Question 1

Evaluate the expression $$-x^2 - 5x$ for x = -4$.

Accepted Answer

$$-16 - 20 = -36$$

Question 2

Simplify the expression $$\left( \dfrac{a^2$ b^3$}{a^3$ b^2$} \$$right)^{-2}$$ using positive exponents only.

Accepted Answer

Question 3

Multiply and simplify: $$(5x + 4)(5x - 4). $$What special product formula is used?

Accepted Answer

$$25x^2 - 16$, difference of squares

Question 4

Multiply and simplify: $$\left( \sqrt{10x} - 9 \right) \sqrt{2x}.$$

Accepted Answer

$$\sqrt{20x^2$} - 9\sqrt{2x}$$

Question 5

Factor the polynomial by grouping: $$2xy - 3x - 10y + 15.$$

Accepted Answer

$$(2xy - 3x) - (10y - 15) = x(2y - 3) - 5(2y - 3) = (x - 5)(2y - 3)$$

Question 6

Simplify: $$\dfrac{16x - 12}{35} \div \dfrac{10}{3 - 4x} ($$Assume all denominators are nonzero).

Accepted Answer

$$\dfrac{(16x - 12)(3 - 4x)}{350}$$

Question 7

Simplify the complex rational expression: $$\dfrac{4 + \dfrac{1}{x^2$}}{1 + \dfrac{1}{x^2$}}.$$

Accepted Answer

$$\dfrac{4x^2$ + 1}{x^2$ + 1}$$

Question 8

How many liters of pure water should be mixed with a $$5-L $$solution of $$80\%$$ acid to produce a mixture that is $$70\%$$ water?

Accepted Answer

$$20 L$$

Question 9

Which of the following is the correct simplification of $$\dfrac{(2x^3$y^2)^2$}{4x^2$y}$$?

Accepted Answer

Question 10

A chemist needs to dilute a $$12\%$$ saline solution to a $$6\%$$ solution. If she has $$100 mL of $$the $$12\%$$ solution, how much pure water should she add?

Accepted Answer

$$100 mL$$

Question 11

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

Accepted Answer

$$2(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15$

Question 12

Which of the following is equivalent to $$\sqrt{50x^3$}$$?

Accepted Answer

$$5x\sqrt{2x}$$

Question 13

A rectangle has a length $$2x + 3$$ and width $$x - 1. $$What is the area in terms of $$x$$?

Accepted Answer

$$2x^2 + x - 3$

Question 14

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x + 3)(x - 3)$$

Question 15

If $$g(x) = \dfrac{1}{x}$$, what is $$g(2x)$$?

Accepted Answer

$$\dfrac{1}{2x}$$

Question 16

Which of the following is the solution to $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 17

Simplify: $$\dfrac{3x^2$y}{6xy^2$}.$$

Accepted Answer

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

Question 18

A car rental company charges a flat fee of $$\20$ plus $$\$$0.15$$ per mile. If a customer paid $$\50$, how many miles did they drive?

Accepted Answer

$$200$$ miles

Question 19

Which of the following is the correct simplification of $$\dfrac{(x^2$ - 4)}{(x + 2)}$$?

Accepted Answer

$$x - 2$$

Precalculus Exam Study Guide: Algebraic Expressions, Exponents, Factoring, and Mixture Problems

Study Guide - Practice Questions

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