SAT MATH REFRESHER
©Art Martirosyan, PhD
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1. NUMBERS Even and Odd Numbers even+even=even odd+odd=even even+odd=odd even-even=even odd-odd=even
Properties of Equality
Quadratic Equation
Transitive Addition
Positive and Negative Numbers
even-odd=odd odd-even=odd even∙even=even odd∙odd=odd even∙odd=even
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2. ALGEBRA (continued)
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positive+positive=positive negative+negative=negative positive−negative=positive negative−positive=negative positive∙positive=positive
two real solutions one real solution no real solution
Subtraction
negative∙negative=positive positive∙negative=negative positive÷positive=positive negative÷negative=positive negative÷positive=negative
Multiplication Division
Quadratic Formula Cross Multiplication
Squares
Divisibility Rules
Zero Product
the last digit of the number is 0, 2, 4, 6, or 8 the sum of the digits is divisible by 3 the last two digits are divisible by 4 the last digit is 0 or 5 the number is divisible by 2 and 3 the sum of the digits is divisible by 9 the last digit is 0 v - speed t - time d - distance
Prime Numbers - A prime number is divisible by 1 and itself only - The first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 - 1 is not a prime number - 2 is the smallest and the only even prime number %
Decimal Fraction
%
Decimal
Fraction
1%
0.01
1/100
40%
0.40
2/5
2%
0.02
1/50
50%
0.50
1/2
5%
0.05
1/20
60%
0.60
3/5
10% 0.10
1/10
75%
0.75
3/4
20% 0.20
1/5
80%
0.80
4/5
25% 0.25
1/4
100% 1.00
Percent
Average Speed Arithmetic Sequence
Geometric Sequence
1
Percent Proportion
Percent Change
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2 3 4 5 6 9 10
Exponents
Transitive Addition Subtraction Multiplication
Division
Rules of Exponents
Rational Exponent
Absolute Value
Radicals
Direct Variation
2. ALGEBRA Algebraic Properties
Rational Expressions
Properties of Inequality
Inverse Variation
FOIL Square of Sum/Difference
3. GEOMETRY Convex Polygons Difference of Two Squares
- The sum of the interior angles is - The sum of the exterior angles is 360° Quadrilaterals
The sum of the interior angles is 360°
Similar Polygons - Corresponding angles are equal - Corresponding sides are proportional
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3. GEOMETRY (continued)
Any side of a triangle is shorter than the sum of the two other sides
Angles of Triangles
1
Pythagorean Theorem
a
30°-60°-90° Triangles
45°-45°-90° Triangles
Equilateral Triangles
45°
30°
60°
2
2
3 90°
90°
a
60°
a 45°
60°
60°
Parallelogram B
Rectangle C
B
O
A
Square C
B O
O D
A
A
D
Area
Perimeter
=
45° 45°
= 2
C
D
Circle
triangle
Triangle
rectangle square
Parallelogram Rectangle
θ/2
θ
Circle
Square
Radius=r Diameter= Circumference= Area=
Trapezoid
Volume
Linear Functions y
Quadrant 2
Quadrant 1
( , +)
(+, +)
Quadrant 3
Quadrant 4
( , )
(+, )
Distance Formula
intercept
x
Point-Slope Form
y
2
run
1
x-intercept: y-intercept:
Quadratic Functions
y
1
rise
Parallel lines
2 x
x
Parallel lines have the same slope Perpendicular Lines
- parabola opens upwards - parabola opens downwards
The product of the slopes of perpendicular lines is -1
Vertical Shift Horizontal Shift
5. PROBABILITY AND STATISTICS Probability of an Event
Odds
Independent Events Dependent Events Geometric Probability
Fundamental Counting Principle If one event can occur in M ways and another event can occur in N ways, then the total number of ways both events can occur is MN.
Central Angle= Mean The mean is the sum of the numbers divided by the number of values in the set.
Factorial Permutations Combinations
Surface Area
Rectangular Solid Cube Right Cylinder
intercept
Slope-Intercept Form
Slope
Solids Solid
Midpoint Formula
x
3, 4, 5 6, 8, 10 5, 12, 13 7, 24, 25 8, 15, 17 9, 12, 15
c
b
3 4
y
Pythagorean Triples
2 m
The Coordinate Plane
In a triangle, the longest side is opposite the largest angle
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Inequalities in Triangles
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4. COORDINATE GEOMETRY
Median
The median is the middle value in an ordered set of numbers.
Mode
The mode is the value that occurs most frequently in a set of numbers.
