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Transcript
SAT Prep A.) Sets means “belongs to” or “is a member of” If C is the set of prime numbers, then 17 C = in either one or the other or both = in both Given X = { 2, 3, 5, 7 } Y = { 1, 3, 5, 7, 9 } X Y = { 1, 2, 3, 5, 7, 9 } X Y = { 3, 5, 7 } B.) Signed Numbers and Operations -,+,0 | a | = distance a is from 0. (NEVER NEGATIVE) | a | = 7 then a = 7 | a – 2 | = 7 then a = 5 or 9 a 2 7 or a 2 7 Add Sub Mult Div + x, *, ( ), · ÷,/ Zero Property sum, total difference product quotient if ab = 0 then a = 0 or b = 0 Ex. What is the product of the integers -3, -2, -1, …3, 4, 5? 0 Prod/Quot of EVEN number of negatives is POSITIVE Prod/Quot of ODD number of negatives is NEGATIVE Reciprocals Sign Changes 1 (a ) 1 a 2 + (-6) = 2 – 6 = -4 2 – (-6) = 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? x x 1 x 2 75 3x 3 75 3x 72 x 24 x 2 26 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. 44 32 11 16 2 2 8 2 2 32 2 2 2 2 2 2 44 2 2 11 GCF 2 2 4 4 2 4 LCM 2 2 2 2 2 11 352 2 E.) EXPONENTS and ROOTS Rules of exponents 3 + 3 + 3 + 3 = 4(3) 3(3)(3)(3) = 34 a0 1 a a 1 c bc a bc a a a b a b c ab b c a ac x 2 Ex. If 32 find the value of x. 2 2 x 5 x 5 Ex. Which of the following, if any are true? I. -210 0 II. - -2 10 Always Negative ---FALSE 0 Always Positive ---TRUE III. 2 (-2 ) 0 Always Positive ---TRUE 10 10 II and III F.) SQUARES and SQUARE ROOTS Know your squares/square roots 1-15/1-225 Know exact values. 2 a always +, a 2 answers +/- Ex. Find the circumference of a circle whose area is 20π A r 2 20 r 20 r . 2 20 r 2 5r 2 C 2 r C 2 2 5 4 5 ab a b Rules of radicals: a a b b 1 n a n a 1 n a na Ex. Evaluate the following A.) 2 3 1 1 3 2 8 B.) 3 8 1 3 82 G.) PEMDAS Careful with negatives on calculator!!!! H.) INEQUALITIES / or x a - SWITCH SIGN!!!! Ex. Solve for a if 5 – 3a < 10. 5 3a 10 3a 5 3a 5 3 3 5 a 3 Properties of Inequalities between 0 and 1. b c 1 1 if b c a a a a if 0 a 1 1 a if 0 a 1 a 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 is % of 100 Ex. Find the following: 1.) 45% of 200 x 45 200 100 100 x 45(200) x 90 90 2.) 90 is 45% of what number? 200 90 45 45 x 90 100 x 100 x 200 3.) 90 is what percent of 200? 90 x 200 100 200 x 90 100 x 45% 45% Percent increase/decrease Increase/Decrease = “is” Original = “of” C.) Ratio and Proportion Part : Part 7:3 compared to Part : Whole 7:10 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? 5 x 13x 90 18 x 90 x 5 13 x 13 5 65 Proportions Cross multiply Ex. Tommy types 35 words per minute. How long would it take Tommy to type 987 words? 35 987 1 x 35 x 987 x 28.2 x 28 min 12 sec Direct Variation Directly Proportional x↑ x↓ vs. vs. y↑ y↓ Inverse Variation or Inversely Proportional x↑ x↓ y = kx y↓ y↑ y = 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. y kx y 3.5 x 7 2k y 3.5 5 3.5 k y 17.5 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? k y x k 120 4 k 120(4) k 480 480 y x 480 y 6 y 80 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? T5 5 85 425 T3 3 83 249 425 249 A 87 2 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