Quarter Review (Ch 7-9)

Chapter 7

100

Rewrite 5³ = 125 as a logarithmic function.

3 = log₅ 125

200

Expand the logarithmic equation 3 ln x²y⁶. 

6 ln x + 18 ln y

300

Solve log₁₂ 4x = log₁₂ 52  

x = 13

400

Solve log₂ (x - 1) = 3

x = 9

500

Solve 2 log₂ x - log₂ (3x -4) = 1

x = 2, 4

Chapter 8

100

Triangle DEF: side DF = 77

Triangle UVW: side UW = 231

If side VW = 33, find side EF.

EF = 11

200

Find the values of the three basic trigonometric functions of the indicated angle using the given information.

Find for angle B, given c = 25 and b = 7

a = 24

sin B = 7/25, cos B = 24/25, tan B = 7/24

300

Use a calculator, find the angle. Round three decimal places. 

sin angle = 7/8

61.045 degrees

400

Convert the given angle to radian without a calculator.

315 degrees

7pi/4

500

Convert the given angle to degrees without a calculator. 

8pi/9

160 degrees

Chapter 9

100

Find the values of the three basic trigonometric functions for an angle in standard position passing through the given point (3, 4).

sin = 4/5

cos = 3/5

tan = 4/3

200

Find the reference angle.

825

75 degrees

300

Determine in which quadrant the angle would lie given the information.

sin angle > 0 and tan angle < 0

quadrant II

400

Solve the equation for the angle. Round to the nearest tenth of a degree.

11 sin angle = 1

5.2 degree, 174.8 degree

500

Solve for the angle using the unit circle.

sin angle = 1/2

30 degrees and 150 degrees

Word Problems

100

Samuel is about to go down a slide that is 11 feet tall and has a slide length of 17 feet. What is the angle of inclination from the ground.

40.32

200

The air pressure in a particular balloon is 20 psi when the temperature is 30F. If the air pressure and temperature are directly proportional, what will the pressure in the balloon be when the temperature is 90? 

60 psi

300

A woodworker is making a triangle art piece. The bottom piece is cut to be 21 feet long and the side piece is 20. How long is the diagonal piece?

29 feet

400

What is the sound level of a sound with an intensity of 2.5 x 10^-6 W/m²?

64.0 dB

500

If a sound measure at 200 decibels, what is the sound intensity?

I = 1 x 10⁸ W/m²

Random

100

If the base of the exponential expression equals the base of the log, the result is the ___?

argument

200

Find the inverse of the function y = x + 10.

y = x - 10 

300

Use a reference triangle to find the exact value of each trigonometric function.

sin 330

30 degrees

400

What is the reciprocal function for cos angle?

sec angle

500

Find the reference angle for 140.

40 degrees