Ch 4 to 6 Cumulative Review
Chapter
Chapter 6
Section
Ch 4 to 6 Cumulative Review
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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}}

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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

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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

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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?

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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?

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Q5

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

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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}

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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}

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Q7b

Is the following an identity.

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

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Q7c

Is the following an identity.

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

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Q7d

What is the measure of x to the nearest unit?

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Q8

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

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Q9

Find \csc \theta.

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Q10

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

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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.

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Q12