Things you should already know but may have forgotten.

Prepared by Joe Brinkley

Symbolics vs. Numbers• We will be using variables and symbolic

expressions to solve problems• Putting in numerical values is the last step

taken when solving any expression• This is a more advanced way of solving

problems and a natural progression from the “plug and chug” techniques you may have used in the past

• If you insist on using numbers only, some problems become very difficult or even impossible to solve

Fractions• Common Mistakes in fraction reduction

• Getting common denominators

• Adding whole numbers to fractions (it’s the Same)

ba

a

bb

1

1or

1

ba

11

ba

a

ab

b 11

ab

a

ab

b

cb

a

b

bc

b

a

1

ab

ba

b

cb

b

a

b

cba

ba

a

This is already reduced as far as it can be!!

Factoring

bybxayax

yxbyxa

yxba

8)2(2 x

628 yy

System of Equations

• Given equations with more than 1 unknown.• Ex: 82 yx

6 yx

yx 28 y28

82 yx

2 y

4 x

• For more than 2 variables, you need one unique equations for each variable.

• If these equations are not unique (i.e. same equation written a different way), you won’t have enough information to solve for the variables.

Quadratic Equations

• Defined as: • Methods

– Factoring (Recognize the most obvious types)• (difference of squares) • (squared addition)• (squared subtraction)

– Quadratic Formula (if it isn’t obvious, use this)

a

acbb

2

42

02 cbxax

222

222

22

)(2

)(2

))((

yxyxyx

yxyxyx

yxyxyx

Geometry• Pythagorean theorem

• Law of cosines

222 bac

cos2222 abbac

a

b

c

Geometry• Parallel lines cut by a transversal• Perpendiculars

adjacent

oppo

site

Trigonometry

• Relationships for right triangles:

hypoppsin hyp

adjcos adjopptan

hypotenuse

• Inverse functions

Trigonometry

• Common Identitiesbatan ba11 tantantan ba1tan

1cossin 22

tancos

sin

2sinsincos2