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### 258 Cards in this Set

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 Positive X Negative = ? Negative Negative X Negative = ? Positive Positive / Negative = Negative Negative / Negative = Positive Odd + Odd = Even Even + Even = Even Odd - Odd = Even Even - Even = Even Odd + Even = Odd Odd - Even = Odd Even x Odd = Even Even x Even = Even Odd x odd x odd x ... = Odd Odd / Even = Not an Integer Even / Odd = Even (or a fraction) Odd / Odd = Odd (or a fraction) Final Value [given X percent change) = (1 + X%/100)Initial Value % change [given Final and Initial values] = (F-I)/I x 100 Simple Interest: R = R = P X (1 + rt) Compound Interest: R = R = P X (1+ r/n)^nt (^nt indicates nt is an exponent) X^a * X^b = X^(a+b) x^a / x^b = x^(a-b) x^a * y^a = (xy)^a (x/y)^a = x^a / y^a (x^a)^b x^(ab) 0! = ? 1 1! = ? 1 2! = ? 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 x^-a 1 / x^a x^0 = 1, unless x = 0 nPk = Permutations (order matters) with n options for k slots n! / (n-k)! nCk = Combinations (order does not matter) with n options for k slots n! / (n-k)!k! nPk = Permutations (order matters) with identical objects k sub i n is the total number of objects and ki is the number of objects of the ith kind n! / k1!k2!...kn! Arrangements in a circle of non-identical things = (n-1)! With two different types of things (men & women) it is (m-1)!w! (only one "anchor" needed) Probability is? number of ways the particular something can happen divided by the number of ways that anything can happen x^(a/b) = b√(x^a) [b root of x to the a power] n√x = [nth root of x] x^(1/n) [x to the 1/n power] Quadratic Formula ? x = (-b+/-√(b^2-4ac))/2a Area of a triangle? A = 1/2 bh Sum of the angles of a triangle? 180 deg The sum of the lengths of any two sides of a triangle is _____ than the length of the third? longer 45-45-90 triangle has what relationship between its sides? 1-1-√2 30-60-90 triangle has what relationship among its sides? 1-√3-2 Right triangle: 3-4-___ 5 Right triangle: ___ -8-10 6 Right triangle: 5-___-13 12 Right triangle: 10-24-____ 26 Right triangle: ___-24-25 7 Right triangle: 8-__-17 15 Equation of a line: y=mx+b slope of a line equals? m=(y2-y1)/(x2-x1) x-intercept of a line = -b/m Area of a rhombus (all sides equal, opposite angles equal, perpendicular diagonals)? A=1/2(d x d) d = diagonal Area of a trapezoid (one pair of sides parallel [sides a and c]) A=1/2(a+c)h Area of a parallelogram (opposite sides equal and parallel, opposite angles equal)? A=bh Measure of all angles of a regular polygon? (n-2)180 Measure of any interior angle of a regular polygon? (n-2)/n ∗ 180 pi ≈ ? (fraction) 22/7 Area of a circle? A=πr^2 Relationship between central angle and arc? L/(2πr) = α /360 deg Area of a sector of a circle? A = (α/360) πr^2 Inscribed angle = ? 1/2 central angle Definition of Central Angle? An angle in a circle which uses the center of the circle as its vertex. Definition of Inscribed Angle? An angle formed by two chords within a circle. Its vertex is on the circle. The measure of an inscribed angle equals 1/2 the measure of its arc. Diagonal of a cube = √3 * length Diagonal of a rectangular solid? D = √(l^2 + w^2 + h^2) Volume of a cylinder? V = π(r^2)h Surface area of a cylinder? A = 2πrh +nπr^2, n= 0,1, or 2 Volume of a sphere? V = 4/3 πr^3 Surface area of a sphere? A = 4πr^2 Exponential growth formula? F = Ia^n Compound interest formula? Earnings = Investment x (1+rate)^t t= no. of periods Average? Add 'em all up and divide by the number of things added. Standard Deviation formula? σ = square root of the sum of the differences between each number and the mean, squared, divided by the number of numbers. √((∑(xi-mean)^2)/n) Permutation formula (order matters)? nPk = n!/(n-k)! Combination formula? nCk = n! / (n-k)!k! Possible circular arrangements of n items? (n-1)! P(A ∩B) = Intersection of independent events (and) P(A) * P(B) P(A∩B) = Intersection of dependent events (and) P(A)*Pa(B) or P(B)*Pb(A) P(A∪B) = Union of two overlapping events (or) P(A) + P(B) - P(A∩B) P(A∪B∪C) = Union of three overlapping events (or) P(A)+P(B)+P(C)-P(A∩B)-P(A∩C)-P(B∩C)+P(A∩B∩C) 12 x 6 72 12 x 7 84 12 x 8 96 12 x 9 108 12 x 12 144 12 x 11 132 13 x 4 52 13 x 5 65 13 x 6 78 13 x 7 91 13 x 8 104 13 x 9 117 13 x 11 143 13 x 12 156 13 x 13 169 14 x 3 42 14 x 4 56 14 x 5 70 14 x 6 84 14 x 7 98 14 x 8 112 14 x 9 126 14 x 11 154 14 x 12 168 14 x 13 182 14 x 14 196 15 x 5 75 15 x 6 90 15 x 7 105 15 x 8 120 15 x 9 135 15 x 11 165 15 x 12 180 15 x 13 195 15 x 14 210 15 x 15 225 1/6 = 0.166... 5/6 = 0.833... 1/8 = 0.125 3/8 = 0.375 5/8 = 0.625 7/8 = 0.875 1/9 = 0.111... 2/9 = 0.222... 17/20 = 0.85 1^2 = 1 1.4^2 ≈ 2 1.7^2 ≈ 3 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 6^2= 36 7^2 = 49 8^2 = 64 9^2= 81 11^2 = 121 12^2= 144 13^2 = 169 14^2= 196 15^2= 225 16^2= 256 17^2= 289 18^2= 324 19^2 = 361 21^2= 441 22^2= 484 23^2= 529 24^2= 576 25^2= 625 √1 = 1 √2 ≈ 1.4 √3 ≈ 1.7 √4 = 2 √9 = 3 √16 = 4 √25 = 5 √36 6 √49 7 √64 = 8 √81 9 √121 11 √144 12 √169 13 √196 14 √225 15 √256 16 √289 17 √324 18 √361 19 √441 21 √400 20 √441 21 √484 22 √529 23 √576 24 √625 25 2^(-3) 1/8 2^(-2) 1/4 2^(-1) 1/2 2^0 1 2^2 4 2^3 8 2^4 16 2^5 32 2^6 64 2^7 128 2^8 256 2^9 512 2^10 1024 3^(-3) 1/27 3^(-2) 1/9 3^(-1) 1/3 3^0 1 3^1 3 3^2 9 3^3 27 3^4 81 3^5 243 3^6 729 3^7 2187 3^8 6561 3^9 19,683 3^10 59,049 1^3 1 2^3 8 3^3 27 4^3 64 5^3 125 3√1 (cubed root of 1) 1 3√8 (cubed root of 8) 2 3√27 (cubed root of 27) 3 3√64 (cubed root of 64) 4 3√125 (cubed root of 125 5 0! 1 1! 1 2! 2 3! 6 4! 24 5! 120 6! 720 7! 5,040 Shortcut for the sum of consecutive integers? 1. Average the first and last term to find the middle point or term 2. Derive the total # of terms 3. The sum = middle point * # of terms Positive x Negative = Negative Negative x Negative = Positive Positive ÷ Negative = Negative Negative ÷ Negative = Positive Odd + Odd = Even Even + Even = Even Odd - Odd = Even Even - Even = Even Odd + Even = Odd Odd - Even = Odd Even x Odd = Even Even x Even = Even Product of an even integer with any other integer is ? Even Product of ALL odd integers is? Odd Odd ÷ Even ≠ Integer Even ÷ Odd = Even (or Fraction) Odd ÷ Odd = Odd (or Fraction) Divisibility test for 2: last digit divisible by 2 Divisibility test for 3: sum of digits Divisibility test for 4: last two digits Divisibility test for 5: Last digit 0 or 5 Divisibility test for 6: test for 2 AND 3 Divisibility test for 8: last three digits (remember powers of 2 -> 64, 128, 256, 512, 1024, etc.) Divisibility test for 9: sum of digits Divisibility test for 12: test for 3 AND 4 Divisibility test for 14: Test for 2 and 7 Divisibility test for 15: Test for 3 and 5 Do Not Multiply Out Intermediate Calculations Simplify later X^2-Y^2 = (X+Y)(X-Y)