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act-facts-and-formulas

# act-facts-and-formulas - ACT Math Facts& Formulas...

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Unformatted text preview: ACT Math Facts & Formulas Numbers, Sequences, Factors Integers: . . . , -3, -2, -1, 0, 1, 2, 3, . . . Rationals: fractions, that is, anything expressable as a ratio of integers Reals: integers plus rationals plus special numbers such as √ 2, √ 3 and π Order Of Operations: PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract) Arithmetic Sequences: each term is equal to the previous term plus d Sequence: t 1 , t 1 + d , t 1 + 2 d , . . . Example: d = 4 and t 1 = 3 gives the sequence 3, 7, 11, 15, . . . Geometric Sequences: each term is equal to the previous term times r Sequence: t 1 , t 1 · r , t 1 · r 2 , . . . Example: r = 2 and t 1 = 3 gives the sequence 3, 6, 12, 24, . . . Factors: the factors of a number divide into that number without a remainder Example: the factors of 52 are 1, 2, 4, 13, 26, and 52 Multiples: the multiples of a number are divisible by that number without a remainder Example: the positive multiples of 20 are 20, 40, 60, 80, . . . Percents: use the following formula to find part, whole, or percent part = percent 100 × whole Example: 75% of 300 is what? Solve x = (75 / 100) × 300 to get 225 Example: 45 is what percent of 60? Solve 45 = ( x/ 100) × 60 to get 75% Example: 30 is 20% of what? Solve 30 = (20 / 100) × x to get 150 www.erikthered.com/tutor pg. 1 ACT Math Facts & Formulas Averages, Counting, Statistics, Probability average = sum of terms number of terms average speed = total distance total time sum = average · (number of terms) mode = value in the list that appears most often median = middle value in the list median of { 3 , 9 , 10 , 27 , 50 } = 10 median of { 3 , 9 , 10 , 27 } = (9 + 10) / 2 = 9 . 5 Fundamental Counting Principle: If an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N × M ways. (Extend this for three or more: N 1 × N 2 × N 3 . . . ) Probability (Optional): probability = number of desired outcomes number of total outcomes Example: each ACT math multiple choice question has five possible answers, one of which is the correct answer....
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act-facts-and-formulas - ACT Math Facts& Formulas...

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