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Name:__________________________________________________________________________________Date: _____/_____/__________
Note: Many problems in this packet will be completed together in class
during review time. Students are not expected to complete every single
problem in the packet. They should complete several problems from each
page-- in addition to studying the notes and past quizzes– in order to be
fully prepared for test.
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TOPICS COVERED ON “The language of algebra” TEST:
Order of Operations
Evaluating Algebraic Expressions (substituting numbers for variables)
Translating Algebraic Sentences
Properties (Commutative, Associative, Distributive, Identity, Inverse,
and Zero Properties)
Vocabulary:
Algebraic Expression v. Equation
Constant
Coefficient
Variable
NOTES SPACE/HELPFUL TIPS (to be filled out in class):
Evaluate – (1) Parentheses, (2) Exponents, (3) Multiply or Divide , & (4) Add or Subtract:
(left to right)
(left to right)
1. 3(12 − 6) −8
2.
12 + 4(5 − 8)²
3.
12 + 4(5 − 8²)
4.
1 + (- 2) − 2 ⋅ 27 ÷ 32
5.
-4 2 + 14(-2)
6.
(-23 −2)2 + 23
7.
3 + 8 – (6 ÷ 3 + 42)
8.
-2 + 2(-8)
3(3)-3
2
Evaluate the following by substituting the given #’s for each variable:
1.
xy – y -- when x = -3 and y = -1
2.
4(m)(p)2 -- when m = 4 and p = -3
3.
(x + y)2 -- when x = -4 and y = 6
4.
(x + y2) -- when x = -4 and y = 6
5.
-3(x + 4y) + 2 -- when x = -7 and y = -2
6.
x2 + (y – x ÷ 2) -- when x = -2 and y = 7
7.
5(n + m2) -- when m = 6 and n = 4
8.
72 ÷ y³ -- when x = 3 and y = -2
3
Translate the following verbal expressions/ sentences into algebraic sentences.
1)
Forty less than a number is five.
2)
Forty less a number is five.
3)
the product of triple a number and eight
4)
the difference of twice a number and two
5)
The total of double a number and six is fifty.
6)
the quotient of a number and ten
7)
twice the sum of a number and four
8)
Triple the difference of a number and six is twelve.
9)
Five less than a number divided by two is four.
10) the quotient of a number squared and two
11)
the product of nine and a number cubed
12)
Double the sum of a number squared and two is thirty-six.
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Be able to identify the following properties! Study, study, study!!
5
Applying Properties:
1) Apply the Commutative Property in order to evaluate the following
expression (give final answer as well): 3 + 13 + 10 = ______________________________
2)
Apply the Associative Property in order to evaluate the following
expression (give final answer as well): (9 + 12) + 8 = ______________________________
3)
Apply the Distributive Property in order to evaluate the following
expression (give final answer as well): 3(4 + 20) = ________________________________
4)
Apply the Inverse Property in order to evaluate the following
expression (give final answer as well): 75( 2/5 ● 5/2) = _____________________________
Name the property represented by the following equations:
5) -35 + 35 = 0 ___________________________________________________________________________
6) (½ xyz)(1) = ½ xyz____________________________________________________________________
7) (¾ y)(0) = 0____________________________________________________________________________
8) -50 + 0 = -50___________________________________________________________________________
Identify the properties used for EACH STEP in order to simplify the following
expressions:
9)
10)
50 + 100 + (-50)
Step 1 = 50 + (-50) + 100
Step 2 = [ 50 + (-50) ] + 100
Step 3 = 0 + 100
Step 4 = 100
4(6 + 7) + 6
Step 1 = 24 + 28 + 6
Step 2 = 24 + 6 + 28
Step 3 = (24 + 6) + 28
Step 4 = 30 + 28
Step 5 = 58
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property
_____________________________ Property of Addition
_____________________________ Property of Addition
6
1)________
Which of the following is an algebraic expression?
A.
8+2
B.
-8 + 2
C.
-8x + 2
D.
8 + -2
2) _________ Which of the following correctly lists the coefficients of the following
expression?
A.
x, y, and z
B.
-9, 6, and 1
C.
-9 and 6
D.
-9, 6, and -1
-9x + 6y – z + 4
3) ________ For the following expression, which operation should be performed first?
(10 – 8 + 3²) ÷ 9 + 3 • 8²
4)________
5)________
A.
10 - 8
B.
3²
C.
8+3
D.
8²
If x = -3, what is x² + x³
A.
-36
B.
-18
C.
18
D.
36
Which property does the following equation represent?
(2x)y = 2(xy)
A. Commutative Property of Multiplication
B. Inverse Property of Multiplication
C. Associative Property of Multiplication
D. Distributive Property
6)________
Bob was given -45 + 17 + 45 + 3 to evaluate. In order to make it
easier to evaluate mentally, he re-wrote the expression as follows:
(-45 + 45) + (17 + 3)
When evaluating, which properties will Bob use?
7)_______
A.
the associative property and the distributive property
B.
the commutative, associative, and inverse properties
C.
the commutative, associative, inverse, and identity properties
D.
the commutative and zero properties
If the number sentence is true, then y is the . . .
𝟏
𝟏
·y =
𝟓
𝟓
A.
a pretty cool variable
B.
the additive identity number
C.
the additive inverse of
1
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D. the multiplicative identity number
8)________
Which property is shown in the following number sentence?
( ½ xyz + 8 ) + 0 = ( ½ xyz + 8)
9)________
A.
multiplicative inverse property
B.
additive identity property
C.
Multiplicative identity property
D.
Additive inverse property
Kate evaluated -32 + 11 , and got 20 as her answer. Is this correct?
Why or why not?
A.
Yes, because she correctly followed the order of operations, and her
calculations are correct.
B.
No, because -32 is -9 , therefore, “2” should be the correct answer.
C.
Yes because Kate always gets the right answer.
D.
No, because she did not follow the order of operations.