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Integers - Any counting numbers (whole numbers), including negatives (e.g., -3, -1, 2, 7... but not 2.5) Real Numbers - All numbers (including fractions, decimals, square roots, negatives, and even π), except for imaginary ones PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction; order of operations Commutative Property - a+b = b+a , a x b = b x a Associative Property - (a + b) + c = a + (b + c) , (a x b) x c = a x (b x c) Distributive Property - a(b + c) = ab + ac , a(b-c) = ab - bc All Prime Numbers below 60 (17) - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59
Divisibility Rules for 3 - sum of digits divisible by 3 Divisibility Rules for 4 - the last two digits of number are divisible by 4 Divisibility Rules for 5 - the last digit is either a 5 or zero Divisibility Rules for 6 - even number and sum of digits is divisible by 3 Divisibility Rules for 8 - f the last three digits are divisible by 8 Divisibility Rules for 9 - sum of digits is divisible by 9 Fast Fractions - 1/x + 1/y = (x+y) / xy; 1/2 + 1/5 = (2+5) / (2x5) = 7/ Absolute Values - The absolute value of a number is its distance from a number line; |x| = x, |-x| = x Ratio - x : y, x to y, or x / y
Pythagorean Triples - 3-4-5, 5-12-13, 8-15-17, 7-24- Triangle Inequality Theorem - Length od the longest side is never greater than the sum of the other two; shortest side is greater than the differenceof other two sides Area of a Circle - = π r² Circumference - = 2 π r Arc Length - = (x/360) 2 π r Area of Sector - = (x/360) π r² Are of Trapezoid - = .5 (Base1 + Base2)/ height Volume of a Cylinder - = r² π h Surface Area of Cylinder - 2 π r² + 2 π r h
Slope - = m = rise/run = (y2-y1) / (x2-x1) Parrel Slopes are - equal slopes Perpendicular slopes are - the opposite reciprocal, for example, perpendicular slope to 3 is -1/ Distance Formula - d = √[(y₂ - y₁)² + ( x₂ - x₁)²] Distance = - Rate x Time Average Speed = - (total distance traveled) / total time Simple Interest - = P [1+(rt/100)]; P is the principal, r is the rate, and t is time Compound Interest - = P [1 + (r/100n)]^nt; P is the principal, r is the rate, t is the time, n is the number of times compounded per year Find the Mean and Median {30, 35, 40, 45, 50} - 40' If numbers are evenly spaced than Median = Mean
P(A OR B) [if the events are independent] - = P(A) + P(B) - P(A and B)
