Sat mathematics formula sheet, Cheat Sheet of Mathematics

Download Sat mathematics formula sheet and more Cheat Sheet Mathematics in PDF only on Docsity! Ivy Global 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 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 = 𝑎𝑚−𝑛 (𝑎𝑚 )𝑛 = 𝑎𝑚𝑛 𝑎𝑚𝑏𝑚 = (𝑎𝑏)𝑚 𝑎𝑚 𝑏𝑚 = ( 𝑎 𝑏 )𝑚 𝑎 𝑚 𝑛 = 𝑎𝑚𝑛 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 Ivy Global Algebra and Functions Difference of squares 𝑎2 − 𝑏2 = (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 = 𝑦2 − 𝑦1 𝑥2 − 𝑥1 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 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 Translation of 𝑦 = 𝑓(𝑥), a units vertically and b units horizontally 𝑦 − 𝑎 = 𝑓(𝑥 − 𝑏) Ivy Global Arc length (L) and area (A) 𝐿 2𝜋𝑟 = 𝑥° 360° 𝐴 𝜋𝑟2 = 𝑥° 360° Volume and surface area of a rectangular solid 𝑉 = 𝑙𝑤𝑕 𝑆𝐴 = 2𝑙𝑤 + 2𝑤𝑕 + 2𝑙𝑕 Diagonal of a rectangular solid 𝑑2 = 𝑙2 + 𝑤2 + 𝑕2 Volume and surface area of a right cylinder 𝑉 = 𝜋𝑟2𝑕 𝑆𝐴 = 2𝜋𝑟2 + 2𝜋𝑟𝑕 Distance formula 𝑑 = (𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2 Midpoint formula ( 𝑥1 + 𝑥2 2 , 𝑦 1 + 𝑦 2 2 ) Ivy Global Data Analysis and Statistics Counting principle If there are m ways to complete the first and n ways to complete the second, then there are 𝑚 × 𝑛 ways to complete the two of them Probability 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 Average 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 = 𝑠𝑢𝑚 𝑛