Q: Which of the following is the correct scientific notation for the number $0.00056$?

$\displaystyle 5.6 \times 10^{-4}$

Question 1

Which of the following is the correct simplification of the expression $\displaystyle \frac{2x^2 - 8}{4x}$ for $x 
eq 0$?

Accepted Answer

$\displaystyle \frac{x-2}{2}$

Question 2

A chemist is mixing two solutions. The concentration of the first is $\displaystyle \frac{3x}{x+2}$ and the second is $\displaystyle \frac{2x}{x-2}$. What is the least common denominator (LCD) when adding these two rational expressions?

Accepted Answer

$\displaystyle (x+2)(x-2)$

Question 3

Which of the following values must be excluded from the domain of $\displaystyle \frac{x^2-9}{x^2-4x+3}$?

Accepted Answer

$\displaystyle x=1$ and $x=3$

Question 4

Simplify the following expression using the properties of exponents: $\displaystyle (2x^3y^2)^2$

Accepted Answer

$\displaystyle 4x^6y^4$

Question 5

Which property of real numbers justifies the following equation: $\displaystyle 5 + (3 + 2) = (5 + 3) + 2$?

Accepted Answer

Associative Property of Addition

Question 6

A biologist is measuring the distance between two points on a petri dish, located at $a = 2.5$ cm and $b = 7.8$ cm. What is the distance between the points?

Accepted Answer

$\displaystyle 5.3$ cm

Question 7

Simplify the following radical expression: $\displaystyle \sqrt{50} + 2\sqrt{8}$

Accepted Answer

$\displaystyle 5\sqrt{2} + 4\sqrt{2} = 9\sqrt{2}$

Question 8

Which of the following is the correct factorization of $\displaystyle x^2 - 16$?

Accepted Answer

$\displaystyle (x-4)(x+4)$

Question 9

A medical researcher is analyzing the growth of bacteria, which doubles every hour. If the initial population is $P_0$, which expression represents the population after $t$ hours?

Accepted Answer

$\displaystyle P_0 \cdot 2^t$

Question 10

Simplify the following expression: $\displaystyle \frac{3x^4y^2}{6x^2y}$

Accepted Answer

$\displaystyle \frac{x^2y}{2}$

Question 11

Which of the following is the correct scientific notation for the number $0.00056$?

Accepted Answer

$\displaystyle 5.6 	imes 10^{-4}$

Question 12

Which of the following is the correct simplification of $\displaystyle (x^2y^3)^4$?

Accepted Answer

$\displaystyle x^8y^{12}$

Question 13

A factory produces $n$ items per hour. The total number of items produced in $t$ hours is modeled by which algebraic expression?

Accepted Answer

$\displaystyle n \cdot t$

Question 14

Which of the following is the correct factorization of $\displaystyle x^3 + 8$?

Accepted Answer

$\displaystyle (x+2)(x^2-2x+4)$

Question 15

Simplify the complex rational expression: $\displaystyle \frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x}}$ for $x 
eq 0, y 
eq 0$.

Accepted Answer

$\displaystyle 1 + \frac{y}{x}$

Question 16

Which of the following is the correct simplification of $\displaystyle \sqrt{18} - \sqrt{8}$?

Accepted Answer

$\displaystyle 3\sqrt{2} - 2\sqrt{2} = \sqrt{2}$

Question 17

Which of the following is the correct result of multiplying $\displaystyle (x-3)(x+5)$?

Accepted Answer

$\displaystyle x^2 + 2x - 15$

Question 18

Which of the following is the correct simplification of $\displaystyle \frac{2x^2y^{-3}}{4x^{-1}y^2}$?

Accepted Answer

$\displaystyle \frac{x^3}{2y^5}$

Question 19

A student is asked to find the intersection of the sets $A = \{1,2,3,4\}$ and $B = \{3,4,5,6\}$. What is $A \cap B$?

Accepted Answer

$\displaystyle \{3,4\}$

Precalculus Fundamentals: Algebraic Expressions, Exponents, Radicals, Polynomials, and Rational Expressions

Study Guide - Practice Questions

Study Guide - Flashcards