Q: A company’s demand function is given by $p = 50 - 2x$, where $p$ is the price per unit and $x$ is the number of units sold. What is the total revenue $R$ when 10 units are sold?

$R = (50 - 2 \times 10) \times 10 = 300$

Q: Given the cost function $C(x) = 5x + 200$, what is the average cost per unit when 20 units are produced?

$C = \frac{5 \times 20 + 200}{20} = 15$

Q: Which of the following is the correct application of the quadratic formula to solve $2x^2 - 4x - 6 = 0$?

$x = \frac{4 \pm \sqrt{(-4)^2 - 4 \times 2 \times (-6)}}{2 \times 2}$

Q: Which of the following is the correct way to rationalize the denominator of $\frac{5}{\sqrt{3}}$?

$\frac{5}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{5\sqrt{3}}{3}$

Q: If $f(x) = x^2 - 4x + 7$, what is $f(3)$?

$f(3) = 3^2 - 4 \times 3 + 7 = 2$

Question 1

A company’s demand function is given by $p = 50 - 2x$, where $p$ is the price per unit and $x$ is the number of units sold. What is the total revenue $R$ when 10 units are sold?

Accepted Answer

$R = (50 - 2 	imes 10) 	imes 10 = 300$

Question 2

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

Accepted Answer

$(x - 4)(x + 4)$

Question 3

Given the cost function $C(x) = 5x + 200$, what is the average cost per unit when 20 units are produced?

Accepted Answer

$C = \frac{5 	imes 20 + 200}{20} = 15$

Question 4

Simplify the expression $\frac{2x^2y}{4xy^2}$ to lowest terms.

Accepted Answer

$\frac{x}{2y}$

Question 5

If $x^2 = 25$, what are the possible values of $x$?

Accepted Answer

$x = \pm 5$

Question 6

Which of the following is equivalent to $\frac{a}{b} \div \frac{c}{d}$?

Accepted Answer

$\frac{ad}{bc}$

Question 7

Find the slope of the line passing through the points $(2, 5)$ and $(6, 13)$.

Accepted Answer

$m = \frac{13 - 5}{6 - 2} = 2$

Question 8

Which of the following is the correct application of the quadratic formula to solve $2x^2 - 4x - 6 = 0$?

Accepted Answer

$x = \frac{4 \pm \sqrt{(-4)^2 - 4 	imes 2 	imes (-6)}}{2 	imes 2}$

Question 9

A business has a revenue function $R(x) = 20x$ and a cost function $C(x) = 8x + 120$. What is the profit function $P(x)$?

Accepted Answer

$P(x) = 20x - (8x + 120) = 12x - 120$

Question 10

Which of the following is the correct way to rationalize the denominator of $\frac{5}{\sqrt{3}}$?

Accepted Answer

$\frac{5}{\sqrt{3}} 	imes \frac{\sqrt{3}}{\sqrt{3}} = \frac{5\sqrt{3}}{3}$

Question 11

Given the function $f(x) = \frac{1}{x-2}$, what is the domain of $f(x)$?

Accepted Answer

$x 
eq 2$

Question 12

Which of the following is the correct factorization of $x^2 + 6x + 9$?

Accepted Answer

$(x + 3)^2$

Question 13

A company’s supply and demand functions are $S(x) = 2x + 10$ and $D(x) = 50 - x$. Find the equilibrium quantity $x_0$ where supply equals demand.

Accepted Answer

$2x + 10 = 50 - x \implies 3x = 40 \implies x_0 = \frac{40}{3}$

Question 14

Simplify the expression $\frac{3x^2y^3}{9xy}$.

Accepted Answer

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

Question 15

If $f(x) = x^2 - 4x + 7$, what is $f(3)$?

Accepted Answer

$f(3) = 3^2 - 4 	imes 3 + 7 = 2$

Question 16

Which of the following is the correct simplification of $\frac{2}{\sqrt{5} - 1}$?

Accepted Answer

$\frac{2(\sqrt{5} + 1)}{(\sqrt{5} - 1)(\sqrt{5} + 1)} = \frac{2(\sqrt{5} + 1)}{5 - 1} = \frac{2(\sqrt{5} + 1)}{4}$

Question 17

Which of the following is NOT a valid property of exponents?

Accepted Answer

$x^n + x^m = x^{n+m}$

Question 18

A company’s cost function is $C(x) = 4x + 100$ and its revenue function is $R(x) = 10x$. What is the break-even quantity?

Accepted Answer

$4x + 100 = 10x \implies 6x = 100 \implies x = \frac{100}{6}$

Question 19

Which of the following is the correct point-slope form for the line passing through $(1, 2)$ with slope $m = -3$?

Accepted Answer

$y - 2 = -3(x - 1)$

College Algebra: Essential Formulas and Concepts for Business Applications

Study Guide - Practice Questions

Study Guide - Flashcards