Q: Which of the following is the correct expression for the double angle identity for cosine?

$$\cos(2\theta) = 2\cos^2$\theta - 1$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 2

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/3}$$

Question 3

Which of the following is the correct expression for the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$?

Accepted Answer

$$\frac{f(4) - f(1)}{4 - 1} = \frac{16 - 1}{3} = 5$$

Question 4

Which of the following is the correct transformation for $$f(x) = x^2$ to g(x$$) = $$(x-2)^2 + 3$?

Accepted Answer

Shift right by 2 units and up by 3 units

Question 5

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

Accepted Answer

$$2x^2 + 1$

Question 6

Which of the following is the correct inverse of $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+5}{3}$$

Question 7

A pharmaceutical company models the concentration of a drug in the bloodstream by $$C(t) = 50e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) = 50e$$^{-1}$$ \approx 18.4$$

Question 8

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

Accepted Answer

$$x = 32$$

Question 9

Which of the following is the correct value for $$\sin(\frac{\pi}{6})$$?

Accepted Answer

$$\frac{1}{2}$$

Question 10

A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?

Accepted Answer

$$5$$

Question 11

Which of the following is the correct law of sines?

Accepted Answer

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

Question 12

Which of the following is the correct law of cosines?

Accepted Answer

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$ \cos C$$

Question 13

Which of the following is the correct expression for the sum of angles identity for sine?

Accepted Answer

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

Question 14

Which of the following is the correct value for $$\cos(\frac{\pi}{3})$$?

Accepted Answer

$$\frac{1}{2}$$

Question 15

Which of the following is the correct expression for the double angle identity for cosine?

Accepted Answer

$$\cos(2	heta) = 2\cos^2$	heta - 1$$

Question 16

Which of the following is the correct polar coordinate for the point $$(x, y) = (1, \sqrt{3})$$?

Accepted Answer

$$(2, \frac{\pi}{3})$$

Question 17

Which of the following is the correct solution to $$e^{x} = 7$?

Accepted Answer

$$x = \ln 7$$

Question 18

Which of the following is the correct expression for the graph of $$y = 3 \sin(x)$$?

Accepted Answer

Amplitude is $$3$$, period is $$2\pi$$

Question 19

Which of the following is the correct solution to $$\cos(	heta) = 0$$ for $$0 \leq 	heta \u003c 2\pi$$?

Accepted Answer

$$	heta = \frac{\pi}{2}, \frac{3\pi}{2}$$

Precalculus Syllabus and Course Structure: Math 121 (Fall 2026)

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