Q: Given $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \circ g)(2)$?

$\displaystyle f(g(2)) = (2 + 1)^2 = 9$

Q: If $f(x) = \frac{1}{x-2}$, which of the following statements is true?

$\displaystyle f(x)$ \text{ is undefined at } x = 2$

Q: Which of the following is the correct expansion of $\displaystyle (x + 2)^3$ using the binomial theorem?

$\displaystyle x^3 + 6x^2 + 12x + 8$

Question 1

Which of the following is the correct simplification of the expression $\displaystyle \frac{2x^2 - 8}{4x}$ for all $x 
eq 0$?

Accepted Answer

$\displaystyle \frac{x - 2}{2}$

Question 2

Solve the equation $\displaystyle 3^{2x} = 27$ for $x$.

Accepted Answer

$\displaystyle x = \frac{3}{2}$

Question 3

A biologist models the population of a bacteria culture with the function $P(t) = 500e^{0.3t}$, where $t$ is in hours. What is the population after 4 hours? (Round to the nearest whole number.)

Accepted Answer

$\displaystyle 500e^{1.2} \approx 1660$

Question 4

Which of the following is the inverse function of $f(x) = 2x + 5$?

Accepted Answer

$\displaystyle f^{-1}(x) = \frac{x - 5}{2}$

Question 5

Which of the following is the correct solution set for the inequality $x^2 - 5x + 6 < 0$?

Accepted Answer

$\displaystyle (2, 3)$

Question 6

Given $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \circ g)(2)$?

Accepted Answer

$\displaystyle f(g(2)) = (2 + 1)^2 = 9$

Question 7

Which of the following is the domain of the function $f(x) = \sqrt{5 - x}$?

Accepted Answer

$\displaystyle (-\infty, 5]$

Question 8

A chemist needs to prepare a solution by mixing a 10% saline solution with a 30% saline solution to obtain 20 liters of a 25% saline solution. How many liters of the 30% solution should be used?

Accepted Answer

$\displaystyle 15$

Question 9

Which of the following is the correct simplification of $\displaystyle \log_2(8x)$?

Accepted Answer

$\displaystyle 3 + \log_2(x)$

Question 10

Solve for $x$: $\displaystyle \frac{1}{x} + \frac{2}{x+1} = 1$

Accepted Answer

$\displaystyle x = 2$

Question 11

Which of the following is the sum of the first 5 terms of the geometric sequence where $a_1 = 3$ and $r = 2$?

Accepted Answer

$\displaystyle 93$

Question 12

If $f(x) = \frac{1}{x-2}$, which of the following statements is true?

Accepted Answer

$\displaystyle f(x)$ 	ext{ is undefined at } x = 2$

Question 13

Which of the following is the solution to the equation $\displaystyle \sqrt{x + 3} = x - 1$?

Accepted Answer

$\displaystyle x = 4$

Question 14

A car's value depreciates according to the function $V(t) = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value of the car after 3 years? (Round to the nearest dollar.)

Accepted Answer

$\displaystyle 12250$

Question 15

Which of the following is the correct expansion of $\displaystyle (x + 2)^3$ using the binomial theorem?

Accepted Answer

$\displaystyle x^3 + 6x^2 + 12x + 8$

Question 16

Which of the following is the solution to the system of equations: $\displaystyle \begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$\displaystyle x = 2, y = 3$

Question 17

Which of the following is the correct solution to $\displaystyle \log_{10}(x^2 - 4) = 1$?

Accepted Answer

$\displaystyle x = 2, x = -2$

Question 18

Which of the following is the correct result of performing the operation $\displaystyle (3x^2 - 2x + 5) + (x^2 + 4x - 3)$?

Accepted Answer

$\displaystyle 4x^2 + 2x + 2$

Question 19

Which of the following is the correct solution to the equation $\displaystyle 2^{x+1} = 16$?

Accepted Answer

$\displaystyle x = 3$

College Algebra Syllabus and Course Overview – Math 130 (Mt. San Antonio College)

Study Guide - Practice Questions

Study Guide - Flashcards