Calculus 42S Assignments
2015-2016
Approximate Timeline:
September
October
November
December
January
February
March
March/April
Ch. 2 Limits and Continuity
Ch. 3 Derivatives
Ch. 4 Applications of Derivatives
Ch. 5 The Definite Integral
Ch. 3-5 Trig, Log, and Exp’l Derivs and Integrals
Ch. 6 Differential Equations and Mathematical Modeling
Ch. 7 Applications of Definite Integrals
Review – Past Exams
Mar. 25 – Apr. 1 – Spring Break
Apr. 6-14 – Music Tour
April _____ MBCI Calculus Exam
Thurs. May 5 AP Calculus AB Exam
Hand in Books in class
Wind-up Video & Food
Section Page Topic
Assigned Questions
1.1
7
Lines
-increments
-slope of a line
-parallel and perpendicular lines
-equations of lines
-applications
1-37, 43 odds, try 45, 51
1.2
17
Functions and Graphs
-domains and ranges
-viewing and interpreting graphs
-even and odd f'ns (symmetry)
-piece-wise f'ns, absolute value f'n
-composite f'ns
1-49 odds
Review: try 37, 39, 41, 43, 60, 61
UNIT 1 Limits and Continuity
Section Page Topic
Assigned Questions
2.1
62
Rates of Change and Limits
-average and instantaneous speed
definition of limit
properties of limits,
one-sided and two-sided limits
1-51 odds (omit trig and log questions)
try 59, 61
given graph find limit (1-5)
given f'n, find limit by substitution (7-19)
given f'n find limit by graphing (21-29, 53-55)
various (31-43)
piecewise limits (45-51)
2.2
71
Limits Involving ∞
1-49 odds (omit trig and log questions)
-finite limits as x goes to +/- infinity
lim x --> +/- ∞ (1-7, 23-27, 43-47)
infinite limits as x goes to a
lim x --> a+/- (9-15)
-end behavior models
VA (17-21)
-"seeing" limits as x goes to +/- infinity
end behavior model and HA (29-41)
2.3
80
Continuity
-continuity at a point
-continuous functions
1-41 odds, try 43
discontinuity (1-9, 19-23)
limit exist and continuity (11-17)
-algebraic combinations
-composites
-intermediate value theorem (IVT) for
continuous functions
2.4
extend f'n to be cont. (25-29)
given f'n, cont? (31-33)
87
Rates of Change and Tangent Lines
-average rates of change
-tangent to a curve
-slope of a curve
-normal to a curve
-speed revisited
1-33 odds (omit trig and log questions)
given f'n find avg rate change (1-5)
given f'n find slope at pt. and eq'n tangent/normal (9-13)
piecewise, does tangent exist? (15-17)
real life q's (23-33)
91
Review
1-48 all (omit trig and log questions)
given f'n find limit (1-14)
given graph, does limit exist? (15-20)
given graph, is it coninuous at pts? (21-24)
given graph, find lim. and cont. (25-26)
VA (27-28)
piecewise f'n lim. and cont (29-30, 39-40)
given f'n, discontinuity (31-32)
end behavior and HA (33-36)
given lim, sketch graph )41-42
rate of change, slope, and lines (43-48)
UNIT 2 Derivatives
Section Page Topic
Assigned Questions
3.1
101
Definition of the Derivative
1-25 odds, except 13
-definition of derivative
finding derivative of a simple f'n (1-5)
-notation
match graph of f'n with graph of derivative (7-10)
-relationship bet. the graphs of f and f’
graphs and derivatives (13-17)
-graphing the derivative from data
table and derivative (19)
-one-sides derivatives
3.2
111
Differentiability
-how f’(a) might fail to exist
-diferentiability implies local linearity
-derivatives on a calculator
-ifferentiability implies continuity
-int. value theorem for derivatives
1-23 odds, 24-27 all
RH and LH derivatives on a graph (1-4)
graphs: differentiability and continuity (5-10)
discontinuity and eq'n of f'n (11-16)
differentiability domain and eq'n of f'n (17-22)
graphing nDeriv (24-28)
3.3
120
Rules of Differentiation
-positive integer powers
-multiples, sums, and differences,
products and quotients
-negative integer powers of x
-second and higher order derivatives
1-39 odds
first and second derivative: power rul (1-12)
derivative using quotient/product rule (13-21)
u/v composite f'ns (23, 24)
derivatives and tangent lines of eq'ns of f'ns (25-32)
derivatives and practical problems (33-39)
3.4
129
Applications of Derivatives
-instantaneous rates of change
-motion along a line: d, s, v, a
1, 3, 5, 9, 13, 21-33 odds
eq'ns of f'ns and derivatives (1-20, 27, 31,33)
tables and graphs (21-25, 29)
172
Review
1, 2, 4, 7, 43-44, 53, 55, 57-64, 71-73
find the derivative of eq'n of f'n (1, 2, 7, 8)
find all derivative of eq'n of f'n (43-44)
diff. and continuity of eq'n of g'n (54, 55, 57-58)
graphs of f'ns and derivatives (59-63)
speed and practical problems (71-73)
UNIT 3 Derivatives and Graphs
Section Page Topic
Assigned Questions
3.6
146
The Chain Rule
-derivative of a composite function
-"outside-inside" rule
-repeated use of the chain rule
-power chain rule
9, 15, 33, 37,45, 57, 59, 63, 65
3.7
155
Implicit Differentiation
-implicitly defined functions
-lenses, tangents, and normal lines
-derivatives of higher order
-rational powers of differentiable
functions
(1-7 review), 9-13, 21-31, odds, 37a, 41, 43, 45, try 47, 49
4.1
184
Extreme Values
-absolute (global) extreme values
-local (relative) extreme values
-finding extreme values
1-9, 17-29, 35-43, 45, 46, 47-49 odds, 46, 48
4.2
192
Mean Value Theorem
-mean value theorem for derivatives
-physical interpretation
-increasing and decreasing functions
-other consequences (antiderivative)
1-9, 17-29, 35-43 odds, try 45-51
4.3
203
f, f', f''
-first derivative test for local extrema
-concavity
-pts of inflection
-second derivative test for local
extrema
-learning about f'ns from derivatives
1-15, 19, 25-47 odds
172
Review ch. 3
4, 8, 35-42 all, 45, 47, 48, 77, 80
242
Review ch. 4
1, 2, 4, 5, 7, 8, 14-18, 21, 22, 24-26
UNIT 4 Applications of Derivatives
Section Page Topic
Assigned Questions
4.4
214
Optimization
-examples from busines and industry:
area and volume
-examples from mathematics
1-13, 17, 19, 25-33 odds, try 47, 49, 51
4.5
229
Linearization
-linear approximation
-Newton's method (extra)
1, 3, 7, 11, 13, 15-16, try 19, 25, 33, 39
4.6
237
Related Rates
-related rate equations
-solution strategy
1-17, 29 (shadow), 33 odds
244
Review
45-54 all
58-62 all
optimization
related rates
UNIT 5 The Definite Integral
Section Page Topic
Assigned Questions
5.1
254
Estimating with Finite Sums
-distance traveled
-rectangular aproximation method
(RAM):LRAM, RRAM, MRAM
-volume of a sphere
1, 2
equation
9, 11
tables
17-25 Volumes
5.2
267
Definite Integrals
-Riemann Sums
-terminology and notation
-definite integral and area
-constant functions
-integrals on a calculator
-discontinuous integrable functions
1-5
7-11
13-27
29-37
39,41
43,45
5.3
274
Definite Integrals and Antiderivatives
-properties of definite integrals
-average value of a function,
-mean value theorem for definite
integrals
-connecting differential and integral
calculus
1-5
Properties
7-11
Evaluate
17-23 Find area of graphs and x-axis
25-29 average value
41
word problem
5.4
286
Fundamental Theorem of Calculus
-f-undamental theorem, part 1
-graphing using fNint
-fundamental theorem, part 2
-area connection
-more applications
3, 5, 13 evaluate using FTC-2
15, 17
area bet. Curve and x-axis
19
can FTC-2 be used?
25
area
35
finding K
37, 47, 49, 53, 55 FTC-1
5.5
295
Trapezoidal Rule
-trapezoidal approximations
1-9 odds
298
Review
-do odds AND evens
1-6 L/M/RRAM
9
Rules
13 area bet. Curve and x-axis
15, 16, 18-22, 26, 30-33 evaluate using FTC-2
41, 42, 45-47, 49, 54 FTC-1
50-51
graphs, trapezoidal table, word problem
notation
evaluation constants
evaluate using graphs and areas
evaluate using graphs and areas and known integral
evaluate using fNint
discontinuous integrals
UNIT 6 Derivatives of Special Functions (Trig, Exp, Logs)
Section Page Topic
Assigned Questions
3.5
Trigonometric Functions
-derivative of the sine function
-derivative of the cosine function
-simple harmonic motion, jerk
-derivatives of the other basic
trigonometric functions
1-9
trig deriv
11-21 eq’ns and tangents
23
motion
27-33 further deriv.
Inverse Functions
-derivatives of inverse functions
Handout sheet
Inverse Trigonometric Functions
-derivative of the arcsine
-derivative of the arctangent
-derivative of the arcsecant
1-17
19-21
23
140
3.8a
3.8b
162
inverse trig deriv.
tangent line
motion
-derivatives of the other three
3.9a
170
Exponential Functions
-derivative of e^x, derivative of a^x
1-17
3.9b
170
Logarithmic Functions
-derivative of lnx
-derivative of logx base a
-power rule for arbitrary real powers
19-39 exp. and log. Deriv
41
tangent line
43-45 log. Differentiation
47-49 exp. equations
Rev.
172
Review
3, 5-6, 9-30
31-32
41
implicit
46
tangent/normal
54,56 continuous/differentiable
66d-f numerical values
68
70
particle motion
76
horizontal tangent
78
f’n Q’s … max
79
graph composite trig f’n
#3 signs reversed:
+2cos2x -2sin2x
4.3
204
f, f', f''
21, 23
4.5
229
Linearization
5
5.4
286
FTC
7, 9, 11
27
31
39-46
exp. deriv
max/min, inc/dec, conc
FTC part 2
area
average value
FTC part 1
UNIT 7 Differential Equations and Mathematical Modeling
Section Page Topic
Assigned Questions
6.1
312
Antiderivatives and Slope Fields
-solving initial value problems
-antiderivatives and indefinite integrals
-properties of indefinite integrals
-applicaitons
1-5
find antiderivative
7-23
evaluate the indefinite integral
25
graph of initial value problem (IVP)
27-29
solve IVP and overlay on slope field
31-37
solve IVP
39, 41
motion: s, v, and a
43
overlay graph on slopefield
45, 47, 53 confirm integration by differentiation
6.2
321
Integration by Substitution
-power rule in integral form
-trigonometric integrands
-substitution in indefinite integrals
-substitution in definite integrals
-separable differential eq'ns
1-29
31-37
39, 41
43
6.4
338
Exponential Growth and Decay
-law of exponential change
-radioactivity
-Newton’s law of cooling
1, 3, 5
solve diff’l equation
11
growth problem
13
decay problem
15
find exponential f’n given two points
17, 19, 21, 29 decay problems
Rev.
358
Review
-do all questions (odds and evens)
1-16 (not 14)
evaluate indefinite integrals
21-28
solve IVP
29-32
function notation and antiderivatives
33-35
match indefinite integral with graph
36
does IVP have solution?
evaluation integral by substitution
evaluation using u(a) to u(b)
evaluate using separation of variable
solve IVP using sep’n
37
38
45,48,49
51
54
56
58
motion problem
sketch graph given slopefield and initial value
radioactive decay
differential equation
show integral is solution of IVP
provide graphical support
f and g antiderivatives
UNIT 8 Applications of Definite Integrals
Section Page Topic
Assigned Questions
7.1
371
Integral as Net Change
-linear motion revisited
-general strategy
-consumption over time
-net change from data
1-11
12-19
21, 23
28
7.2
380
Areas in the Plane
-area between curves
-area enclosed by intersecting curves
-boundaries with changing functions
-integrating with respect to y
-saving time with geometric formulas
1-9
area bet. Curves given the graph
11-35
area bet. Curves without the graph
Try 37-43 odds
7.3
391
Volumes
-volume as an integral
-square cross sections
-circular cross sections
-cylindrical shells (optional)
1-9
13-25
27
29-33
35,37
39-47
Review
1-5
consumption (7.1)
6-18
areas bet. Curves (7.2)
20-23, 25
volumes of revolution (7.3)
24,39
cross-sectional solids on a base (7.3)
Rev’w 413
velocity f’n
graphs of vel. f’n
consumption of a quanitity
solids on a base
solid revolved about x-axis
solid revolved about given line
solid revolved about y-axis
solid revolved about given lines
cylindrical shells method (optional)
UNIT 9 Review – Barron’s AP Calculus Manual
9.1 Limits and Continuity (Ch. 2)
9.2 Differentiation (Ch. 3)
9.3 Applications of Differential Calculus (Ch. 4)
9.4 Integration and Definite Integrals (Ch. 5-6)
9.5 Applications of Integrations and Differential Equations (Ch. 7-9)
Unit 10 Former AP Exams
10.1 Free Response Questions
10.2 Multiple Choice Questions
10.3 MBCI FINAL EXAM
AP CALCULUS FINAL EXAM