Final Exam Review (MC)

Complex Numbers

100

What is the value of i?

sqrt (-1)

200

Solve

(2 + i) + (3 - 5i)

5 - 4i

300

Solve

(5 + 4i) - (3 - i)

2 + 5i

400

Solve

(5 + i)(5 - i)

26

500

Solve

(2 + i)²

(2 + i)(2 + i)

4 + 2i + 2i + i^2

4 + 4i - 1

3 + 4i

Solving Quadratics

100

Solve for x:

x² = 4

2 and -2

200

Solve for x: 

x² + 9 = 0

+ or - 3i

300

Solve for x:

(x + 1)² = 100

x + 1 = 10, x + 1 = -10

x = 9 or x = -11

400

Solve for x:

x² + 5x + 6 = 0

(x + 3)(x + 2) = 0

x = -3 and -2

500

Solve for x: (Use Quadratic Formula)

x² - 6x + 10 = 0

Quadratic Formula

x = 3+- i

Log Functions

100

Convert log to exp:

log ₂ 8 = 3

2³ = 8

200

Convert exp to log:

3² = 9

log₃9 = 2

300

Solve for x:

3^x = 27

3

400

Solve for x:

4^x = 1/16

-2

500

Convert from exp to log and solve for x.

2*4^x=32

4^x = 16

log₄ 16 = x

x = 2

Transformations

100

Given: af(x - h) + k

What does the value h do to the graph?

- h shifts the graph to the right

+ h shifts the graph to the left

200

Describe what happens to the graph g(x).

3g(x) + 1

vertical stretch of 3 units

shifts up 1 unit

300

Describe what happens to the graph g(x).

-g(x + 1) - 4

Flips over x-axis

Shifts left 1 unit

Shifts down 4 units

400

What is the horizontal asymptote of the graph
y = 2^x + 3?

y = 3

500

What is the vertical asymptote for y = log ₂ (x - 5)?

x = 5

Misc/Trig

100

Write the inverse point of (3, - 5)

(-5, 3)

200

Describe an ODD function

rotational symmetry of 180 degrees

300

Name the quadrant where sine function is negative and tangent is negative.

Quadrant 4

400

Convert 7pi/6 into degrees

210

500

Imagine you are at the top of a ferris wheel. Sketch a graph that would represent the height of the ferris wheel as a function of time.

See Sketch.