Name Date. Show all work! Exact answers only unless the problem asks for an approximation.

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1 Advanced Calculus & AP Calculus AB Summer Assignment Name Date Show all work! Eact answers only unless the problem asks for an approimation. These are important topics from previous courses that you must be comfortable doing before you can be successful in Advanced Calculus. This packet is to be completed in full and turned in on the first day of class. It will be graded and counted as your first quiz grade. If you find that you need some assistance, please feel free to Google or YouTube the concepts. Within the directions of each problem, you will see key words that you should be using in your research. I also recommend that you use the Desmos app for your phone or desmos.com on your computers to analyze the graph of functions if you do not have a graphing calculator. 1) Solve the linear equation ) Solve the linear equation ) Solve the linear equation ) Solve the equation algebraically ) Solve the equation algebraically ) Solve the inequality, write the solution in interval notation & graph the solution set. 3 8 Interval Notation Advanced Calculus & AP Calculus AB Summer Assignment 1

2 7) Solve the inequality, write the solution in interval notation & graph the solution set. 0 4 Interval Notation 8) Graph the linear function (slope-intercept form). y 9) Graph the linear function (slope-intercept form). 1 y 3 10) Graph the linear function (slope-intercept form). y 3 11) Graph the linear functions. 4 and y Advanced Calculus & AP Calculus AB Summer Assignment

3 1) Graph the linear function (standard form). 6 y 8 13) Graph the linear function (standard form). 3 6y 1 14) Write the equation in slope-intercept form for the line that is graphed. Slope-intercept form 15) Write the equation in slope-intercept form for the line that is graphed. Slope-intercept form 16) Determine the slope of the line that goes through the points. 11, 7 & 4,3 Advanced Calculus & AP Calculus AB Summer Assignment 3

4 17) Determine the slope of the line that goes through the points. 5,6 &,6 18) Determine the slope of the line that goes through the points. 11, 7 & 11,3 19) Find the equation for a line with the given properties. Slope 0 & containing the point 5,6 0) Find the slope-intercept equation for a line with the given properties. 3 4 Slope & containing the point 8, 16 1) Find the slope-intercept equation for a line with the given properties. Containing the points 4, 4 & 6,1 ) Find the slope & y-intercept of the line. y 4 Slope 3) Find the slope & y-intercept of the line. 5 Y-intercept Slope Y-intercept 4) Find the slope-intercept equation for a line with the given properties. Parallel to 7 y & containing the point 7,6 5) Find the slope of the line perpendicular to the line containing the points., 5 & 6, 9 Advanced Calculus & AP Calculus AB Summer Assignment 4

5 6) Find the slope-intercept equation for a line with the given properties. Perpendicular to ,9 y & containing the point 7) Find the equation for a line with the given properties. Perpendicular to 4 y & containing the point 11, 9 8) Simplify using properties of eponents y 3 y 9) Simplify using properties of eponents y y 10 z z 6 30) Rewrite the epression using rational eponent notation ) Rewrite the epression using radical notation ) Evaluate the epression ) Evaluate the epression ) Evaluate the epression ) Subtract the polynomials Advanced Calculus & AP Calculus AB Summer Assignment 5

6 36) Multiply the polynomials ) Factor the polynomial. 1 16y 4 38) Factor the polynomial ) Factor the polynomial ) Factor the polynomial ) Factor the polynomial ) Factor the polynomial ) Factor the polynomial ) Factor the polynomial ) Factor the polynomial ) Factor the polynomial ) Factor the polynomial Advanced Calculus & AP Calculus AB Summer Assignment 6

7 48) Graph the quadratic function (standard form). y Identify the following: 4 3 Direction of Opening Y-intercept Ais of Symmetry Verte X-intercept(s) 49) Graph the quadratic function (standard form). Identify the following: y Direction of Opening Y-intercept Ais of Symmetry Verte X-intercept(s) 50) Solve the quadratic equation (factor or quadratic formula) ) Solve the quadratic equation (factor or quadratic formula) ) Solve the quadratic equation (factor or quadratic formula). 5 53) Solve the quadratic equation (factor or quadratic formula) Advanced Calculus & AP Calculus AB Summer Assignment 7

8 54) Solve the quadratic equation (square root method) ) Solve the square root equation (be sure to check for etraneous solutions) ) Evaluate the function notation. h Find h 3 57) Evaluate the function notation. 3 f Find f 7 58) Find the value of in the function notation equation. g Find so that g 10 Use the graph of p to answer the following questions. 59) Find p 9 60) Find p4 61) Find p8 6) Find so that p( ) 5 63) Find so that p( ) 4 64) Find so that p( ) 1 Advanced Calculus & AP Calculus AB Summer Assignment 8

9 65) Find the eact distance between the points & the midpoint of the line segment joining the points., 5 & 6, 9 Distance Midpoint 66) Find the domain and range of the function in interval notation. f Domain Range 67) Find the domain and range of the function in interval notation. g 4 Domain Range 68) Find the domain and range of the function in interval notation. 3 h Domain Range Let f 5, g 3 and h 1. Perform the indicated operation (composition & inverse of functions). 69) h f 11 70) g h10 71) f g 4 7) f g 73) g f 74) h f 1 75) f Advanced Calculus & AP Calculus AB Summer Assignment 9

10 76) h 1 Graph the following piecewise linear functions. 77) f Find f 3 Find f 7 1, 3 1 4, 3 3 Find so that f ( ) 3 Find so that f ( ) 0 78) g 7, 3 1, 1 6, g 4 Find Find g 8 Find so that g ( ) 5 Find so that g ( ) 1 79) Write a piecewise function h for the graph. h,,, Advanced Calculus & AP Calculus AB Summer Assignment 10

11 The graph of function functions using transformations. f is given. Use the graph of 80) f ) 4 f to graph each of the following f 8) Sketch a graph of the power functions. 7 y 1 y 9 y 10 y 83) Find all local maima & minima of the polynomial function. Then identify the interval(s) on which the function is increasing or decreasing in interval notation y Maima Minima Increasing Decreasing Advanced Calculus & AP Calculus AB Summer Assignment 11

12 For the polynomial functions (in factored form), list each real zero & its multiplicity, determine whether the graph crosses or touches the -ais at each -intercept, determine the end behavior model and then graph y Zeros (include multiplicity & if the graph crosses or touches) 84) End behavior model y 3 Zeros (include multiplicity & if the graph crosses or touches) 85) 3 End behavior model 86) Simplify the sum of the rational epressions ) Solve the rational equation Advanced Calculus & AP Calculus AB Summer Assignment 1

13 Identify the hole(s), vertical asymptote(s), horizontal asymptote, oblique asymptote, - intercept(s) & y-intercept of each rational function. Then graph each function. 88) f Hole(s) Vertical asymptote(s) Horizontal asymptote Oblique asymptote X-intercept(s) Y-intercept 89) g 9 8 Hole(s) Vertical asymptote(s) Horizontal asymptote Oblique asymptote X-intercept(s) Y-intercept 90) h Hole(s) Vertical asymptote(s) Horizontal asymptote Oblique asymptote X-intercept(s) Y-intercept Advanced Calculus & AP Calculus AB Summer Assignment 13

14 Evaluate the logarithms. 1 log ) 5 9) ln e 93) Graph the logarithmic function and determine its domain, range and asymptote(s). Use interval notation for the domain and range. f log Domain Range Asymptote(s) 94) Graph the logistic function and determine its domain, range and asymptote(s). Use interval notation for the domain and range. g Domain Range Asymptote(s) 95) The number N of bacteria present in a culture at time t (in hours) obeys the function 0.05t N t 789e. A) What is the population after 6 hours? B) When will the number of bacteria reach 000? Advanced Calculus & AP Calculus AB Summer Assignment 14

15 kt 96) Determine the eponential function At A e round k to 3 decimal places whose initial amount is 8 milligrams and halving every 9 years. 0 97) The number of students infected with the flu at Main Street High School after t days is modeled by the function Ft t 1 59e. A) What was the initial number of infected students? B) How many students will be infected after 9 days? C) The school will close when 00 of the 600 student body are infected. When will school close? Graph the implicitly defined functions. 98) 4 y 5 99) y Advanced Calculus & AP Calculus AB Summer Assignment 15

16 100) Complete the unit circle (you are epected to have it memorized). Determine the eact value of the si trigonometric functions of ) 4 sin csc cos sec tan cot Advanced Calculus & AP Calculus AB Summer Assignment 16

17 10) 4 3 sin csc cos sec tan cot Evaluate the eact value of the trigonometric functions. 103) 104) 3 3 cos sec 4 105) 106) 13 sin 6 107) 108) 10 csc 3 15 tan 4 35 cot 6 Graph the sinusoidal function using transformations. Then determine the domain, range, amplitude, period and midline (vertical shift). Use interval notation for the domain and range. y 3sin 109) 1 Domain Range Amplitude Period Midline Advanced Calculus & AP Calculus AB Summer Assignment 17

18 A is an acute angle in a right triangle satisfying the given condition. Find eact value of the remaining 5 trigonometric functions. Then find the m A in degrees (round answers to decimal places). 110) 7 sin A 8 cos A csca sec A tan A cot A ma 111) sin A csca cos A tan A sec A cot A ma Evaluate the eact value in radians of the inverse trigonometric functions. sin ) 113) cos ) tan ) sin ) cos ) tan 1 3 Advanced Calculus & AP Calculus AB Summer Assignment 18

AP CALCULUS AB,...) of Topical Understandings ~

AP CALCULUS AB,...) of Topical Understandings ~ Name: Precalculus Teacher: AP CALCULUS AB ~ (Σer) ( Force Distance) and ( L, L,...) of Topical Understandings ~ As instructors of AP Calculus, we have etremely high epectations of students taking our courses.