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Name:____________________________________________________________________________________Date:_____/_____/__________
Study guide/ practice
Unit 3 Test, “The Language of Algebra”
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.
Topics:
Order of Operations
Evaluating Algebraic Expressions
Verbal Math Sentences (translating)
Properties
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Commutative
Associative
Distributive
Identity
Inverse
Zero Property
Sequences (Arithmetic and Geometric)
Vocabulary (study the below)
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Expression– math sentence that does NOT contain an equals (=) symbol
Equation– math sentence that MUST contain an equals (=) symbol
Term-- parts of a math sentence separated by either plus signs or minus signs
Variable– letter used in a math sentence that represents a number
Coefficient– the number “with” a variable (3x – “3” is the coefficient)
Constant– a number that stands alone (2x + 5 – “5” is the constant)
On the back of this cover page is the Unit 3 “Quick Guide” – for your reference.
Unit 3, “The Language of Algebra” Quick Guide
Add
Subtract
Multiply
Divide
Sum
Difference
Product
Quotient
total
less
less than
twice (x2)
split
“Seven less than a number is five”
x–7=5
“Seven less a number is five”
7–x=5
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
3
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
4
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.
5
Be able to identify the following properties! Study, study, study!!
Circle ALL of the choices that represent the following property:
1.
2.
Commutative of
Multiplication
Inverse of Addition
4x(-5) = -5(4x)
x+y=y+x
4(xy) = (4x)y
2•½=1
(-2)(x + 3) = (x + 3)(-2)
5(0) = 0
5 + (-3 + 3) = 5 + 0
4(0) = 06
𝟑
𝟖
𝟖
• 𝟑 =1
4x + (-4x) = 0
9 •
𝟏
𝟗
= 1
2–2=0
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
7
Fill-in-the-Blanks:
An arithmetic sequence is a sequence where the next term is found by either adding or
__________________________________ by the SAME #, and the “rule” for determining what comes next is
described as the common _______________________________ .
A geometric sequence is a sequence where the next term is found by either multiplying or
__________________________________ by the SAME #, and the “rule” for determining what comes next is
described as the common _______________________________ .
Sequence
Rule
(Common
Diff. or Ratio)
1)
-5, -3, -1, 1, 3 . . .
2)
1, 3, 9, 27 . . .
3)
16, 8, 4, 2, 1, ½ . . .
4)
2, -6, 18, -54. . .
5)
10, 6, 2, -2, -6 . . .
What
Comes next?
Arithmetic
or
Geometric?
Multiple Choice:
1) Which of the following sequences is a geometric
sequence?
A.
B.
C.
1, -4, 16, -64 . . .
2, 4, 6, 8. . .
2, -2, -6, -10 . . .
2) What would be the 6th term of the following
arithmetic sequence?
4, 1, -2, -5 . . .
A.
B.
C.
-8
-11
8
3)
Which variable term describes what would come
next in the following sequence?
6, 2, -2, -6 . . .
A.
B.
C.
x+4
4x
x–4
4)
What is the common difference in the following
arithmetic sequence?
1, -4, -9, -14 . . .
A.
B.
C.
-5
5
1/
5
5)
What is the common ratio in the following
geometric sequence?
50, 10, 2, 2 /5 . . .
A.
B.
C.
5
-5
1/
5
Variable
Expression
1.
2.
3.
4.
Which of the following is an
algebraic expression?
For the following expression,
which operation should be
performed first?
(10 – 8 + 3²) ÷ 9 + 3 • 8²
If x = -3, what is x² + x³
Which property does the
following equation represent?
A.
8+2
B.
-8 + 2
C.
-8x + 2
D.
8 + -2
A.
10 - 8
B.
3²
C.
8+3
D.
8²
A.
-36
B.
-18
C.
18
D.
36
A. Commutative Property of Multiplication
B. Commutative Property of Addition
C. Associative Property of Multiplication
D. Distributive Property
5.
Which choice correctly lists
the coefficients of the
following expression?
-9x + 6y – z + 4
A.
x, y, and z
B.
-9, 6, and 1
C.
-9 and 6
D.
-9, 6, and -1
6.
Bob was given:
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
A.
a pretty cool variable
B.
the additive identity number
C.
the additive inverse of
-45 + 17 + 45 + 3
Bob re-wrote the expression
as: (-45 + 45) + (17 + 3)
When evaluating, which
properties will Bob use?
7.
If the number sentence is true,
then y is . . .
𝟏
𝟓
·y =
𝟏
𝟓
1
5
D. the multiplicative identity number
8.
Which property is shown in
the following number
sentence?
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?
A.
Yes, because she correctly followed the
order of operations, and her
calculations are correct.
Why or why not?
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.
A.
2x
B.
x – 12
C.
1
2
( ½ xy + 8 ) + 0 = ( ½ xy + 8)
9.
10.
Which variable expression
describes the following
sequence?
48, 24, 12, 6, 3 . . .
x