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SAT MATH CHECKLIST:
Facts and Formulas
Numbers and Arithmetic
Sum of consecutive integers 𝑛 + 𝑛 + 1 + 𝑛 + 2 …
Sum of the consecutive integers from 1 to an integer n
( n + 1 ) × 𝑛^2
Adding or multiplying even or odd integers
even + even = even odd + odd = even odd + even = odd
even ⨯ even = even odd ⨯ odd = odd odd ⨯ even = even
Cross-multiplication If^
, then 𝑎𝑑 = 𝑏𝑐.
Percent increase or percent decrease
× 100%
Exponent rules
𝑎^1 = 𝑎
𝑎^0 = 1
𝑎−𝑚^ =
𝑎𝑚^ 𝑎𝑛^ = 𝑎𝑚+𝑛
𝑎𝑛^
(𝑎𝑚^ )𝑛^ = 𝑎𝑚𝑛
𝑎𝑚^ 𝑏𝑚^ = (𝑎𝑏)𝑚
𝑏𝑚^
𝑚 𝑛 (^) = 𝑛𝑎𝑚
Absolute value
If 𝑥 = 4 , then 𝑥 = 4 𝑜𝑟 𝑥 = − 4 If 𝑥 < 4 , then − 4 < 𝑥 < 4 If 𝑥 > 4 , then 𝑥 < − 4 𝑜𝑟 𝑥 > 4
Algebra and Functions
Difference of squares 𝑎^2 −^ 𝑏^2 =^ (𝑎^ +^ 𝑏)(𝑎^ −^ 𝑏)
Properties of inequalities
The inequality is reversed by taking the negative of both sides taking the reciprocal of both sides multiplying or dividing both sides by a negative number
Rates 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑟𝑎𝑡𝑒 × 𝑡𝑖𝑚𝑒
Domain of a function The set of^ all the “input” numbers for which the function still works
Range of a function The set of all the “output” numbers
Formula for slope 𝑚^ =^
rise run
Facts about slope
Horizontal lines have slopes of zero. Vertical lines have undefined slopes. Non-vertical parallel lines have equal slopes. Non-vertical perpendicular lines have slopes whose product is -1.
Linear functions 𝑦^ =^ 𝑚𝑥^ +^ 𝑏
Quadratic functions 𝑦 = 𝑎𝑥^2 + 𝑏𝑥 + 𝑐
Translation of 𝑦 = 𝑓(𝑥), a units vertically and b units horizontally
Classification of triangles
Pythagorean Theorem 𝑎^2 + 𝑏^2 = 𝑐^2
Special right triangles
Triangle inequality
The sum of the lengths of two sides of a triangle is always greater than the length of the third side
Area of a triangle 𝐴 =
Area of a parallelogram or rectangle (^) 𝐴 = 𝑏
Area of a trapezoid 𝐴 =
Area and circumference of a circle 𝐴^ =^ 𝜋𝑟
2 𝐶 = 𝜋𝑑 = 2 𝜋𝑟
Arc length ( L ) and area ( A )
𝜋𝑟^2
Volume and surface area of a rectangular solid
Diagonal of a rectangular solid 𝑑^2 =^ 𝑙^2 +^ 𝑤^2 +^ ^2
Volume and surface area of a right cylinder
𝑉 = 𝜋𝑟^2
𝑆𝐴 = 2 𝜋𝑟^2 + 2 𝜋𝑟
Distance formula (^) 𝑑 = (𝑥 2 − 𝑥 1 )^2 + (𝑦 2 − 𝑦 1 )^2
Midpoint formula (
