AP CALCULUS ASSIGNMENT SHEET
I – FUNCTIONS
TopicProblems solved in class Homework
PageQuestion
1) Domain and range12225, 7, 23, 29, 31, 47
2) Algebraic combinations of 13, 144629, 31
functions
3) Even and odd functions15, 162259, 63
4) The composition of functions17, 18, 19, 204635, 43, 47, 51, 55ad, 61b
5) One-to-one functions and inverses21, 22, 23733, 5, 7, 9, 11, 13, 15, 17, 23, 25, 31
Review2237, 39, 45, 61
7327, 29
75(true-false) 1, 3, 5, 7
761(skip e), 5, 17abd, 19, 20, 23*,24
Test
II – LIMITS AND RATES OF CHANGE
TopicProblems solved in class Homework
PageQuestion
1) The idea of limit24, 25991, 5, 7, 9, 12, 13, 15
2) Some limit theorems (limit 30 – 35109(1 – 21)odd, 25, 27, 29ac, 37, 39, 43, 46
properties)
3) Continuity36, 37, 381313, 5, 9, 11, 19, 35, 39
The Intermediate Value Theorem13145, 47, 51
4) Bisection Method39 – 42
Horizontal and vertical asymptotes144(7-23)odd, 31, 37, 52
5) Tangents and velocity43, 441547, 9, 11, 13, 15, 17, 19
Review994, 8, 19, 21, 23, 25
174 (true-false) (1 – 11)odd
175 1, 2, (3 – 19)odd, 31, 35, 37, 39
Test
III – DERIVATIVES
(Part 1)
TopicProblems solved in class Homework
PageQuestion
1) Derivatives – definition 43, 44, 4617549
17119, 21, 23, 25
2) Differentiability45, 47171(1 – 13)odd, 33, 42, 45
3) Differentiation formulae48189(3 – 17, 21 – 27)odd, 39, 43, 45, 47, 49
1951, 7, 11, 15, 21, 23, 27, 31, 35
4) Derivatives of trigonometric functions49 – 522131, 3, 5, 9, 13, 19, 21, 23, 29, 31,
35, 37, 39
Review(1)267(true – false)1, 7, 11, 13
26811, 53, 55, 61, 81, 85, 87
18953, 57, 59
19539, 41ab, 43
(Part 2)
5) The Chain Rule53 – 56 221(7 – 13)odd, 19, 27, 33,
(39 – 45, 51 – 57)odd, 63
6) Implicit differentiation57, 58, 592303, 5, 9, 11, 13, 19, 21, 23, 25, 27
7) Higher derivatives60 – 642371, 7, 9, 11, 17, 23, (27 – 33)odd, 37,
39, 47, 53
8) Related rates65, 66, 6721333
257(3 – 9)odd, 11*, 13, 15*, 19*, 21, 23*,
(25 – 33)odd
9) Linear (tangent)68 – 71 2645, 9, 13, 35(use lin. approx.)
and quadratic approximations
10) Newton’s method723495, 7, 9, 11, 15
Review (2)22165
23063, 65
23759
267 (true-false) 3, 5, 9
268 1, 3, 5, 9, 13, 15, 21, 23, 25, 33, 35, 37
47, 49, 59, 65, 67, 69, 75, 77, 89, 91,
93, 95a
Test
IV – THE MEAN VALUE THEOREM AND CURVE SKETCHING
TopicProblems solved in class Homework
PageQuestion
1) Maximum and minimum values73284(3 – 7, 11 – 21)odd, 25, 31, 33,
37, 49, 59, 71
2) The Mean Value Theorem74 – 77 2931, 3, 7, 11, 17, 21, 23, 25
3) Monotonic functions and78, 793021ab, 5, (11, 15)ab, (33, 37)ab, 61
The First Derivative Test
4) Concavity and points of inflection81, 823021cde, 7, 9, (11, 15)c, (21 – 27)odd,
29abcd, (33, 37)c
5) Curve sketching83, 8430243, 45
3217, 9, 19, 27, trigonometric: 31, 33, 37
6) Max/min (optimization) problems85, 86, 873343, 5, 9, 11, 15, 17, 19, 29, 31, 39, 41
Review359(true – false) (1 – 17)odd
3601, 5, 15, 17, 23, 27, 35, 59
Test
V – TRANSCENDENTAL FUNCTIONS
TopicProblems solved in class Homework
PageQuestion
1) Exponential functions and 88, 89633, 7, 11, 13, 15, 17, 21
their derivatives9935
1449
PagePage
2) Exponential function with 90 – 93 175 21221 5, 15, 21, 35, 37, 47, 67
the base e 189 19230 17
195 3, 5, 17, 25, 29237 19, 35, 40, 57
264 7
3) Logarithmic functions94 – 100 7319, 27, (35 – 43, 47 – 51)odd, 57
4) Derivatives of logarithmic functions101 – 103 245(3 – 15)odd, (19 – 23, 27 – 31)odd, 47, 49
5) Logarithmic differentiation104, 10524535, 37, 39, 41, 43, 45
6) Inverse trigonometric functions110 – 113 A34(in the back of the book) 83, 87, 89, 95
23041, 43, 45, 47, 49, 51
7) L’Hospital’s Rule114 – 116 3111, 5, 9, 13, 17, 21, 23, 27, 37, 43, 51
Page Page
Review A34 85, 91* 268 7, 19, 29, 31, 39, 57, 71, 73, 79
77 23, 25 311 3, 7, 11, 15, 19, 25, 29, 41
267 (true – false)7
Test
VI – INTEGRALS
TopicProblems solved in class Homework
PageQuestion
1) Sigma (∑) notation117 – 119 A411, 3, 5,9,(13–21)odd, 27,31, 33, 36, 43, 45
2) Area 120, 1213761, 3, 5, 11, 15, 19
3) The definite integral122, 1233881, 3, 5, 7, 15, 17, 29, 31, 33, 35
4) Approximate integration.124 – 127 3889, 11, 19, 21, 37, 43, 45, 51, 53
Properties of definite integrals.5201, 3, 19ab, 33a
5) The Fundamental Theorem 128 – 130 3981, 5, 9, 11, 15, 17, 19, 23, 25, 27, 31
of Calculus 35, 39, 51*, 55*, 57*
6) Indefinite integral.131 – 133A407(1 – 11)odd, 13*, (19 – 29)odd, 39, 47
Applications of the Fundamental Theorem:49, 53, 55
Position/velocity/acceleration4621, 11, 13
Average value of a function (M.V.T. for integrals)
7) Integration by substitution134 – 136 4161, 3, 5, 9, 11, 15, 17, 19, 29, 35, 39*
49, 53, 55, 65, 67, 77, 81*
Page Page
Review426 (true – false) 1, 2, 3, 4, 7, 11, 13462 3, 9, 15, 17
426(1 – 7)odd, 13, 15, 19, 21, 27, 29, 45,520 7a, 9a, 13ab, 31ab
47, 51, 57, 59, 61, 67*, 71*
Test
VII – APPLICATIONS OF INTEGRALS
TopicProblems solved in class Homework
PageQuestion
1) Areas between curves138 – 140 4381,3,9,13,17,21,25,27,29,33, 35, 41, 45, 47
2) Volume : ∫A(x) dx140 A, B, C44845, 47, 49, 53, 55
3) Volume : Disk Method141, 1424481, 3, 5, 15, 19, 29, 39
4) Volume : Washer Method1434487, 9, 11, 27, 33, 35, 37
5) Separable differential equations144 – 146 6003, 7, 15, 17, 33
6) Exponential growth and decay106 – 109 6103, 5, 9, 13bc, 15, 17a
7) Slope fields5931, 3 – 6, 9, 11, 13
Review4631, 3, 5, 7, 13, 15, 23, 25
635 (true-false) 1, 3
635 1, 2, 5, 9
Test