Formulas to Remember for the Math Section of SAT
Algebra
Percents:
Percent Change= Change/Original × 100
Part = Percent /100 × Whole
Examples:
75% of 300 is what?
Solve x = (75/100) × 300 to get 225
45 is what percent of 60?
Solve 45 = (x/100) × 60 to get 75%
Example: 30 is 20% of what?
Solve 30 = (20/100) × x to get 150
Average Speed = total distance/total time
Distance =rate × time
FOIL: (x + a)(x + b) = x ^2 + (b + a)x + ab
Difference of Squares:
a) a ^2 − b ^2 = (a + b)(a − b)
b) a ^2 + 2ab + b^ 2 = (a + b)(a + b)
c) a ^2 − 2ab + b^ 2 = (a − b)(a − b)
Distance Formula: SQRT (x2 − x1) ^2 + (y2 − y1) ^2
Mid-point of the segment AB: x1 + x2 /2, y1 + y2/2
Slope of the line: y2 − y1 / x2 − x1 = rise run
Geometry
Opposite Angles are equal, so a+b and 180 degrees.
All the “a’s” are equal and all the “b’s” are equal. Any “a” plus any “b” equals 180 degrees.
Right Triangle Formulas***
Triangle area= ½*b*h ***
Angles in a triangle add up to 180 degrees.***
Circles
Area of a Circle = πr2 ***
Circumference = 2πr ***
Full circle = 360◦ ***
Length Of Arc = (n ◦ /360◦ ) × 2πr
Area Of Sector = (n ◦ /360◦ ) × πr2
Total number of degrees in the interior of an n-sided polygon= (n-2) × 180 where n is the number of sides.
For example, an eight-sided polygon (or octagon) has:
(8 – 2) · 180 = 6 · 180 = 1080 degrees
Arithmetic
Arithmetic sequence formula: an=a1+d(n-1)
a1=first term, d =distance between the numbers, and n= term to find
Example: Find tenth term in 3,7,11….
a10=3+4(10-1)= 63
Geometric sequence formula: an=a1×r(n-1)
a1=first term, r =rate between the numbers, and n= term to find
Example: Find 6th term in 3,6,12…
a6=3×2(6-1) = 3×2 5=3×32= 96
Functions
I was putting together a cheat sheet for studying for the math section of the SAT. Hope this helps some of you! :)
*** on the SAT given formulas, but still good to know by heart.