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Sat mathematics formula sheet, Cheat Sheet of Mathematics

Sat math formula sheet in given numbers and arithmetic’s, algebra and functions, geometry, data analysis and structures.

Typology: Cheat Sheet

2021/2022

Uploaded on 02/07/2022

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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) ×𝑛2
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 𝑎
𝑏 =𝑐
𝑑 , then 𝑎𝑑 =𝑏𝑐.
Percent increase or percent decrease
𝑐𝑕𝑎𝑛𝑔𝑒 𝑖𝑛 𝑎𝑚𝑜𝑢𝑛𝑡
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡 ×100%
Exponent rules
𝑎1=𝑎
𝑎0= 1
𝑎−𝑚 =1
𝑎𝑚
𝑎𝑚𝑎𝑛=𝑎𝑚+𝑛
𝑎𝑚
𝑎𝑛=𝑎𝑚𝑛
(𝑎𝑚)𝑛=𝑎𝑚𝑛
𝑎𝑚𝑏𝑚= (𝑎𝑏)𝑚
𝑎𝑚
𝑏𝑚= (𝑎
𝑏)𝑚
𝑎𝑚
𝑛= 𝑎𝑚
𝑛
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
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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 (