Question 1

Simplify the expression $$\left( \dfrac{a}{b^4$} \$$right)^5$$ \left( \dfrac{b}{3a} \$$right)^2$$ and eliminate any negative exponents.

Accepted Answer

$$\dfrac{a^3$}{9b$$^{18}$$}$$

Question 2

Given the expression $$\dfrac{2 - \dfrac{y}{x}}{2 + \dfrac{y}{x}}$$, simplify it as much as possible.

Accepted Answer

$$\dfrac{2x - y}{2x + y}$$

Question 3

Rationalize the denominator and simplify: $$\dfrac{1}{\sqrt{x} - \sqrt{y}}$$

Accepted Answer

$$\dfrac{\sqrt{x} + \sqrt{y}}{x - y}$$

Question 4

Rationalize the numerator and simplify: $$\dfrac{\sqrt{5 + h} - \sqrt{2}}{h + 3}$$

Accepted Answer

$$\dfrac{5 + h - 2}{(h + 3)(\sqrt{5 + h} + \sqrt{2})}$$

Question 5

Write the point-slope equation for the line through the point $$P(2, 5)$$ with slope $$m = -2.$$

Accepted Answer

$$y - 5 = -2(x - 2)$$

Question 6

Find the equation of the line passing through the points $$(3, 2)$$ and $$(-1, 4).$$

Accepted Answer

$$y = -\dfrac{1}{2}x + \dfrac{7}{2}$$

Question 7

Given the line $$2x - 5y = 12$$, what is its slope and $$y-$$intercept?

Accepted Answer

Slope $$= \dfrac{2}{5}$$, $$y-$$intercept $$= -\dfrac{12}{5}$$

Question 8

A patient receives a drug with an initial amount of 18 mg. If the amount increases by 0.3 mg per minute, which formula gives the amount $$A$$ after $$t$$ minutes?

Accepted Answer

$$A = 18 + 0.3t$$

Question 9

For the quadratic function $$f(x) = x^2$ + 6x + 8$$, what is the vertex?

Accepted Answer

$$(-3, -1)$$

Question 10

What are the $$x-$$intercepts of $$f(x) = x^2$ + 6x + 8$$?

Accepted Answer

$$x = -2,\ x = -4$$

Question 11

Factor the quadratic $$x^2 - 9x + 20$.

Accepted Answer

$$(x - 4)(x - 5)$$

Question 12

Simplify the expression $$\dfrac{x$$^{4/3}$$y^{1/2}$$}{$$x^{5/3}y$$^{-5/2}$$}.$$

Accepted Answer

$$\dfrac{y^3$}{x}$$

Question 13

Given $$g(x) = -4x^2$ + 4x + 3$$, what is the $$y-$$intercept?

Accepted Answer

$$3$$

Question 14

Which of the following is the correct factorization of $$5x^2 - 12x + 4$?

Accepted Answer

$$(5x - 2)(x - 2)$$

Question 15

A medication is administered with an initial amount of 18 mg and decreases by 0.3 mg per minute. What is the formula for the amount $$A$$ after $$t$$ minutes?

Accepted Answer

$$A = 18 - 0.3t$$

Question 16

For $$m(x) = 2x^2$ - 4x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 17

Which of the following is the correct factorization of $$12x^2 + 11x - 15$?

Accepted Answer

$$(3x + 5)(4x - 3)$$

Question 18

A biologist is studying a population that grows linearly. If the population is 18 at time $$t = 0$$ and increases by 0.3 per minute, what is the population after 10 minutes?

Accepted Answer

$$21$$

Question 19

Given the quadratic $$g(x) = -4x^2$ + 4x + 3$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = -0.5,\ x = 1.5$$

Algebraic Foundations and Linear/Quadratic Functions: Practice Exam Study Guide

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