Unit III Review

Lessons 15 & 16

100

Convert 4  /3 radians to degrees

240

200

Convert 150 degrees to radians

5  /6

300

Given: polar coordinates (Q, R)

The Q represents:

distance along the hypotenuse on a right triangle

400

Rewrite the rectangular coordinates (-3  3 , -3) as polar coordinates and graph.

(-6, 30 )

500

Give three other ways to express (5, 125 ) using degrees.

(5, -235 )

(-5, -55 )

(-5, 305 )

Lessons 17 & 18

100

The point r cos 0 in polar coordinates is the same as _____________ with rectangular coordinates.

"x"

200

Write the equation x² + y² = 16 in terms of polar coordinates

r = 4

300

Rewrite the equation 2y = x² in terms of polar coordinates

r = 2 tan 0 / cos 0

400

Graph the following equation:

r =   -2 / 5 sin 0 - 3 cos 0

Use 45 , 90 , 225 , 270

See graph (straight line)

500

The first vector was (110, 45 ). The resultant vector was (85, 65 ). What were the polar coordinates of the second vector?

(42, 181.1 )

Lessons 19 & 20

100

Any set of ordered pairs is a ____________ .

relation

200

The set of possible x coordinates for a function is the ________________ .

domain

300

Which of the following are functions?

A. x² + y² = 25             B. -y = x²

C. x = 4y                      D. y = ln x

B, C, and D

(A is a circle)

400

What is h[j(-1)]?

h(x) = x² - 8

j(x) = -3x

1

500

What is r[r(p)]?

r(p) = p² + 1

p⁴ + 2p² + 2

Lessons 21 & 22

100

Common logarithms are in base 10. Natural logarithms are in base ____________ .

"e"

200

Solve for x: log_x2A/B

log_x2A - log_xB

300

Factor: ln² x - ln x - 2

(ln x - 2)(ln x + 1)

400

Solve for x: e^2x = ln 5

(answer rounded to hundredths)

x = .24

500

Suppose that at time t (hours), the number of bacteria in a culture is given by N(t) = 2000e^0.3t

A. How many bacteria are in the culture after two hours?

B. How long will it take for the bacteria count to reach 50,000? (Answer rounded to nearest hour)

A. 3,644 bacteria

B. about 11 hours

*Lessons 20 & 22*

100

The natural logarithm function, ln x, is the inverse of:

e^x

200

Given the following functions, find the composite functions.

f(w(p))

-6e^x

300

Given the following functions, find the composite functions.

z(w(p))

x + 2

400

Given the following functions, find the composite functions.

z(p) + w(p) + r(p)

ln x + e^x + p² + 3

500

Given the following functions, find the composite functions.

z(w(f(-2)))

14