Useful notes about functions for people who want to take the SAT II Math Level 2 Subject Test
Useful notes about conic sections for people who wish to take the SAT II Math Level 2 Subject Test.Full description
Useful notes about matrices for people who want to take the SAT II Math Level 2 Subject TestFull description
Useful notes about polar coordinates for people who want to take the SAT II Math Level 2 Subject TestFull description
Full description
Maths
MA 92
Useful notes about arithmetic and algebra for students who wish to take the SAT II Math Level 2 Subject TestFull description
Useful notes about arithmetic and algebra for students who wish to take the SAT II Math Level 2 Subject Test
Preparation Booklet 2006 - 2007
Preparation Booklet 2006 - 2007
Chemistry Subject Test for SATFull description
Scanned Version
Scanned Version
Syllabus of SAT PHYSICS, CHEMISTRY AND BIOLOGY compiledFull description
_Master_SAT_II_Math
Combinatorics Factorials
n! is read as “n “n factorial” n! = n(n – 1)( – 1)(n n – 2) – 2) … 3 ∙ 2 ∙ 1 0! = 1
Permutations
Definition: A permutation A permutation is any arrangement of the elements of a set in definite definite order of n things taken r r at at a time n P r r = P (n,r ) = the number of permutations of n n P r r = n! (n – – r r )! )! n = number of items r = r = number of spots A permutation of n of n things where there are a of one kind and b of another kind: permutations = n! a!b! Circular arrangement (can be viewed from only one side): permutations = (n – – 1)! 1)! Circular arrangement (can be viewed from either side): permutations = (n – – 1)! 1)! 2 The box-counting procedure: Sketch the number of positions pos itions available, fill the number of objects available o for each position, and multiply those numbers to gether Examples of when to use permutations p ermutations:: o Forming a committee in which there are d ifferent ifferent positions (president, vice president, etc.)
Combinations
Definition: A combination is any arrangement of the elements of a set in which order is NOT important of n things taken r r at at a time nC r r = C (n,r ) = n = the number of combinations of n r r factors factors of n of n! nC r r = n P r r = the product of the largest r r ! r ! Examples of when to use combinations: o The selection of co mmittees mmittees (with (w ith no distinctive positions) Forming teams o Toppings on a pizza o
Binomial Theorem n
Observations in expanding the binomial (a (a + b) : There are n + 1 terms in each expansion o o The sum of the exponents in each term equals n The exponent of b of b is 1 less than the number of the term o The coefficient of each term equals n o either exponent
Probability
Definition: The probability The probability of an event happening is a number defined to be the number of ways an event can happen successfully divided by the total number of ways the event can happen Sample Space the set of all outcomes of an experiment exper iment o often used in dice experiments o The probabili pro bability, ty, p p,, of any event is a number such that 0 ≤ p ≤ p ≤ 1 If p p = 0, the event CANNOT happen o If p p = 1, the event MUST happen o The odds in favor of an event happening are defined d efined to be the probabili pro bability ty of the event happening successfully divided by the probabili pro bability ty of o f the event not happening successfully Independent Events events that have no effect on each other o Two events are independent if P P ( A A ∩ B B)) = P = P ( A) A) ∙ P ∙ P ( B) B) o sets A and B and B o A ∩ B is the intersection of sets A If two events are not independent, t hey are said to be dependent The probability of event A event A happening OR event B event B happening: ( A A U B B)) = P = P ( A) A) + P + P ( B) B) – P P ( A A ∩ B B)) o P sets A and B and B o A U B is the union of sets A If P P ( A A ∩ B) B) = 0, the events are said to be mutually exclusive (cannot occur at o the same time) You can find the probabili pro bability ty that something so mething WILL NOT happen by subtracting the probability probability that it WILL happen from 1 The probability of multiple events occurring together is the product of the probabilities probabilities of the events occurring individually
