Question 1

Factor the following function completely:  $f(x)=27x^3-9x^2-12x+4$

Accepted Answer

$(3x-2)(3x+2)(3x-1)$

Answer

$(3x-2)^2(3x-1)$

Answer

$(9x^2-4)(3x-1)$

Answer

$(9x^2+4)(3x-1)$

Question 2

If the probability of Mr. Carroll being absent is $0.08$, the probability of having homework is $0.85$, and the probability that Mr. Carroll is absent OR having homework is $0.65$, find the probability that Mr. Carroll is absent AND having homework.

Accepted Answer

$0.28$

Answer

$0.12$

Answer

$0.582$

Answer

$0.798$

Question 3

Solve the following for x.  $\sqrt{m-1}+5=m-2$

Accepted Answer

$\{10\}$

Answer

$\varnothing$

Answer

$\{5,10\}$

Answer

$\{5\}$

Question 4

Solve for x to the nearest hundredth:   $5^{x+2}=4$

Accepted Answer

$-1.14$

Answer

$0.43$

Answer

$-0.84$

Answer

$-1.20$

Question 5

Simplify the following: $(4i-6)(2i+5)$

Accepted Answer

$-38+8i$

Answer

$8i^2+8i-30$

Answer

$-22+8i$

Answer

$-1+6i$

Question 6

Given the function: $f(x)=\frac{3}{2x+1}$, find $f^{-1}(x)$

Accepted Answer

$f^{-1}(x)=\frac{3-x}{2x}$

Answer

$f^{-1}(x)=\frac{1}{x}$

Answer

$f^{-1}(x)=\frac{2x+1}{3}$

Answer

$f^{-1}(x)=\frac{3x-1}{2}$

Question 7

Given the function $f(x)=(2^{-1.5x})(cos\frac{4x\pi}{15})$, find the average rate of change over the interval $[-4,2.5]$ to the nearest hundredth.

Accepted Answer

$-3.19$

Answer

$1.67$

Answer

$-2.50$

Answer

$-8.78$

Question 8

The expression $\frac{2x^{2}+5x-3}{9-x^{2}}$ is equivalent to which of the following?

Accepted Answer

$\frac{2x-1}{3-x}$

Answer

$\frac{2x-1}{x-3}$

Answer

$\frac{2x+1}{3+x}$

Answer

$\frac{(x+6)(x-1)}{(3-x)(3+x)}$

Question 9

Determine the remainder when $g(x)=x^{5}-3x^{4}+5x^{2}-16x+3$ is divided by $x+3$

Accepted Answer

$-390$

Answer

$42$

Answer

$6$

Answer

$0$

Question 10

In Calculus, Kevin has taken 21 math tests throughout the year.  His test average is an 88 with a standard deviation of 9.  Assuming his test scores model a normal distribution, how many of his tests are less than a 76?

Accepted Answer

$3$

Answer

$5$

Answer

$15$

Answer

$16$

Question 11

Which of the following is equivalent to $(\frac{64x^{\frac{1}{2}}}{8x^{4}})^{\frac{-1}{3}}$

Accepted Answer

$\frac{\sqrt[6]{x^{7}}}{2}$

Answer

$\frac{\sqrt[7]{x^{6}}}{2}$

Answer

$\sqrt[6]{x^{7}}$

Answer

$\sqrt[7]{x^{6}}$

Question 12

A recursive formula for the sequence  3, 7, 15, 31, 63, ... is

Accepted Answer

$a_{1}=3$; $a_{n+1}=2a_{n}+1$

Answer

$a_{1}=3$; $a_{n+1}=a_{n}+4n$

Answer

$a_{n}=2a_{1}+1$

Answer

$a_{n}=a_{1} +4n$

Question 13

What is the equation of the directrix of the parabola: $-36(y-4)^{2}=(x+2)^{2}$?

Accepted Answer

$y=13$

Answer

$y=0$

Answer

$y=-5$

Answer

$y=-2$

Question 14

Which of the following is the correct function to the graph pictured above?

Accepted Answer

$f(x)=2\cos{2x}$

Answer

$f(x)=2\cos{x}$

Answer

$f(x)=2\sin{x}$

Answer

$f(x)=2\sin{2x}$

Question 15

Which of the following statements is false regarding the equation: $f(x)=-4\cos{(\frac{x}{4}+\frac{\pi}{2})-3}$

Accepted Answer

The function shifted $\frac{\pi}{2}$ units left

Answer

The maximum value is $1$

Answer

The period is $8\pi$

Answer

The amplitude is $4$

Question 16

Which factorization is incorrect?

Accepted Answer

$3x^{2}-4x+6-3x-x^{2}-10=(2x-1)(x+4)$

Answer

$x^{4}-16=(x^{2}+4)(x-2)(x+2)$

Answer

$6x^{3}+3x^{2}-10x-5=(2x+1)(3x^{2}-5)$

Answer

$8x^{3}+y^{3}=(2x+y)(4x^{2}-2xy+y^{2})$

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