Question 1

Simplify the expression $$ (3 - 4i)(-2 + 4i) . $$What is the result?

Accepted Answer

Question 2

Solve the quadratic equation $$ x^2$ - 5x - 14 = 0 . $$What are the solutions?

Accepted Answer

$$ x = 7, x = -2 $$

Question 3

A car rental agency rents a Nissan Versa for $$40 per day with unlimited mileage or 24 $$per day plus $$0.20 per mile. How many miles can a customer drive per day for the 24 $$option to cost no more than the unlimited mileage option?

Accepted Answer

$$ 80 $$ miles

Question 4

Solve the equation $$ (x-4$$)^{3/2}$$ = 27 . $$What is the value of $$ x $$?

Accepted Answer

$$ x = 13 $$

Question 5

Given the function $$ f(x) = -2x^2$ + x - 1 $$, what is the simplified form of the difference quotient $$ \frac{f(x+h) - f(x)}{h} $$?

Accepted Answer

$$ -4x - 2h + 1 $$

Question 6

Solve the inequality $$ -11 \u003c 2x - 1 \u003c -5 . $$What is the solution set for $$ x $$?

Accepted Answer

$$ -5 \u003c x \u003c -2 $$

Question 7

Given the points $$ (-3, 5) $$ and $$ (1, 9) $$, what is the equation of the line passing through these points in slope-intercept form?

Accepted Answer

$$ y = x + 6 $$

Question 8

Find the center and radius of the circle $$ (x+6)^2$ + (y+1)^2$ = 16 .$$

Accepted Answer

Center $$ (-6, -1) $$, radius $$ 4 $$

Question 9

Solve the equation $$ 4|1 - \frac{3}{4}x| + 7 = 10 . $$What is the solution set for $$ x $$?

Accepted Answer

Question 10

Given $$ f(x) = x^3$ - 8 $$, find $$ f$$^{-1}$$(x) $$ and verify that $$ f(f$$^{-1}$$(x)) = x .$$

Accepted Answer

$$ f$$^{-1}$$(x) = (x+8$$)^{1/3}$$ $$; Yes, $$ f(f$$^{-1}$$(x)) = x $$

Question 11

Find the average rate of change of $$ f(x) = x^3$ $$ from $$ x = 2  to$$ $$ x = 6 .$$

Accepted Answer

$$ 108 $$

Question 12

Which of the following equations does NOT represent $$ y  as a $$function of $$ x $$?

Accepted Answer

$$ x^2$ + y^2$ = 9 $$

Question 13

A toll road charges $$5.00$$ per use, but with a $$30$$ electronic pass, the toll is reduced by $$30\%. $$What is the minimum number of times the road must be used for the pass to be a better deal?

Accepted Answer

$$ 12 $$

Question 14

Find the distance between the points $$ (-1, 2) $$ and $$ (12, 4) .$$

Accepted Answer

$$ 13 $$

Question 15

Write the equation of the line parallel to $$ y = 2x + 3 $$ passing through $$ (4, 8) .$$

Accepted Answer

Question 16

Solve the equation $$ 2|x-3| - 6 = 10 . $$What is the solution set for $$ x $$?

Accepted Answer

$$ x = 11, x = -5 $$

Question 17

Given $$ f(x) = 3x^2$ + 7 $$, what is the simplified form of the difference quotient $$ \frac{f(x+h) - f(x)}{h} $$?

Accepted Answer

$$ 6x + 3h $$

Question 18

Solve the equation $$ x^3$ + x^2$ = 4x + 4 . $$What are the real solutions?

Accepted Answer

Question 19

Write the equation $$ 7x - 9y = 0  in $$slope-intercept form.

Accepted Answer

$$ y = \frac{7}{9}x $$

Question 20

Find the $$ x - $$and $$ y -$$intercepts of the line $$ 3x + 2y - 4 = 0 .$$

Accepted Answer

College Algebra Exam 1 Review – Step-by-Step Study Guidance

Study Guide - Practice Questions

Study Guide - Flashcards