Math Midterm 7: Hunter College High School 2017
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Commutative Property of Addition
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b + a = a + b
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Commutative Property of Multiplication
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a x b = b x a
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Associative Property of Addition
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(a+b) + c = a + (b + c)
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Associative Property of Multiplication
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(a x b) x c = a x (b x c)
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Distributive Property of Multiplication over addition/subtraction
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a(b + c) = ab + bc
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Inverse Property of Addition (Additive Inverse)
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(-a) + a = 0
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Inverse Property of Multiplication (Multiplicative Inverse)
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a x 1/a = 1
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Identity Property of Addition
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a + 0 = 0 + a = a
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Identity Property of Multiplication
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a x 1 = 1 x a = a
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Zero Property of Multiplication
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a x 0 = 0 x a = 0
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Closure Property of Addition of Whole Numbers
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a E W and b E W then a + b E W
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Closure Property of Multiplication of Whole Numbers
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a E W and b E W then ba E W
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Prime
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A natural number with only 2 divisors, one and itself
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Composite
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A natural number with more than 2 divisors
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Find the no. of subsets of a given set: Formula
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Let n = the number of elements in the set. 2n = the number of subsets.
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Complement of a set
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The complement Å of a set A, is the set of all elements, in U, which are not in set A.
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R, Z, W, N: Stand for...
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R = real. Z = integers (...-2, -1, 0, 1, 2...) W = whole (every whole number: (0, 1, 2, 3, 4...) N = natural (every whole number except 0: (1, 2, 3, 4, 5...)
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Divisibility Test: 2
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If it is even, it's divisible by 2. ex.: 6 is even and divisible by 2.
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Divisibility Test: 3
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A number is divisible by 3 if the sum of its digits is divisible by 3. ex.: 342: 3 + 4 + 2 = 9, 9/3 = 3
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Divisibility Test: 5
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The # must end in 5 or 0.
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Divisibility Test: 7
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Example: 5308:1 5308 -2 530:6 530 -12 51:8 -16 35 35/7 = 5 So it is divisible by 7.
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Divisibility Test: 11
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A number is divisible by 11 if the difference of the sums of alternating sets of digits is divisible by 11 or 0.
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How do you find the number of factors a number has: Formula
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Put the number into prime factorization. Then take the exponents, add one, and multiply the exponents by each other. Ex: 345 = 3^1 x 5^1 x 23^1. (1+1)(1+1)(1+1) = 8. 345 has 8 divisors. Ex 2: 81 = 9^2 = (3^2)^2 = 3^4. 4 + 1 = 5.
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Hehe guess:
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A number is divisible by 5^n iff the 5 rightmost n digits form a number divisible by 5^n.
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The union
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The union of sets A & B is the set of all the elements which are in either Set A or Set B, or possibly both AUB = union of A & B.
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Universal Set
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the universal set is the set of all elements considered in a particular problem U
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Subset & Element Signs
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C = subset E = element ø = empty set
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Intersection
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Intersection (n) of sets A & B is the set of all elements which are both in set A and set B.
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Algebraic Expression
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An algebraic expression is an expression involving constants, variables, and arithmetic operations. The variables represent numbers although specific values are not always given.
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Multiplicative Property of Equality
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if a = b then ac = bc
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Addition Property of Equality
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if a = b then a+c = b+c
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KESCA
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Key Equation Solution Check Answer Make a key, an equation, get a solution, check it, and there's your answer ;)
