Mz. H: OLYMPIAD 2010

ALGEBRA NOTES

LESSON 1.1 EVALUATING EXPRESSIONS

ALGEBRAIC DEFINITION OF SUBTRACTION: (add-op)

a - b = a + -b ex) 5 - 2 = 5 + -2 = 3 4 - -10 = 4 + 10 = 14

ALGEBRAIC DEFINITION OF DIVISION:

a divided by b = a/b = a * 1/b

ASSOCIATIVE PROPERTY (addition and multiplication): move the groupings

(a + b) + c = a + (b + c)

(ab)c = a(bc) ex) (1.735 * 25) *4 = 1.735 * (25 * 4) = 173.5

TRANSITIVE PROPERTY

If a = b and b = c then a = c ex) if .5 = 50% and 50% = 1/2 then .5 = 1/2

PEMDAS- Order of operations

LESSON 1.2 PATTERNS

INSTANCE- Example *numbers*

PATTERN- general idea *variable*

instance

ex1) (5 + 8) + 10 = 5 + (8 + 10) ex2) 2 * 5 = 5 + 5

(2 + 7) + 9 = 2 + (7 + 9) 2 * 3 = 3 + 3

(4 + 2 ) + 6 = 4 + ( 2 + 6) 2 * .7 = .7 + .7

pattern

(x + y) + n = x + (y + n) 2 * a = a + a

pattern

ex3) wp = pw

instances

7*4 = 4*7

5*6 = 6*5

.8* 7 = 7*.8

COMMUTATIVE PROPERTY (addition and multiplication)

switch the order

LESSON 1.3 PATTERNS

sequence- a collection of numbers/objects in a specific order

terms- objects of the sequence

*if 2 expressions yield the same results they are equivalent

counterexample- an instance that proves the pattern is not true

LESSON 1.4 PICTURING EXPRESSIONS

scatterplot- graph with individual points not connected

connected graph use when there is a measure being graphed (length, time, area, or weight)

domain all the values that may be meaningfully substituted for the variable

set grouping numbers or objects {use the brackets}

roster {list}

set builder notation {x: x < 7}

name of set (domain)	description	elements
whole numbers	{0, 1, 2, 3, ...}	5, 16/2, 7 million, 0
integers	{...-2, -1, 0, 1, 2 ...} whole #’s and their opposites (no parts/pcs)	-21/3, -17.00, 50
real numbers	set of all numbers	0, .3, -3.001, 4, ∏
non-negative real numbers	pos set of numbers and 0 {x: x > 0}	0, 3.2, 6000