surround the vegetable garden?

  1. A18
  2. B45
  3. C310
  4. D360
DProblem Solving and Data Analysis / Percents
2

Which expression is equivalent to 19(x^2-6) ?

  1. A19x^2-114
  2. B19x^2-25
  3. C19x^2-6
  4. D19x^2+13
AAdvanced Math / Operations of polynomials
3

5,8,11,17,29
What is the mean of the data shown?

  1. A11
  2. B14
  3. C17
  4. D29
BProblem Solving and Data Analysis / Mean, mode, median
4

A sleep study consisted of 77 participants, of which 69 participants each had an average of more than 120 minutes of rapid eye movement (REM) sleep per night. If a participant from this sleep study is selected at random, what is the probability of selecting a participant that had an average of more than 120 minutes of REM sleep per night?

  1. A69/100
  2. B77/100
  3. C69/77
  4. D77/69
CProblem Solving and Data Analysis / Ratios and proportion

For certain air temperatures, the table gives wind chill temperatures for two different wind speeds.

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5

According to the table, what is the wind chill temperature, in degrees Fahrenheit (°F ), when the air temperature is 41 °F and the wind speed is 45 miles per hour (mph)? (Disregard the degree symbol when entering your answer.)

28Problem Solving and Data Analysis / Table Data
6

A soccer team's goal is to earn at least $1,320 by selling coupon books. The team earns $12 from selling each coupon book. Which of the following inequalities describes all possible values for the number of coupon books, n, the team can sell to meet the goal?

  1. An+12≤1,320
  2. Bn+12≥1,320
  3. C12n≤1,320
  4. D12n≥1,320
DAlgebra / Linear inequality word problem
7

1.5c+3d=84
The given equation describes the relationship between the number of cats, c, and the number of dogs, d, that can be cared for at a pet care business during a week. If the business cares for 28 dogs during a week, how many cats can it care for during this week?

  1. A0
  2. B3
  3. C42
  4. D84
AAlgebra / Linear equation word problem
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8

For the triangles shown, triangle ABC is dilated by a scale factor of 4 to obtain triangle XYZ, where d = 16. What is the measure, in degrees, of angle X?

  1. A15
  2. B56
  3. C60
  4. D64
CGeometry and Trigonometry / Congruence and similarity
9

What is the y-intercept of the graph of y=8^(x+3) in the xy-plane?

  1. A(0,512)
  2. B(0,0)
  3. C(0,3)
  4. D(0,8)
AAdvanced Math / Nonlinear equation graphs
10

The function g is defined by g(x)=(√cx)/c+17, where c is a negative constant. What is the value of g(25c)?

12Advanced Math / Radical and rational exponent problems
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11

The area of triangle ABC is 230 square centimeters. What is the height h, in centimeters, of this triangle?

  1. A10
  2. B23
  3. C46
  4. D92
CGeometry and Trigonometry / General triangle
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12

In the right triangle shown, the value of tan x° is c/39. What is the value of c?

  1. A79
  2. B40
  3. C39
  4. D1
BGeometry and Trigonometry / Trigonometric functions
13

The graph of the polynomial function f in the xy-plane, where y=f(x), has x-intercepts of (-2,0) and (8,0). Which of the following must be true?

  1. Af(0)=-2
  2. Bf(8)=-2
  3. Cf(-2)=0
  4. Df(-2)=8
CAdvanced Math / Polynomial factors and graphs
14

(x-20)(x-18)(x+9)(x+17)=0
What is a positive solution to the given equation?

20,18Advanced Math / Polynomial factors and graphs
15

y=x^2-22x+80
The given equation relates the variables x and y. For what value of x does the value of y reach its minimum?

  1. A-22
  2. B11
  3. C22
  4. D80
BAdvanced Math / Transform of quadratic expressions
16

y=x^2-16x+44
The given equation relates the variables x and y. For what value of x does the value of y reach its minimum?

  1. A-16
  2. B8
  3. C16
  4. D44
BAdvanced Math / Transform of quadratic expressions
17

In the xy-plane, the graph of the equation (x-4)^2+(y-2)^2=16 is a circle. The point (8,c), where c is a constant, lies on this circle. What is the value of c?

2Geometry and Trigonometry / Circle equation
18

6(x-8)=(x-8)+6
If x is the solution to the given equation, what is the value of x-8?

6/5,1.2Algebra / Solve linear equation
19

9/2x+7y=30
5/2x+7y=26
The solution to the given system of equations is (x, y). What is the value of 19/2x+21y?

  1. A2
  2. B3
  3. C56
  4. D82
DAlgebra / Solving systems of linear equations
20

The graph of a line in the xy-plane passes through the point (1,7) and crosses the x-axis at the point (3,0). The line crosses the y-axis at the point (0,b). What is the value of b?

21/2,10.5Algebra / Graphing linear equations
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21

The table shows three values of x and their corresponding values of y. The linear relationship between x and y can be represented by an equation written in the form Ax+By=C, where A, B, and C are constants, What is the value of A/B?

-6Algebra / Linear functions word problem
22

7x+5y=4
21x+15y=12
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,-7r/5+4/5)
  2. B(-7r/5+4/5,r)
  3. C(-7r/5+4,7r/5+12)
  4. D(r/3+4,-r/3+12)
AAlgebra / Solving systems of linear equations

Module 2 (Advanced)

1

The function g is defined by g(x)=-18-9x. For what value of x does g(x)=-216?

  1. A-26
  2. B22
  3. C26
  4. D1,926
BAlgebra / Linear functions word problem
2

The population of a certain city doubled every 25 years from 1660 to 1760. The population of this city was 208,000 in 1760. What was the population of this city in 1660?

  1. A13,000
  2. B26,000
  3. C104,000
  4. D416,000
AAdvanced Math / Exponential word problems
3

The function f(x)=600(0.5)^(x/11) gives the predicted intensity of a beam f(x), in number of photons in the beam, x millimeters below the surface of a certain material. What is the best interpretation of f(11)=300?

  1. AA beam at the surface of the material has a predicted intensity of 11 photons in the beam.
  2. BA beam at the surface of the material has a predicted intensity of 300 photons in the beam.
  3. CA beam 11 millimeters below the surface of the material has a predicted intensity of 300 photons in the beam.
  4. DA beam 300 millimeters below the surface of the material has a predicted intensity of 600 photons in the beam.
CAdvanced Math / Interpreting nonlinear expressions
4

For the linear function h, h(0)=0 and h(11)=5. Which equation defines h?

  1. Ah(x)=5/11x
  2. Bh(x)=5/11x+5
  3. Ch(x)=11/5x
  4. Dh(x)=11/5x+11
AAlgebra / Graphing linear equations
5

Hassan put up wire fencing along each edge of a rectangular garden with a length of x feet and a width of y feet. Hassan put up a total length of 44 feet of wire fencing. Which equation represents this situation?

  1. A2x+2y=44
  2. Bx+y=44
  3. C2xy=44
  4. Dxy=44
AGeometry and Trigonometry / General polygons
6

How many solutions does the equation 7x-19=19-7x have?

  1. AZero
  2. BExactly one
  3. CExactly two
  4. DInfinitely many
BAlgebra / Solve linear equation
7

y>17
4x+y<21
The point (x, 54) is a solution to the given system of inequalities in the xy-plane. Which of the following could be the value of x?

  1. A9
  2. B5
  3. C-5
  4. D-9
DAlgebra / Solving systems of linear inequalities
8

A linear function f gives a company's profit, in dollars, for selling x items. The company's profit is $190 when it sells 4 items, and its profit is $670 when it sells 10 items. Which equation defines f?

  1. Af(x)=180x-670
  2. Bf(x)=67x
  3. Cf(x)=80x-10x
  4. Df(x)=80x-130
DAlgebra / Linear functions word problem
9

Which quadratic equation has no real solutions?

  1. A-2x^2=0
  2. B-2x^2+2=0
  3. C-2x^2+2x=0
  4. D-2x^2+2x-2=0
DAdvanced Math / Solving quadratic equations
10

The circumference of the base of a right circular cylinder is 6π meters, and the height of the cylinder is 19 meters. What is the volume, in cubic meters, of the cylinder?

  1. A57π
  2. B114π
  3. C171π
  4. D684π
CGeometry and Trigonometry / Volume
11

A zoologist observed the nests of wood ducks in an area.Each year, the zoologist recorded the number of eggs in each of the first 30 nests that were observed and created a frequency table for the data set. Which of the following frequency tables represents the data set with the smallest standard deviation?

  1. A
    image
  2. B
    image
  3. C
    image
  4. D
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DProblem Solving and Data Analysis / Spread of distribution
12

A carnival receives $10 for each adult admission ticket sold and $5 for each child admission ticket sold. On a particular day, the carnival received a total of $4,100 from selling adult and child admission tickets. If 220 adult admission tickets were sold on that day, how many child admission tickets were sold?

380Algebra / Linear equation word problem
13

y-x=32
y=x^2-30x
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 y?

  1. A32
  2. B33
  3. C63
  4. D64
DAdvanced Math / linear and quadratic systems
14

c(r)=2/5(2πr)
The function c gives the partial length, in centimeters (cm), of the circumference of a circle with a radius that measures r cm. According to the function, for each increase of 18 cm in the length of the radius, this partial length of the circumference increases by kπ cm. What is the value of k?

72/5,14.4Algebra / Linear functions word problem
15

f(x)=25(1.40)^(x/3)
For the given function f, the value of f(x) increases by p% for every increase of x by 6. What is the value of p?

  1. A40
  2. B49
  3. C80
  4. D96
DAdvanced Math / Exponential word problems
16

The function k is defined by k(s)=√s+110. If k(53p)=p, where p is a constant, what is the value of p?

55Advanced Math / Radical and rational exponent problems
17

If 121x^2=-110x+56 , what is the value of 11x+5, where 11x+5>0?

9Advanced Math / Solving quadratic equations
18

A computer program models the population of a certain insect in an environment where the insect has no natural predators. According to the model, the estimated total mass of the population of insects at the end of every 5-week period is 158% greater than the estimated total mass of the population of insects at the end of the previous 5-week period. The estimated total mass of the population of insects at the end of 15 weeks is 627.7 grams. Which equation best represents this model, where M is the estimated total mass, in grams, of the population of insects at the end of t weeks?

  1. AM=538.92(1.58)^(5/t)
  2. BM=457.66(2.58)^(5/t)
  3. CM=159.14(1.58)^(t/5)
  4. DM=36.55(2.58)^(t/5)
DAdvanced Math / Exponential word problems
19

The value of an autographed baseball increased by 178% from the end of 2012 to the end of 2013 and then decreased by 21% from the end of 2013 to the end of 2014. What was the net percentage increase in the value of the autographed baseball from the end of 2012 to the end of 2014?

  1. A119.62%
  2. B140.62%
  3. C157.00%
  4. D236.38%
AProblem Solving and Data Analysis / Percents
20

If n and k are numbers greater than 1 and 4√n^5 is equivalent to 5√k^2, for what value of a is n^(2a+1) equal to k?

17/16Advanced Math / Radical and rational exponent problems
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21

For triangle ABC, the length of AB is 11 less than the length of AC. Point D (not shown) lies on AC such that BD (not shown) is perpendicular to AC . What is the value of BC/BD?

28/17,1.647Geometry and Trigonometry / Congruence and similarity
22

The area of a rectangular region is increasing at a rate of 280 square feet per hour. Which of the following is closest to this rate in square meters per minute? (Use 1 meter = 3.28 feet.)

  1. A0.43
  2. B1.42
  3. C15.31
  4. D26.03
AProblem Solving and Data Analysis / Units