Download Math Final Review

Chapter 1
Chapter 2
Chapter 3
Chapter 7
Chapter 11
Chapter 12
Chapter 13
Chapter 4
Chapter 6
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
Ch. 1.
1. Problem Solving Plan: a. read and understand b. make a plan c. solve the problem d. look
back
2. Frequency Table -A table that groups data into intervals
3. Histogram -A graph where data is broken up into intervals
4. Numerical Expression-A mathematical statement using numbers and operations
5. Evaluate-To find the answer
6. Order of Operations: a. Grouping symbols b. Exponents c. Multiply and Divide from left to right
d. Add and Subtract from left to right
7. Solve This Problem:
5 x (18 - 12) + ( 14 + 4) / 6 + 3 - 2 x 4 +9 =
Click on underlined terms
5 x 6 + 18 / 6 + 3 - 8 + 9 =
to see an example.
30 + 3 + 3 - 8 +9 =
33 + 3 - 8 + 9 =
36 - 8 + 9 =
37
8. Algebra-The area of math where we use letters
9. Variable Expression-Its an Expression that contains numbers, variables, and at least 1 operation
10. Exponent-How many of the base to multiply
11. Base-The number that is multiplied together
12. Power-When a product is written as a base and an exponent 
8 to the 2nd Power
13. Squared-To the second power
14. Cubed-To the third power
15. Equation-A math sentence that has an equals sign
16. Solving Equations-Find the number that makes the equation true
17. Solution-The number that makes an equation true
18. Write an Equation and Solve It: 3 x 9 - 2 x 527 - 1017
19. Formulas-an equation that relates two or more quantities
20. Perimeter-The distance around/ sum of all sides P = 2L x 2 W
21. Area-The space inside of a shape A = LxW22. Variable A letter that
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represents a number
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Chapter 1
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Chapter 1
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Chapter 1
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Integers - the positive and negative
numbers
Absolute Value - How many places the
number is from zero on a number line
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Problems:
1. -6 + -8 = -14
2. -5 + 7 = 2
3. 3 + 15 = 18
4. 12 -18 =
12 + -18 = -6
5. 4 - (-7) = 11
6. -12 x -7 = 84
7. 11 x - 8 = -88
8. -3 x 2 = -6
9. -14 / -2 = 7
10. 12 / -3 = -4
Coordinate System - is two intersecting
number lines used to graph things
X Axis - the horizontal number line in a
coordinate system
Y Coordinate - Tells how far up or down the Y axis a point
is in a coordinate system
Y Axis - the vertical number line in a
coordinate system
8 Integer rules:
1. The sum of two positive integers will always be POSTIVE
To get the answer you ADD
Origin - The point where the number lines
intersect in a coordinate system.
Quadrant - The coordinate system is
broken into 4 sections called quadrants.
They get labeled with roman numerals.
Ordered Pair - Two numbers that give
the exact location of a point in a
coordinate plane.
X Coordinate - Tells how far across the X
axis a point is in a coordinate system
2. The sum of two negative integers will always be
NEGATIVE
To get the answer you ADD
3. The sum of two negative integers with different signs will
have THE SIGN OF THE LARGER #
To get the answer SUBTRACT
4. To subtract two integers, change the subtraction to
ADDTION and change the sign of the second number to
its OPPOSITE
11. -15 / 5 = -3
5. The product of two integers with the same sign will
always be POSITVE
To get the answer you MULTIPLY
Commutative Property - going back and
forth will be the same
6. The product of two integers with different signs will
always be NEGATIVE
To get the answer you MULTIPLY
Associative Property - grouping symbols, can
be moved without changing the problem
Identity Property - it doesn't change
Multiplicative Inverse - Flip the Fraction
Distributive Property - it gives an equal
amount
7. The quotient of two integers with the same sign will
always be POSTIVE
To get the answer you DIVIDE
8. The quotient of two integers with different signs will
always be NEGATIVE
To get the answer you DIVIDE
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Chapter 2
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
x+24=31
-24 -24
x=7
1. To solve an equation you always try to find the number that
makes the equation true.
2.You do the order of operations backwards.
-3a=81
-3 -3
a+ -27
3. Add:
add, plus, more than, increased by, total, sum, greater than
2x+10=46
-10 -10
2x=46
22
x=23
Subtract:
minus, difference, decrease, fewer than, less than
- 6y > - 96
_
-6 -6
y > -16
y/9 = 14
x9x9
y = 126
c - 12 = 26
+ 12 + 12
c = 38
x - 14 < 35
+14 + 14
x < 49
Multiply:
times, product, multiply, of
Dividing:
divide, quotient, per
4. inequality - a statement formed by placing an inequality
symbol between expressions
5. solution of an inequality - the set of numbers that you can
substitute for the variable to make the inequality true
6. You reverse the inequality symbol when dividing or multiplying
by a negative.
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Multiple - a number that can be equally divided by another number
4:4,8,12,16,20,24,28,32,36,40, etc.
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Prime Numbers - a number
greater than 1 whose only
factors are 1 and itself.
Composite Number - a
number greater than 1 that
has more factors beside 1
and itself
Factor Tree - used to find
prime factorization
Prime Factorization - is
finding which numbers are
prime and multiply together
to get the original number
ex.36=2x2x3x3
Common Multiple - a number that can be equally divided by the numbers that is
shared by the numbers
LCM - the lowest number that can be equally divided by all the numbers that is
shared by all the numbers
8:8,16,24,32,40
10:10,20,30,40
To multiply two powers with the same base, you simply add the exponents.
7 = x11
x4 * x 

To
divide two powers with the same base, you simply subtract the exponents.
8
y
__ =y
4
4
y
Factors - numbers that divide into the
original number evenly
48:
1,2,3,4,6,8,12,16,24,48
GCF - The highest number that goes into
all of the numbers equally
To change a number with a negative exponent, you make it into a fraction with
one as the numerator and the power as the denominator, but change it from a
negative to a positive.
-2 = 
ex. 2
1
_
2
2
Anything to the zero power is equal to 1.
12:1,2,3,4,6,12
Scientific Notation - A shorter way to write very large or very small numbers
60:1,2,3,4,5,6,10,12,15,20,30,60
1.23 * 1
010
The GCF is 12
Standard Form - The regular way to write numbers
0.000000045
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Write the order in which you solve
multi-step equations (i.e. combining
like terms, solving a 2-step
equation, distributing, getting
variables on one side)
A. 1. distribute 2. get variables on
one side 3. combine like terms 4. two
step equation
How can you tell if you have to
combine like terms?
A. If there is more than one
coefficient followed by the same
variable
How can you tell if you have to
distribute?
A. If there is a number outside of a
group of numbers in parentheses.
How can you tell if you have to move
variables to the same side?
A. If there are variables on both
sides.
Solve the following equations:
5(x + 6) = 45
X=3
6y + 12 – 3y + 15 = 51
Y=8
2x + 14 = 4x – 10
X=6
3(x + 4) + 9x = 48
X=3
6(x – 7) + 8x = 7(x + 4)
X=-1
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Ratio- write this ratio as a fraction in
simplest form and two other ways: 15 Scale Drawing – a drawing of
to 40
something in a size relative to its size
on Earth*
3
Scale – the relation between size of a
8
drawing and size on Earth
3 to 8
3:8
A map has a scale of 1in = 150 miles.
If two cities are 400 miles apart, how
Rate – comparing things with two
many inches apart are they on the
unlike units
map? 2 2/3 inches
Unit Rate – a rate with a denominator
of 1
Using the same scale as above, if
two towns are 4.5 inches apart on the
How do you change a rate to a unit map, how far apart are they in real
rate? You divide both numbers by
life? 675 miles
what you want the unit to be. For
mph, you divide by how many hours.
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Relation – a relation between
mathematical expressions
Input – what goes into the table to
become an output
Output – what number comes out
of an input table
Function – what you do to the
input to get the output
Domain – all the possible input
values
Range – set of all possible values
Scatter Plot – a plot
Solution of an equation with two
variables
Linear equation – an equation
that, when graphed, forms a
straight line
Is the following a function? (2,3), (3,5),
(7,2), (9,1) A. yes
Name the domain and the range of the
set of points above. Domain: 2,3,7,9
Range:3,5,2,1
Find three solutions of y = 6x + 5, and
tell if this is a linear equation.
(Y=17 x=2) (y=11 x=1) (y=23 x=3)
Does the number of days we’ve been in
school and how many days are left in
the school year have a positive
relationship, a negative relationship, or
no relationship? A. Positive relationship
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Range – the largest number subtracted by the smallest
Mean – all of the numbers added then divided by how many there are
Median – the middle number when the set of data is in order from least to greatest
Mode – the number that occurs most often in the set of data
Circle graph – a graphical display that shows data as part of a whole
Line graph – points connected by line segments to show how things change over time
Tree diagram – used to show all possible outcomes of an event
Fundamental Counting Principal – way to calculate the number of possible outcomes
Complementary – angles that measure to 90 degrees
Unfavorable outcome – what you don’t want to happen
Odds – the amount of favorable outcomes to the number of unfavorable outcomes
Probability – the number of favorable outcomes to the total number of possible outcomes
Independent events – an event where the outcome is not affected by another event
Dependent events – an event that the outcome is affected by another event
Use the following set of data to find the range, mean, median, and mode.
8, 10, 11, 8, 12, 19, 13, 12, 8, 10, 13, 8, 1
Range – 18
Mean – 10.2
Median – 13
Mode – 8
If Sally has 8 shirts, 4 pairs of jeans, and 3 pairs of shoes, use either a tree diagram or the fundamental
counting principal to figure out how many different outfits she can make. Then find the probability
that she wears her green shirt, dark jeans, and brown shoes. A. 96 outfits, 1/96
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Monomial – a single term
Binomial – an expression
with two terms
Trinomial – an expression
with three terms
Polynomial – an expression
with more than one term
Standard Form – in a
polynomial where the
exponents are in order
from greatest to least
What do you do to multiply
monomials? – you add the
exponents and multiply
numbers with the same
variable
What do you do to raise a
power to a power? – you
multiply the exponents
together
Do the following problems:
Simplify: 3x2 + 5x5 - 4x + 12 – 2x5 +
10, put it in standard form and
classify it. A. 3x5 + 3x2 – 4x + 22,
polynomial
Add: (3y3 + 2y2 – 6y + 9) + (4y3 – 8y2
+ 8y – 4) A. 7y3 – 6y2 + 2y - 5
Subtract: (6x2 – 4x + 13) – (8x2 – 9x +
5) A. -2x2 + 5x - 8
Multiply: 6c3 (5c7) = 30c10
Multiply: 4d3(3d + 7d2) = 4d4 + 28d5
Simplify: (a5b4c8)3 = a 15 b1 c 24
Simplify: (2x5)3 = 23 x15
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