Download Algebra 2CP - Madison Local Schools

Algebra 2CP
Day 1
Introduction
1.1 Properties of Real Numbers
1.2 Algebraic Expressions
o Assign Seats
o Pass out Syllabus
i) Review how fast the course will be
ii) 1st Assignment – the sheet needs to be signed and returned tomorrow
o Pass out book (Algebra 2)
o Fill out Note Cards
o Pass out Daily Openers
1.1 Properties of Real Numbers
Natural Numbers (Counting Numbers) → {1, 2, 3, 4, 5, …}
Whole Numbers → {0, 1, 2, 3, 4, 5, …}
Integers → {…-3, -2, -1, 0, 1, 2, 3, …}
Rational Numbers → #’s that can be written as a fraction of two integers.
→ can be written as a terminating decimal or a repeating decimal.
→ examples: 0.35, 0.444 , ¾, ⅝
Irrational Numbers → #’s that cannot be written as a fraction of two integers.
→ non-terminating, non-repeating decimals.
→ examples: 3 , 10 , π
PROPERTIES OF REAL NUMBERS
PROPERTY OF ADDITION
PROPERTY OF MULTIPLICATION
Commutative
m+n=n+m
m∙n=n·m
Associative
(m +n) + p = m + (n + p)
(m ∙ n) ∙ p = m ∙ (n ∙ p)
Identity
m+0=m
m∙1=m
Inverse
m + (-m) = 0
Closure
m + n is a real number
Distributive Property
m(n + p) = mn + mp
m∙
1
=1
m
mn is a real number
Ex. Identify the property:
(a) 4 + 5 = 5 + 4
(c) x + 0 = x
(b) (x ∙ y) ∙ 2 = x ∙ (y ∙ 2)
(d)
3 4
4
k  = 9
4 3
3
(e) 2ab = 2ba
Ex. Simplify: 10yz – 12zy – z3y – 7yz3
absolute value – the distance a number is from zero on a number line.
Ex. Compare with  and .
(a) 7 ▓  8
(b)  3 ▓  5
(c)   9 ▓ 11
1.2 Algebraic Expressions
variable – a symbol, letter, that represents a number.
expression – a group of numbers and variables, [no =].
algebraic expression – expression that contains one or more variables.
term – expressions separated by addition or subtraction signs.
coefficient – the number in front of a variable.
Ex. How many terms?
(a) 4x2yz – 5yz3 + 2xz
(b) 0.565a 5 b 6 c 7  0.1875ab 8 c 9
like terms – terms with exactly the same variable part.
unlike terms – terms with different variable parts.
simplify – combining like terms.
NOTE: a problem is simplified when only unlike terms are left
Ex. Simplify: 3c  8d  5c  10d  18c  6d
Ex. Simplify: 2(4 x  5 y )  3(2 x  3 y )
2
2
2
2
Ex. Simplify: 2mn  5mn  3m n  6mn  2mn  5m n
Ex. Simplify: 56 j  (80 j )  200k  3(75k )
Ex. Simplify:
5
1
3
4
m m p p
8
6
4
5
Ex. Simplify:
2 2 1
1
7
1
x  x  x2  x  x2
5
5
3
15
2
 Copy chart on page 13 if necessary.
Homework – pages 8–9 #1–11, 12–62 even
pages 15–16 #2–52 even, 54–63 all
Daily Openers – 1. Evaluate: 2 x  8 y , when x = 5 and y = -3
2. Simplify: 3x 2  8x  9  22 x 2  12 x  7
3. Simplify: 4 x 3  5 x 9  x
1
1
5
x  x
2
6
24
5. Evaluate: 40  24  8  2 2  1
4. Solve: