2024.6 A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

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1

In the figure, line n intersects lines r and s. Line r is parallel to line s. What is the value of x?

152Geometry and Trigonometry / Angles and Arc length
2

During a portion of a flight, a small airplane's cruising speed varied between 125 miles per hour and 145 miles per hour. Which inequality best represents this situation, where s is the cruising speed, in miles per hour, during this portion of the flight?

  1. As≤20
  2. Bs≤125
  3. Cs≤145
  4. D125≤s≤145
DAlgebra / Linear inequality word problem
3

If 4x = 7, what is the value of 24x?

  1. A1
  2. B13
  3. C34
  4. D42
DAlgebra / Solve linear equation
4

Which expression is equivalent to (x^3+8x^2-7x)+6(x^2+5) ?

  1. Ax^3+6x^2-7x+30
  2. Bx^3+8x^2-7x+30
  3. Cx^3+14x^2-7x+30
  4. Dx^3+5x^2-7x+30
CAdvanced Math / Operations of polynomials
5

The function f is defined by f(x)=x^3+19 . What is the value of f(2)?

27Advanced Math / Function notations and transforms
6

The function g is defined by g(x)=x/2 . For what value of x does g(x)=224 ?

448Algebra / Solve linear equation

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

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7

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

  1. Ay=0.8+8.5x
  2. By=0.8-8.5x
  3. Cy=8.5+0.8x
  4. Dy=8.5-0.8x
DAlgebra / Graphing linear equations
8

The y-intercept of the graph of y=x^2+15 in the xy-plane is (0, y). What is the value of y?

15Advanced Math / Nonlinear equation graphs
9

4x - 3y = - 24
For the given equation, which table gives three values of x and their corresponding values of y ?

  1. A
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  2. B
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  3. C
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  4. D
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AAlgebra / Linear equation word problem
10

A chemist combines water and isopropanol to make a mixture with a volume of 38 milliliters (mL). The volume of isopropanol in the mixture is 10 mL. What is the volume of water, in mL, in the mixture? (Assume that the volume of the mixture is the sum of the volumes of water and isopropanol before they were mixed.)

28Algebra / Linear functions word problem
11

y=-1/8x
y=1/10x
The solution to the given system of equations is (x, y). What is the value of x?

  1. A-8
  2. B0
  3. C2
  4. D10
BAlgebra / Solving systems of linear equations
12

A company has a customer loyalty program. In January 2018, there were 800 customers enrolled in the loyalty program. For the next 24 months after January 2018, the total number of customers enrolled in the loyalty program each month was 5% greater than the total number enrolled the previous month, Which equation gives the total number of customers, c, enrolled in the company's loyalty program m months after January 2018, where m < 24?

  1. Ac=800(0.05)^m
  2. Bc=800(1.05)^m
  3. Cc=800(1.5)^m
  4. Dc=800(5)^m
BAdvanced Math / Exponential word problems
13

The function f(t)=60,000(2)^(t/580) gives the number of bacteria in a population t minutes after an initial observation, How much time, in minutes, does it take for the number of bacteria in the population to double?

580Advanced Math / Exponential word problems
14

For x > 0, the function f is defined as follows:
f (x) equals 293% of x
Which of the following could describe this function?

  1. ADecreasing exponential
  2. BDecreasing linear
  3. CIncreasing exponential
  4. DIncreasing linear
DProblem Solving and Data Analysis / Linear growth
15

y=3/8x+2
One of two equations in a system of linear equations is given. The system has infinitely many solutions. What is the slope of the graph of the second equation?

  1. A-8/3
  2. B-3/8
  3. C3/8
  4. D8/3
CAlgebra / Solving systems of linear equations
16

If 4x^2-32x-40=0 , what is the value of x^2-8x ?

  1. A0
  2. B4
  3. C8
  4. D10
DAdvanced Math / Solving quadratic equations
17

The function f is defined by f (x)=(x - 5)(x - 9)( x + k), where k is a constant. In the xy-plane, the graph of y = f (x) passes through the point (-3, 0). What is the value of f (0)?

  1. A-288
  2. B-3
  3. C11
  4. D135
DAdvanced Math / Polynomial factors and graphs
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18

Line k is shown in the xy-plane. Line j (not shown) is perpendicular to line k and passes through the point (-20, -23). Which equation defines line j?

  1. Ay=3/4x-8
  2. By=3/4x-38
  3. Cy=4/3x-8
  4. Dy=4/3x-38
AAlgebra / Graphing linear equations
19

In right triangle ABC, angles A and B are acute, side AC has a length of 29.5, and tanB = 1/9 . What is the length of side BC, rounded to the nearest tenth?

  1. A870.2
  2. B265.5
  3. C5.4
  4. D3.3
BGeometry and Trigonometry / Trigonometric functions
20

A rectangular banner has an area of 3,200 square inches, A copy of the banner is made in which the length and width of the original banner are each increased by 20%. What is the area of the copy, in square inches?

  1. A3,220
  2. B3,240
  3. C3,840
  4. D4,608
DGeometry and Trigonometry / Congruence and similarity
21

f(x)=(x-4)^2+6
What is the minimum value of the given function?

  1. A2
  2. B4
  3. C6
  4. D10
CAdvanced Math / Nonlinear equation graphs
22

Point F lies on a unit circle in the xy-plane and has coordinates (1, 0). Point G is the center of the circle and has coordinates (0, 0), Point H also lies on the circle and has coordinates (-1, y), where y is a constant. Which of the following could be the positive measure of angle FGH, in radians?

  1. A37π/2
  2. B39π/2
  3. C34π
  4. D35π
DGeometry and Trigonometry / Angles and Arc length

Module 2 (Advanced)

1

Which of the following is a graph of a decreasing exponential function?

  1. A
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  2. B
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  3. C
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  4. D
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DAdvanced Math / Nonlinear equation graphs
2

What is the y-intercept of the graph of y=6x^2+4x+3 in the xy-plane?

  1. A(0, 3)
  2. B(0, 4)
  3. C(0, 6)
  4. D(0, 7)
AAdvanced Math / Nonlinear equation graphs
3

The product of a positive number x and the number that is 7 less than x is equal to 18. What is the value of x?

  1. A3.5
  2. B9
  3. C11
  4. D25
BAdvanced Math / Quadratic word problems
4

A cylinder has a diameter of 6 inches and a height of 21 inches. What is the volume, in cubic inches, of the cylinder?

  1. A9π
  2. B126π
  3. C189π
  4. D756π
CGeometry and Trigonometry / Volume
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5

In triangle PQR, QR is extended to point S. The measure of ∠PQR is 132°, and the measure of ∠PRS is 166°. What is the measure of ∠QPR?

  1. A14°
  2. B24°
  3. C34°
  4. D48°
CGeometry and Trigonometry / General triangle
6

Eli used wax to make candles. The function f (x)= - 9x + 54 approximates the weight, in ounces, of wax Eli had remaining after making x candles. Which statement is the best interpretation of the y-intercept of the graph of y = f (x) in the xy-plane in this context?

  1. AEli used approximately 9 ounces of wax for each candle.
  2. BEli had approximately 9 ounces of wax when he began to make the candles.
  3. CEli had approximately 54 ounces of wax when he began to make the candles.
  4. DEli used approximately 54 ounces of wax for each candle.
CAlgebra / Interpreting linear equation
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7

The graph shows the relationship between the number of shares of stock from Company A, x, and the number of shares of stock from Company B, y, that Sayen can purchase. Which equation could represent this relationship?

  1. Ay=9x+16
  2. B9x+16y=720
  3. Cy=16x+9
  4. D16x+9y=720
BAlgebra / Linear functions word problem
8

ak=b/12(8+m)
The given equation relates the positive variables a, b, k, and m. Which equation correctly expresses m in terms of a, b, and k?

  1. Am=(12(ak-8))/b
  2. Bm=ak-8-b/12
  3. Cm=ak-8b/12
  4. Dm=12ak/b-8
DAdvanced Math / Isolating quantities
9

The function g is defined by g(x)=10^(4x-2) . What is the value of x when g(x) is equal to 10,000?

  1. A5/4
  2. B3/2
  3. C3
  4. D4
BAdvanced Math / Radical and rational exponent problems
10

If z/y=3x/y=3 and 2x/ty=18 , what is the value of t ?

  1. A1/3
  2. B2/3
  3. C3/2
  4. D3
AAdvanced Math / Rational transformation
11

A piece of string with a length of 53 inches is cut into two parts. One part has a length of x inches, and the other part has a length of y inches. The value of x is 8 more than 2 times the value of y. What is the value of x?

38Algebra / Systems of linear equations word problem
12

Which equation has no solution?

  1. A-13x-1/9=-13x-1/9
  2. B-13x-1/9=-13x+1/9
  3. C-13x-1/9=13x-1/9
  4. D-13x-1/9=13x+1/9
BAlgebra / Solve linear equation
13

F(x)=9/5(x-273.15)+32
The function F gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x kelvins. If a temperature increased by 13.30 kelvins, by how much did the temperature increase, in degrees Fahrenheit?

  1. A23.94
  2. B55.94
  3. C467.73
  4. D499.73
AAlgebra / Linear functions word problem
14

An environmental scientist is investigating the volatility of 175 organic compounds by finding the boiling point of each compound. The mean boiling point of all 175 compounds is 167 degrees Celsius. The scientist classifies each of these compounds as either semivolatile or volatile. Of the 175 compounds, 50 compounds were classified as semivolatile, and these 50 compounds have a mean boiling point of 322 degrees Celsius. The remaining 125 compounds were classified as volatile. What is the mean boiling point, in degrees Celsius, of the 125 compounds classified as volatile compounds?

105Problem Solving and Data Analysis / Mean, mode, median
15

f(x)=26(1.20)^(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. A20
  2. B31
  3. C40
  4. D44
DProblem Solving and Data Analysis / Exponential growth
16

A carpenter charges a flat rate of $228 for the first 2 hours of work and $95 for each additional hour of work. Which equation gives the total amount y, in dollars, that the carpenter charges for x hours of work, where x > 2?

  1. Ay=95x+228
  2. By=228x+418
  3. Cy=95x+38
  4. Dy=228x+95
CAlgebra / Linear functions word problem
17

y=-6.5
y=x^2+8x+a
In the given system of equations, a is a positive integer constant. The system has no real solutions. What is the least possible value of a?

10Advanced Math / linear and quadratic systems
18

5√272n(6√272n)^2
For what value of x is the given expression equivalent to (272n)^30x , where n >1?

4/225,.0177,.0178,0.018,0.017Advanced Math / Radical and rational exponent problems
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19

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age?

  1. A5/21
  2. B5/14
  3. C17/35
  4. D5/7
BProblem Solving and Data Analysis / Ratios and proportion
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20

The table shows three values of x and their corresponding values of g(x), where g(x)=(f(x))/(x+4) ? and f is a linear function. What is the y-intercept of the graph of y = f (x) in the xy-plane?

  1. A(0, 36)
  2. B(0, 9)
  3. C(0, 4)
  4. D(0, -9)
AAlgebra / Linear functions word problem
21

The mass of object A is 438% of the mass of object B, and the mass of object A is 0.073% 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/1000 ?

600Problem Solving and Data Analysis / Percents
22

1/cx=x/72+1/c
In the given equation, c is a constant. If the equation has exactly one solution, what is the value of c?

-18Advanced Math / Rational transformation