Question 1

Evaluate the following expression using the order of operations: $$3 + 4 	imes 2^2$ - (6 \div 3). $$What is the result?

Accepted Answer

$$15$$

Question 2

Given $$a = -2$$ and $$b = 5$$, evaluate the expression $$2a^2 - 3b + 4$.

Accepted Answer

$$-19$$

Question 3

Factor the expression completely: $$x^2 - 9x + 20$.

Accepted Answer

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

Question 4

Simplify the rational exponent expression: $$\$$left(27x^6$$\$$right)^{1/3}$$.

Accepted Answer

$$3x^2$$

Question 5

A store reduces the price of a laptop by $$15\%$$ during a sale. If the original price was $$\800$, what is the sale price?

Accepted Answer

$$\680$

Question 6

Solve the absolute value inequality: $$|2x - 5| \u003c 7.$$

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 7

Divide the complex numbers: $$\dfrac{3 + 4i}{1 - 2i}.$$

Accepted Answer

$$-1 + 2i$$

Question 8

Solve the polynomial equation by factoring: $$x^3$$ - $$4x^2 - 21x = 0$.

Accepted Answer

$$x = 0, x = -3, x = 7$$

Question 9

Solve the rational equation: $$\dfrac{2}{x} + 1 = 3.$$

Accepted Answer

$$x = 2$$

Question 10

Solve the radical equation: $$\sqrt{x + 5} = x - 1.$$

Accepted Answer

$$x = 2$$

Question 11

Find the midpoint of the segment joining the points $$(2, 5)$$ and $$(8, -3).$$

Accepted Answer

$$(5, 1)$$

Question 12

Find the distance between the points $$(-1, 2)$$ and $$(3, -2).$$

Accepted Answer

$$\sqrt{32}$$

Question 13

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

Accepted Answer

$$y = -3x + 5$$

Question 14

Find the domain of the function $$f(x) = \dfrac{1}{x - 4}.$$

Accepted Answer

$$x 
eq 4$$

Question 15

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, find (f$$ \circ g)(2)$$.

Accepted Answer

$$9$$

Question 16

Find the vertex of the parabola $$y = x^2$ - 6x + 8.$$

Accepted Answer

$$(3, -1)$$

Question 17

Use the Rational Zero Theorem to list all possible rational zeros of $$f(x) = 2x^3$ - 3x^2$ + x - 6.$$

Accepted Answer

$$\pm1, \pm2, \pm3, \pm6, \pm\dfrac{1}{2}, \pm\dfrac{3}{2}$$

Question 18

Use Descartes’s Rule of Signs to predict the number of positive real zeros for $$f(x) = x^3$ - 4x^2$ + 5x - 2.$$

Accepted Answer

$$2 or$$ $$0$$

Question 19

Solve the rational inequality: $$\dfrac{x - 2}{x + 1} \u003e 0.$$

Accepted Answer

$$x  2$$

Question 20

Find the inverse of the function $$f(x) = 3x - 7.$$

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x + 7}{3}$$

Precalculus Study Guide: Key Concepts and Problem Types

Study Guide - Practice Questions