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.

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