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SAT MATH CHECKLIST: Facts and Formulas. Numbers and Arithmetic. Sum of consecutive integers.
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

Adding or multiplying even or odd integers

(n + 1) Γ— 𝑛 2 even + even = even odd + odd = even odd + even = odd

If

Cross-multiplication

π‘Ž1 = π‘Ž π‘Ž0 = 1

Absolute value

π‘Ž 𝑐 = , then π‘Žπ‘‘ = 𝑏𝑐. 𝑏 𝑑

π‘π‘•π‘Žπ‘›π‘”π‘’ 𝑖𝑛 π‘Žπ‘šπ‘œπ‘’π‘›π‘‘ Γ— 100% π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘

Percent increase or percent decrease

Exponent rules

even β¨― even = even odd β¨― odd = odd odd β¨― even = even

1 π‘Žπ‘š π‘š 𝑛 π‘Ž π‘Ž = π‘Žπ‘š +𝑛 π‘Žπ‘š = π‘Žπ‘šβˆ’π‘› π‘Žπ‘› π‘Žβˆ’π‘š =

(π‘Žπ‘š )𝑛 = π‘Žπ‘šπ‘› π‘Žπ‘š π‘π‘š = (π‘Žπ‘)π‘š π‘Žπ‘š π‘Žπ‘š π‘š =( ) 𝑏 𝑏 π‘š

π‘Žπ‘› =

𝑛

π‘Žπ‘š

If π‘₯ = 4, then π‘₯ = 4 π‘œπ‘Ÿ π‘₯ = βˆ’4 If π‘₯ < 4, then βˆ’ 4 < π‘₯ < 4 If π‘₯ > 4, then π‘₯ < βˆ’4 π‘œπ‘Ÿ π‘₯ > 4

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Algebra and Functions

π‘Ž2 βˆ’ 𝑏2 = (π‘Ž + 𝑏)(π‘Ž βˆ’ 𝑏)

Difference of squares

Properties of inequalities

The inequality is reversed by ο‚· taking the negative of both sides ο‚· taking the reciprocal of both sides ο‚· multiplying or dividing both sides by a negative number

Rates

Domain of a function

π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’ = π‘Ÿπ‘Žπ‘‘π‘’ Γ— π‘‘π‘–π‘šπ‘’

The set of all the β€œinput” numbers for which the function still works

Range of a function

The set of all the β€œoutput” numbers

π‘š=

Formula for slope

Facts about slope

ο‚· ο‚· ο‚· ο‚·

rise 𝑦2 βˆ’ 𝑦1 = run π‘₯2 βˆ’ π‘₯1

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. 𝑦 = π‘šπ‘₯ + 𝑏

Linear functions Quadratic functions

𝑦 = π‘Žπ‘₯ 2 + 𝑏π‘₯ + 𝑐

Translation of 𝑦 = 𝑓(π‘₯), a units vertically and b units horizontally

𝑦 βˆ’ π‘Ž = 𝑓(π‘₯ βˆ’ 𝑏)

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Geometry

ο‚· ο‚· Angle sums

ο‚· ο‚·

The sum of any number of angles that form a straight line is 180Β°. The sum of any number of angles around a point is 360Β°. Two angles that add to 90Β° are called complementary angles. Two angles that add to 180Β° are called supplementary angles.

Sum of the interior angles of a polygon with n sides

180Β°(𝑛 βˆ’ 2)

Vertical angles

π‘Ž = 𝑑 and 𝑏 = 𝑐

Transversals

π‘Ž=𝑑=𝑒=𝑕 𝑏=𝑐=𝑓=𝑔 𝑐 + 𝑒 = 180Β° and 𝑑 + 𝑓 = 180Β°

Exterior angle of a triangle

𝑑=π‘Ž+𝑏

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Classification of triangles

π‘Ž2 + 𝑏2 = 𝑐 2

Pythagorean Theorem

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 1 𝐴 = 𝑏𝑕 2

Area of a triangle

Area of a parallelogram or rectangle

Area of a trapezoid

𝐴 = 𝑏𝑕

1 𝐴 = 𝑕(π‘Ž + 𝑏) 2

𝐴 = πœ‹π‘Ÿ 2 𝐢 = πœ‹π‘‘ = 2πœ‹π‘Ÿ

Area and circumference of a circle

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𝐿 π‘₯Β° = 2πœ‹π‘Ÿ 360Β° Arc length (L) and area (A)

Volume and surface area of a rectangular solid

Diagonal of a rectangular solid

Volume and surface area of a right cylinder

𝐴 π‘₯Β° = 2 πœ‹π‘Ÿ 360Β°

𝑉 = 𝑙𝑀𝑕 𝑆𝐴 = 2𝑙𝑀 + 2𝑀𝑕 + 2𝑙𝑕

𝑑2 = 𝑙2 + 𝑀 2 + 𝑕2

𝑉 = πœ‹π‘Ÿ 2 𝑕 𝑆𝐴 = 2πœ‹π‘Ÿ 2 + 2πœ‹π‘Ÿπ‘•

Distance formula

𝑑=

(π‘₯2 βˆ’ π‘₯1 )2 + (𝑦2 βˆ’ 𝑦1 )2

(

Midpoint formula

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π‘₯1 + π‘₯2 𝑦1 + 𝑦2 ) , 2 2

Data Analysis and Statistics

Counting principle

Probability

If there are m ways to complete the first and n ways to complete the second, then there are π‘š Γ— 𝑛 ways to complete the two of them π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘“π‘Žπ‘£π‘œπ‘Ÿπ‘Žπ‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘  π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘ π‘ π‘–π‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 

π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ =

Average

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π‘ π‘’π‘š 𝑛

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