Summary

Math Concepts Review Types of triangles:

right equilateral isosceles scalene

Angle rules:

All the angles of a triangle add up to 180 degrees.
If a line MEETS another line, the two angles it makes add up to 180 degrees.
If two lines cross, the angles ACROSS from each other are the same.
Negative numbers:

Adding and subtracting Multiplying and dividing
Add: move RIGHT along the number line.
Subtract: move LEFT

<====== SUBTRACT |---|---|---|---|---|---| -2 -1 0 1 2 3 4 ADD ===========>
If the numbers you are multiplying or dividing have the SAME sign, then the result is POSITIVE(+).
If they have different signs, then the result is NEGATIVE (-)
Example 1: -3 x -3 = +9 (same signs)
Example 2: -3 x +3 = -9 (different signs)
Evaluate expressions:

Multiply Divide Parentheses
A letter and a number together means multiply:
3x = 3 times x These mean divide:
Things inside parentheses are done first:
3x(5 - 2) = 3 x 3 = 9

The circle:

Diameter Circumference Area
D = 2R C = D A = R²

Translating words to expressions:
Word Phrase Expression Comment
three times a number 3x A number next to a variable means multiply
half of a number x/2 "half of", "third of", "one fifth of" all mean multiply by fractions, or divide by the denominator
one minus 3 times a number 1 - 3x
one less than 3 times a number 3x - 1 Tricky! "less than" means subtract from what follows the "less than"
a number increased by 5 x + 5 The word "increase" means add
a number decreased by 8 x - 8 The word "decrease" means subtract
8 more than 5 times a number 5x + 8 "more than" means add
6 less than 3 times a number 3x - 6 "less than" means subtract from what follows the "less than"
Statistics:

Mean Mode Median Range
Mean means average:
The average of {3,8,4} is:
(3+8+4)/3 = 5 Mode means the most common:
The mode of {2,3,3,8} is 3 Median is the one in the middle. The median of
{2,8,5,4,1} is 4 (crossing off the highest and lowest) The range is the highest - the lowest
The range of {2,8,5,4,1} is 8 - 1 = 7
Probability:
Example Problem Answer
1 What is the probability of
a flipped coin turning up heads? because there is 1 head and the coin has 2 sides.

2 What is the probability of pulling,
at random, the ace of spades
out of a deck of 52 cards? because there is only 1 ace of spades and there are 52 cards in the deck.
3 What is the probability of drawing
any ace out of a deck of 52 cards? because there are 4 aces in a deck of 52 cards.
4 What is the probability of drawing a red marble out of a bag containing 2 red marbles and 5 blue marbles?
because there are 2 red marbles
and 7 marbles in all.

Translating words to expressions:
Word Phrase	Expression	Comment
three times a number	3x	A number next to a variable means multiply
half of a number	x/2	"half of", "third of", "one fifth of" all mean multiply by fractions, or divide by the denominator
one minus 3 times a number	1 - 3x
one less than 3 times a number	3x - 1	Tricky! "less than" means subtract from what follows the "less than"
a number increased by 5	x + 5	The word "increase" means add
a number decreased by 8	x - 8	The word "decrease" means subtract
8 more than 5 times a number	5x + 8	"more than" means add
6 less than 3 times a number	3x - 6	"less than" means subtract from what follows the "less than"

Example	Problem	Answer
1	What is the probability of a flipped coin turning up heads?	because there is 1 head and the coin has 2 sides.
2	What is the probability of pulling, at random, the ace of spades out of a deck of 52 cards?	because there is only 1 ace of spades and there are 52 cards in the deck.
3	What is the probability of drawing any ace out of a deck of 52 cards?	because there are 4 aces in a deck of 52 cards.
4	What is the probability of drawing a red marble out of a bag containing 2 red marbles and 5 blue marbles?	because there are 2 red marbles and 7 marbles in all.