# Mathematics Placement/Pretest 2

26 Questions | Total Attempts: 40

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This is Part 2 of the Mathematice Placement/Pre-test.

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• 1.
Expand the expression   log (6x5 / y)   as a sum, difference, and/or constant multiple of logarithms.
• A.

5(log 6x - log y)

• B.

30(log x) - log y

• C.

5(log 6x) - log y

• D.

Log 6 + 5(log x) - log y

• E.

Log (6x^5 / y)

• 2.
Find all solutions of the following equation in the interval [0, 2π).
• A.

X = 0, π/6, 5π/6, 7π/6, 11π/6

• B.

X = 0, π/2, π, 3π/2

• C.

X = 0, π/4, 7π/4

• D.

X = 0, π/3, 2π/3, π, 4π/3, 5π/3

• E.

X = 0, π/4, 3π/4, π, 5π/4, 7π/4

• 3.
Solve the following equation. 2 cos x -1 = 0
• A.

X = (π/6) + 2nπ and x = (5π/6) + 2nπ, where n is an integer

• B.

X = (π/3) + 2nπ and x = (5π/3) + 2nπ, where n is an integer

• C.

X = (π/4) + 2nπ and x = (5π/4) + 2nπ, where n is an integer

• D.

X = (π/6) + 2nπ and x = (7π/6) + 2nπ, where n is an integer

• E.

X = (2π/3) + 2nπ and x = (4π/3) + 2nπ, where n is an integer

• 4.
Using the factors (x - 1) and (x + 4), find the remaining factor(s) of F(x) = x3 + 5x2 + 2x – 8.   and write the polynomial in fully factored form.
• A.

F(x) = (x - 1)(x + 4)(x + 2)

• B.

F(x) = (x - 1)(x + 4)^2

• C.

F(x) = (x - 1)(x + 4)(x - 2)

• D.

F(x) = (x - 1)^2(x + 4)

• E.

F(x) = (x - 1)(x + 4)(x + 6)

• 5.
Find the exact value of log4 12 – log4 3 without using a calculator.
• A.

1/2

• B.

1

• C.

3

• D.

3/2

• E.

4

• 6.
The point (7, 24) is on the terminal side of an angle in standard position. Determine the exact value of tan θ.
• A.

Tan θ = -7/24

• B.

Tan θ = 25/24

• C.

Tan θ = 24/25

• D.

Tan θ = -25/24

• E.

• 7.
State the quadrant in which θ lies if cos θ < 0 and csc θ < 0.
• A.

• B.

• C.

• D.

• 8.
Write the quadratic function, f(x) = -x2 + 2x + 8, in standard form.
• A.

F(x) = - (x + 1)^2 + 9

• B.

F(x) = (x - 9)^2 - 1

• C.

F(x) = (x - 1)^2 - 9

• D.

F(x) = -(x - 1)^2 + 9

• E.

F(x) = -(x + 9)^2 - 1

• 9.
Condense the expression 1/3[log x + log 7] - [log y] to the logarithm of a single term.
• A.

Log ((7x)^3/y)

• B.

Log (7x/3y)

• C.

Log ((7x / y)^(1/3))

• D.

Log (((7x)^(1/3)) / y)

• E.

Log ((7x)^(1/3)) - log y

• 10.
Find the exact value of csc θ, using the triangle shown in the figure below, if a = 7 and b = 24.
• A.

25/24

• B.

25/7

• C.

7/24

• D.

24/25

• E.

7/25

• 11.
Determine the exact value of sin θ when cot θ = (7/24) and csc θ > 0.
• A.

Sin θ = 26/25

• B.

Sin θ = 24/25

• C.

Sin θ = 49/25

• D.

Sin θ = 48/25

• E.

Sin θ = 23/24

• 12.
Determine the vertex of the graph of the quadratic function  f(x) = x2 - 3x + 13/4
• A.

(-3/2, 11/2)

• B.

(3, 13/4)

• C.

(3/2, 13/4)

• D.

(3/4, 5/4)

• E.

(-3/2, 1)

• 13.
Identify all intercepts of f(x) = x2 / (x2 + 9).
• A.

X-intercept: none; y-intercept: (0, 4)

• B.

X-intercept: (0, 0); y-intercept: (0, 0)

• C.

X-intercept: none; y-intercept: (0, 1)

• D.

X-intercept: (-3, 0) and (3, 0); y-intercept: (0, 1)

• E.

X-intercept: none; y-intercept: none

• 14.
Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x) = 2 / (x - 3)
• A.

Horizontal: x = 0; vertical: y = 3

• B.

Horizontal: y = -3; vertical: x = 0

• C.

Horizontal: y = 2; vertical: x = 3

• D.

Horizontal: y = 0; vertical: x = 3

• E.

Horizontal: x = 3; vertical: y = -2

• 15.
Identify the vertical asymptote of the function f(x) = 2 + log(x + 3).
• A.

X = 0

• B.

X = -2

• C.

X = -3

• D.

X = 3

• E.

The function has no vertical asymptote.

• 16.
Given  f(x) = x2 + 3x -2    x + 5 determine the equations of any slant and vertical asymptote.
• A.

Slant: y = x - 2; vertical: x = -5

• B.

Slant: y = x + 8; vertical: none

• C.

Slant: y = x + 2; vertical: x = -2

• D.

Slant: y = x - 7; vertical: x = 3

• E.

Slant: none; vertical: none

• 17.
Write F(x) = x3 – 3x2 + 4x - 12 as a product of linear factors.
• A.

X = (x - 3)(x + 2)^2

• B.

X = (x - 3)^2(x - 2i)

• C.

X = (x - 3)(x - 2)^2

• D.

X = (x - 3)(x + 2i)(x - 2i)

• E.

X = (x - 3)(x + 3)(x + 2)

• 18.
If sin x = 1/2 and cos x = √(3)/2, evaluate the following function.   csc x
• A.

Csc x = √( 3)/2

• B.

Csc x =2

• C.

Csc x = √ 3

• D.

Csc x = 1/3

• E.

Csc x = 2√ 3/3

• 19.
Use an inverse function to write θ as a function of x.
• A.

θ = arctan (4 / (2x + 1))

• B.

θ = arctan ((2x + 1) / 4)

• C.

θ = arctan ((x + 1) / 2)

• D.

θ = arctan (1 / (x + 1))

• E.

θ = arctan (2x + 1)

• 20.
Use the One-to-One Property to solve the following equation for x.  (1/3)7x-1 = 27
• A.

4/7

• B.

-3/7

• C.

1/7

• D.

-2/7

• E.

1/3

• 21.
Which of the following is equivalent to the expression below? cot θ - 1 1 - tan θ
• A.

Cot θ

• B.

Csc θ

• C.

Sec θ

• D.

1

• E.

Tan θ

• 22.
Sketch the graph of the function below. y = cos (x - (π/2))
• A.

Graph A

• B.

Graph B

• C.

Graph C

• D.

Graph D

• E.

Graph E

• 23.
Identify the x-intercept of the function y = 3 + log3 X .
• A.

27

• B.

1/27

• C.

-3

• D.

9

• E.

The function has no x-intercept.

• 24.
An initial investment of \$1000 grows at an annual interest rate of 8% compounded continuously. How log will it take to double the investment?
• A.

8.66 years

• B.

9.66 years

• C.

9.00 years

• D.

8.00 years

• E.

1 year

• 25.
Find the exact value of
• A.

3/4

• B.

8/5

• C.

3/5

• D.

3/8

• E.

4/3