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facts-and-formulas-2a - SAT Subject Math Level 1 Facts...

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SAT Subject Math Level 1 Facts & Formulas Numbers, Sequences, Factors Integers: . . . , -3, -2, -1, 0, 1, 2, 3, . . . Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π , etc.) 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 , . . . The n th term is t n = t 1 + ( n - 1) d Number of integers from i n to i m = i m - i n + 1 Sum of n terms S n = ( n/ 2) · ( t 1 + t n ) (optional) Geometric Sequences: each term is equal to the previous term times r Sequence: t 1 , t 1 · r , t 1 · r 2 , . . . The n th term is t n = t 1 · r n - 1 Sum of n terms S n = t 1 · ( r n - 1) / ( r - 1) (optional) Prime Factorization: break up a number into prime factors (2, 3, 5, 7, 11, . . . ) 200 = 4 × 50 = 2 × 2 × 2 × 5 × 5 52 = 2 × 26 = 2 × 2 × 13 Greatest Common Factor: multiply common prime factors 200 = 2 × 2 × 2 × 5 × 5 60 = 2 × 2 × 3 × 5 GCF(200 , 60) = 2 × 2 × 5 = 20 Least Common Multiple: check multiples of the largest number LCM(200 , 60): 200 (no), 400 (no), 600 (yes!) Percentages: use the following formula to find part, whole, or percent part = percent 100 × whole http://www.erikthered.com/tutor pg. 1
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SAT Subject Math Level 1 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 (which must be sorted) Example: median of { 3 , 10 , 9 , 27 , 50 } = 10 Example: 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 . . . ) Permutations and Combinations: The number of permutations of n things is n P n = n ! The number of permutations of n things taken r at a time is n P r = n ! / ( n - r )! The number of combinations of n things taken r at a time is n C r = n ! / ( ( n - r )! r ! ) Probability: probability = number of desired outcomes number of total outcomes The probability of two different events A and B both happening is P ( A and B ) = P ( A ) · P ( B ), as long as the events are independent (not mutually exclusive). If the probability of event A happening is P ( A ), then the probability of event A not happening is P (not A ) = 1 - P ( A ). Logic (Optional): The statement “event A implies event B ” is logically the same as “ not event B implies not event A ”. However, “event A implies event B ” is not logically the same as “event B implies http://www.erikthered.com/tutor pg. 2
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SAT Subject Math Level 1 Facts & Formulas event A ”. To see this, try an example, such as A = { it rains } and B = { the road is wet } . If it rains, then the road gets wet ( A B ); alternatively, if the road is not wet, it didn’t rain (not B not A ). However, if the road is wet, it didn’t necessarily rain ( B 6⇒ A ).
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