0-1 to 0-3 Review

Sets

100

What is the universal set?

The set of all possible elements of a situation

200

Write the following in set notation: W is the set of whole numbers less than 10.

W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

300

Given the following sets, is A ⊂ U?

U = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A = {11, 15, 19}

Yes. All elements of A are present in U.

400

Given the following sets, find C'.

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A = {1, 3, 5, 10}

B = {4, 9, 11}

C = {2, 3, 8, 10, 12}

C' = {1, 4, 5, 6, 7, 9, 11, 13, 14, 15}

500

Given the following sets, find A ∩ B.

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A = {2, 4, 9, 11, 13, 18}

B = {0, 3, 5, 8, 10, 14, 17, 19, 20}

∅

Complex Numbers

100

What is the standard form of a complex number (define the variables, too!)?

a + bi, where a is the real number part and b is the imaginary part.

200

Simplify: i¹⁰

-1.

(10 ÷ 4 = 2 R 2. Since R = 2, iⁿ = -1).

300

(17 + 3i) - (12 + 7i)

5 - 4i

400

(8 - 5i)(2 + 3i)

31 + 14i

500

(-2+i)/(-1-8i)

(-6-17i)/65

Quadratic Functions

100

What is the standard form of a quadratic function?

y = ax² + bx + c OR f(x) = ax² + bx + c

200

What is the y-intercept of this function? 

f(x) = 2x² - 17x + 39

(0, 39)

300

What is the equation of the axis of symmetry for the following function? 

f(x) = 3x² - 9x + 13

x = 3/2

400

What is the vertex of the following function? 

f(x) = x² - 8x + 13

(4, -3)

500

Find the y-intercept, maximum/minimum, domain, and range of the following function.

f(x) = 2x² - 16x + 33

y-intercept: (0, 33)

Minimum: 1 at x = 4

Domain: All real numbers

Range: y > 1

Quadratic Equations

100

What are the two methods to solving quadratic equations that we covered in class?

Factoring and completing the square

200

Solve:

(x + 1)(x - 5) = 0

x = -1, 5

300

Solve by factoring:

b² + 2b - 35 = 0

b = -7, 5

400

Solve by completing the square: 

x² + 14x - 15 = 0

x = -15, 1

500

Solve by completing the square: 

8x² + 16x = 42

x = -7/2, 3/2

0-1 to 0-3

100

Simplify: i³⁷¹

-i

(371 / 4 = 92 R 3. R = 3, so iⁿ = -i).

200

Given the following sets, find A' ∩ B

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A = {2, 5, 8, 10, 11, 13}

B = {3, 4, 5, 6, 11, 15, 18, 20}

{3, 4, 6, 15, 18, 20}

300

Find the y-intercept, maximum/minimum, domain, and range of the following function:

f(x) = -x²/4 + x - 9

y-intercept: (0, -9)

Maximum: -8 at x = 2

Domain: All real numbers

Range: y < -8

400

Solve by factoring:

3x² - 16x - 7 = 5

x = -2/3, 6

500

Solve by completing the square: 

2x² - 10x + 2 = 0

x = (5 + √21)/2, (5 - √21)/2