Calculus
Calculus is the study of limits, derivatives, integrals and their applications. This is a College in the High School class where students can earn college credits(4). For more information, click here.
Here is a list of topics and assignments covered.
TOPIC
Aug/Sept
Review of course and syllabus . . . .
1.1 Limits by tables and graphs
HW: p. 68 # 1 - 18
QUIZ
1.2 Limits and properties
HW: p. 74 # 1 - 31 odds second assignment p. 74 # 2 - 32 evens
QUIZ
1.3 Limits using Algebraic techniques
HW: p. 82 # 1 - 39 odds, 51, 52
QUIZ
1.4 Continuity
HW: p. 92 # 1 - 69 every other odd, 52, 70 - 73, 86
QUIZ
1.5 Infinite Limits
HW: p. 101 # 1 - 51 odds
QUIZ
Sept/Oct
2.1 The derivative, the tangent line problem, linearizations and differentials
HW: p. 112 # 1 - 25 odds, 27 - 32
QUIZ
2.2 Rules, rates of change and derivatives of trig functions
HW: p. 123 # 1 - 53 odds, 54, 71 - 74, 79, 86
QUIZ
2.3 Product and quotient rules
HW: p. 134 # 1 - 63 odds, 65 - 67, 72 - 80 evens, 81, 83, 84, 95, 96
QUIZ
2.4 The chain rule
HW1: p. 143 # 1 -20
HW2: p. 143 # 21 - 29, 39, 43, 47, 51, 55, 59, 63
QUIZ
TEST on derivatives and rules
2.5 Implicit Differentiation
HW: p. 151 # 9, 13, 17, 21, 25, 27
2.6 Related rates
HW1: p. 158 # 11, 14 - 20
HW2: p. 158 # 21 - 24, 38, 40, 80
QUIZ
Nov/Dec
3.1 Extrema
HW: p. 170 # 1 - 26, 35 - 38
QUIZ
3.2 Rolle’s Theorem and Mean Value Theorem
HW: p. 177 # 1 - 21 odds, 22, 25 - 33 odds, 39, 40
QUIZ
3.3 Increasing and decreasing functions and the first derivative test
HW: p. 186 # 1 - 49 every other odd except 33
QUIZ
3.4 Concavity and the second derivative test
HW: p. 194 # 1 - 35 odds, 55
QUIZ
3.5 Limits at Infinity (horizontal asymptotes)
HW: p. 203 # 1 - 8, 9 - 27 odds, 37, 43, 62, 64
QUIZ
3.6 Summary of curve sketching (domain & range, extrema, inflection pts, vertical & horizontal asymptotes)
HW: p. 211 # 1, 3, 13, 17, 18, 24, 27, 28, 41, 46
QUIZ
3.7 Optimization
HW: p. 218 # 3, 16, 23, 40, 45, 49
QUIZ
January
4.1 Antiderivatives and indefinite integration
HW: p. 256 # 1 - 33 odds
QUIZ
4.2 Area
HW: p. 267 # 1 - 29 every other odd
QUIZ
4.3 Riemann sums and definite integrals
HW: p. 277 # 1 - 33 odds, 39, 41, 43, 52
QUIZ
4.4 The fundamental theorem of Calculus
HW: p. 289 # 1 - 49 odds
QUIZ
4.5 Integration by Substitution
HW: p. 301 # 1 - 69 odds
QUIZ
4.6 Numerical Integration
HW: p. 311 # 1, 7, 10, 21
QUIZ
Feb/March
5.1 The natural log function and differentiation
HW: 324 # 3 - 6, 13, 15 - 30, 31 - 59 odds
QUIZ
5.2 The natural log function and integration
HW: p. 333 # 1 - 49 odds except 39, 41, 43
QUIZ
5.3 Inverse Functions
HW p. 341 # 1 - 21 every other odd, 23, 27, 29, 59, 63
5.4 Exponential functions: Differentiation and Integration
HW: p. 350 # 1 - 17 odds, 19 - 22, 25 - 57 odds, 67 - 85 odds
QUIZ
5.5 Bases other than e
HW: p. 359 # 1, 5, 9, 13, 21, 25 - 39 odds, 45, 53
5.6 Growth and Decay
HW: 367 # 1, 3, 5, 11, 13, 15, 17, 19, 26, 27, 37, 38, 52
QUIZ
March/April
6.1 Area of a region between curves
HW: 409 # 1 - 41 odds
QUIZ
6.2 Volume: Disc method (washer method)
HW: p. 420 # 1, 3, 9, 11, 13, 23, 25, 31, 43
QUIZ
6.3 Volume: Shell method (cylindrical shell method)
HW: p. 429 # 1, 3, 7, 13, 15, 22
QUIZ
Test: Volume
6.4 Arc Length, surfaces of revolution and volume by cross sections
HW: p. 439 # 3 - 8, 24, 29, 30, 31
April/May
7.2 Integration by parts
HW: p. 486 # 9 - 29 odds, 37 - 41 odds
QUIZ
7.4 Trig Substitution
HW: p. 506 # 5, 9, 13, 19, 23, 27, 31, 35
QUIZ
7.5 Partial Fractions
HW: p. 517 # 7 - 33 odds
QUIZ
7.6 Integration by tables
HW: # 15 - 45 odds
QUIZ
7.7 Indeterminate forms and L’Hopitals rule
HW: p. 532 # 1 - 39 odds
QUIZ
7.8 Improper Integrals
HW: p. 543 # 1 - 31 odds
QUIZ