Question 1

Simplify the expression $$ (5 - 3i) - (11 + 4i) . $$What is the result?

Accepted Answer

$$ -6 - 7i $$

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. For how many miles per day will the $$24$$ option 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

$$ x = 31 $$

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

Find the equation of the line passing through the points $$ (-3, 5) $$ and $$ (1, 9) . $$What is its $$ y -$$intercept?

Accepted Answer

$$ y = x + 8 $$; $$ y -$$intercept is $$ 8 $$

Question 8

Given the circle $$ (x + 6)^2$ + (y + 1)^2$ = 16 $$, what are the center and radius?

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?

Accepted Answer

$$ x = -4,\ x = 8 $$

Question 10

Is the equation $$ 2x + y^2$ = 6  a $$function of $$ x $$? Why or why not?

Accepted Answer

No, because for some $$ x $$ values, there are two corresponding $$ y $$ values.

Question 11

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

Accepted Answer

$$ 68 $$

Question 12

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

Accepted Answer

$$ f$$^{-1}$$(x) = \sqrt[3]{x + 8} $$

Question 13

Solve the equation $$ 8x$$^{5/3}$$ - 24 = 0 . $$What is the value of $$ x $$?

Accepted Answer

$$ x = 3$$^{3/5}$$ $$

Question 14

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

Accepted Answer

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

Question 15

A toll road costs $$5.00$$ per use, but with a $$30$$ electronic pass, the toll is reduced by $$30\%. $$How many times must the road be used for the pass to be a better deal?

Accepted Answer

$$ 9 $$ times

Question 16

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

Accepted Answer

$$ 13.15 $$

Question 17

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

Accepted Answer

$$ x = 1,\ x = -2 $$

Question 18

Given the points $$ (0, 1) $$ and $$ (5, 17) $$, what is the equation of the line passing through them and its $$ x -$$intercept?

Accepted Answer

$$ y = 3.2x + 1 $$; $$ x -$$intercept is $$ -0.3125 $$

Question 19

Solve the absolute value equation $$ 2|x - 3| - 6 = 10 . $$What are the solutions?

Accepted Answer

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

Question 20

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

Accepted Answer

$$ 6x + 3h $$

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

Study Guide - Practice Questions

Study Guide - Flashcards