Question 1

Which of the following correctly represents the union of sets $$A = \{1, 2, 3\}$$ and $$B = \{3, 4, 5\}$$?

Accepted Answer

$$\{1, 2, 3, 4, 5\}$$

Question 2

A pharmaceutical company needs to mix two solutions. Solution A contains $$x mg of a $$drug, and Solution B contains $$y mg. If $$the total amount after mixing is $$z mg$$, which equation best represents this scenario?

Accepted Answer

$$x + y = z$$

Question 3

Simplify the expression $$\sqrt{50} + \sqrt{8}.$$

Accepted Answer

$$7\sqrt{2}$$

Question 4

Which of the following is the correct solution to the quadratic equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 5

A biologist models population growth with the exponential function $$P(t) = 1000 \cdot 2^t. $$What is the population after 3 hours?

Accepted Answer

$$8000$$

Question 6

Which of the following is the correct simplification of the rational expression $$\frac{x^2$ - 9}{x - 3}$$ for $$x 
eq 3$$?

Accepted Answer

$$x + 3$$

Question 7

A medical researcher needs to solve the system of equations for drug concentrations: $$x + y = 10$$ and $$x - y = 2. $$What are the values of $$x$$ and $$y$$?

Accepted Answer

$$x = 6$$, $$y = 4$$

Question 8

Which of the following is the correct definition of a function?

Accepted Answer

A relation in which each input has exactly one output.

Question 9

If $$f(x) = 2x + 1$$, what is $$f(3)$$?

Accepted Answer

$$7$$

Question 10

A chemical reaction follows the equation $$C = 5e$$^{0.2t}$$, where C$ is concentration and t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$$C = 5e$$^{1}$$ \approx 13.59$$

Question 11

Which of the following is the correct solution to the linear inequality $$2x - 3 \u003c 7$$?

Accepted Answer

$$x \u003c 5$$

Question 12

A business uses the quadratic function $$R(x) = -2x^2$ + 12x to $$model revenue, where $$x is $$the number of units sold. What is the maximum revenue, and at how many units is it achieved?

Accepted Answer

Maximum revenue is $$36 at$$ $$x = 3$$ units.

Question 13

Which of the following is the correct simplification of $$\frac{2x^2$ - 8}{x^2$ - 4}$$?

Accepted Answer

$$\frac{2(x - 2)}{x + 2}$$

Question 14

Which of the following is the correct solution to the exponential equation $$3^x = 81$$?

Accepted Answer

$$x = 4$$

Question 15

A patient’s medication level is modeled by $$M(t) = 50e$$^{-0.1t}$$. What is the medication level after 10 hours?

Accepted Answer

$$M(10) = 50e$$^{-1}$$ \approx 18.39$$

Question 16

Which of the following is the correct solution to the logarithmic equation $$\log$$_{2}$$x = 5$$?

Accepted Answer

$$x = 32$$

Question 17

A company wants to expand its product line. The number of possible ways to select 3 products from a list of 10 is:

Accepted Answer

$$\binom{10}{3} = 120$$

Question 18

Which of the following is the correct expansion of $$(x + 2)^3$ using the Binomial Theorem?

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 19

Which of the following is the correct solution to the absolute value equation $$|x - 4| = 7$$?

Accepted Answer

$$x = 11 or$$ $$x = -3$$

College Algebra Syllabus & Core Concepts Study Guide

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