Question 1

Which of the following is the simplified form of $$ \sqrt{50} + 2\sqrt{8} $$?

Accepted Answer

$$ 7\sqrt{2} $$

Question 2

A chemist mixes two solutions. The first contains $$ 3x^2$y $$ and the second contains $$ 5xy^2$ . $$What is the product of these two expressions?

Accepted Answer

$$ 15x^3$y^3$$ $

Question 3

Factor the trinomial $$ x^2$ - 5x + 6 .$$

Accepted Answer

$$ (x - 2)(x - 3) $$

Question 4

Solve the rational equation $$ \frac{2}{x} + 1 = \frac{5}{x} $$ for $$ x .$$

Accepted Answer

$$ x = 3 $$

Question 5

A store increases the price of a $$ \50$$ $$ item by  20$$\% $. What is the new price?

Accepted Answer

$$ \60$$ $

Question 6

Multiply the complex numbers $$ (2 + 3i) $$ and $$ (4 - i) .$$

Accepted Answer

Question 7

Simplify $$ \sqrt{-16} + \sqrt{-9} .$$

Accepted Answer

$$ 7i $$

Question 8

Solve the quadratic equation $$ x^2$ - 4x - 5 = 0 $$ using any method.

Accepted Answer

$$ x = 5, x = -1 $$

Question 9

Given the graph of $$ f(x) $$, which of the following is always true about the domain?

Accepted Answer

The domain is all real numbers unless there are breaks or restrictions in the graph.

Question 10

Which function is odd?

Accepted Answer

$$ f(x) = x^3$ $$

Question 11

Find the slope of a line perpendicular to the line $$ y = 2x + 3 .$$

Accepted Answer

$$ -\frac{1}{2} $$

Question 12

The graph of $$ f(x) = x^2$  is $$translated 3 units right and 2 units up. What is the new equation?

Accepted Answer

$$ f(x) = (x - 3)^2$ + 2 $$

Question 13

Find the inverse of $$ f(x) = 2x + 5 .$$

Accepted Answer

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

Question 14

Find the distance between the points $$ (1, 2) $$ and $$ (4, 6) .$$

Accepted Answer

$$ 5 $$

Question 15

Which is the standard form of the equation of a circle with center $$ (2, -3) $$ and radius $$ 4 $$?

Accepted Answer

$$ (x - 2)^2$ + (y + 3)^2$ = 16 $$

Question 16

If $$ f(x) = \sqrt{x} $$, what is the domain of $$ f(x) $$?

Accepted Answer

$$ x \geq 0 $$

Question 17

Which value of $$ x $$ makes the denominator zero in $$ \frac{3}{x - 2} $$?

Accepted Answer

$$ x = 2 $$

Question 18

Which of the following is the equation of a line parallel to $$ y = -\frac{1}{3}x + 7 $$ and passing through $$ (0, 2) $$?

Accepted Answer

$$ y = -\frac{1}{3}x + 2 $$

Question 19

Given $$ f(x) = x^2$ $$ and $$ g(x) = \sqrt{x} $$, which graph is symmetric about the y-axis?

Accepted Answer

$$ f(x) = x^2$ $$

College Algebra Final Exam Blueprint: Key Topics and Study Guide

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