Q: Which of the following is the correct general solution to $$\tan 5\theta = -1$$?

$$\theta = -\frac{\pi}{20} + k\frac{\pi}{5}$$

Q: Which of the following is the correct general solution for $$\sin \theta = \frac{1}{2}$$?

$$\theta = \frac{\pi}{6} + 2k\pi or$$ $$\theta = \frac{5\pi}{6} + 2k\pi$$, $$k \in \mathbb{Z}$$

Q: Which of the following is the correct value for $$\sin(2\theta) in $$terms of $$\sin \theta$$ and $$\cos \theta$$?

$$\sin(2\theta) = 2 \sin \theta \cos \theta$$

Question 1

Which of the following correctly describes the set of all real numbers $$x$$ that satisfy $$|2x + 4| \u003c 1$$?

Accepted Answer

$$x \in (-5, -3)$$

Question 2

A pharmaceutical company needs to design a circular pill with a diameter of $$1.2 cm. $$What is the area of the pill in terms of $$	ext{cm}^2$$?

Accepted Answer

$$A = \pi 	imes 0.6^2$

Question 3

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - x$$

Question 4

A ladder leans against a wall and slides down while keeping contact with both the wall and the floor. The path traced by a point not at the ends of the ladder is:

Accepted Answer

An ellipse

Question 5

Which of the following is the correct general solution to $$	an 5	heta = -1$$?

Accepted Answer

$$	heta = -\frac{\pi}{20} + k\frac{\pi}{5}$$

Question 6

A function $$f(x) is $$defined as $$f(x) = \frac{1}{\sqrt{x-1}}. $$What is the natural domain of $$f$$?

Accepted Answer

$$x \in (1, \infty)$$

Question 7

A car wheel has a diameter of $$60 cm $$and the car moves at $$80 km/h. $$How many revolutions per minute does the wheel make? (Use $$\pi \approx 3.14)$$

Accepted Answer

$$\approx 710$$ rpm

Question 8

Which of the following is the correct binomial expansion for $$(a + b)^3$?

Accepted Answer

$$a^3$$ + $$3a^2b$$ + $$3ab^2$$ + $$b^3$$

Question 9

Which of the following is the correct expression for $$\cos x + \sqrt{3} \sin x in $$the form $$R \cos(x - 	heta)$$?

Accepted Answer

$$2 \cos(x - \frac{\pi}{3})$$

Question 10

If $$f(x) = x^2$ - 2x + y^2$ = 0$$, what type of conic section does this equation represent?

Accepted Answer

Circle

Question 11

Which of the following is the correct formula for the area $$A of a $$sector with radius $$r$$ and angle $$\alpha (in $$radians)?

Accepted Answer

$$A = \frac{1}{2} r^2$ \alpha$$

Question 12

Which of the following is the correct solution set for $$4x + 3x - x^2$ + 2x \leq 0$$?

Accepted Answer

$$x \in (1, 2) \cup [8, \infty)$$

Question 13

Which of the following is the correct general solution for $$\sin 	heta = \frac{1}{2}$$?

Accepted Answer

$$	heta = \frac{\pi}{6} + 2k\pi or$$ $$	heta = \frac{5\pi}{6} + 2k\pi$$, $$k \in \mathbb{Z}$$

Question 14

Which of the following is the correct formula for the sum of the first $$n$$ positive integers?

Accepted Answer

$$\sum_{r=1}^n r = \frac{n(n+1)}{2}$$

Question 15

Which of the following is the correct domain for the function $$g(x) = \frac{1}{|x| - 2}$$?

Accepted Answer

$$x \in \mathbb{R} \setminus \{2, -2\}$$

Question 16

Which of the following is the correct value for $$\sin(2	heta) in $$terms of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

$$\sin(2	heta) = 2 \sin 	heta \cos 	heta$$

Question 17

Which of the following is the correct formula for the binomial coefficient $$\binom{n}{k}$$?

Accepted Answer

$$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$

Question 18

Which of the following is the correct conversion from $$120^\circ to $$radians?

Accepted Answer

$$\frac{2\pi}{3}$$

Comprehensive Study Notes: College Algebra (MATH1034A Lecture Manual)

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