2024.11 US A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

If 6x=60, what is the value of 7x+3?

  1. A73
  2. B63
  3. C55
  4. D45
AAlgebra / Solve linear equation
2

The function j is defined by j(x)=x/8. What is the value of j(48)?

  1. A48
  2. B40
  3. C8
  4. D6
DAlgebra / Linear functions word problem
3

k(x)=-1/2x^2+8x+20
The function k gives the estimated number of students in a school organization x years after the organization was established, where 0≤x≤10. Which statement is the best interpretation of k(4) = 44?

  1. AIt is estimated there were 4 students in the school organization when it was established.
  2. BIt is estimated there were 44 students in the school organization when it was established.
  3. CIt is estimated there were 44 students in the school organization 4 years after it was established.
  4. DIt is estimated there were 44 students in the school organization 10 years after it was established.
CAdvanced Math / Interpreting nonlinear expressions
4

The function t(x)=-3x+74 gives the estimated temperature, in degrees Fahrenheit, of a town x hours after 6 p.m., where 0≤x≤5. What is the best interpretation of -3 in this context?

  1. AThe estimated temperature decreases 3 degrees Fahrenheit each hour.
  2. BThe estimated temperature decreases 7474 degrees Fahrenheit each hour.
  3. CAt 6 p.m., the estimated temperature is --3 degrees Fahrenheit.
  4. DAt 6 p.m., the estimated temperature is 5 degrees Fahrenheit.
AAlgebra / Interpreting linear equation

The graph of the function f is shown, where y=f(x).

image
5

Which of the following best describes the function f?

  1. AIncreasing linear
  2. BDecreasing linear
  3. CIncreasing exponential
  4. DDecreasing exponential
CProblem Solving and Data Analysis / Exponential growth
6

Which expression is equivalent to 10x^2+130?

  1. A10(13x^2)
  2. B10(x^2+13)
  3. C130(10x^2)
  4. D130(10x^2+1)
BAdvanced Math / Operations of polynomials
7

An event planner is planning an ice-skating event. It costs the event planner a onetime fee of $30 to rent the skating rink and $10.25 per attendee. The event planner has a budget of $250. What is the greatest number of attendees possible without exceeding the budget?

21Algebra / Linear inequality word problem
8

The function f is defined by f(x)=4√x. For what value of x does f(x)=28?

  1. A4
  2. B7
  3. C16
  4. D49
DAdvanced Math / Radical and rational exponent problems
9

Triangle PQR is similar to triangle STU, where P, Q, aSTUnd R correspond to S, T, and U, respectively. In triangle PQR, the length of PQ is 6 and the length of QR is 24. In triangle STU, the length of ST is 8. What is the length of overlineTUTU?

  1. A8
  2. B14
  3. C32
  4. D48
CGeometry and Trigonometry / Congruence and similarity
image
10

The graph of a system of a linear and a quadratic equation is shown. What system is represented by the graph?

  1. Ay=-7/25x^2
    y=-7/5x
  2. By=-7/25x^2
    y=7/5x
  3. Cy=7/25x^2
    y=-7/5x
  4. Dy=7/25x^2
    y=7/5x
DAdvanced Math / linear and quadratic systems
11

The function f is defined by f(x)=4^(x-2)+8. What is the value of f(2)?

9Advanced Math / Exponential word problems
12

If the graph of 12x+22y=132 is shifted down 4 units in the xy-plane, what is the y-intercept of the resulting graph?

  1. A(0,2)
  2. B(0,7)
  3. C(0,10)
  4. D(0,18)
AAlgebra / Graphing linear equations
image
13

The table shows three values of x and their corresponding values of j(x) for exponential function j. When the graph of y=j(x) in the xy-plane is shifted up 20 units, the resulting graph is defined by function h. Which table gives three values of x and their corresponding values of h(x)?

  1. A
    image
  2. B
    image
  3. C
    image
  4. D
    image
BAdvanced Math / Exponential word problems
14

A landscaping company mixes oil with gasoline to power its tools. A chainsaw requires 8 ounces of oil per gallon of gasoline. A lawnmower requires 4 ounces of oil per gallon of gasoline. The company uses a total of 21 ounces of oil in its mixes for the chainsaw and lawnmower. Which of the following equations represents this situation, where x represents the amount of gasoline, in gallons, in the mix for the chainsaw and y represents the amount of gasoline, in gallons, in the mix for the lawnmower?

  1. A2(x+2y)=21
  2. B2(2x+y)=21
  3. C4(x+2y)=21
  4. D4(2x+y)=21
DAlgebra / Linear equation word problem
image
15

What is the value of cos B in the right triangle shown?

0.6,3/5Geometry and Trigonometry / Trigonometric functions
16

Rectangles ABCD and EFGH are similar. The length of each side of rectangle EFGH is 7 times the length of the corresponding side of rectangle ABCD. The area of rectangle ABCDEFGH is 68 square units. What is the area of rectangle EFGH, in square units?

3332Geometry and Trigonometry / Congruence and similarity
17

18 is 10% of what number?

  1. A28
  2. B100
  3. C162
  4. D180
DProblem Solving and Data Analysis / Percents
18

h(t)=-16t^2+b
The function h estimates an object's height, in feet, above the ground t seconds after the object is dropped, where b is a constant. The function estimates that the object is 2.56 feet above the ground when it is dropped at t = 0. How many seconds after being dropped does the function estimate the object will hit the ground?

0.4,2/5Advanced Math / Quadratic word problems
19

The measure of angle S is 8π/13 radians. The measure of angle T is 3 times the measure of angle S. Which expression represents the measure, in degrees, of angle T?

  1. A8/13(90)(3)
  2. B8/13(180)(3)
  3. C8/13π(90)(3)
  4. D8π/13(180)(3)
BGeometry and Trigonometry / Angles and Arc length
20

(x-7)/5+(y+8)/4=0
3x+4y=0
The solution to the given system of equations is (x, y). What is the value of x + y?

  1. A-12
  2. B-5
  3. C-4
  4. D12
AAlgebra / Solving systems of linear equations
21

Each of the following frequency tables represents a data set. Which data set has the greatest mean?

  1. A
    image
  2. B
    image
  3. C
    image
  4. D
    image
AProblem Solving and Data Analysis / Mean, mode, median
22

Jackson mows lawns in the summer. When Jackson mows a lawn with a fence he charges $1.03 per minute. When Jackson mows a lawn without a fence, he charges $0.56 per minute. Jackson spends a total of 15 hours mowing lawns with and without a fence in a week and charges a total of $701.40 for mowing lawns during that week. How many minutes does Jackson spend mowing lawns with a fence during that week?

420Algebra / Systems of linear equations word problem

Module 2 (Advanced)

1

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, 47). Which equation defines g?

  1. Ag(x)=37x
  2. Bg(x)=37x+5
  3. Cg(x)=5x
  4. Dg(x)=5x+37
DAlgebra / Graphing linear equations

The table gives the number of hours, h, of labor and a plumber's total charge f(h), in dollars, for two different jobs.

image
2

There is a linear relationship between hand f(h). Which equation represents this relationship?

  1. Af(h)=85h+55
  2. Bf(h)=55h+85
  3. Cf(h)=110h+30
  4. Df(h)=30h+110
BAlgebra / Linear functions word problem

The table shows the frequency of values in a data set.

image
3

What is the minimum value of the data set?

  1. A1
  2. B7
  3. C20
  4. D44
CProblem Solving and Data Analysis / Table Data
4

Exactly how many x-intercepts does the graph of f(x)=x(x-10)^2(x-11)^3 have in the xy-plane, where y=f(x)?

  1. A0
  2. B1
  3. C2
  4. D3
DAdvanced Math / Polynomial factors and graphs
5

2x^2+2y^2+tx+ty-78=0
The given equation, where t is a positive constant, defines a circle in the xy-plane. The radius of this circle is √41. What is the value of t?

4Geometry and Trigonometry / Circle equation
6

In triangle RST, the measure of angle R is 29 degrees. Which statement provides sufficient information to prove that triangle RST is isosceles?

  1. AThe measure of angle S is 151 degrees.
  2. BThe measure of angle S is 61 degrees.
  3. CThe measure of angle S is 58 degrees.
  4. DThe measure of angle S is 29 degrees.
DGeometry and Trigonometry / General triangle
7

Ifa=6k+5r and b=9k-12r+3, which expression is equivalent to a-b?

  1. A-3k+17r-3
  2. B-3k+17r+3
  3. C-3k-7r+3
  4. D-3k-7r-3
AAdvanced Math / Operations of polynomials
8

x^2-49/16=0
How many distinct real solutions does the given equation have?

  1. AZero
  2. BExactly one
  3. CExactly two
  4. DInfinitely many
CAdvanced Math / Solving quadratic equations
9

y>-7/2x+17
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
AAlgebra / Solve linear inequality
10

A polygonal chain is a connected series of line segments whose length is defined as the sum of the lengths of the line segments it is made of. A polygonal chain with a length of 33 centimeters (cm) is extended by adding line segments that each have a length of 8-r cm. Which function f represents the total length, in cm, of the extended polygonal chain after x line segments are added?

  1. Af(x)=33(8-r)+x
  2. Bf(x)=8x-rx+33
  3. Cf(x)=8x-r+33
  4. Df(x)=(41-r)x
BAlgebra / Linear functions word problem
11

If 9/6(x-5)-36=7/6(x-5)+28, what is the value of x-5?

192Algebra / Solve linear equation
12

A chemist combines 30 grams of compound A, 45 grams of compound B, and x grams of compound C. The resulting mixture has a mass of 135 grams. What is the value of x?

  1. A15
  2. B30
  3. C45
  4. D60
DAlgebra / Linear equation word problem
image
13

Line k is shown in the xy-plane. Line j(not shown) is perpendicular to line k and passes through the point (19, 23). What is the y-coordinate of the y-intercept of line j?

39/5,7.8Algebra / Graphing linear equations
14

For a study, a group of chipmunks will be selected from a habitat consisting of 220 chipmunks, and a group of prairie dogs will be selected from a habitat consisting of 190 prairie dogs. Some of the chipmunks and prairie dogs will be in a treatment group, and some of the chipmunks and prairie dogs will be in a control group. Which of the following is necessary for this study to attempt to establish a cause-and-effect relationship between two variables?

  1. AThe number of chipmunks in the treatment group is equal to the number of prairie dogs in the treatment group, and the number of chipmunks in the control group is equal to the number of prairie dogs in the control group.
  2. BThe chipmunks and the prairie dogs are randomly assigned to the treatment and control groups.
  3. CThe chipmunks and the prairie dogs are randomly selected from their respective habitats.
  4. DThe average age of the chipmunks in the treatment group is equal to the average age of the prairie dogs in the treatment group, and the average age of the chipmunks in the control group is equal to the average age of the prairie dogs in the control group.
BProblem Solving and Data Analysis / Sample and conclusion
15

A certain investment account offers a special interest rate for the first 4 months the account is open followed by a lower interest rate for the remainder of the time the account is open. Akeyla opened one of these accounts with an original account balance of $700.00 and did not make any other deposits or withdrawals. 4 months after Akeyla opened the account, the balance had increased by 0.6% of the original balance. 6 months after Akeyla opened the account, the balance had increased by an additional 0.1% of the balance at the end of the first 4 months. Every 2 months after the first 6 months, the balance had increased by an additional 0.1% of the balance 2 months before. Which of the following equations could represent the account balance B(x), in dollars, x months after the account was opened, where x≥4?

  1. AB(x)=704.20(1.001)^((x-4)/2)
  2. BB(x)=700.00(1.001)^((x-4)/2)
  3. CB(x)=704.20(1.001)^(2(x-4))
  4. DB(x)=700.00(1.001)^(2(x-4))
AAdvanced Math / Exponential word problems
16

As the size of a firework's shell increases, the height above the ground when the firework bursts increases. For a firework to burst l,075 feet above the ground, a firework's shell in the shape of a sphere with a volume of 542.68 cubic inches could be used. To the nearest whole number, what is the volume of this firework's shell in cubic centimeters? (1 inch = 2.54 centimeters)

8893Problem Solving and Data Analysis / Units
17

√(x+15)^2=x+15
What is the least value of x that is a solution to the given equation?

  1. A-16
  2. B-15
  3. C0
  4. D15
BAdvanced Math / Radical and rational exponent problems
18

The function f is defined by f(x)=a^x-b, where a and b are constants. In the xy-plane, the graph of y=f(x) passes through the points (c, 7) and (2c, 117), where c is a constant. Which of the following could be the value of b?

  1. A4
  2. B117
  3. C110
  4. D124
AAdvanced Math / Exponential word problems
19

4/5x+6/5y=g
8/13x+hy=k
In the given system of equations, g, h, and k are constants. The system has infinitely many solutions. What is the value of g/k?

13/10,1.3Algebra / Solving systems of linear equations
20

34z^18+bz^9+30
In the given expression, b is a positive integer. If qz^9+r is a factor of the expression, where q and r are positive integers, what is the greatest possible value of b?

1021Advanced Math / Transform of quadratic expressions
21

A right rectangular prism has a base area of 16t square centimeters (cm²). The length of the base of the rectangular prism is 8/3 cm, and the height of the rectangular prism is 9 cm. Which expression represents the surface area, in cm², of the right rectangular prism?

  1. A32t+96
  2. B140t+48
  3. C800t+48
  4. D144t
BGeometry and Trigonometry / Volume
22

The mass of object A is 498% of the mass of object B, and the mass of object A is 0.830% of the mass of object C. If the mass of object C is p% of the mass of object B, what is the value of p?

60000Problem Solving and Data Analysis / Percents