# Planning Guide

#### Learning …

Learning is hard work. It is not easy to force the mind to go the distance. Focus has to be created and kept. You may have heard the famous quote that ‘genius is one percent inspiration and ninety-nine percent perspiration’. It was only after six-seven years of continuous hard work and many more years of prerequisite learning that Andrew Wiles was able to arrive at the proof of Fermant’s Last Theorem. Think of your famous writers, artists, scientists, mathematicians, doctors,…, your famous einsteins churned and brooded over ideas for decades for their own $e=mc^2$. Our memory of their name is a celebration of their force and distance - a celebration of perspiration.

Different individuals learn their own way. Here is one prescription for learning:

• Put in the time to wrestle with questions until the essence of the questions and the logic to their solutions is clear to you.
• Combine research to wrestling and build your knowledge by studying different perspectives and solutions.
• Rehearse the knowledge that you have built via research and wrestling with frequency.
• Communicate to relay, rehearse, and check the wisdom of your wrestling, research, and rehearsals versus the perspectives of other minds.
• Collaborate to remain in gravity and to contribute + grow via communication.

Further, combine the above prescription with Gorge Polya’s steps for problem-solving. View this summary document from UC Berkley Mathematics. These are simple to read but hard work to turn into a conscious learning habit.

#### Get Organized → Create a Schedule

# Lesson Time (1 Session = 90min Double Period Class)
1 Equation and its graph 1 Session
2 Functions 2 Sessions !important review and introduction
Learning Check - 1
3 Limit 1 Session
4 Limit Laws 1 Session
5 Limit techniques 1 Session
6 Continuous Functions 1 Session
7 Intermediate Value Theorem 1 Session
8 Infinite Limits and Vertical Asymptotes 1 Session
Learning Check - 2
9 Tangent line to a curve 1 Session
10 Derivative Function 1 Session
11 Differentiability and Continuity 1 Session
12 Alternate form of the derivative 1 Session
13 Differentiation Rules 1 Session
14 Product Rule 1 Session
15 Quotient Rule 1 Session
16 Derivatives of Trigonometric Functions 1 Session
17 Chain Rule 1 Session
18 Chain Rule – Trigonometric Functions 1 Session
19 Implicit Differentiation 1 Session
Learning Check - 3
20 Velocity Acceleration 2-3 Sessions
21 Related Rates 2-3 Sessions
Learning Check - 4
22 Extreme Values 1 Session
23 Rolle’s Theorem and Mean Value Theorem 1 Session
24 Increasing Decreasing Functions 1 Session
25 Concavity and Second Derivative Test 1-2 Sessions
26 Horizontal Asymptotes 1 Session
27 Summary of Curve-Sketching 2 Sessions
28 Optimization 2 Sessions
29 Newton’s Method 1 Session
Learning Check - 5
30 Antiderivative 1 Session
31 Sigma Notation 1 Session
32 Area of a Plane Region 2-3 Sessions
33 Fundamental Theorem of Calculus 1 Session
34 Mean Value Theorem for Integrals 1 Session
35 Second Fundamental Theorem 1 Session
36 U-Substitution 1 Session
37 Trapezoidal Rule 1 Session
38 Simpsons Rule – BC 1 Session
Learning Check - 6
39 Natural Log function 1 Session
40 Derivative of a log function 1 Session
41 Log rule for integration 1 Session
42 Derivatives of Inverse Functions 2 Sessions
43 Natural Exponential Function 1 Session
44 Functions with bases other than e 1 Session
45 Derivatives and integrals of Inverse Trig Functions 1 Session
Learning Check - 7
46 Slope Fields 1 Session
47 Euler’s Method – BC 1 Session
48 Separable Equations 1 Session
49 Growth-Decay-Logistic 1 Session
Learning Check - 8
50 Area Between Two Curves 1 Session
51 Volumes by Cross-section 1 Session
52 Volumes Disk Method 1 Session
53 Washer Method 1 Session
54 Shell Method 1 Session
55 Arc length – BC 1 Session
Learning Check - 9
56 Basic integration Rules 1 Session
57 Integration by parts 1-2 Sessions
58 Partial fractions 1 Session
59 L’hopital’s Rule and indeterminate forms AB 1 Session
60 Improper Integrals 1 Session
Learning Check - 10
61 Sequences – Definition and Limit 1 Session
62 Series and Convergence 1 Session
63 Integral Test and P-series 1 Session
64 Comparison of Series 1 Session
65 Alternating Series 1 Session
66 Conditional and absolute convergence 1 Session
67 Taylor Polynomials and Approximations 1 Session
68 Power Series 1 Session
69 Geometric power series 1 Session
70 Taylor and Maclauren Series 1 Session
Learning Check - 11
71 Parametric Equations 1-2 Sessions
72 Polar Equations 1 Session
73 Derivatives and integrals of polar graphs 1-2 Sessions
Learning Check - 12
TOTAL Sessions (including exam & review days) ~100 Days Minimum
74 AP Calculus Review Click the lesson link for review resources.
Currently includes flashcards. More will be added soon.