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Common Core Algebra 8A
Test: Properties and Linear Equations
ANSWERS
Part I: Answer each multiple choice question and put the letter of
your answer choice in the column to the right.
1. Which equation illustrates the
multiplicative identity element?
21x 4 y 3 z
7x2 y2 z3
2
A) 3x yz
2
3x 2 y
z3
3x 2 y
C)
z2
3x 2
D) 2
z
4. If 2x2 – 4x + 6 is subtracted from
5x2 + 8x – 2, the difference is
B)
3. Which of the following do not represent
a rational number?
4.
5.
6.
7.
3
2
B) 0.29
C) 7
A)
A)
B)
C)
D)
2
3x + 4x + 4
-3x2 + 4x + 4
-3x2 – 12x + 8
3x2 + 12x – 8
16
5. The product of
2.
3.
A) x + 0 = x
B) x · 1 = x
C) x – x = 0
1
D) x · = 1
x
D)
2. Find the quotient:
1.
1 3
1
x and x5 is
2
4
1 8
x
8
3 8
B)
x
4
1
C) x15
8
1
D) x8
6
6. Solve the given equation for the
variable: 3(y – 5) = 2(y + 2)
A)
7. Find the quotient of the given
24 x 6  30 x 3  6 x
expression:
6x
A) 4x6 – 5x3 + 1
B) 4x5 – 5x2 + 1
C) 18x5 – 36x2
D) 4x5 – 5x2 + x
A)
B)
C)
D)
17
19
-7
7
8. Solve for p:
p
 7  11
5
A) -90
B) -0.8
C) 20
D) -20
8.
When solving the equation
4(3x2 + 2) – 9 = 8x2 + 7, Emily wrote
4(3x2 + 2) = 8x2 + 16 as her first step.
Which property justifies Emily’s first
step?
9.
A)
B)
C)
D)
Addition property of equality
Commutative property of addition
Multiplication of equality
Distributive property of
multiplication over addition
10. Find the product:
(x – 3)(2x + 5)
9.
10.
A) 2x2 – x – 15
B) 2x2 + x + 15
C) 2x2 + 11x + 15
D) 2x2 + 11x – 15
11. Solve the equation for h in simplest 12. Determine the number of solutions for
the given equation:
2h  3 2

form:
5h
3
5(x – 2) – 3 = 5x + 10
A)
ANSWERS
9
4
11.
12.
13.
14.
15.
9
B) 
4
4
C) 
9
4
D)
9
A)
B)
C)
D)
13. Translate: Eight less than the
product of three and a number.
A) 8x – 3
B) 3x – 8
C) 8 – 3x
D) 3 – 8x
15. Name the property illustrated
below:
-3 + 6 = 6 + (-3)
A) Commutative property of
addition
B) Associative property of addition
C) Property of additive inverse
D) Distributive property
All real numbers
No solution
One solution
Two solutions
14. Which property is being illustrated?
(7 ∙ 5) ∙ 2 = 7 ∙ (5 ∙ 2)
A) Commutative property of
multiplication
B) Property of multiplicative inverse
C) Associative property of
multiplication
D) Identity property for multiplication
16. Which property is being illustrated in
the following equation?
5 + (-5) = 0
A)
B)
C)
D)
Identity property for addition
Addition property of equality
Property of additive inverse
Commutative property of
addition
16.
Part II: Show all work in the space provided.
17. Fill in the blanks of this proof showing that (k + 2)(k + 3) is equivalent to k2 + 5k + 6 by
writing the name of the property being illustrated (associative, commutative or distributive).
1.
2.
3.
4.
(k + 2)(k) + (k + 2)(3)
k(k + 2) + 3(k + 2)
k2 + 2k + 3k + 6
k2 + (2k + 3k) + 6
k2 + 5k + 6
18. Simplify: (-3x)3(4y)2
19. Find the value of x so that the figures have the same perimeter. Write an equation and solve
for x.
5x + 1
3x + 4
2x
2x + 5
x + 13
20. Which value of m satisfies the equation
7
9
(m  )  20 ?
3
28
Circle the correct answer and PROVE or JUSTIFY your answer below:
A) 8.25
B) 8.89
C) 19.25
D) 44.92
21. Solve for y: 0.4y – 1 + 0.2y + 5 = 2(0.3y + 2)
**BONUS
a) Multiply and satisfy the given polynomials: (x – 3)(x2 + x + 3)
b) Write the set of all real numbers greater than -3 and less than or equal to 8 in interval
and set-builder notation:
Interval Notation
Set-builder Notation