SAT Prep

A.) Sets means “belongs to” or “is a member of” If C is the set of prime numbers, then = in either one or the other or both = in both Given X = { 2, 3, 5, 7 }Y = { 1, 3, 5, 7, 9 } = { 1, 2, 3, 5, 7, 9 } = { 3, 5, 7 }

B.) Signed Numbers and Operations -, +, 0 | a | = distance a is from 0. (NEVER NEGATIVE) | a | = 7 then a = | a – 2 | = 7 then a =

Add +sum, total Sub-difference Multx, *, ( ), · product Div÷, / quotient Zero Propertyif ab = 0 then a = 0 or b = 0 Ex. What is the product of the integers -3, -2, -1, …3, 4, 5?

Prod/Quot of EVEN number of negatives is POSITIVE Prod/Quot of ODD number of negatives is NEGATIVE Reciprocals Sign Changes 2 + (-6) = 2 – 6 = -4 2 – (-6) = = 8

C.) INTEGERS Number ≠ Integer Consecutive integers x, x+1, x+2, x+3, … Consecutive odd/even integers x, x+2, x+4, … Ex. The sum of three consecutive integers is less than 75. What is the largest possible value of the first of the three consecutive integers?

D.) FACTORS Factors – Finite set of values - Know your “goes intos” Multiples – Infinite set of values GCF and LCM – use product of primes GCF = product of common primes(1 time) LCM = product of common primes(1 time) and uncommon primes.

Ex. Find the GCF and the LCM of 32 and 44.

E.) EXPONENTS and ROOTS Rules of exponents = 4(3) 3(3)(3)(3) = 3 4

Ex. If find the value of x. Ex. Which of the following, if any are true?

F.) SQUARES and SQUARE ROOTS Know your squares/square roots 1-15/1-225 Know exact values. always +, 2 answers +/- Ex. Find the circumference of a circle whose area is 20π.

Rules of radicals: Ex. Evaluate the following A.) B.)

G.) PEMDAS Careful with negatives on calculator!!!! H.) INEQUALITIES / or x a -SWITCH SIGN!!!! Ex. Solve for a if 5 – 3a < 10.

Properties of Inequalities between 0 and 1.

A.) Fractions and Decimals Comparing: Decimals – same # of places – larger # is larger number Fractions – same denom. – bigger numer. is larger fraction same numer. – smaller denom. is smaller fraction

Powers of 10 - move decimal place – + exponent – move to right – exponent – move to the left Rounding - know rules - do not need to round grid-ins Operations with fractions Add/sub:like denominators Multiply:numerators and denominators Divide:multiply by reciprocals “of” means multiply

B.) Percents Ex. Find the following: 1.) 45% of 200

2.) 90 is 45% of what number? 3.) 90 is what percent of 200?

Percent increase/decrease Increase/Decrease = “is” Original = “of” C.) Ratio and Proportion Part : Part compared to Part : Whole 7:37:10 or 3:10 Two numbers in a ratio of a to b – Apply an x to each.

Ex. Two acute angles of a right triangle are in a ratio of 5:13. What is the measure of the larger acute angle? Proportions  Cross multiply Ex. Tommy types 35 words per minute. How long would it take Tommy to type 987 words?

Direct Variationvs.Inverse Variation or Directly Proportional vs.Inversely Proportional x ↑y ↑x ↑y ↓ x ↓y ↓x ↓y ↑ y = kxy = k/x or k = xy Ex. If y is directly proportional to x and y = 7 when x = 2, find the value of y when x is 5.

Ex. If it takes 4 workers 2 hours to complete a certain job, how many minutes would it take 6 workers to complete the same job?

A.) Average = Mean = Sum/count Know the average then sum = average x count Ex. After 5 tests Tony has an 85 average. If Tony had an 83 average after his first three tests, what was his average on the last two tests?

B.) Median = Middle # ARRANGE THEM IN ORDER FIRST!!! Odd # of scores - Find middle # Even # of scores - Find average of middle 2 #’s C.) Mode = Number that occurs the MOST