Chapter 1 Review - Alg2

Order of Operations

100

What operation can be done the same time as division?

Multiplication

200

Solve when x = 4.

7x - 3x² + 9 

-11

300

Solve.

5^3 + (8-4)/2 * ( 15 -2)-12 

135

400

Solve.

(125-13*2+34)/(3*4-5*(24+5) 

-1

500

Solve.

6/4-(-10-3)*5

66 1/2

Algebraic Properties

100

True or False

An example of the inverse property is

3 + 0 = 3

** Write your answer down for me to check. Do not call it out.

False, 

Inverse Property: a + (-a) = 0

200

Give an example of the identity property of multiplication.

Answers will vary.

Identity Property of Multiplication: 

a*1 = a

300

Give an example of the distributive property.

Answers will vary. 

Distributive Property: a(b + c) = ab + ac

400

Which one is the commutative property?

1.)   c + (b + a) = (c + b) + a

2.)  (c + b) + a = a + (c + b)

**Write the number on your board and do not say it out loud. Raise your hand and I will come check it.

2

500

Give an example of the associative property.

Answers will vary.

Associative Property: (x + y) + z = x + (y + z)

Exponent Properties

100

Simplify both

x^2 * 3x

x^2 + 3x^2

3x³

4x²

200

Simplify

(x³)³

x⁹

300

Write without denominators.

(6y^2z^3)/(3x^2y^4)

2x^-2y^-2z³

400

Write without negative exponents.

(8x^2y^5)/(2x^4y

(4y^4)/x^2

500

Write without negative exponents.

(65x^3y^-1z)/(100c^3x^-4z^-3)

(13x^7z^4)/(20c^3y)

Operations w/ Polynomials

100

Simplify.

(-3x² - 6x + 8) + (8x² + 7x - 14)

5x² + x - 6

200

Simplify.

(x² + x - 5) - (3x² + 7x - 14)

-2x² - 6x + 9

300

Simplify. 

(x² - 2y)(x² + 2y) 

x⁴ - 4y²

400

Simplify.

(4x - 5)(2x² + 5x - 5)

8x³ + 10x² - 45x + 25

500

(2y² + 3y - 4)(y² - 6y + 2)

2y⁴ - 9y³ - 18y² + 30y - 8

Expanding Polynomials

100

(x - 1)²

x² - 2x + 1

200

Expand.

(2x + 4y)²

4x² + 16xy + 16y²

300

Expand.

(y + 1)³

y³ + 3y² + 3y + 1

400

(2x - y)³

8x³ - 12x²y + 6xy² - y³

500

(2k + 4w)³

8k³ + 40k²w + 64kw² + 32w³

Polynomial Division

100

Divide.

(n^2 + 5n - 50)/ (n-5)

n + 10

200

Divide.

(a^3 + 13a^2 + 39a - 18)/ ( a+6)

a² + 7a - 3

300

Divide. 

(8p^3 + 2p^2 - 10) / (p-1)

8p² + 10p + 10

400

Divide.

(x^3 + 3x^2 - 2x + 6)/ (x-1)

x^2 + 4x + 2 + 8/(x-1)

500

(2x^4 + 4x^2 - 1) / (x+1)

2x^3 - 2x^2 + 6x - 6 + 5/(x +1)

Factoring

100

Factor.

25m² - 40m + 16

(5m - 4)²

200

Factor.

4a² - 25

(2a - 5)(2a + 5)

300

Factor.

2n² + 16n + 32

2(n+4)²

or 

(2n+8)(n+4)

400

Factor.

5b² - 125

5(b+5)(b-5)

500

Factor. 

3k² - 10k + 7

(3k - 7)(k - 1)