2024.11 A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

image
1

The graph of the function f is shown, where y=f(x). What is the value of f(0)?

  1. A-6
  2. B-4
  3. C-3
  4. D-2
AAdvanced Math / Nonlinear equation graphs
image
2

In the figure, two lines intersect at a point. If r=61 , what is the value of s?

61Geometry and Trigonometry / Angles and Arc length
3

The function f is defined by f(x)=5x^2. What is the value of f(7)?

  1. A35
  2. B45
  3. C70
  4. D245
DAdvanced Math / Quadratic word problems
4

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

  1. A1.2
  2. B5
  3. C6
  4. D12
CAlgebra / Solving systems of linear equations
5

Which expression is equivalent to 6x(x+3)?

  1. A6x^2+3
  2. B6x^2+18x
  3. C7x^2+3
  4. D7x^2+9x
BAdvanced Math / Operations of polynomials
6

The function f is defined by f(x)=3x^5. In the xy-plane, the graph of y=g(x) is the result of shifting the graph of y=f(x) up 9 units. Which equation defines the function g?

  1. Ag(x)=3x^5+9
  2. Bg(x)=3x^5-9
  3. Cg(x)=3x^45
  4. Dg(x)=27x^5
AAdvanced Math / Function notations and transforms
7

For the linear function f, the graph of y=f(x) in the xy-plane has a slope of 69 and f(0)=3. Which equation defines f?

  1. Af(x)=3x
  2. Bf(x)=3x+3
  3. Cf(x)=69x
  4. Df(x)=69x+3
DAlgebra / Graphing linear equations
8

5% of w is 741.41. What is the value of w?

  1. A778.481
  2. B3,707.05
  3. C14,828.2
  4. D70,433.95
CProblem Solving and Data Analysis / Percents
image
9

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

  1. Ay=-7/16x^2
    y=-7/4x
  2. By=-7/16x^2
    y=7/4x
  3. Cy=7/16x^2
    y=-7/4x
  4. Dy=7/16x^2
    y=7/4x
DAdvanced Math / linear and quadratic systems
10

W(x)=4x+80
The function W gives the total time, in minutes, it takes for a gardener to water x plants and mow the grass. According to the function, how many minutes does it take the gardener to mow the grass?

80Algebra / Linear functions word problem
11

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

  1. A9
  2. B10
  3. C14
  4. D19
CAlgebra / Solving systems of linear equations
12

x^2-16x+y^2-10y-55=0
In the xy-plane, the graph of the given equation is a circle. If this circle is inscribed in a square, what is the perimeter of the square?

  1. A24
  2. B48
  3. C96
  4. D220
CGeometry and Trigonometry / Circle equation
13

If 5(3x+6)=3(3x+6)+78, what is the value of3x+6?

  1. A78
  2. B39
  3. C33
  4. D11
BAlgebra / Solve linear equation
14

If f(x)=x+5 and g(x)=5x, what is the value of 7f(4)-g(4)?

  1. A-11
  2. B13
  3. C35
  4. D43
DAlgebra / Linear functions word problem
15

C(t)=240(53/52)^(t-15)+7
The function C gives the estimated number of cephalopods, a class of marine animal, in a certain area, where t is the number of months since a study began. How many months after the study began was the number of cephalopods in the area estimated to be 247?

15Advanced Math / Exponential word problems
16

An object moves at a speed of 3/17 feet per second. What is this speed in yards per second? (3 feet = 1 yard)

1/17,0.0588,.0588Problem Solving and Data Analysis / Units
image
17

For the linear function g, the table shows four values of x and their corresponding values of g(x). The function can be written as g(x)=mx+b, where m and b are constants. What is the value of b?

37Algebra / Linear functions word problem
18

The current value of a house is $174,000, and this value increases by 2.4% each year from the value of the previous year. Which function f gives the value, in dollars, of the house x years from now?

  1. Af(x)=174,000(0.024)^x
  2. Bf(x)=174,000(0.24)^x
  3. Cf(x)=174,000(1.024)^x
  4. Df(x)=174,000(1.24)^x
CAdvanced Math / Exponential word problems
19

What is the value of sin 18π?

  1. A0
  2. B1/2
  3. C(√2)/2
  4. D1
AGeometry and Trigonometry / Trigonometric functions
image
20

In triangle QRS shown, QR<RS . Which expression represents the length of QS ?

  1. A17cosQ
  2. B17sinQ
  3. C17/(cos Q)
  4. D17/(sin Q)
DGeometry and Trigonometry / Trigonometric functions
21

1/9x-3r/7y=34
One of the equations in a system of two linear equations is given, where r is a nonzero constant. The system has no solution. If the other equation in the system is graphed in the xy-plane, what is the slope of the graph?

  1. A-27r/7
  2. B-27/7r
  3. C7r/27
  4. D7/27r
DAlgebra / Solving systems of linear equations
22

A machine makes 8-inch, 9-inch, and 3-inch parts. During a certain day, the number of 8-inch parts that the machine makes is 4 times the number n of 9-inch parts, and the number of 3-inch parts is 30. During this day, the machine makes 100 parts total. Which equation represents this situation?

  1. A8(4n)+9n+3(30)=100
  2. B8n+9n+3n=100
  3. C4n+30=100
  4. D5n+30=100
DAlgebra / Linear equation word problem

Module 2 (Advanced)

1

The ratio of the base to the height of a triangle is 1 to 8. The base of the triangle is 104 centimeters. What is the height, in centimeters, of the triangle?

  1. A13
  2. B52
  3. C104
  4. D832
DProblem Solving and Data Analysis / Units
2

q(x)=15(3^x)
Which table gives three values of x and their corresponding values of q(x) for function q?

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

A plant nursery classifies a perennial flower species as tall if its typical height when fully grown is more than 100 centimeters. Each of the following inequalities represents the possible heights h, in centimeters, for a specific perennial flower species when fully grown. Which inequality represents the possible heights h, in centimeters, for a tall perennial flower species?

  1. A14<h<95
  2. B41<h<93
  3. C78<h<100
  4. D107<h<160
DAlgebra / Linear inequality word problem
4

A linear function f gives a company's profit, in dollars, for selling x items. The company's profit is $170 when it sells 4 items, and its profit is $590 when it sells 10 items. Which equation defines f?

  1. Af(x)=170x-590
  2. Bf(x)=59x
  3. Cf(x)=70x-10x
  4. Df(x)=70x-110
DAlgebra / Linear equation word problem
5

Each year, the value of an investment increases by 0.69% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?

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

Line p in the xy-plane is defined by y=x+8/3 and passes through the points (a, 0) and (0, b), where a and b are constants. What is the value of a?

-8/3,-2.666,-2.667Algebra / Graphing linear equations
7

25x/(x^2-25)=x/(x-5)+20/(x+5)
What is the positive solution to the given equation?

10Advanced Math / Rational transformation
8

How many solutions does the equation7(x+12)+5x=12(x+7) have?

  1. AExactly one
  2. BExactly two
  3. CInfinitely many
  4. DZero
CAlgebra / Solve linear equation
9

The manager of a gym selected a sample of 142 members at random to estimate the percentage of the gym's members that would continue to pay for a membership if the price increased. From the survey, the manager estimates that 89% of the gym's members would continue to pay for a membership if the price increased, with an associated margin of error of 5.15%. If the survey is repeated with a random sample of 284 members and the results are calculated in the same way, which of the following will be the most likely effect of using the larger random sample compared to the smaller random sample?

  1. AThe margin of error will be lower.
  2. BThe margin of error will be higher.
  3. CThe estimate of the percentage of the gym's members that would continue to pay for a membership if the price increased will be lower.
  4. DThe estimate of the percentage of the gym's members that would continue to pay for a membership if the price increased will be higher.
AProblem Solving and Data Analysis / Spread of distribution
10

The function f is defined by f(x)=-9x+9. What is the y-coordinate of the y-intercept of the graph of y=f(x) in the xy-plane?

9Algebra / Graphing linear equations
image
11

The histogram summarizes a data set of the weights, in pounds, of 14 salmon. If an additional weight of 68 pounds is added to the original data set to create a new data set of 15 weights of salmon, which of the following measures must be greater for the new data set than for the original data set?
Ⅰ. The median
Ⅱ. The mean

  1. AⅠ only
  2. BⅡ only
  3. CⅠ and Ⅱ
  4. DNeither Ⅰ nor Ⅱ
  5. AⅠ only
  6. BⅡ only
  7. CⅠ and Ⅱ
  8. DNeither Ⅰ nor Ⅱ
BProblem Solving and Data Analysis / Mean, mode, median
image
12

The table shows three values of x and their corresponding values of y, where a and b are constants. There is a linear relationship between x and y. In the xy-plane, the y-intercept of the line representing this relationship is (0, -16). What is the value of a + b?

  1. A-32
  2. B-31
  3. C-22
  4. D-21
AAlgebra / Linear functions word problem
13

(x+k)^2+37=37
In the given equation, k is a constant. How many distinct real solutions does this equation have?

  1. AZero
  2. BExactly one
  3. CExactly two
  4. DInfinitely many
BAdvanced Math / Solving quadratic equations
14

For a certain circuit, its power P, in watts, current C, in amperes; voltage V, in volts; and resistance R, in ohms, are related as (CV^2)/P=√PR, where P, C, V, and R are positive. When R=18, which equation correctly expresses P in terms of C and V?

  1. AP=(CV^2)/(√18P)
  2. BP=(CV^2)/(√18)
  3. CP=3√(C^2V^4)/18
  4. DP=3√18/(C^2V^4)
CAdvanced Math / Isolating quantities
15

y<-5x-21
y>-3x-8
For which of the following tables are all the values of x and their corresponding values of y solutions to the given system of inequalities?

  1. A
    image
  2. B
    image
  3. C
    image
  4. D
    image
DAlgebra / Solving systems of linear inequalities
16

A circle is inscribed in a square such that the circumference of the circle touches the midpoint of each side of the square. The length of the diagonal of the square is 228 units. What is the area, in square units, of the circle?

  1. A6,498π
  2. B12,996π
  3. C25,992π
  4. D51,984π
AGeometry and Trigonometry / Circle theorems
17

The expression kx represents the result of decreasing a positive force, x, acting on an object by 0.34%. What is the value of k?

.9966,0.996,0.997,0.9966Problem Solving and Data Analysis / Percents
18

A polygon has exactly 87 sides. If the measure of each of the 87 interior angles of this polygon is (180p)°, what is the value of p?

85/87,0.977,.977,.9770Geometry and Trigonometry / General polygons
19

The number of bacteria in a liquid medium doubles every hour. There are 66,000 bacteria in the liquid medium at the start of an observation. Which of the following represents the number of bacteria, y, in the liquid medium t hours after the start of the observation?

  1. Ay=1/2(66,000)^t
  2. By=2(66,000)^t
  3. Cy=66,000(1/2)^t
  4. Dy=66,000(2)^t
DAdvanced Math / Exponential word problems
20

The function f(n)=7(20.44)^(n/4) gives each term of a sequence as a function of the term's position, n, in the sequence, where n is a whole number. The value of the term in position 14 is p% more than the value of the term in position 10. What is the value of p?

  1. A20.44
  2. B44
  3. C1,944
  4. D2,044
CAdvanced Math / Exponential word problems
21

A right square pyramid has a total surface area of 28,160 square inches, and the combined surface area of the four lateral faces of this pyramid is 16,060 square inches. What is the height, in inches, of this pyramid?

  1. A48
  2. B55
  3. C73
  4. D110
AGeometry and Trigonometry / Volume
22

The expression 6x^4+17x^2+7 can be rewritten as (3x^2+a)(2x^2+b), where a and b are positive integers, or as (3x^2+c)(2x^2+d), where c and d are positive nonintegers. What is the value of a+c?

17/2,8.5Advanced Math / Transform of quadratic expressions