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Algebra II Chapter 1 Notes
Notes#1 Section 1.1: Properties of real numbers
Real Numbers
Graph on a number line: 
5
and
4
3
Period:______
Put in descending order:
7 , -2, 1.5, -0.75, -0.5
Properties of Addition and Multiplication
Property
Addition
Closure
Commutative
Associative
Identity
Inverse
Distributive
Name the property that each equation illustrates:
Multiplication
1.) 83 + 6 = 6 + 83
2.) (1)(4y) = 4y
3.) 15x + 15y = 15(x + y)
4.) (8 ∙ 7) ∙ 6 = 8 ∙ (7 ∙ 6)
5.) (8 ∙ 7) ∙ 6 = (7 ∙ 8) ∙ 6
6.) 0 + (-5m) = -5m
7.) 0 = 0 ∙ 18
8.) -2xy + 2xy = 0
2
9.) 1.5    1
3
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Section 1.2: Algebraic expressions
Evaluate and simplify Algebraic expressions
7 3 = 7∙ 7 ∙ 7 = _____
Base:
5 4 =
vs.
Exponent:
(5)4 =
Order of operations:
1.) Substitute a value for the variable (use _______________________!)
2.) Parentheses: do operations that occur with grouping symbols first
3.) Exponents: evaluate the powers
4.) Multiplication and division: Do operations left to right
5.) Addition and subtraction: Do operations left to right
Evaluate:
10.) 4 x 2  6 x  11 when x  3
11.) 5 x( x  2) when x  6
12.)
13.) ( z  3)3 when z  1
14.) -25
15.) (-2)5
16.) (a3  b2 )  a , for a = 2, b = 6
17.)  x 2  2 x  3 when x  2 18.) -42 + 3(15 – 23 ÷ 4)
a  2b
, for a = 1, b=2
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Combining like terms: When adding or subtracting algebraic expressions, look for “buddies” (terms that
have the same _________________). Add/subtract the coefficients but leave the variables/exponents the same.
Simplify each expression.
19.) 4m – 3p – (-m) + 2p
20.) 17k – 4w + w – (-5k)
22.) 2(3h + 2) – 4h
23.) 5(t2 – 3t) – 2t
21.)
5
2
1
4
x y x y
6
3
2
5
24.) 4(2 f  3g )  0.5(6 g  f )
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Section 1.3: Solve linear equations
Solving Linear equations
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Practice:
1.) Solve
2.) Solve
4
x  8  20
5
4x  9  21
3.) Solve:
4.) Solve:
7 x  41  13
3
 x 1  4
5
5.) Solve:
6.) Solve:
3(5 x  8)  2( x  7)  12 x
2
5
1
x  x
3
6
2
HW#1: Pg. 6 #2-20 even, Pg.13 #3-48x3 (3, 6, 9, 12, …), Pg. 21 #3-60x3 (3, 6, 9, 12, …)
Signatures on: syllabus, electronics contract, academic honest contract
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Notes#2: Section1.4 - Rewrite formulas and Equations
Formula:
Solve for a variable:
Solve for r: D = rt
Solve for h: A = ½ bh
Solve for b1: A = ½ ( b1 + b2) h
Solve for r: A = πr2
Solve and find the value of a variable:
Solve: 9x – 4y = 7 for y. Then find value of y
when x = -5.
Solve: 2y + xy = 6 for y. Then find the value
of y when x = -3.
1. Solve for y:
1.Use distributive property to get y by itself
2. Solve for y.
2. Substitute the value for x and solve for
y.
3. Substitute the given value into rewritten
equation.
Practice: Solve each equation for y. Then find the value of y when x = 2.
1. y – 6x = 7
2. 5y – x = 13
3. 3x + 2y = 12
4. 2x + 5y = -1
5. 3 = 2xy – x
6. 4y – xy = 28
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7.) 4xy = 7y – 3
8.) 14 – 5xy = 9y
Translating Sentences to Equations (Use n to represent the number) First write whether each
expression implies addition, subtraction, multiplication, or division:
sum
difference
more than
quotient
product
twice
minus
added to
less than
9. One-third of a number is 12 less than the
number itself.
total
plus
three times
10. Twice a number divided by 6 is 42.
11. Four less than a number, multiplied by 6, is 12. One-half of a number is 7 less than the
25.
number itself.
13. Forty-five divided by a number is 5.
14. Seven more than one-third of a number is
15.
15. Five more than one-third of a number is
18.
16. Nine less than 3 times a number, divided
by four, is 12.
Write an equation and solve. Use n for the number.
17. Four less than a number is 172. Find the
18. Twelve less than a number is -14. Find the
number.
number.
HW#2: Pg. 30 # 2-32 even, Signatures on: syllabus, electronics contract, academic honest contract
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Notes# 3: Sec. 1.6 –Solving Linear Inequalities
1. Graph: x < 2
2. Graph x  1
_______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
_______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
3. Graph: -1 < x < 2
4. Graph: x  2 or x > 1
_______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
_______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
When solving inequalities remember: Flip the inequality sign if you multiply or divide by a negative
number.
5. Solve then graph: 5x + 2 > 7x – 4
6. Solve and graph: 1 – 3x > -14
__________________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
7. Solve and graph: 3 – x > x – 9
8. Solve and graph: 4x + 9 < 25
________________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
When solving an “and” compound inequality:
1. get variable by itself in-between inequality signs
2. “and” problems will graph as a connected line with no arrows
10. Solve and graph: -10 < 3x + 5 < 8
9. Solve and graph: 4  6x 10  14
_______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
11.) Solve and graph: 5  2x  1  8
12.) Solve and graph: 2   x  3  4
_______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
_______________________________
-7 -6 -5 -4 -3 -2 -1 0 1
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When solving an “or” compound inequality:
1. Get variable by itself in each equation
2. Graph will have arrows pointing away or “oars”
13. Solve and graph:
14. Solve and graph:
3x + 5 < 11 or 5x – 7 > 23
2x – 1 ≤ -7 or 4x + 3 ≥ 7
___________________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
_______________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5
15.) Solve and graph:
3x + 2 < -7 or -4x + 5 < 1
16.) Solve and graph:
4v + 3 < -1 or
___________________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
___________________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Write and equation and solve:
17. Jerry is twice as old as Mary. If Jerry is twelve
years old, how old is Mary?
18. John is four times as old as his son. If John is 44
years old, how old is his son?
19. The length of a rectangle is four times the width. If
the length is 20 inches, what is the width?
20. The length of a rectangle is six times the width. If
the length is 18 inches, what is the width?
21. Two-thirds of the students in class are male. If 18
of the students are male, how many are in the class?
22. Three-fourths of the student body attended the pep
rally. If there were 1230 at the pep rally, how many
students are there in all?
23. If
-2v + 7 < 1
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yard of fabric costs $3.75, what does one yard cost?
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HW #3: Pg. 44 #2-50 even, Signatures on: syllabus, electronics contract, academic honest contract
Chapter 1 Test and Notes check on Friday!! (Sections 1.1-1.6)
Print Chapter 2 Notes Packet by Monday
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