Download Math Review

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:
1.
(a )( a )  a
2.
(ab)  a b
3.
(a m ) n  a mn
4.
a 1
5.
6.
m
n
m
m
0
m
a
mn

a
n
a
1
m
a  m
a
mn
m
Exponents Practice
• Practice: Simplify these two expressions.
Answers will still have exponents in them.
• 1) 550 x 512 = ?
• 2)
25
?
3
2
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
2.
0
0
a
0
a 1
3.
0 0
4.
a0  0
1.
a
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
Associative Property:
a+(b+c) = (a+b)+c
Distributive Property:
ab = ba
a(bc) = (ab)c
a(b+c) = ab+ac
Additive Identity:
0+a = a
Multiplicative Identity:
1a = a
Additive Inverse:
a-a = a+(-a) = 0
Multiplicative Inverse:
a
1
 a   1
a
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
These are done together at the
Division
same time, LEFT to RIGHT.
Addition
These are done after × and ÷, LEFT
to RIGHT.
Subtraction
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:
y
2 _
1 _
|
-5
|
-4
|
-3
|
-2
|
-1
-1 _
-2 _
|
1
|
2
|
3
|
4
|
5 x
Formulas For Lines
• Slope-Intercept Form: y=mx+b
m = slope b = y-intercept
y 2  y1
x2  x1
or
m
rise
run
run
y
2 _
rise
• Slope:
m
1 _
|
-5
|
-4
|
-3
|
-2
|
-1
-1 _
-2 _
|
1
|
2
|
3
|
4
|
5 x
b: y-intercept
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)
Geometry
• Include the following two diagrams on your
note sheet:
X
a
X
c
b
Geometry
• The following formulas will be useful for
squares and triangles.
Squares
Perimeter: P = (x+x+x+x) = 4x
Area: A = x2
Volume of a cube: V = x3
Triangle
Pythagorean Theorem: a2 + b2 = c2
Area: 1/2ba
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
Opposite Side (o)
• Trigonometry will deal only with Right
Triangles, and deals with their angles (θ).
• Include the following diagram on your note
sheet:
θ
Adjacent Side (a)
Trigonometry
• The following are the equations used in
trigonometry: sin   opposite
hypotenuse
adjacent
cos  
hypotenuse
opposite
tan  
adjacent
• Pneumonic:
• An easy way to remember this is “soh cah toa”
or Some Old Hippie Caught Another Hippie
Trippin on Acid
Trigonometry Practice
• Solve the Following problem:
• What would tanθ be for the following
triangle?
10 meters
11 meters
θ
5 meters