Question 1

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

Accepted Answer

$$ -6 + 12i + 8i - 16i^2$ = -6 + 20i + 16 = 10 + 20i $$

Question 2

Solve the quadratic equation $$ x^2$ - 5x - 14 = 0  by $$factoring.

Accepted Answer

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

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 $$ 6x^2$ - x = 5 $$ using the quadratic formula.

Accepted Answer

$$ x = \frac{1 \pm \sqrt{121}}{12} $$

Question 5

An electric pass for a toll road costs $$30. The toll is normally 5.00 $$but is reduced by 30% for those who purchase the pass. Determine the minimum number of times the road must be used so that the electronic pass is a better deal.

Accepted Answer

$$ 12 $$ times

Question 6

Solve the absolute value equation $$ 2|x - 3| - 6 = 10 .$$

Accepted Answer

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

Question 7

Find and simplify the difference quotient for $$ f(x) = -2x^2$ + x - 1 .$$

Accepted Answer

$$ \frac{-2(x+h)^2$ + (x+h) - 1 - [-2x^2$ + x - 1]}{h} $$

Question 8

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

Accepted Answer

$$ y = x + 2 $$; $$ y -$$intercept is $$ 2 $$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

Center: $$ (-6, -1) $$, Radius: $$ 4 $$

Question 11

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

Accepted Answer

$$ 54 $$

Question 12

Solve the compound inequality $$ -11 \u003c 2x - 1 \u003c -5 .$$

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

$$ \sqrt{(12 - (-1))^2$ + (4 - 2)^2$} = \sqrt{169 + 4} = \sqrt{173} $$

Question 16

Solve the equation $$ (x - 4$$)^{3/2}$$ = 27 .$$

Accepted Answer

$$ x = 13 $$

Question 17

Given the points $$ (0, 1) $$ and $$ (5, 17) $$, write the equation of the line passing through these points. What is the $$ x -$$intercept?

Accepted Answer

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

Question 18

Solve the equation $$ x^3$ + x^2$ = 4x + 4 .$$

Accepted Answer

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

Question 19

Find and simplify the difference quotient for $$ f(x) = 3x^2$ + 7 .$$

Accepted Answer

$$ \frac{3(x+h)^2$ + 7 - [3x^2$ + 7]}{h} $$

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

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