Question 1

Convert $$12.5664$$ radians to degrees. Which of the following is the correct answer?

Accepted Answer

$$720^{\circ}$$

Question 2

Express $$440^{\circ} in $$radian measure in terms of $$\pi. $$Simplify your answer.

Accepted Answer

$$\frac{11\pi}{9}$$

Question 3

A machine rotates at $$800$$ rpm (revolutions per minute). What is its angular speed in radians per second?

Accepted Answer

$$40\pi$$	ext{ rad/s}$

Question 4

A sector has area $$A = 16.5\ 	ext{m}^2$$ and radius $$r = 4.02\ 	ext{m}. $$What is the arc length $$s$$?

Accepted Answer

$$s = \frac{2A}{r}$$

Question 5

The paddles of a riverboat have a radius of $$2.59\ 	ext{m}$$ and revolve at $$20$$ rev/min. What is the speed of the tip of one paddle in m/s?

Accepted Answer

$$5.42\ 	ext{m/s}$$

Question 6

Solve $$x^2 + 30 = 11x$. What are the solutions?

Accepted Answer

$$x = 6, x = 5$$

Question 7

Factor $$x^3 - 27$. Which of the following is the correct factorization?

Accepted Answer

$$(x - 3)(x^2$ + 3x + 9)$$

Question 8

Find the discriminant $$D of$$ $$4x^2 - 6 = 5x$. Which formula gives the discriminant?

Accepted Answer

$$D = b^2$ - 4ac$$

Question 9

Given $$\cot 	heta = 2.368$$ and $$0 \leq 	heta \u003c 360$$^{\circ}$$, which of the following is a possible value for $$	heta$$?

Accepted Answer

$$	heta = 22.8$$^{\circ}$$

Question 10

If $$\csc 	heta = -3.1392$$ and $$0 \leq 	heta \u003c 2\pi$$, which quadrant is $$	heta$$ located in?

Accepted Answer

Quadrant III

Question 11

Solve the triangle $$ABC$$ given $$a = 9.3$$, $$b = 18.3$$, $$c = 27.1. $$Which law is most appropriate to use?

Accepted Answer

Law of Sines

Question 12

Factor completely: $$3x^4 - 243$. Which is the correct factorization?

Accepted Answer

$$3(x^2$$ - $$9)(x^2 + 9$$)$$

Question 13

Simplify $$\frac{4}{y-4} - \frac{2}{y^2$}. $$Which is the correct simplified form?

Accepted Answer

$$\frac{4y - 16 - 2}{y^2$(y-4)}$$

Question 14

Solve $$2x^2 + 7x = 4$. What is the correct solution?

Accepted Answer

$$x = \frac{-7 \pm \sqrt{49 - 8}}{4}$$

Question 15

Solve for $$R_2 in$$ $$\frac{1}{R_T} = \frac{1}{R_1$} + \frac{1}{R_2$}. $$Which formula is correct?

Accepted Answer

$$R_2$$ = \frac{$$R_1 R_T$$}{$$R_1 - R_T$$}$$

Question 16

A developer increases both the length and width of a rectangular lot by $$x$$ meters, resulting in new dimensions $$50 m by$$ $$100 m $$and an area increase of $$2000 m$^2. $$What equation must be solved to find $$x$$?

Accepted Answer

$$(50)(100) - (50 - x)(100 - x) = 2000$$

Question 17

Crew A can assemble 2 cars in 24 hours, Crew B can assemble 2 cars in 36 hours. How long will it take both crews, working together, to produce 10 cars?

Accepted Answer

$$60$$ hours

Question 18

The length of a tennis court is $$12.8 m $$more than its width. If the area is $$262 m$^2$$, what are the dimensions?

Accepted Answer

Width $$= 12.8 m$$, Length $$= 25.6 m$$

Precalculus Study Guide: Sample Test 2 (Math 1100, Spring 2026)

Study Guide - Practice Questions

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