Question 1

Which of the following numbers is NOT a real number?

Accepted Answer

$\sqrt{-1}$

Question 2

Simplify the expression: $2^3 	imes 2^4$.

Accepted Answer

$2^{7}$

Question 3

Evaluate the following using the order of operations: $3 + 6 	imes (5 + 4) \div 3 - 7$.

Accepted Answer

$11$

Question 4

Which of the following is the result of adding $3x^2 - 2x + 5$ and $-x^2 + 4x - 3$?

Accepted Answer

$2x^2 + 2x + 2$

Question 5

Factor the polynomial: $x^2 - 5x + 6$.

Accepted Answer

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

Question 6

Solve for $x$: $2x - 7 = 9$.

Accepted Answer

$x = 8$

Question 7

Simplify the expression: $\frac{3}{4} \div \frac{2}{5}$.

Accepted Answer

$\frac{15}{8}$

Question 8

Which of the following is equivalent to $\sqrt[3]{x^6}$?

Question 9

Rewrite $16^{3/4}$ using radical notation.

Accepted Answer

$\sqrt[4]{16^3}$

Question 10

A chemist mixes two solutions: $x$ liters of a $20\%$ acid solution and $y$ liters of a $50\%$ acid solution to obtain $10$ liters of a $30\%$ acid solution. Which equation represents the total amount of acid in the final mixture?

Accepted Answer

$0.2x + 0.5y = 3$

Question 11

Which of the following is a rational number?

Accepted Answer

$\frac{2}{3}$

Question 12

If $f(x) = x^2 - 4x + 3$, what is $f(2)$?

Accepted Answer

$-1$

Question 13

Simplify: $\left(\frac{27x^6}{3x^2}\right)^{1/3}$.

Question 14

Which of the following is the correct factorization of $4x^2 - 9$?

Accepted Answer

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

Question 15

A patient is prescribed a medication that requires the dosage to be halved every 6 hours. If the initial dose is $80$ mg, what is the dose after 18 hours?

Accepted Answer

$10$ mg

Question 16

Which of the following is equivalent to $\frac{5x^2y}{10xy^2}$?

Accepted Answer

$\frac{x}{2y}$

Question 17

If $a = 2$ and $b = -3$, evaluate $a^2 + 2ab + b^2$.

Accepted Answer

$1$

Question 18

Which of the following expressions is equivalent to $\sqrt{50}$?

Accepted Answer

$2\sqrt{5}$

Question 19

Simplify: $\frac{2}{x} + \frac{3}{x}$.

Accepted Answer

$\frac{5}{x}$

Question 20

Which of the following is the solution to $x^2 = 25$?

Accepted Answer

$x = 5$ or $x = -5$

Fundamental Concepts in the Real Number System

Study Guide - Practice Questions

Study Guide - Flashcards