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SAT Prep
A.) Sets
 means “belongs to” or “is a member of”
If C is the set of prime numbers, then 17  C
= in either one or the other or both
= in both
Given X = { 2, 3, 5, 7 }
Y = { 1, 3, 5, 7, 9 }
X
Y = { 1, 2, 3, 5, 7, 9 }
X
Y = { 3, 5, 7 }
B.) Signed Numbers and Operations
-,+,0
| a | = distance a is from 0.
(NEVER NEGATIVE)
| a | = 7 then a =
7
| a – 2 | = 7 then a =
5 or 9
a  2  7 or a  2  7
Add
Sub
Mult
Div
+
x, *, ( ), ·
÷,/
Zero Property
sum, total
difference
product
quotient
if ab = 0 then a = 0 or b = 0
Ex. What is the product of the integers -3, -2, -1, …3, 4, 5?
0
Prod/Quot of EVEN number of negatives is POSITIVE
Prod/Quot of ODD number of negatives is NEGATIVE
Reciprocals
Sign Changes
1
(a )  1
a
2 + (-6) = 2 – 6 = -4
2 – (-6) = 2 + 6 = 8
C.) INTEGERS
Number ≠ Integer
Consecutive integers
x , x+1, x+2, x+3, …
Consecutive odd/even integers x , x+2, x+4, …
Ex. The sum of three consecutive integers is less than
75. What is the largest possible value of the first of the three
consecutive integers?
x   x  1   x  2  75
3x  3  75
3x  72
x  24
x  2  26
D.) FACTORS
Factors – Finite set of values - Know your “goes intos”
Multiples – Infinite set of values
GCF and LCM – use product of primes
GCF = product of common primes(1 time)
LCM = product of common primes(1 time) and
uncommon primes.
Ex. Find the GCF and the LCM of 32 and 44.
44
32
11
16
2
2
8
2
2
32  2  2  2  2  2
2
44  2  2 11
GCF  2  2  4
4
2
4
LCM  2  2  2  2  2 11  352
2
E.) EXPONENTS and ROOTS
Rules of exponents
3 + 3 + 3 + 3 = 4(3)
3(3)(3)(3) = 34
a0  1
a a
1
c
bc

 a bc
a a a
b
a
b c
ab
b c

a
ac
x
2
Ex. If  32 find the value of x.
2 2
x 5
x
5
Ex. Which of the following, if any are true?
I. -210  0
II. -  -2
10
Always Negative ---FALSE
0
Always Positive ---TRUE
III. 2  (-2 )  0 Always Positive ---TRUE
10
10
II and III
F.) SQUARES and SQUARE ROOTS
Know your squares/square roots 1-15/1-225
Know exact values.
2
a always +, a 2 answers +/-
Ex. Find the circumference of a circle whose area is 20π
A r
2
20   r
20
r
.
2
20  r
2 5r
2
C  2 r


C  2 2 5  4 5
ab  a b
Rules of radicals:
a
a

b
b
1
n
a  n
a
1
n
a na
Ex. Evaluate the following
A.)
2
3
1 1

3
2
8
B.)
3
8
1
3
82
G.) PEMDAS
Careful with negatives on calculator!!!!
H.) INEQUALITIES
/ or x a -
SWITCH SIGN!!!!
Ex. Solve for a if 5 – 3a < 10.
5  3a  10
3a  5
3a 5

3 3
5
a
3
Properties of Inequalities between 0 and 1.
b
c
1 1
     if b  c
a a
a  a if 0  a  1
1
 a if 0  a  1
a
A.) Fractions and Decimals
Comparing:
Decimals – same # of places – larger # is
larger number
Fractions – same denom. – bigger numer. is
larger fraction
same numer. – smaller denom. is
smaller fraction
Powers of 10 - move decimal place –
+ exponent – move to right
– exponent – move to the left
Rounding
- know rules
- do not need to round grid-ins
Operations with fractions
Add/sub: like denominators
Multiply: numerators and denominators
Divide:
multiply by reciprocals
“of” means multiply
B.) Percents
is
%

of 100
Ex. Find the following:
1.) 45% of 200
x
45

200 100
100 x  45(200)
x  90
90
2.) 90 is 45% of what number?
200
90 45 45 x  90 100

x 100
x  200
3.) 90 is what percent of 200?
90
x

200 100
200 x  90 100
x  45%
45%
Percent increase/decrease
Increase/Decrease = “is”
Original = “of”
C.) Ratio and Proportion
Part : Part
7:3
compared to
Part : Whole
7:10 or 3:10
Two numbers in a ratio of a to b – Apply an x to each.
Ex. Two acute angles of a right triangle are in a ratio of 5:13.
What is the measure of the larger acute angle?
5 x 13x  90
18 x  90
x 5
13 x  13  5  65
Proportions  Cross multiply
Ex. Tommy types 35 words per minute. How long would it
take Tommy to type 987 words?
35 987

1
x
35 x  987
x  28.2
x  28 min 12 sec
Direct Variation
Directly Proportional
x↑
x↓
vs.
vs.
y↑
y↓
Inverse Variation or
Inversely Proportional
x↑
x↓
y = kx
y↓
y↑
y = k/x or k = xy
Ex. If y is directly proportional to x and y = 7 when x = 2, find
the value of y when x is 5.
y  kx
y  3.5 x
7  2k
y  3.5  5
3.5  k
y  17.5
Ex. If it takes 4 workers 2 hours to complete a certain job,
how many minutes would it take 6 workers to complete the
same job?
k
y
x
k
120 
4
k  120(4)
k  480
480
y
x
480
y
6
y  80
A.) Average = Mean = Sum/count
Know the average then sum = average x count
Ex. After 5 tests Tony has an 85 average. If Tony had an 83
average after his first three tests, what was his average on
the last two tests?
T5  5 85  425
T3  3 83  249
425  249
A
 87
2
B.) Median = Middle #
ARRANGE THEM IN ORDER FIRST!!!
Odd # of scores - Find middle #
Even # of scores - Find average of middle 2 #’s
C.) Mode = Number that occurs the MOST