Ch 4 to 6 Cumulative Review
Chapter
Chapter 6
Section
Ch 4 to 6 Cumulative Review
Solutions 31 Videos

Which of the following is equal to -7?

(a) \displaystyle 25^{\frac{1}{2}}+ 16^{\frac{3}{4}} 

(b) \displaystyle 8^{\frac{2}{3}}- 81^{\frac{3}{4}}+4^2 

(c) \displaystyle 8^{-\frac{3}{4}}- 81^{-\frac{3}{4}}+8^{-3} 

(d) \displaystyle 81^{-\frac{3}{4}}+ 16^{-\frac{3}{4}}-16^{-\frac{1}{2}} 

Q1

Which of the following will be true when x = 2?

(a) \displaystyle 3^{3x -1} = 27 

(b) \displaystyle 6^{2x -3} = \sqrt{6} 

(c) \displaystyle 5^{3x + 2} = \frac{1}{5} 

(d) \displaystyle (2^{2x})(2^{x-1}) = 32 

Q2

Identify the expression that simplifies to 1.

(a) \displaystyle (a^{10 + 2p})(a^{-p-8}) 

(b) \displaystyle (2x)^{3 -2m}(\frac{1}{x})^{2m} 

(c) \displaystyle [c^{2n -3m}](c^3)^m\div(c^2)^m 

(d) \displaystyle [(x^{4n -m})(\frac{1}{x})]^6 

Q3

The population of a town is growing at an average rate of 5% per year. In 2000, its population was 15 000. What is the best estimate of the population in 2020 if the town continues to grow at this rate?

Q4

Point P(-7. 24) is on the terminal arm of an angle in standard position. What is the measure of the related acute angle and the principal angle to the nearest degree?

Q5

What is the exact value of \csc 300^o?

Q6

Is the following an identity.

\displaystyle (1 -\tan^2\theta)(1 - \cos^2\theta) = \frac{\sin^2\theta -2\sin^4\theta}{1 -\sin^2\theta} 

Q7a

Is the following an identity.

\displaystyle \frac{\tan x \sin x}{\tan x +\sin x} = \frac{\tan x \sin x}{\tan x \sin x} 

Q7b

Is the following an identity.

\displaystyle \frac{\cos^2x -\sin^2x}{\cos^2x + \sin x \cos x} = 1 -\tan x 

Q7c

Is the following an identity.

\displaystyle \frac{\cos x}{\tan x} = \frac{1-\cos x}{\sin x} 

Q7d

What is the measure of x to the nearest unit?

Q8

What is the measure of \theta to the nearest degree?

Q9

Find \csc \theta.

Q10

If \tan \theta = \frac{4}{5}  and \theta lies in the third quadrant, find \cos \theta.

Q11

A weather balloon is spotted from two angles of elevation, 57° and 85°, from two different tracking stations. The tracking stations are 15 km apart. Determine the altitude of the balloon if the tracking stations and the point directly below the balloon lie along the same straight line.

Q12

At a concert, a spotlight is placed at a height of 12.0 m. The spotlight beam shines down at an angle of depression of 35°. How far is the spotlight from the stage?

Q13

In \triangle ABC, \angle A = 32^o, \angle C = 81^o, and a = 24.1. Solve the triangle.

Q14

Sketch y = 2\cos2(\theta + 45^o) + 4.

Q15

Sketch y = 2\cos 2\theta.

Q16

A sine function has an amplitude of 5, a period of 720°, and range {y \in \mathbb{R} \vert 2 \leq y \leq 12}. Identify the correct equation of this function.

Q17

A circular dining room at the top of a skyscraper rotates in a counterclockwise direction so that diners can see the entire city. A woman sits next to the window ledge and places her purse on the ledge as shown. Eighteen minutes later she realizes that her table has moved, but her purse is on the ledge where she left it. The coordinates of her position are (x, y) = (20 \cos (7.5t)^o, 20 \sin (7.5t)^o), where t is the time in minutes and x and y are in metres. What is the shortest distance she has to walk to retrieve her purse?

A. 54.1 m

B. 37.0 m

C. 114.0 m

D. 62.9 m

Q19

In \triangle ABC, \angle A = 85^o, c = 10 cm, and b = 15 cm. A possible height of \triangle ABC is

A. 10.0 cm

B. 8.6 cm

C. 13.8 cm

D. 12.5 cm

Q22

Find the exact value of \cos(-420^o).

Find the period of y = \sin 4\theta.
If 3x^{\frac{1}{2}} = 12, then find the value of x.