Question 1

Simplify the expression: $$-4\sqrt{20} + \sqrt{80} + \sqrt{45}$$

Accepted Answer

$$-\sqrt{5}$$

Question 2

Expand and simplify: $$(\sqrt{5} - 4)^2$

Accepted Answer

$$11 - 8\sqrt{5}$$

Question 3

Given the polynomial $$2x^3$$ - $$3x^2 + 4x + 3$$ - $$x(7x^2 - 6x + 2$$)$$, simplify the expression.

Accepted Answer

$$-5x^3$$ + $$3x^2 + 2x + 3$

Question 4

Rationalize the denominator: $$\dfrac{\sqrt{7}}{2 - \sqrt{7}}$$

Accepted Answer

$$\dfrac{7 + 2\sqrt{7}}{-7}$$

Question 5

Rationalize the denominator: $$\dfrac{\sqrt{3}}{\sqrt{2} + 3\sqrt{3}}$$

Accepted Answer

$$\dfrac{9}{25}$$

Question 6

Simplify the rational expression: $$\dfrac{2x + 10}{x^2$ - 25}$$

Accepted Answer

None of the above

Question 7

Factor the polynomial completely: $$x^2 - 4x - 32$

Accepted Answer

$$(x - 8)(x + 4)$$

Question 8

Factor the polynomial completely: $$3x^2 + 10x + 3$

Accepted Answer

$$(3x + 1)(x + 3)$$

Question 9

Solve for $$x$$: $$x(2x - 5) = (2x + 2)(x - 3)$$

Accepted Answer

$$x = -6$$

Question 10

Solve the quadratic equation: $$x^2 + 5x + 6 = 0$

Accepted Answer

$$x = -2 or$$ $$x = -3$$

Question 11

Solve for $$x$$: $$\sqrt{2x - 4} = 4$$

Accepted Answer

$$x = 10$$

Question 12

Solve the inequality: $$2x - 5 \u003e 3$$

Accepted Answer

$$x \u003e 4$$

Question 13

Solve the compound inequality: $$-15 \leq 9 - 4x \leq 25$$

Accepted Answer

$$-4 \leq x \leq 6$$

Question 14

Write the equation of a line passing through $$(1, 3)$$ with slope $$2.$$

Accepted Answer

$$y = 2x - 1$$

Question 15

Write the equation of a circle with center at $$(-3, 2)$$ and radius $$4.$$

Accepted Answer

$$(x + 3)^2$ + (y - 2)^2$ = 16$$

Question 16

Find the domain of the function $$f(x) = \sqrt{x - 2}.$$

Accepted Answer

$$x \geq 2$$

Question 17

Find the domain of the function $$g(x) = \dfrac{5}{x + 4}.$$

Accepted Answer

$$x 
eq -4$$

Question 18

A rectangular garden has a length that is 3 meters less than twice its width. If the area is $$665$$ square meters, what is the width?

Accepted Answer

$$w = 19.5$$

Question 19

Given $$f(x) = (x + 1)^2$ - 2$$, which transformation is applied to the graph of $$g(x) = x^2$ to obtain f(x$$)$$?

Accepted Answer

Shift left 1 unit and down 2 units

Question 20

A chemical solution's concentration $$C (in $$mol/L) is modeled by $$C(t) = \dfrac{5}{t + 4}$$, where $$t is $$time in hours. What is the concentration after 2 hours?

Accepted Answer

$$C(2) = 0.833$$

College Algebra Midterm Study Guidance (MATH 206)

Study Guide - Practice Questions

Study Guide - Flashcards