Question 1

Which of the following is NOT a property of real numbers?

Accepted Answer

The Exponential Property: $$a^b = b^a$$ for all real numbers $$a$$ and $$b$$

Question 2

Which set contains both rational and irrational numbers?

Accepted Answer

Set of real numbers

Question 3

Simplify the expression $$\sqrt{x^6$ y^4$}$$ for $$x, y \geq 0.$$

Accepted Answer

$$x^3$$ $$y^2$$

Question 4

Which of the following is the result of rationalizing the denominator of $$\frac{2}{\sqrt{5}}$$?

Accepted Answer

$$\frac{2\sqrt{5}}{5}$$

Question 5

Which of the following is a polynomial in $$x$$?

Accepted Answer

$$\frac{3x^3$ - 5x^2$}{10}$$

Question 6

Subtract $$(4x^2y + 6x - 3$$)$$ from (3x^2$y - 2x + 1)$$ and simplify.

Accepted Answer

$$-x^2y - 8x + 4$

Question 7

Which of the following is the factored form of $$x^2 - 9$?

Accepted Answer

$$(x + 3)(x - 3)$$

Question 8

What is the result of dividing $$x^3$$ + $$2x^2 + x$ by x$?

Accepted Answer

$$x^2 + 2x + 1$

Question 9

Simplify the fraction $$\frac{x^2$ - x - 6}{x^2$ + 7x + 12}$$ for $$x 
eq -3.$$

Accepted Answer

$$\frac{x - 3}{x + 4}$$

Question 10

Which operation does NOT always produce equivalent equations?

Accepted Answer

Multiplying both sides by an expression involving the variable

Question 11

Solve the linear equation $$5x - 6 = 3x.$$

Accepted Answer

$$x = 3$$

Question 12

Which of the following is a literal equation?

Accepted Answer

$$(a + c)x + x^2$ = (x + a)^2$

Question 13

Solve the fractional equation $$\frac{5}{x - 4} = \frac{6}{x - 3}.$$

Accepted Answer

$$x = 9$$

Question 14

Solve the radical equation $$\sqrt{y - 3} - \sqrt{y} = -3.$$

Accepted Answer

$$y = 4$$

Question 15

Which of the following is the quadratic formula for the roots of $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 16

Which of the following is the factored form of $$x^2 + 8x + 16$?

Accepted Answer

$$(x + 4)^2$

Question 17

If $$x^2 = -1$, what is the solution for x$ in the set of real numbers?

Accepted Answer

No real solution

Question 18

Which of the following is the result of $$\sqrt{(-3)^2$}$$?

Accepted Answer

$$3$$

Question 19

Which of the following is the result of $$x^0$$ for $$x 
eq 0$$?

Accepted Answer

$$1$$

Question 20

Which of the following is the result of $$\frac{a}{b} \cdot \frac{c}{d}$$?

Accepted Answer

$$\frac{ac}{bd}$$

Review of Algebra: Fundamental Concepts for Precalculus

Study Guide - Practice Questions