Question 1

Solve the following linear equation for $$x$$: $$5x - 3 = 2x + 9.$$

Accepted Answer

$$x = 4$$

Question 2

Which of the following is the solution to the inequality $$2x + 7 \u003c 15$$?

Accepted Answer

$$x \u003c 4$$

Question 3

What is the solution to the absolute value equation $$|3x - 5| = 7$$?

Accepted Answer

$$x = 4,\ x = -\frac{2}{3}$$

Question 4

Given the points $$(2, 5)$$ and $$(6, 13)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = 2$$

Question 5

Which of the following relations is a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4)\}$$

Question 6

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

Accepted Answer

$$16$$

Question 7

Solve the system of equations: $$x + y = 7$$ and $$x - y = 1.$$

Accepted Answer

$$x = 4,\ y = 3$$

Question 8

Which of the following is the result of multiplying the polynomials $$(x + 2)(x - 3)$$?

Accepted Answer

$$x^2 - x - 6$

Question 9

Factor the trinomial $$x^2 + 7x + 12$.

Accepted Answer

$$(x + 3)(x + 4)$$

Question 10

Simplify the rational expression $$\frac{x^2$ - 9}{x + 3}.$$

Accepted Answer

$$x - 3$$

Question 11

Solve the radical equation $$\sqrt{x + 5} = 4.$$

Accepted Answer

$$x = 11$$

Question 12

If $$y$$ varies directly as $$x$$ and $$y = 10$$ when $$x = 2$$, what is $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 25$$

Question 13

What is the standard form of the complex number $$3 - 4i$$?

Accepted Answer

$$3 - 4i$$

Question 14

Evaluate $$i^5$$ where $$i is $$the imaginary unit.

Accepted Answer

$$i$$

Question 15

A chemist mixes a solution with a concentration of $$x$$ grams per liter. If the total amount of solute is $$30$$ grams and the volume is $$5$$ liters, what is $$x$$?

Accepted Answer

$$x = 6$$

Question 16

Which of the following is NOT a polynomial?

Accepted Answer

$$\frac{1}{x}$$

Question 17

Simplify the radical expression $$\sqrt{50}.$$

Accepted Answer

$$5\sqrt{2}$$

Question 18

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

Accepted Answer

$$4$$

Question 19

Which of the following equations represents a line parallel to $$y = 2x + 5$$?

Accepted Answer

$$y = 2x - 3$$

Question 20

A medical researcher is analyzing the growth of bacteria, which doubles every hour. If the initial population is $$P_0 = 100$, what is the population after 3$ hours?

Accepted Answer

$$800$$

Intermediate Algebra Syllabus and Course Competencies Study Guide

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