Q: Solve for $$\theta$$: $$4 \sin \theta + 5 = 3$$

$$\theta = \arcsin(-\frac{1}{2})$$

Q: Which of the following is the correct solution to $$2\sin^2$ \theta - \sin \theta - 1 = 0$$?

$$\sin \theta = 1, \sin \theta = -\frac{1}{2}$$

Q: Which of the following is the correct solution to $$\sin \theta \cdot \sec \theta = \tan \theta$$?

True for all $$\theta$$ where defined

Q: Solve for $$\theta$$: $$\sqrt{2} \cos^2$ \theta - \cos \theta = 0$$

$$\cos \theta = 0, \cos \theta = \frac{1}{\sqrt{2}}$$

Question 1

What is the domain of the function $$H(x) = \frac{x^2$ - 27}{x^2$ - 5x + 6}$$?

Accepted Answer

$$x 
eq 2, x 
eq 3$$

Question 2

Which of the following describes the vertical asymptotes of $$R(x) = \frac{x^2$}{x^2$ - x - 6}$$?

Accepted Answer

$$x = 2, x = -3$$

Question 3

Given $$F(x) = \frac{x^3$ - 64}{x^2$ - 5x + 4}$$, which $$x-$$values are excluded from the domain?

Accepted Answer

$$x = 4, x = 1$$

Question 4

What is the horizontal asymptote of $$T(x) = \frac{2x^2$}{x^4$ - 81}$$?

Accepted Answer

$$y = 0$$

Question 5

Solve for $$x$$: $$\log_2$ (2x + 5) = 3$$

Accepted Answer

Question 6

If $$200 is invested at 10\%$$ compounded quarterly for $$\frac{3}{2}$$ years, what is the final amount? (Round to the nearest cent)

Accepted Answer

$$A = 232.30$$

Question 7

A population doubles every 21 months. If the current population is 30,000, what will it be in 3 years? (Assume continuous growth)

Accepted Answer

$$P \approx 113,137$$

Question 8

Solve for $$	heta$$: $$4 \sin 	heta + 5 = 3$$

Accepted Answer

$$	heta = \arcsin(-\frac{1}{2})$$

Question 9

Solve for $$x$$: $$e^{5x} + 4 = 13$

Accepted Answer

$$x = \frac{1}{5} \ln 9$$

Question 10

A pizza is baked at $$450^\circF $$and removed to a $$74^\circF $$room. After 5 minutes, the pizza is $$300^\circF. At $$what time can you eat the pizza if you want it to be $$125^\circF$$? (Use Newton's Law of Cooling)

Accepted Answer

After approximately 18 minutes

Question 11

Solve for $$x$$: $$\log_2$ (x+5) = 2x + 5$$

Accepted Answer

No real solution

Question 12

What is the present value needed to have $$5000$$ after $$\frac{13}{4}$$ years at $$8\%$$ compounded daily?

Accepted Answer

$$P \approx 3,047.13$$

Question 13

Solve for $$	heta$$: $$\sqrt{3} 	an 	heta - 1 = 0$$

Accepted Answer

$$	heta = \arctan(\sqrt{3})$$

Question 14

Which of the following is the correct solution to $$2\sin^2$ 	heta - \sin 	heta - 1 = 0$$?

Accepted Answer

$$\sin 	heta = 1, \sin 	heta = -\frac{1}{2}$$

Question 15

If $$60 is invested at 6\%$$ compounded continuously for 3 years, what is the final amount?

Accepted Answer

$$A = 71.97$$

Question 16

Solve for $$x$$: $$\frac{1}{2} \log_4$ x = 3 \log_4$ 5$$

Accepted Answer

$$x = 5^6$

Question 17

Which of the following is the correct domain for $$R(x) = \frac{7}{x^2$ - 36}$$?

Accepted Answer

$$x 
eq 6, x 
eq -6$$

Question 18

Which of the following is the correct solution to $$\sin 	heta \cdot \sec 	heta = 	an 	heta$$?

Accepted Answer

True for all $$	heta$$ where defined

Question 19

Given $$G(x) = \frac{2x}{(x+7)^2$}$$, what is the $$x-$$intercept?

Accepted Answer

$$x = 0$$

Question 20

Solve for $$	heta$$: $$\sqrt{2} \cos^2$ 	heta - \cos 	heta = 0$$

Accepted Answer

$$\cos 	heta = 0, \cos 	heta = \frac{1}{\sqrt{2}}$$

Precalculus Exam 1 Study Guide: Rational Functions, Logarithms, Exponentials, and Trigonometry

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