Question 1

Given the points $A(2, 3)$ and $B(8, 11)$, what is the distance between them?

Accepted Answer

$10$

Question 2

Which of the following is the equation of the line passing through the points $(1, 2)$ and $(4, 8)$?

Question 3

A chemist is mixing two solutions. The first solution contains 30% salt and the second contains 80% salt. How many liters of each should be mixed to obtain 10 liters of a 50% salt solution?

Accepted Answer

4 liters of 30% and 6 liters of 80%

Question 4

If $f(x) = 2x + 3$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$f(g(2)) = 2 \cdot 4 + 3 = 11$

Question 5

Which of the following is the inverse of the function $f(x) = 3x - 5$?

Accepted Answer

$f^{-1}(x) = \frac{x + 5}{3}$

Question 6

Solve the quadratic equation $x^2 - 6x + 5 = 0$.

Accepted Answer

$x = 1$ or $x = 5$

Question 7

A ball is thrown upward from the ground with an initial velocity of $32$ ft/s. Its height after $t$ seconds is given by $h(t) = -16t^2 + 32t$. When does the ball hit the ground?

Accepted Answer

$t = 0$ and $t = 2$

Question 8

Which of the following is the domain of the function $f(x) = \frac{1}{x-4}$?

Accepted Answer

$x 
eq 4$

Question 9

Solve the inequality $2x - 5 > 7$.

Accepted Answer

$x > 6$

Question 10

Given $f(x) = x^2 - 4x + 7$, what is the range of $f(x)$?

Accepted Answer

$[3, \infty)$

Question 11

If $\log_2(x) = 5$, what is the value of $x$?

Accepted Answer

$x = 32$

Question 12

Expand $\log(2x^3)$ using logarithm properties.

Accepted Answer

$\log 2 + 3\log x$

Question 13

Solve the exponential equation $2^{x+1} = 16$.

Accepted Answer

$x = 3$

Question 14

A radioactive substance decays according to $A(t) = 100e^{-0.05t}$. How much of the substance remains after 20 years?

Accepted Answer

$A(20) = 100e^{-1} \approx 36.79$

Question 15

Solve the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$

Question 16

A business invests $\$5000$ in an account that earns 6% annual interest compounded monthly. What will the balance be after 5 years? (Use $A = P(1 + \frac{r}{n})^{nt}$)

Accepted Answer

$A \approx \$6740.24$

Question 17

Which of the following is the solution to the system of equations: $\begin{cases} x + y + z = 6 \ 2x - y + z = 3 \ x + 2y - z = 4 \end{cases}$?

Accepted Answer

$(x, y, z) = (1, 2, 3)$

Question 18

A population of bacteria triples every 4 hours. If the initial population is 200, what will the population be after 12 hours?

Accepted Answer

$200 	imes 3^3 = 5400$

Question 19

Which of the following is the correct formula for the sum of a geometric series with first term $a$ and common ratio $r$ (where $|r| < 1$)?

Accepted Answer

$S = \frac{a}{1 - r}$

Math 142 Final Exam Review: College Algebra Study Guide

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