Unit 4: Expressions and Equations
Quiz (Lessons 27 to 30)
Name: ______________________
Date: ________________
1. Evaluate the expression with n = 5.
b) 16 − 3n
a) 6n
2. In the expression 2x + y − 12, what is …
a) the coefficient of x? __________
b) the coefficient of y? __________
c) the constant term? __________
3. To go bowling, you pay a flat fee of $5 to rent the shoes plus an hourly rate of $6.
a) Write an expression for the cost to go bowling for h hours. _________________________
b) How much would you pay to go bowling for 1.5 hours? ____________________________
4. Compete the table and then solve for x.
3x − 7 = 2
x
3x − 7
True?
1
2
3
4
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x = __________
5. Solve for x by doing the same thing to both sides of the equation.
a) 7x = 35
b) x − 7 = –3
Sample Unit Quizzes and Tests for AP Book 8.1
c) x ÷ 9 = 2
d) 9 = x + 1
K-49
Unit 4: Expressions and Equations
continued
Quiz (Lessons 27 to 30)
6. Replace the variable with the given number and evaluate.
a) 5n + 2,
n=
2
3
b)
n
+ (−9),
4
n = −16
7. Solve the equation by adding or subtracting the same number from both sides.
a) x + 2
3
7
= 4
5
10
b) 2.5 = x − 3.7
8. Check your answer to Question 7.a).
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Bonus► If you multiply Rob’s age by 5 and then subtract 20, you get 65. How old is Rob?
K-50
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 4: Expressions and Equations
Answer Key
Quiz (Lessons 27 to 30)
1.
a)
6(5) = 30
b)
16 − 3(5)
b)
6.2 = x
= 16 − 15
8.
=1
2.
3.
4.
a)
2
b)
1
c)
−12
a)
6h + 5
b)
6(1.5) + 5
x
1
2
3
4
2.5 + 3.7
= x − 3.7 + 3.7
1
3
2 +2
10
5
1
6
= 2 +2
10
10
7
= 4
10
Bonus
=9+5
Let x be Rob’s age.
= $14
5x − 20 = 65
3x − 7
True?
3(1) − 7
= −4
3(2) − 7
= −1
3(3) − 7
=2
3(4) − 7
=5


5x − 20 + 20 = 65 + 20
5x = 85
5x ÷ 5 = 85 ÷ 5
x = 17
or
(65 + 20) ÷ 5 = 17
Rob is 17 years old.


x=3
5.
a)
7x ÷ 7 = 35 ÷ 7
x=5
b)
x − 7 + 7 = −3 + 7
x=4
c)
x÷9×9=2×9
x = 18
d)
9−1=x+1−1
8=x
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6.
a)
æ2 ö
5 çç ÷
+ 2
÷
çè3 ÷
ø
10 6
=
+
3
3
16
1
=
= 5
3
3
b)
(- 16)
−9
4
= −4 − 9
= −13
7.
a)
3
3
x+ 2 - 2
5
5
7
3
= 4 - 2
10
5
7
6
x= 4 - 2
10
10
1
x= 2
10
Sample Unit Quizzes and Tests for AP Book 8.1
K-51
Unit 4: Expressions and Equations
Name: ______________________
Quiz (Lessons 31 to 34)
Date: ________________
1. Solve for the variable by undoing one operation at a time in the equation.
a) 5x + 8 = 28
c)
x
− 4 = −6
8
b) 3x − 7 = 14
d) 5 − x = 18
2. Add and subtract.
a) 7x + 3x
b) 4x − 5x + 8x + x − 3x
a) 7x + 3 + 4x
b) 5x + 12 + 10x − 6
c) (2x + 8) + (3x − 4)
d) (9x + 6) − (7x − 2)
e) 3.5x − (2.4x − 6.2)
æ2
1ö æ
1 2 ö
f) çç x + ÷
- çç - x ÷
÷
÷
÷
÷
èç9
3 ø èç6 9 ø
K-52
Sample Unit Quizzes and Tests for AP Book 8.1
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3. Combine like terms to simplify the expression.
Unit 4: Expressions and Equations
continued
Quiz (Lessons 31 to 34)
4. Write an equivalent expression without brackets.
a) 5(x + 6) = ________________
b) 3(2x + 1) = ________________
c) 4(5x − 2) = ________________
d) 7(−4x − 3) = ________________
Bonus► Which property is being used? Write “commutative,” “associative,” or “distributive.”
a) 5(6x) = (5 × 6)x
____________________________
b) 3(t + 1) = 3t + 3
____________________________
c) a + 5 = 5 + a
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____________________________
Sample Unit Quizzes and Tests for AP Book 8.1
K-53
Unit 4: Expressions and Equations
Answer Key
Quiz (Lessons 31 to 34)
1.
a)
5x + 8 − 8 = 28 − 8
5x = 20
5x ÷ 5 = 20 ÷ 5
x=4
b)
3x − 7 + 7 = 14 + 7
3x = 21
3x ÷ 3 = 21 ÷ 3
x=7
c)
x
− 4 + 4 = −6 + 4
8
x
= −2
8
x
× 8 = −2 × 8
8
x = −16
d)
5 − x − 5 = 18 − 5
−x = 13
−x ÷ (−1) = 13 ÷ (−1)
x = −13
2.
a)
10x
b)
13x − 8x
= 5x
3.
a)
11x + 3
b)
15x + 6
c)
2x + 8 + 3x − 4
= 5x +4
d)
9x + 6 − 7x + 2
= 2x + 8
e)
3.5x − 2.4x + 6.2
= 1.1x + 6.2
4.
f)
2
1 1 2
x+ + x
9
3 6 9
4
1
= x+
9
6
a)
5x + 30
b)
6x + 3
c)
20x − 8
d)
−28x − 21
a)
associative
b)
distributive
c)
commutative
K-54
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Bonus
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 4: Expressions and Equations
Name: ______________________
Quiz (Lessons 35 to 38)
Date: ________________
1. Write the expression without brackets and then simplify.
a) 6 + 5(3x – 2)
b) 7x – 4(6 – 5x)
2. Solve the equation.
a) 7x = 5x + 6
c)
b) 5(x – 3) = 3x – 1
5
1
(3x – 2) = (1 – 3x)
3
6
3. Solve the equation. Is there one solution, no solution, or an infinite number of solutions?
b) x + 7 – 2x = 1 + 3x + 6 – 4x
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a) 5(x + 2) = 5x + 2
Sample Unit Quizzes and Tests for AP Book 8.1
K-55
Unit 4: Expressions and Equations
continued
Quiz (Lessons 35 to 38)
4. The sum of three consecutive numbers is 81. Write and solve an equation to find the numbers.
3x – 8
5. a) Write a simplified expression for the perimeter of the trapezoid.
x
x–1
2x
b) If the perimeter is 26 cm, what are the unknown side lengths? Label the diagram.
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Bonus► There are 550 trees in a forest. There are 100 more spruce trees than fir trees.
There are four times as many pine trees as fir trees. How many spruce trees,
fir trees, and pine trees are in the forest?
K-56
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 4: Expressions and Equations
Answer Key
Quiz (Lessons 35 to 38)
1.
a)
b)
2.
a)
6 + 15x − 10
b)
7x − 9 = 26
= 15x − 4
7x = 26 + 9
7x − 24 + 20x
7x = 35
= 27x − 24
x=5
7x − 5x = 6
Side lengths are:
2x = 6
3x − 8 = 3(5) − 8
= 15 − 8
x=3
b)
=7
5x − 15 = 3x − 1
5x − 3x = −1 + 15
x=5
2x = 14
2x = 2(5)
= 10
x=7
5
5
(3 x ) - (2)
6
6
1
1
= (1) - (3 x )
3
3
5
5 1
x= - x
2
3 3
5
2
1 5
x+ x= +
2
2
3 3
7
x= 2
2
7
x = 2¸
2
2
x = 2´
7
4
x=
7
c)
3.
a)
5x + 10 = 5x + 2
x−1=5−1
=4
Bonus
spruce: x + 100
fir: x
pine: 4x
x + 100 + x + 4x = 550
6x + 100 = 550
6x = 550 − 100
6x = 450
x = 450 ÷ 6
x = 75
There are 175 spruce
trees, 75 fir trees, and
300 pine trees.
5x − 5x = 2 − 10
0x = −8
no solution
b)
x − 2x − 3x +4x
=1+6−7
0x = 0
infinite number of
solutions
4.
x + (x + 1) + (x +2) = 81
3x + 3 = 81
3x + 3 − 3 = 81 − 3
3x = 78
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x = 78 ÷ 3
x = 26
The numbers are 26, 27,
and 28.
5.
a)
P = 3x − 8 + x + 2x
+x−1
P = 7x − 9
Sample Unit Quizzes and Tests for AP Book 8.1
K-57
Unit 4: Expressions and Equations
Name: ______________________
Test (Lessons 27 to 38)
Date: ________________
1. Evaluate the expression with the given variable.
a) 6x, x = 4
b) 5x − 8, x = 7
c) 3x + 9.5, x = 1.1
d) 2(6x + 3), x =
1
3
2. Simplify the expression.
a) 7x − 3x
b) 14x − 6 + 5x − 4
c) 4(10x + 11)
d) (x + 14) − 9(3x − 5) + 2(5x − 6)
3. Solve the equation.
a) 6 + x = 15
b) 5x = 30
c) 5x − 7 = 33
d) 4(5x + 9) = 96
e) 12x + 11 = 5(x + 5)
f)
COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC
4
1
x−5= 9
9
4. Check your answer to Question 3.f).
K-58
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 4: Expressions and Equations
continued
Test (Lessons 27 to 38)
5. Solve the equation. Is there one solution, no solution, or an infinite number of solutions?
a) 7(x + 4) − 14 = 4(2x + 3) − x + 2
b)
1
1
2
1
x+
= x−
2
3
3
2
6. Explain why there is no solution to the given equation.
3(x + 4) = 8x + 3 − 5x
7. Write the algebraic expression. Let x represent the number.
a) Five times a number.
b) A number increased by fourteen.
c) One less than three times a number.
d) Two more than a number divided by five.
8. Solve the problem by first writing an equation.
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a) Five times six more than a number is 45. What is the number?
b) A box contains 25 red and yellow beads. There are four times as many
red beads as yellow beads. How many of each color of beads are there?
Sample Unit Quizzes and Tests for AP Book 8.1
K-59
Unit 4: Expressions and Equations
continued
Test (Lessons 27 to 38)
9. Solve the problem by first writing an equation.
a) The sum of three consecutive odd numbers is 63. What are the three numbers?
b) There are oranges, apples, and bananas in a fruit bowl. There are four more
oranges than apples. There are three times as many oranges as bananas.
If there are 17 pieces of fruit in the fruit bowl, how many of each kind of fruit
are there?
COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC
Bonus► Write an equation with the solution x = 0.5 that has at least one variable term
on each side and brackets on one side.
K-60
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 4: Expressions and Equations
Answer Key
Test (Lessons 27 to 38)
1.
3(1.1) + 9.5
1
2
1 1
x- x= - 2
3
2 3
1
5
- x= 6
6
5æ
6ö
ç
x = - ç- ÷
÷
6 çè 1 ø÷
= 3.3 + 9.5
x= 5
= 12.8
one solution
a)
6(4) = 24
b)
5(7) − 8
b)
= 35 − 8
= 27
c)
d)
æ æ1ö
2çç6 çç ÷
÷+
çè èç3 ÷
ø
ö
÷
3÷
÷
ø÷
6.
= 2(2 + 3)
= 2(5)
= 10
2.
a)
4x
b)
19x − 10
c)
40x + 44
d)
x + 14 − 27x + 45
+ 10x −12
7.
a)
b)
x = 21 ×
3
7
a)
5x
x=3×3
b)
x + 14
c)
3x − 1
d)
x÷5+2
a)
b)
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5.
a)
5(x + 3) = x + 17
red: 4x
There are 5 yellow
beads and 20 red
beads in the box.
12x − 5x = 25 − 11
4
1
(11) - 5 = 9
9
44 45
1
=9
9
9
1
1
- =9
9
Sample answer:
x+6=9
x=5
12x + 11 = 5x + 25
4.
5(x + 6) = 45
5x = 25
x=3
4
8
x= 4
9
9
44 9
x=
´
9 4
x = 11
Answers will vary. Teacher
to check.
x + 4x = 25
20x = 60
f)
Bonus
x
+2
5
yellow: x
20x + 36 = 96
x=2
There are 9 oranges,
5 apples, and
3 bananas.
The number is 3.
5x = 33 + 7
7x = 14
x=9
x=3
x=8
e)
1
x = 21
3
It is impossible to multiply
by 0 and get a number that
is not 0.
x = 30 ÷ 5
5x = 40
d)
2
1
x = 17
3
7
3
x=6
c)
x+x+
x = 21 ÷
or
8.
1
x
3
bananas:
0x = −9
x = 15 − 6
x=9
oranges: x
apples: x − 4
3x + 12 = 8x − 5x + 3
= −16x + 47
3.
b)
9.
a)
x + (x + 2) + (x + 4)
= 63
3x + 6 = 63
3x = 57
x = 19
The numbers are 19,
21, and 23.
7x + 28 − 14
= 8x + 12 − x +2
0x = 0
infinite number of
solutions
Sample Unit Quizzes and Tests for AP Book 8.1
K-61