This packet is a review of the prerequisite concepts for AP Calculus. It is to be done NEATLY and on a SEPARATE sheet of paper. All problems are to be done WITHOUT a graphing calculator. Points will be awarded only if the correct work is shown, and that work leads to the correct answer. Have a great summer and I am looking forward to seeing you in September. Part I. Simplify. Show the work that leads to your answer. ) 8 ) 5 5 ) 6 Part II. Find the equations of all vertical asymptotes ye ) yln( ) ) 8 ) 5 Part III. Simplify each epression. 8 ) h 6 9 0 Part IV. Given: f ( ) and g( ) (f+g)( ) (g-f)(5) ) ( f g )( ) ( g f )(7) 5) gg ( ( )) 6) g ( f ( )) Use the table at right to answer #7-0. 7) rs ( ()) 8) 0) Why does s ( ) not eist? sr ( (0)) 9) r r s ( ( ()) r() s() - - 0-6 0 5 - - - -
7 Part V. Miscellaneous: Follow the directions for each problem. Given f() =, find f ( h) f ( ). ( points) h ) Find the slope of the secant line that runs through the maimum and minimum points of the graph of 5sin when graphed on the interval[0,]. (5 points) Part VI. Factor 7 5 ( ) 0 ( ) ) ( 7) 8( 7) ) 8( 5) ( 5) ( 5) ) 5v 5v 0v 6 Part VII. Simplify ln e ) log ) ln ) ln e 7 5) log ½ 8 6) ln ½ 7) ( ln ) e For #8-9, epand each logarithm into a sum and or difference of logs. 8) log ( ) 9) ln For #0-, condense each epression into a single logarithm. 0) log log log( 7) (ln a ln b) ln c
5 8 Part VIII. Using the point-slope form y y = m(, write an equation for the line with slope, containing the point (,) ) Containing the points (,-) and (-5,) ) With slope 0, containing the point (,) ) Parallel to y = 7 and passes through (5, 5) Perpendicular to the line in problem #, containing the point (,) 0 8 Part IX. Without a calculator, determine the eact value of each epression. Please note: You MUST be able to do this in your sleep by the time you get back to school WITHOUT A CALCULATOR!!! This is one of the single most important skills necessary for success in AP Calculus! sin 0 7 ) cos 6 5) sin 6) cos 9) sin 0) tan 7 ) tan 6 7) tan tan ) cos(sin - ½ ) 8) sin - (sin ) sin( ) 7 ) 6 ) cos cos 5) tan 6) If sin and, find the values of the other five trig functions for. 5 7 7) cos csc 8) tansin 9) cos cot 0) tan Part X. Simplify or verify each identity. tan tan ) cos sin sec csc
Part XI Graph: (a) sin( ) (b) y cos( ) Part XII. For each function, determine its domain and range. (#- are point each) y = ) y = ) y = ) ln f ( ) 5) e log( 5) Part XIII. Determine all points of intersection without the use of a calculator. y = + AND y = 5 + ) y =cos and y =sin in the st quadrant on [0, ] 6 Part XIV. Graph each function, without the aid of a graphing calculator. Consider each trigonometric function to be on the interval [0, ]. y = sin ) y = cos ) y = tan ) y ( ) 5) 6) y = 7) y = e 8) y = 9) y = 0) y = ln y = + - ) y = ) y = if 0 if 0 if
Write the equation for the piecewise function shown below: y 6 8 Part XV. For #- below, find the its, if they eist.(#- are pt each) 7 ) 9 9 ) 5 ) 8 For #5-7, eplain why each function is discontinuous and determine if the discontinuity is removable or nonremovable. 5), g ( ) 5, ( 6) b ( ) 5 7) h ( ) 05 5
For #8-, determine if the following its eist, based on the graph below of p(). If the its eist, state their value. Note that = - and = are vertical asymptotes. y 8) p ( ) 9) p ( ) 0) p ( ) p ( ) ) p ( ) ) p ( )
Use the graph of f(), shown below, to answer #-6. ( pt each). For what value of a is a f ( ) noneistent? 5) f ( ) 6) f ( )