Math Review

Gallery Walk

Laws of Exponents

• These rules deal with simplifying numbers when there is more than one exponent in an equation. The letters a, b, m and n represent whatever number happens to show up in a particular problem (2, 5, 2000, 1.4, …).

The Laws of Exponents Are:

mm

nmn

m

mnnm

mmm

nmm

aa

aa

a

a

aa

baab

aaa n

1

1

)(

)(

))((

0

1.

2.

3.

4.

5.

6.

Exponents Practice

• Practice: Simplify these two expressions. Answers will still have exponents in them.

• 1) 550 x 512 = ?

• 2) ?2

23

5

Rules of Zero

• These are rules showing how to simplify when there are zeros in an expression, and when you cannot simplify ( A number is undefined)

Rules of Zero

00

00

1

00

0

a

a

a

a

1.

2.

3.

4.

Rules of Zero

• Practice: Simplify the following two expressions:

• 1. 19500 = ?• 2. 01,000,000 = ?

Algebraic Simplification

• Basic rules that can be used to simplify or rearrange formulas.

• These are most useful when using variables in equations, but can also be useful with numbers too.

Algebraic Simplification• Commutative Property:• a+b = b+a ab = ba • Associative Property:• a+(b+c) = (a+b)+c a(bc) = (ab)c• Distributive Property:• a(b+c) = ab+ac• Additive Identity:• 0+a = a• Multiplicative Identity:• 1a = a• Additive Inverse:• a-a = a+(-a) = 0• Multiplicative Inverse: 1

1

a

aa

a

Algebraic Simplification

• Practice: Rewrite the following two expressions using the rules of simplification:

• 1. a(b+c) = ?

• 2. a(bc) = ?

Order of Operations

• In order to correctly simplify a formula, you have to do the math in a certain order. Use the Pneumonic PEMDAS to help you remember that order.

Order of Operations

• Parenthesis- do all math inside () first.• Exponents- group or simplify any exponents• Multiplication• Division• Addition• Subtraction

These are done together at the same time, LEFT to RIGHT.

These are done after × and ÷, LEFT to RIGHT.

Order of Opperations

• Simplify the following into a single numerical answer:

• 1. (3+2)2 = ?• 2. 5+3*4-2 = ?

Lines

• With lines, you need to be able to calculate slope and recognize Slope-Intercept Form for the equation of a line. Copy the following diagram onto your review sheet:

-5 -4 -3 -2 -1 1 2 3 4 5 x

y2

1

-1

-2

| | | | | | | | | |

_

_

_

_

Formulas For Lines

• Slope-Intercept Form: y=mx+bm = slope b = y-intercept

• Slope: or12

12

xx

yym

run

risem

-5 -4 -3 -2 -1 1 2 3 4 5 x| | | | | | | | | |

_

_

_

_

y2

1

-1

-2b: y-intercept

rise

run

Practice with Lines

• Complete the following two problems:• 1.) Write the equation for the line shown in

the diagram using slope-intercept form.

• 2.) What is the slope of a line with equation: y = 12x - 4

Geometry

• In Geometry, we will be using formulas dealing with circles, squares, and triangles.

• Include the following diagram on your handout:

r: radius

Circle Formulas

• The following formulas will be useful for circles and spheres:

• Perimeter: 2πr• Area: πr2

• Surface Area of a Sphere: 4πr2

• Volume of a Sphere: 4/3πr3

Note: π is just a number that never changes (π=3.14 always)

• Include the following two diagrams on your note sheet:

a c

b

Geometry

X

X

• The following formulas will be useful for squares and triangles.SquaresPerimeter: P = (x+x+x+x) = 4xArea: A = x2

Volume of a cube: V = x3

TrianglePythagorean Theorem: a2 + b2 = c2

Area: 1/2ba

Geometry

Geometry Practice

• Solve for the following:• 1.) What is the Volume of a cube that

measures 2cm to a side?

• 2) What is the length of side c of this traingle?

3 c

4

Trigonometry

• Trigonometry will deal only with Right Triangles, and deals with their angles (θ).

• Include the following diagram on your note sheet:

θ

Hypotenuse (h)

Opp

osite

Sid

e (o

)

Adjacent Side (a)

Trigonometry

• The following are the equations used in trigonometry:

• Pneumonic:• An easy way to remember this is “soh cah toa”

or Some Old Hippie Caught Another Hippie Trippin on Acid

adjacent

opposite

hypotenuse

adjacent

hypotenuse

opposite

tan

cos

sin

Trigonometry Practice

• Solve the Following problem:• What would tanθ be for the following

triangle?

θ

10 meters 11 meters

5 meters