Download STUDY GUIDE : Chapter 3 : Algebraic

Name: ______________________
Class: _________________
Date: _________
ID: A
STUDY GUIDE : Chapter 3 : Algebraic Expressions (ACC)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Simplify the expression.
4. Which equation is true for all numbers a?
a. a + 0 = a
b. a + 1 = 1
c. a × 0 = a
d. a × 1 = 1
1. 8 + 4c + 8.5 − c
a. 3c + 16.5
b. 19.5c
c. 19.5 + c
d. −3c + 16.5
5. Sheryl earns money for college by walking dogs
and by mowing lawns. She earns $3 for each dog
she walks and $25 for each lawn she mows.
Which expression can be used to determine the
amount of money, in dollars, Sheryl earns from
walking w dogs and mowing m lawns?
a. 3w + 25m
b. 3w + 25
c. 28 ( w + m )
d. 75 ( w + m )
2. The steps Irena took to simplify an expression
are shown below. What should Irena change in
order to simplify the expression correctly?
a.
b.
c.
d.
Multiply 48 and 24 by 12.
Add 12 to(48 + 24)
Divide 48 and 24 by 12.
Multiply 24 by (48 + 12)
Factor the expression using the GCF.
6. 8y − 6x
a. 2(4y − 3x)
b. 2(4y − 6x)
c. 2(4y − 6x)
d. 2y(4 − 3x)
3. An ice cream shop charges $3.39 for a dish of ice
cream. A customer can also order toppings for
$0.59 each. If x represents the number of
toppings, which expression can be used to
determine the total charge, in dollars, for a dish
of ice cream with x toppings?
a. 339x + 0.59
b. 3.39 + 0.59x
c. 3.98 + x
d. 3.98x
7. 10x + 20
a. 10(x + 2)
b. 10(x + 20)
c. 10(x + 4)
d. 10x(1 + 2)
1
Name: ______________________
ID: A
Evaluate the expression when a = 14, b = 10,
and c = 8.
12. A symbol that represents one or more numbers
a. algebraic expression
b. terms
c. variable
d. coefficient
e. constant
f. equivalent expressions
8. 4a + 3
a. 60
b. 56
c. 57
d. 59
13. The numerical factor of a term that contains a
variable
a. algebraic expression
b. terms
c. variable
d. coefficient
e. constant
f. equivalent expressions
Name the word that matches the definition
given.
9. A term without a variable
a. algebraic expression
b. terms
c. variable
d. coefficient
e. constant
f. equivalent expressions
14. Expressions with the same value
a. algebraic expression
b. terms
c. variable
d. coefficient
e. constant
f. equivalent expressions
10. An expression that contains numbers, operations,
and one or more symbols
a. algebraic expression
b. terms
c. variable
d. coefficient
e. constant
f. equivalent expressions
15. Terms of an algebraic expression that have the
same variables raised to the same exponents
a. algebraic expression
b. like terms
c. factoring an expression
d. coefficient
e. constant
f. equivalent expressions
11. The parts of an algebraic expression
a. algebraic expression
b. terms
c. variable
d. coefficient
e. constant
f. equivalent expressions
2
Name: ______________________
ID: A
Write the phrase as an expression.
19. The expression 16 + x + 22 represents the
perimeter of a triangle. Simplify the expression.
a. 38
b. x + 38
c. 54
d. 38x
16. 16 multiplied by the quotient of a number n and
19
ÁÊ n ˜ˆ˜
˜˜
a. 16 ÁÁÁÁ
ÁË 19 ˜˜¯
16
b.
+ 19
n
ÊÁ 16 ˆ˜
˜˜ 19
c. ÁÁÁÁ
˜
ÁË n ˜˜¯
d.
Use the Distributive Property to write and
simplify an expression for the area of the
rectangle.
16
19n
20.
Write an expression for the problem.
17. You wash 30 cars in 3 hours. How many cars do
you wash per hour?
a. Cars washed per hour = 30 • 3
b. Cars washed per hour = 10 ÷ 3
c. Cars washed per hour = 30 ÷ 3
d. Cars washed per hour = 3 ÷ 30
18. A tortoise weighed 72 pounds two years ago.
Today it weighs 89 pounds. How many pounds did
the tortoise gain?
a. Pounds gained = 72 + 89
b. Pounds gained = 89 – 72
c. Pounds gained = 72 • 89
d. Pounds gained = 2(89 – 72)
a.
b.
c.
d.
x+3
3x + 9
3x + 3
3x + 6
a.
b.
c.
d.
340 − 20x
340 − x
20 − 17x
340 − 17x
21.
3
Name: ______________________
ID: A
Numeric Response
Evaluate the expression when a = 4, b = 2,
and c = 8.
Evaluate the expression when x = 4 and y =
1.
1. a + 7
4. (x − 1)(y − 1)
2. bc
5. The running time (in minutes) of a TV episode is
30 – 0.5c where c is the number of commercials
aired during the episode. What is the running time
of an episode with 15 commercials?
3. A player’s score in the game of horseshoes is
based on the number of “ringers” r and the
numbers of horseshoes closest to the stake c that
a player throws. Use the formula below to
determine the score of a player who throws 4
ringers and 7 horseshoes closest to the stake.
3r + c
Short Answer
Identity the terms, coefficients, and
constants of the expression.
Complete the table.
5.
1. 5h + 9
x
1
3
5
2
2. a + 2 + 7b
4x – 1
Write the phrase as an expression.
Write the expression using exponents.
3. r • r • r • r • r • r
6. the sum of 25 and 14
4. 4 • d • d • d
7. a number x multiplied by 3
8. 4 less than a number w
4
Name: ______________________
ID: A
Tell which property the statement
illustrates.
20. 6(8 – x)
9. 6 + (4 + x) = (6 + 4) + x
Simplify the expression.
21. 2(6 + 3n) – 4
10. 5 • (3 • z) = (5 • 3) • z
22. 5a + 7 – 3a – 2
11. 0 + z = z
23. 6a + 2b + 3(a + b)
12. 3(x – 3) = 3x – 9
Factor the expression using the GCF.
13. 3 + z = z + 3
24. 24 – 9
14. 8(1) = 8
25. 54 – 30
15. (2 • 5)c = 2(5 • c)
26. 12y – 8
Simplify the expression. Explain each step.
27. 5x + 60y
16. 3.5 + (x + 2.7)
Write the phrase as an expression. Then
evaluate the expression when x = 3 and y = 6
17. 2 + (g + 5)
28. the product of 8 and a number x
18. 7(4p)
29. the quotient of a number y and 2
Use the Distributive Property to simplify
the expression.
19. 7(x + 3)
5
Name: ______________________
ID: A
30. Complete the table.
31. To find the sales tax on an item, divide the price of the item by 20.
a. Write an algebraic expression to find the sales tax on an item that costs d dollars.
b. Find the sales tax on a television that costs $800.
6
ID: A
STUDY GUIDE : Chapter 3 : Algebraic Expressions (ACC)
Answer Section
MULTIPLE CHOICE
1. ANS:
NAT:
MSC:
2. ANS:
A
PTS: 1
6.EE.2c | 6.EE.3
Knowledge
A
DIF: Level 1
REF: Section 3.4
KEY: simplify | expression
Feedback
A
B
C
D
Correct answer
The student thinks that a number next to a quantity in parentheses represents the
operation of addition.
The student thinks that a number next to a quantity in parentheses represents the
operation of division.
The student thinks that the 24 should be distributed instead of the 12.
PTS:
NAT:
MSC:
3. ANS:
1
DIF: Level 2
6.EE.3 | 6.EE.4
Comprehension
B
REF: Ch 3 Standards Assessment
KEY: Distributive Property
Feedback
A
B
C
D
The student writes an expression that multiplies the cost of a dish of ice cream by
the number of toppings and represents the cost per topping as a one-time charge.
Correct answer
The student adds the charges for a dish of ice cream and one topping and then adds
the number of toppings to this sum.
The student adds the charges for a dish of ice cream and one topping and then
multiplies this sum by the number of toppings.
PTS: 1
NAT: 6.EE.2a
DIF: Level 2
REF: Ch 3 Standards Assessment
KEY: algebraic expression
MSC: Application
1
ID: A
4. ANS: A
Feedback
A
B
C
D
Correct answer.
The student misapplies the multiplication property of one to the operation of
addition, thinking that one added to any number equals one.
The student misapplies the addition property of zero to the operation of
multiplication, thinking that any number multiplied by zero equals the number itself.
The student misapplies the multiplication property of one, thinking that any
number multiplied by one equals one.
PTS:
NAT:
KEY:
MSC:
5. ANS:
1
DIF: Level 2
REF: Ch 3 Standards Assessment
6.EE.3
Multiplication Property of Zero | Multiplication Property of One | Addition Property of Zero
Comprehension
A
Feedback
A
Correct answer
B
The student does not multiply the earnings per lawn by the number of lawns mowed,
representing the earnings per lawn as a one-time charge.
The student adds the earnings per dog and the earnings per lawn and then multiplies
this sum by the sum of the number of dogs and the number of lawns.
The student multiplies the earnings per dog by the earnings per lawn and then
multiplies this product by the sum of the number of dogs and the number of lawns.
C
D
6.
7.
8.
9.
10.
11.
12.
PTS:
NAT:
ANS:
NAT:
KEY:
MSC:
ANS:
NAT:
KEY:
MSC:
ANS:
NAT:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
MSC:
ANS:
TOP:
1
DIF: Level 2
REF: Ch 3 Standards Assessment
6.EE.2a
KEY: algebraic expression
MSC: Application
A
PTS: 1
DIF: Level 1
REF: Extension 3.4
6.EE.3 | 6.NS.4
factor | greatest common factor | GCF | numerical expression | Distributive Property
Knowledge
A
PTS: 1
DIF: Level 1
REF: Extension 3.4
6.EE.3 | 6.NS.4
factor | greatest common factor | GCF | numerical expression | Distributive Property
Knowledge
D
PTS: 1
DIF: Level 1
REF: Section 3.1
6.EE.2c
KEY: evaluate | expression | variable
MSC: Knowledge
E
PTS: 1
DIF: Level 1
REF: Section 3.1
Vocabulary KEY: constant
MSC: Knowledge
A
PTS: 1
DIF: Level 1
REF: Section 3.1
Vocabulary KEY: algebraic expression
MSC: Knowledge
B
PTS: 1
DIF: Level 1
REF: Section 3.1
Vocabulary KEY: terms (of an algebraic expression)
Knowledge
C
PTS: 1
DIF: Level 1
REF: Section 3.1
Vocabulary KEY: variable
MSC: Knowledge
2
ID: A
13. ANS:
TOP:
14. ANS:
TOP:
15. ANS:
TOP:
16. ANS:
NAT:
MSC:
17. ANS:
NAT:
18. ANS:
NAT:
19. ANS:
NAT:
MSC:
20. ANS:
NAT:
MSC:
21. ANS:
NAT:
MSC:
D
PTS: 1
DIF: Level 1
REF: Section 3.1
Vocabulary KEY: coefficient MSC: Knowledge
F
PTS: 1
DIF: Level 1
REF: Section 3.3
Vocabulary KEY: equivalent expressions
MSC: Knowledge
B
PTS: 1
DIF: Level 1
REF: Section 3.4
Vocabulary KEY: like terms
MSC: Knowledge
A
PTS: 1
DIF: Level 1
REF: Section 3.2
6.EE.2a | 6.EE.6
KEY: write an expression
Knowledge
C
PTS: 1
DIF: Level 1
REF: Section 3.2
6.EE.2c
KEY: write an expression
MSC: Comprehension
B
PTS: 1
DIF: Level 1
REF: Section 3.2
6.EE.2c
KEY: write an expression
MSC: Comprehension
B
PTS: 1
DIF: Level 2
REF: Section 3.4
6.EE.2b | 6.EE.3 | 6.EE.4
KEY: addition | properties | simplify
Application
B
PTS: 1
DIF: Level 2
REF: Section 3.4
6.EE.2b | 6.EE.3 | 6.EE.4
KEY: Distributive Property | write an expression | simplify | area
Application
D
PTS: 1
DIF: Level 2
REF: Section 3.4
6.EE.2b | 6.EE.3 | 6.EE.4
KEY: Distributive Property | write an expression | simplify | area
Application
NUMERIC RESPONSE
1. ANS: 11
PTS: 1
DIF: Level 1
KEY: evaluate | algebraic expression
2. ANS: 16
REF: Ch 3 Quiz 1
MSC: Knowledge
NAT: 6.EE.2c
PTS: 1
DIF: Level 1
REF: Ch 3 Quiz 1 NAT: 6.EE.2c
KEY: evaluate | algebraic expression
MSC: Knowledge
3. ANS:
19
Common error: The student makes an order of operations error by first adding 4 and 7 and then multiplying 3
by this sum to get 3(4 + 7) = 33
PTS: 1
NAT: 6.EE.2
4. ANS: 20
DIF: Level 2
REF: Ch 3 Standards Assessment
KEY: algebraic expression | evaluate
MSC: Application
PTS: 1
DIF: Level 1
KEY: evaluate | algebraic expression
REF: Ch 3 Test B NAT: 6.EE.2c
MSC: Knowledge
3
ID: A
5. ANS: 22.5 minutes
PTS: 1
DIF: Level 2
KEY: algebraic expression | evaluate
REF: Ch 3 Test A NAT: 6.EE.2a | 6.EE.6
MSC: Application
SHORT ANSWER
1. ANS:
terms: 5h, 9
coefficient: 5
constant: 9
PTS: 1
DIF: Level 1
REF: Ch 3 Quiz 1 NAT: 6.EE.2c
KEY: algebraic expression | terms (of an algebraic expression) | coefficient | constant
MSC: Knowledge
2. ANS:
terms: a 2 , 2, 7b
coefficients: 1, 7
constant: 2
PTS: 1
DIF: Level 1
REF: Ch 3 Quiz 1 NAT: 6.EE.2c
KEY: algebraic expression | terms (of an algebraic expression) | coefficient | constant
MSC: Knowledge
3. ANS:
6
r
PTS: 1
DIF: Level 1
KEY: algebraic expression
4. ANS:
3
4d
REF: Ch 3 Quiz 1
MSC: Knowledge
NAT: 6.EE.2c
PTS: 1
DIF: Level 1
KEY: algebraic expression
5. ANS:
REF: Ch 3 Quiz 1
MSC: Knowledge
NAT: 6.EE.2c
x
1
3
5
4x – 1
3
11
19
PTS: 1
DIF: Level 2
KEY: algebraic expression | evaluate
6. ANS:
25 + 14
PTS: 1
DIF: Level 1
KEY: numerical expression
REF: Ch 3 Quiz 1 NAT: 6.EE.2c
MSC: Comprehension
REF: Ch 3 Quiz 1
MSC: Knowledge
4
NAT: 6.EE.2a
ID: A
7. ANS:
x•3
PTS: 1
DIF: Level 1
KEY: algebraic expression
8. ANS:
w– 4
REF: Ch 3 Quiz 1
MSC: Knowledge
NAT: 6.EE.2a
PTS: 1
DIF: Level 1
KEY: algebraic expression
9. ANS:
Associative Property of Addition
REF: Ch 3 Quiz 1
MSC: Knowledge
NAT: 6.EE.2a
PTS: 1
DIF: Level 1
REF: Ch 3 Quiz 2
KEY: Associative Properties of Addition and Multiplication
10. ANS:
Associative Property of Multiplication
NAT: 6.EE.3
MSC: Knowledge
PTS: 1
DIF: Level 1
REF: Ch 3 Quiz 2
KEY: Associative Properties of Addition and Multiplication
11. ANS:
Addition Property of Zero
NAT: 6.EE.3
MSC: Knowledge
PTS: 1
DIF: Level 1
KEY: Addition Property of Zero
12. ANS:
Distributive Property
REF: Ch 3 Test A NAT: 6.EE.3
MSC: Knowledge
PTS: 1
DIF: Level 1
KEY: Distributive Property
13. ANS:
Commutative Property of Addition
REF: Ch 3 Test A NAT: 6.EE.3
MSC: Knowledge
PTS: 1
DIF: Level 1
REF: Ch 3 Test B NAT: 6.EE.3
KEY: Commutative Properties of Addition and Multiplication
MSC: Knowledge
14. ANS:
Multiplication Property of One
PTS: 1
DIF: Level 1
KEY: Multiplication Property of One
15. ANS:
Associative Property of Multiplication
REF: Ch 3 Test B NAT: 6.EE.3
MSC: Knowledge
PTS: 1
DIF: Level 1
REF: Ch 3 Test B NAT: 6.EE.3
KEY: Associative Properties of Addition and Multiplication MSC: Knowledge
5
ID: A
16. ANS:
3.5 + (x + 2.7) = 3.5 + (2.7 + x)
= (3.5 + 2.7) + x
= 6.2 + x
Commutative Property of Addition
Associative Property of Addition
Add 3.5 and 2.7.
PTS: 1
DIF: Level 1
REF: Ch 3 Quiz 2 NAT: 6.EE.3
KEY: Associative Properties of Addition and Multiplication | Commutative Properties of Addition and
Multiplication
MSC: Knowledge
17. ANS:
2 + (g + 5) = 2 + (5 + g)
Commutative Property of Addition
= (2 + 5) + g
Associative Property of Addition
=7+g
Add 2 and 5.
PTS: 1
DIF: Level 1
REF: Ch 3 Test A NAT: 6.EE.3
KEY: Associative Properties of Addition and Multiplication | Commutative Properties of Addition and
Multiplication
MSC: Knowledge
18. ANS:
7(4p) = (7 • 4)p
Associative Property of Multiplication
= 28p
Multiply 7 and 4.
PTS: 1
DIF: Level 1
REF: Ch 3 Test A NAT: 6.EE.3
KEY: Associative Properties of Addition and Multiplication MSC: Knowledge
19. ANS:
7x + 21
PTS: 1
DIF: Level 1
KEY: Distributive Property
20. ANS:
48 – 6x
REF: Ch 3 Quiz 2
MSC: Knowledge
NAT: 6.EE.2b | 6.EE.3
PTS: 1
DIF: Level 1
KEY: Distributive Property
21. ANS:
8 + 6n
REF: Ch 3 Quiz 2
MSC: Knowledge
NAT: 6.EE.2b | 6.EE.3
PTS: 1
DIF: Level 1
KEY: Distributive Property | like terms
22. ANS:
2a + 5
REF: Ch 3 Quiz 2
MSC: Knowledge
NAT: 6.EE.3 | 6.EE.4
PTS: 1
DIF: Level 1
KEY: Distributive Property | like terms
23. ANS:
9a – 5b
REF: Ch 3 Quiz 2
MSC: Knowledge
NAT: 6.EE.3 | 6.EE.4
PTS: 1
DIF: Level 1
KEY: like terms | algebraic expression
REF: Ch 3 Test B NAT: 6.EE.3 | 6.EE.4
MSC: Knowledge
6
ID: A
24. ANS:
3(8 – 3)
PTS: 1
DIF: Level 1
REF: Ch 3 Quiz 2 NAT: 6.EE.3 | 6.EE.4 | 6.NS.4
KEY: Distributive Property | greatest common factor | GCF | factor
MSC: Knowledge
25. ANS:
6(9 – 5)
PTS: 1
DIF: Level 1
REF: Ch 3 Test A NAT: 6.EE.3 | 6.EE.4 | 6.NS.4
KEY: Distributive Property | greatest common factor | GCF | factor
MSC: Knowledge
26. ANS:
4(3y – 2)
PTS: 1
DIF: Level 1
REF: Ch 3 Test A NAT: 6.EE.3 | 6.EE.4 | 6.NS.4
KEY: Distributive Property | greatest common factor | GCF | factor
MSC: Knowledge
27. ANS:
5(x + 12y)
PTS: 1
DIF: Level 1
REF: Ch 3 Test B NAT: 6.EE.3 | 6.EE.4 | 6.NS.4
KEY: Distributive Property | greatest common factor | GCF MSC: Knowledge
28. ANS:
8x; 24
PTS: 1
DIF: Level 1
KEY: algebraic expression | evaluate
29. ANS:
y
;3
2
REF: Ch 3 Test A NAT: 6.EE.2a | 6.EE.6
MSC: Knowledge
PTS: 1
DIF: Level 1
KEY: algebraic expression | evaluate
30. ANS:
2, 5, 8, 11, 14
REF: Ch 3 Test A NAT: 6.EE.2a | 6.EE.6
MSC: Knowledge
PTS: 1
DIF: Level 2
KEY: algebraic expression | evaluate
31. ANS:
d
a.
20
b. $40
REF: Ch 3 Test A NAT: 6.EE.2c
MSC: Comprehension
PTS: 1
DIF: Level 2
KEY: algebraic expression | evaluate
REF: Ch 3 Test A NAT: 6.EE.6 | 6.EE.2a
MSC: Application
7