Formula Memorization Sheet - Precalculus I | MATH 121, Study notes of Pre-Calculus

Download Formula Memorization Sheet - Precalculus I | MATH 121 and more Study notes Pre-Calculus in PDF only on Docsity! MATH 121 Formulas Properties of Exponents 1. n m n ma a a 2. n n m m a a a   3. rn m nr mra b a b       4. rn nr m mr a a b b   1 5. r r b b Quadratic Formula     2 4 2 b b ac x a Vertex of Parabola           , 2 2 b b f a a   2( ) ( )f x a x h k Vertex at ( , )h k Circle    2 2 2( ) ( )x h y k r   ( , )center h k radius r Properties of Logarithms  1. log yby x iff b x 2. log 1b b 3. log pb b p 4. log 1 0b  log5. b pb p 6. log logpb bm p m    7. log log logb b bmn m n        8. log log logb b b m m n n   109. log( ) loga a  10. ln( ) logea a Change of Base Formula  10 10 log ln log log ln b x x x b b Properties of Radicals    1. m m mnn nb b b 2. n n nb b ab 3. m n mnb b  4. , 0 n n n a a b bb Distance Formula        22 2 1 2 1d x x y y        1 21 2 , 2 2 y yx x M Equations for Graphing Lines      2 1 2 1 , y y m y mx b x x    1 1y y m x x Exponential Growth Model:  0( ) ktP t P e Doubling Time:  ln 2 T k Exponential Decay Model:  0( ) ktP t P e Half Life:  ln 2 T k Special Product Formulas    2 2 21. ( ) 2a b a ab b    2 2 22. ( ) 2a b a ab b    2 23. ( )( )a b a b a b Sum or Difference of Cubes     3 3 2 24. ( )( )a b a b a ab b     3 3 2 25. ( )( )a b a b a ab b Absolute Value Inequalities    E k iff k E k    E k iff E k or E k Interest Formulas Compound        1 nt r A P n Continuous  rtA Pe Remainder Theorem: For any polynomial ( )P x , the remainder obtained when dividing ( )P x by x r is ( )P r . Rational Root Theorem: Let      1 1 1 0( ) n n n nP x a x a x a x a , where all coefficients are integers and n is a positive integer. If c d is a root of ( )P x then c is a factor of 0a and d is a factor na . Note: Students are not allowed to use this formula sheet during any tests or final exams.