Question 1

Convert $18^{\circ}$ to radians (in terms of $\pi$).

Accepted Answer

$\frac{\pi}{12}$

Question 2

Find the value of $\sin^{-1}\left(\frac{1}{2}\right)$.

Accepted Answer

$\frac{\pi}{6}$

Question 3

What is the amplitude, period, and phase shift of $y = 2\sin\left(4x + \frac{\pi}{3}\right)$?

Accepted Answer

Amplitude: $2$, Period: $\frac{\pi}{2}$, Phase shift: $-\frac{\pi}{12}$

Question 4

For the function $f(x) = \frac{1}{x-2}$, what is the domain?

Accepted Answer

$x 
eq 2$

Question 5

Given $f(x) = x^2$ and $g(x) = \sqrt{x}$, what is the domain of $f \circ g$?

Accepted Answer

$x \geq 0$

Question 6

Consider $f(x) = \log_2(x-3)$. What is the domain of $f$?

Accepted Answer

$x > 3$

Question 7

Evaluate $\ln\left( x^2 - \sqrt{3}x + 1 \right)$ as a sum of logarithms with powers as factors.

Accepted Answer

$\ln(x^2) + \ln(1 - \frac{\sqrt{3}x}{x^2} + \frac{1}{x^2})$

Question 8

Solve $\log_3(x^2 - 4) = 2$.

Accepted Answer

$x = 5, x = -5$

Question 9

Solve $5^{2x} = 125$.

Accepted Answer

$x = \frac{3}{2}$

Question 10

A polynomial that satisfies degree 3 and zeros 1 and 4 is:

Accepted Answer

$a(x-1)^2(x-4)$

Question 11

Find the domain of $f(x) = \frac{1}{x^2 - 4x + 3}$.

Accepted Answer

$x 
eq 1, x 
eq 3$

Question 12

Determine whether $f(x) = x^3 - 4x$ is even, odd, or neither.

Accepted Answer

Odd

Question 13

Suppose the quantity supplied $q$ and quantity demanded $D$ of baseball caps at price $p$ are given by $q = 2p + 100$ and $D = 400 - 3p$. What is the equilibrium price?

Accepted Answer

$p = 60$

Question 14

An object is traveling around a circle with a radius of 100 meters. If it is 24 seconds per revolution, what is the linear speed?

Accepted Answer

$\frac{100\pi}{12}$ m/s

Question 15

A radioactive substance decays at a rate $A = A_0e^{-kt}$. If 80% decays in 5 hours, what is the value of $k$?

Accepted Answer

$k = \frac{\ln 0.2}{5}$

Question 16

Graph $y = 4\sin(2x + \frac{\pi}{2})$ and identify the phase shift.

Accepted Answer

Phase shift: $-\frac{\pi}{4}$

Precalculus Semester 1 Exam Review (Chapters 1–6): Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards