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

$$x \u003e 3$$

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

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