Q: A medical device rotates at an angular speed of $$6$$ revolutions per second. What is its angular speed in radians per minute?

$$6 \times 2\pi \times 60 = 720\pi$$ radians/min$

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

$$\theta = -\frac{\pi}{20} + k\frac{\pi}{5}$$, $$k \in \mathbb{Z}$$

Q: A patio is in the shape of a sector with radius $$3 m $$and angle $$60^\circ. $$Tiler A charges R100 per square metre, Tiler B charges R50 per metre around the perimeter. Which tiler offers better value for money?

Tiler B, because the perimeter is $$2r + r\alpha = 6 + 3 \times \frac{\pi}{3} = 6 + \pi m$$, so cost is $$50(6 + \pi) R.$$

Q: Which of the following is the correct expression for $$\sin^4$ \theta in $$terms of cosine functions, without even powers?

$$\frac{3}{8} - \frac{1}{2} \cos(2\theta) + \frac{1}{8} \cos(4\theta)$$

Question 1

Which of the following statements correctly describes the set of irrational numbers?

Accepted Answer

The set of irrational numbers consists of all real numbers that are not rational numbers, and can be denoted by $$\mathbb{R} \setminus \mathbb{Q}.$$

Question 2

A chemical reaction produces a temperature change that can be modeled by $$T(t) = 5t^2$ - 3t + 2$$, where $$t is $$time in minutes. What is the natural domain of $$T$$?

Accepted Answer

The domain is $$\mathbb{R}$$, since $$T is a $$polynomial.

Question 3

Which of the following is the correct solution set for the inequality $$|2x + 4| \u003c 1$$?

Accepted Answer

$$(-5/2, -3/2)$$

Question 4

A medical device rotates at an angular speed of $$6$$ revolutions per second. What is its angular speed in radians per minute?

Accepted Answer

$$6 	imes 2\pi 	imes 60 = 720\pi$$ radians/min$

Question 5

Let $$f(x) = \sqrt{x-1}$$ and $$g(x) = \frac{1}{|x|-2}. $$What is the natural domain of $$g$$?

Accepted Answer

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

Question 6

Which of the following functions is odd?

Accepted Answer

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

Question 7

A ladder leans against a wall and slips downward, keeping contact with the floor and wall. The path traced by a point not at the endpoints of the ladder is:

Accepted Answer

An arc of an ellipse

Question 8

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

Accepted Answer

$$	heta = -\frac{\pi}{20} + k\frac{\pi}{5}$$, $$k \in \mathbb{Z}$$

Question 9

A patio is in the shape of a sector with radius $$3 m $$and angle $$60^\circ. $$Tiler A charges R100 per square metre, Tiler B charges R50 per metre around the perimeter. Which tiler offers better value for money?

Accepted Answer

Tiler B, because the perimeter is $$2r + r\alpha = 6 + 3 	imes \frac{\pi}{3} = 6 + \pi m$$, so cost is $$50(6 + \pi) R.$$

Question 10

Which of the following is the correct binomial expansion for $$(a + b)^4$?

Accepted Answer

$$a^4$$ + $$4a^3b$$ + $$6a^2b^2$ + 4ab^3$ + b^4$

Question 11

A point in the plane has polar coordinates $$(r, 	heta) = (2, 5\pi/4). $$What are its Cartesian coordinates?

Accepted Answer

$$(x, y) = (-\sqrt{2}, -\sqrt{2})$$

Question 12

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 13

Which of the following is the correct expression for $$\sin^4$ 	heta in $$terms of cosine functions, without even powers?

Accepted Answer

$$\frac{3}{8} - \frac{1}{2} \cos(2	heta) + \frac{1}{8} \cos(4	heta)$$

Question 14

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 15

Which of the following is the correct canonical form for the ellipse $$x^2 + 2x$$ + $$2y^2 - 8y + 7 = 0$ after completing the square?

Accepted Answer

$$\frac{(x+1)^2$}{2} + (y-2)^2$ = 1$$

Question 16

Which of the following is the correct general solution for $$|a| \u003c b$$ where $$b \geq 0$$?

Accepted Answer

$$-b \u003c a \u003c b$$

Question 17

Which of the following is the correct formula for converting degrees to radians?

Accepted Answer

Multiply by $$\frac{\pi}{180}$$

College Algebra and Trigonometry: Structured Study Notes

Study Guide - Practice Questions

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