Question 1

Which of the following correctly describes the union of two sets $$A$$ and $$B$$?

Accepted Answer

The set of all elements that are in $$A or$$ $$B (or $$both).

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 required is $$500 mg$$, which equation represents this scenario?

Accepted Answer

$$x + y = 500$$

Question 3

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

Accepted Answer

$$5\sqrt{2} + 2\sqrt{2} = 7\sqrt{2}$$

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 is tracking the population growth of bacteria, which doubles every hour. If the initial population is $$P_0$$, what is the population after $$t$$ hours?

Accepted Answer

$$P_0$$ \cdot 2^t$$

Question 6

Which of the following is NOT a function?

Accepted Answer

A relation where an input is paired with two different outputs.

Question 7

Solve the system of equations: $$\begin{cases} 2x + 3y = 12 \ x - y = 1 \end{cases}$$

Accepted Answer

Question 8

A chemical reaction requires mixing two solutions in a ratio described by the equation $$\frac{x}{y} = 4. If$$ $$y = 10 mL$$, how much of solution $$x is $$needed?

Accepted Answer

$$x = 40 mL$$

Question 9

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

Accepted Answer

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

Question 10

A medical researcher models the spread of a virus using the exponential function $$N(t) = N_0$ e$$^{kt}$$. If N_0$ = 100$$, $$k = 0.05$$, and $$t = 10$$, what is the population size after 10 days?

Accepted Answer

$$N(10) = 100 e$$^{0.5}$$

Question 11

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 12

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 1$

Question 13

A company wants to expand its product line. The number of ways to choose 3 products from 10 is given by:

Accepted Answer

$$\binom{10}{3}$$

Question 14

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

Accepted Answer

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

Question 15

Which of the following is the correct definition of a complex number?

Accepted Answer

A number of the form $$a + bi$$, where $$a$$ and $$b$$ are real numbers and $$i^2 = -1$

Question 16

A sequence is defined by $$a_n = 3n + 2. $$What is the 5th term of the sequence?

Accepted Answer

$$a_5 = 17$

Question 17

Which of the following is the correct solution to the logarithmic equation $$\log_{2}(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 18

A circle is defined by the equation $$(x - 2)^2$ + (y + 3)^2$ = 16. $$What is the radius of the circle?

Accepted Answer

$$4$$

College Algebra Syllabus & Core Concepts Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard