8th Grade Math Unit 1 - Algebra

8th Grade Math Unit 1 - Algebra - Introduction

____________ are symbols used to represent unspecified numbers or values in an algebraic expression.

Review Algebra Language
Select which of the following are algbebraic expressions:
1. 4y
2. z
3. 6 + a/b
4. 23 + 42
5. (t)(s)
Which of the following is the algebraic expression for:

the product of 17 and m raised to the sixth power
1. 17 + m⁶
2. 17m⁶
3. (17m)⁶
4. m(17⁶)
If the length of a rectangle is m and the width of the rectangle is n, which of the following are algebraic expressions for the perimeter of the rectangle.
1. 2(m+n)
2. 2(mn)
3. 2m + 2n
4. 2m + n
5. (m+n)2
Which of the following rules should you perform first to evaluate this expression:

7[ 130 - (25 ÷ 5)³]

Review Order of Operations
1. Do all multiuplications and/or divisions from left to right.
2. Evaluate all powers.
3. Evaluate innermost expressions first .
4. Do all additions and/or subtractions left to right,
Evaluate the following expression:

2+ [ 7 + (24 ÷ 8)]²
Evaluate the folllowing expression:

[(2a - b) / (c ÷ a)] + [(b² - c) / (a³ - 22]

if a = 3, b= 4, and c= 6
Which value in the replacement set below is the solution for the following equation:
5x + 19 = 34
1. 2
2. 3
3. 4
4. 5
5. 6
Find the solution of the following equation using the given replacement set.

18(x + 3) = 75.6; {1.1, 1.2, 1.3, 1.4}

x = _________
Find the difference:

(8m³ - 6m² + 5)
- (- 9m³ + 19m + 22)
1. m³ - 6m² - 19 m + 27
2. 17m³ - 6m² - 19 m - 17
3. -17m³ - 6m² - 19 m + 17
4. -m³ - 6m² - 19 m + 27
If x = - 4, and y = 8, what is the product of:

- 4 xy(-2y² + 9)
What is the product of:
- 6a(3a² - 4a + 2)
1. - 42a² -12a
2. - 18a³ - 24a² - 12a
3. - 18a³ +24a² -12a
4. 18a³ +24a² -12a
Sam buys several cans of soda at the convenience store. He hands the cashier a $10 bill. Write an expression for the amount of change he will receive if s represents the cost of the soda.
Write an algebraic expression for the sum of 52 and y.
Which algebraic expressions below represent:

one third the cube of x
1. x³/3
2. 3/x³
3. (1/3) • x³
4. 1/3x³
A store sells a package of blank DVD's for $8.85 and a package of blank CD's for 5.95.
Which algebraic expression below represents the cost of buying m packages of DVD's and n packages of CD's.
1. (8.85 + 5.95) • (m + n)
2. 8.85 • n + 5.95 • n
3. (5.95 • n) + (8.85 • m)
4. mn ( 8.85 + 5.95)
Sketch a rectangular prism. Label the length (l), width (w), and height (h).
WHich algebraic expressions below represent the surface area of the prism?
1. 2 [ (l • w) + (l • h) + (h• w)]
2. (l • h) + (l • w) + (h • w)
3. 2( l • w • h)
4. 2(l • w) + 2(l • h) + 2(w • h)
If you write 6 • 6 • 6 • 6 • m • m • m • m • m using exponents, you get:
1. 6³m⁵
2. 6⁴m⁴
3. 6⁴m⁵
4. 6⁴m⁴
Evaluate:

24 ÷ 4 • 3 - 3²
Evaluate:

384 ÷ [4( 8 + 4)]
Evaluate:

[ (8 + 6) (5 – 2)3 ] – (5 • 14 ÷ 7)
[ (28 ÷ 7) ÷ 2]
Evaluate the following expression if x = 11, y = 6, and z = 4:

[ xy² – 2z] / 4
If the three sides of a triangle are l, m, and n, what is the perimeter of thie triangle if:
l = 11 in , m = 14 in , and n = 9 in ?

Perimeter = ______ in
Using a calculator, evaluate the following expression if y = 14.67:

[ 3 y³ ] / [ y² - 2y ]

Enter your answer to the nearest tenth.
Which solutions belong in the solution set for the following inequality using the given replacement set:

4(16 - x) - 3 ≤ 30; {6.8, 7.5, 7.8, 8.0}

Check all that shluld be included.
1. 6.8
2. 7.5
3. 7.8
4. 8.0
Find the solution of the following equation using the given replacement set.

18(y + 3) = 79.2; {1.1, 1.3, 1.4, 1.6, 1.8}

y = ________
Solve the following equation:

m = 1/4 [ 8 (2⁴ + 5(4² - 6(3)]
Check the members of the solution set for the following inequality using the given replacement set:

3c < 9; { 2.5, 2.9, 3.0, 3.1, 3.2}
1. 2.5
2. 2.9
3. 3.0
4. 3.1
5. 3.2
Check the members of the solutions set for the following inequality if the replacement set for n is:
{4, 6, 7, 8, 13}

[ (4 • n)² +6 ] / [ (8 • 3²) - 2n ] < 32
1. 4
2. 6
3. 7
4. 8
5. 13
The set of whole numbers is closed under division.
1. True
2. False
Which of the following are like terms:
1. xy³ and 4x3y³
2. 3a² and 5a
3. m⁴ and 4m³
4. 6ax² and -2ax²
Which expression below is the result of applying the Distributive Property to the following expression:

3(7a + 6b - 8c)
1. 10a + 18b - 11c
2. 21a + 18b + 24c
3. 21a + 18b - 24c
4. 10a +18b - 24c
Using the distributive property, find the product:

24(2 5/8)
Simplify the following expression:

4a³ - a⁴ + 7a³

Select the correct answer below.
1. 10a³
2. 11a³
3. 11a³ -a⁴
4. a⁴ + 11a³
Simplify:

4(2x + y) + 3(x + 3y) - 5y
Simplify:

x + x/5 + x • 2/5

Check the correct answer below.
1. (1 3/5 )x
2. (3 1/5)x
3. x/5
4. (21/5)x
Evaluate:

(3)(3/7) • (21) • (8)(1/4)
The ice cream store sells coffee ice cream for $2.99, and vanilla ice cream for $2.79. They are having a two for one sale for chocolate ice cream where the price for one is $2.89. You buy 3 coffee ice creams, 5 vanilla ice creams and 10 chocolate ices creams.

Which expression below represents the total cost?
1. 3 • 2.99 + 5 • 2.79 + 10 • 2.89
2. 18 • (2.99 + 2.79 + 2.89)
3. (18/2) • (2.99 + 2.79 + 2.89)
4. 3 • 2.99 + 5 • 2.79 + (10/2) • 2.89
Simplify this expression:

4(3a + b) + 6a
Simplify this expression:

4x + 2/5(x/4 + 3y) + 3/4

Check the correct answer below.
1. (4 1/10)x + (6/5)y + 3/4
2. (4 8/5)x + (3/5)y + 3/4
Which of the expressions below represents:

the product of five and the cube of x, increased by the sum of eight, x³, and 5.
1. 5x³ (x³ + 13
2. 5x³ + 8 + 5x³
3. 6x³ + 13
4. 6x³ + 13x³
Simplify:

5(ac + 4b) + 2ac
Which numbers are counterexamples of the following statement:

If a number x is squared, then x² > x

Check all that apply.
1. x = -2
2. x = 1
3. x = 1/2
4. x = 0
Dylan is bouncing a tennis ball on the ground. After the ball strikes the ground, how many seconds does it take it to reach its maximum height off the ground?

__________ seconds
Simpify:

4m - m + 6n - 3n
Write an algebraic expression for the following verbal expression. Then simplify the algebraic expession.

5 times the cube of y minus the sum of y cubed and 6 times y.

Which of the following is the correct expression?
1. 6y³ + 6y
2. 4y³ + 6y
3. 4y³ -6y
4. 5y³ - 5y
Which property below matches the following statement:

For any number x, y, and z, if x = y, and y = z, then x = z.

Review Algebra Properties
1. Substitution Property of Equality
2. Symetric Property of Equality
3. Transitive Property of Equality
4. Reflexive Property of Equality
Write the following expression in its simplest form.

4(3x + y) - 7x + 6y
Which property was used in the following step?

9x + 3x + 8xy = (9 + 3)x + 8y

Review Algebra Properties
1. Commutative
2. Distributive
3. Substitution
4. Associative
In the equation d = 60 • t, which is the dependent variable?

Review Graphs & Function
1. d
2. 60
3. t