Q: A ladder leans against a wall forming a $$60^{\circ}$$ angle with the ground. If the ladder is $$10$$ feet long, how high up the wall does it reach? (Use $$\sin 60$$^{\circ}$$ = \dfrac{\sqrt{3}}{2})$$

$$10 \times \dfrac{\sqrt{3}}{2} = 5\sqrt{3}$$ feet

Question 1

Which of the following expressions simplifies to $$2x - 3$$?

Accepted Answer

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

Question 2

Given the function $$f(x) = x^2$ - 4x + 3$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 3

If $$g(x) = \sqrt{x-2}$$, what is the range of $$g(x)$$?

Accepted Answer

$$g(x) \geq 0$$

Question 4

Which of the following is the equation of a line passing through the point $$(2, 5)$$ with slope $$-3$$?

Accepted Answer

$$y = -3x + 11$$

Question 5

A function $$h(x) is $$defined as $$h(x) = x^3$. Which of the following statements is true?

Accepted Answer

$$h(x) is an $$odd function

Question 6

Convert $$150^{\circ} to $$radians.

Accepted Answer

$$\dfrac{5\pi}{6}$$

Question 7

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

Accepted Answer

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

Question 8

Given $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 1$

Question 9

A ladder leans against a wall forming a $$60^{\circ}$$ angle with the ground. If the ladder is $$10$$ feet long, how high up the wall does it reach? (Use $$\sin 60$$^{\circ}$$ = \dfrac{\sqrt{3}}{2})$$

Accepted Answer

$$10 	imes \dfrac{\sqrt{3}}{2} = 5\sqrt{3}$$ feet

Question 10

Which of the following is the solution set for $$2x^2 - 8 = 0$?

Accepted Answer

$$x = 2, x = -2$$

Question 11

If $$f(x) = |x - 3|$$, which of the following describes the graph of $$f(x)$$?

Accepted Answer

A V-shaped graph with vertex at $$(3, 0)$$

Question 12

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 1)$$

Question 13

Which of the following is the period of the function $$f(x) = \sin(2x)$$?

Accepted Answer

$$\pi$$

Question 14

If $$	an 	heta = \dfrac{3}{4}$$ and $$	heta is in $$the first quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$\dfrac{3}{5}$$

Question 15

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 16

A car rental company charges a flat fee of $$\20$ plus $$\$$0.15$$ per mile driven. Which of the following equations represents the total cost $$C$$ for $$m$$ miles driven?

Accepted Answer

$$C = 0.15m + 20$$

Question 17

Which of the following is the solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 18

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

Accepted Answer

$$(x + 1)^2$

Question 19

Which of the following is the correct solution to $$\sin x = \dfrac{1}{2}$$ for $$x in$$ $$[0, 2\pi]$$?

Accepted Answer

$$x = \dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

Precalculus Unit 1: Foundations, Functions, and Trigonometry Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards