MA1200 Calculus I

Text: Open Educational Resource, free online math book:    https://openstax.org/details/books/calculus-volume-1

Please feel free to download a PDF. So if you don't have internet access, you could still read the book.

Concept Maps: 

Chapter 2 Limits                Chapter 3 Derivatives                Chapter 4 Application of Derivatives                Chapter 5 Integrals

In-class worksheets/Handouts: 

      Lecture Videos    YouTube Playlist                                                    YouTube videos about Calculus

      Link to all blank notes as Word document files

      Algebra formula sheet,    Trig formula sheet,    Trig graph,    Calculus formula sheet,       

      chapter 1  Review of function                                  Notes with answers

      chapter 2.1-2.3 limits law                                        Notes with answers

      chapter 2.4-2.6 infinite limits, continuity                 Notes with answers

      chapter 3.1-3.3 derivative rule                                Notes with answers

      chapter 3.4-3.6 trig derivative, app, chain rule        Notes with answers

      chapter 3.7-3.10 exp log inverse trig derivative, related rates           Notes with answers

      chapter 4.1-4.2 max and min                                    Notes with answers

      chapter 4.4-4.6 Optimization linear approx. MVT     Notes with answers

      chapter 4.7 L'hopital's rule                                       Notes with answers

     chapter 4.8-5.4 antiderivative, FTC                          Notes with answers

Homework assignments: 

Go to Canvas and click the corresponding homework links. 

You have unlimited attempts for the homework. So you can re-do some homework questions to get a perfect score. You can attempt each problem three times and then the system will generate a new but similar question as many times as necessary.  

Down below is a sample homework solution. I strongly recommend that you review class notes and then work on your homework. 

If you have trouble with a question, read the solution and follow the steps to work on that question. Save your work on scratch paper so you can study later to prepare for exams. Cheers! 

When you have questions, come to ask me! Cheers! ^o^   

Homework 1 (algebra review) Solution          

Homework 2 (section 2.1-2.3) Solution           

Homework 3 (section 2.4-2.6) Solution       

Homework 4 (section 3.1) Solution       

Homework 5 (section 3.2-3.3) Solution       

Homework 6 (section 3.4-3.5) Solution       

Homework 7 (section 3.6-3.7) Solution       

Homework 8 (section 3.8) Solution        

Homework 9 (section 3.9-3.10) Solution       

Homework 10 (section 4.1-4.2) Solution        

Homework 11 (section 4.4-4.5) Solution         

Homework 12 (section 4.6-4.7) Solution         

Homework 13 (section 4.8-5.2) Solution         

Homework 14 (section 5.3-5.4) Solution         

Practice exams and solutions:                            Exam scores

1.  Practice exam 1           Solution               

2. Practice exam 2            Solution                    Derivative formula sheet blank                Answer

3. Practice exam 3            Solution

4. Practice final exam             Solution                  Anti-derivative formula sheet blank        Answer                 New formula sheet        Answer              

    For the last problem of the practice exam, change to this type of Riemann sum question:   Riemann Sum + antiderivative exercise       Answer 

More exercises on Related rate and Optimization problems. Do not need to turn in. You can review your notes and homework problems first, then try:

Application Related Rates              Solution

Application Optimization                 Solution

True of False exercises: Some students find T or F problems very challenging, because these problems require a deeper understanding of the concepts compared with computational problems. Here are some exercises from (Briggs & Cochran, Calculus: Early Transcendentals, Pearson,   2011, ISBN: 9780321570567)

Chapter 2 Limit T or F              Answer

Chapter 3 Derivatives T or F              Answer

Chapter 4 Application of derivatives T or F              Answer

Chapter 5 Integrals T or F              Answer

Extra Exercises:

Please be aware that our section numbers differ from those in Opentax. This variation is due to the switch in our textbook to Openstax. To locate the corresponding section exercises in Openstax for practice, please refer to the following mapping.

Section number in Worksheets/videos               Section number in OpenStax                                        Suggested exercises

Review of Functions                                                 1.1Review of Functions                                                             15, 17, 19, 21, 29, 33, 39, 41, 53, 55

                                                                  1.2Basic Classes of Functions                                                   61, 67, 71, 81, 95, 97

                                                                  1.3Trigonometric Functions                                                       113, 115, 119, 123, 127, 129, 131, 139, 143,  

                                                                                                                                                                             145, 155, 159, 163, 169, 173, 181

                                                                  1.4Inverse Functions                                                                  185, 189, 193, 197, 201, 205, 207, 211, 213,  217, 223        

                                                                              1.5Exponential and Logarithmic Functions                              243, 251, 261, 265, 273, 279, 289, 301, 307

2.1-2.2 Definition of limits                                   2.1A Preview of Calculus                                                            7, 13

                                                                                 2.2The Limit of a Function                                                         30, 31, 35, 41, 43, 46-64, 77, 79

2.3  Techniques of Computing Limits               2.3The Limit Laws                                                                       84, 85, 90, 95, 97, 99, 101, 102, 105, 109, 111, 115, 117, 119, 121,

                                                                                                                                                                                         123, 125

2.4  Infinite Limits 

2.5  Limits at infinity                                            4.6Limits at Infinity and Asymptotes                                         253, 259, 265, 267, 270, 277, 281, 282, 283, 

2.6  Continuity                                                     2.4Continuity                                                                                125, 137, 138, 139, 141, 143, 144, 147, 148, `49, 153, 154, 157, 

3.1 Introducing the derivative                                    3.1Defining the Derivative                                                          3, 5, 8, 9, 15, 19, 23, 26, 41, 43, 48, 51, 

                                                                                   3.2The Derivative as a Function                                            59, 61, 63, 65, 67, 69, 73, 74, 77, 78, 79, 80, 

3.2 Rules of differentiations                                     3.3Differentiation Rules                                                              109, 111, 113, 115, 117, 119-121, 126-129, 131-132, 139, 141, 147

3.3 The product & quotient rule

3.4 Derivatives of Trigonometric function                    3.5Derivatives of Trigonometric Functions                             175, 177, 181, 183, 187, 189, 191, 192, 195, 198, 203, 213

3.5 Derivatives as rates of change                                 3.4Derivatives as Rates of Change                                          151, 155, 160, 163, 165, 

3.6 The Chain Rule                                                    3.6The Chain Rule                                                                       223, 224, 227, 231, 233, 235, 236, 237, 239, 241, 245-251, 255,

                                                                                                                                                                                         256, 257, 

3.7 Implicit differentiation                                3.8Implicit Differentiation                                                           303, 305, 307, 313, 317, 321, 323, 

1.3 Inverse, Exp & Log functions                                1.4Inverse Functions                                                                  185, 189, 193, 197, 201, 205, 207, 211, 213,  217, 223 

3.8 Derivatives of Log and Exp functions              3.7Derivatives of Inverse Functions                                         261, 265, 268, 271, 273, 275, 277, 281, 283, 287

                                                                                   3.9Derivatives of Exponential and Logarithmic Functions     333, 337, 341, 343, 344, 345, 347, 349, 353, 355,  

3.9 Derivatives of Inverse Trig functions  

3.10 Related rates                                                     4.1Related Rates                                                                         3, 6, 9, 10, 14, 19, 22, 25, 29, 30, 31, 37, 39

4.1 Maxima & Minima                                               4.3Maxima and Minima                                                                101-103, 109, 111, 113, 114, 115, 117, 119, 121, 123, 126, 127,                                                                                                                                                                                           131,  133, 135, 139

4.2 What derivatives tell us                                        4.5Derivatives and the Shape of a Graph                                  202, 207, 210, 215, 221, 223, 227, 233, 237, 239, 

4.4 Optimization Problems                                         4.7Applied Optimization Problems                                            316, 319, 322, 326, 343, 353, 

4.5 Linear Approximation and Differentials                  4.2Linear Approximations and Differentials                              51, 55, 59, 61, 63, 69-71, 75, 83, 85, 

4.6 Mean Value Theorem                                           4.4The Mean Value Theorem                                                      155,  159, 163, 167, 173, 175, 177, 186, 189, 

4.7 L’hopital’s rule                                                     4.8L’Hôpital’s Rule                                                                       163, 371, 375, 378, 381, 390, 394, 395, 399, 401, 403, 405, 

4.8 Antiderivatives                                                     4.10Antiderivatives                                                                      473, 479, 485, 487, 495, 497, 501, 505, 508, 517, 

5.1 Approximating Areas under curves                      5.1Approximating Areas                                                              13, 15, 23, 25, 41, 43, 

5.2 Definite integrals                                              5.2The Definite Integral                                                                67, 70, 71, 75, 79, 81, 111, 115, 

5.3 Fundamental Theorem of Calculus                        5.3The Fundamental Theorem of Calculus                                   151, 155, 157, 167, 173, 185, 193, 195, 203

5.4 Working with integrals                                          5.4Integration Formulas and the Net Change Theorem               207, 208, 221, 227, 231, 249

                                                            5.6Integrals Involving Exponential and Logarithmic Functions       321, 323, 325, 331, 333, 335, 339, 341, 357, 365

                                                            5.7Integrals Resulting in Inverse Trigonometric Functions             395, 397, 400, 402, 407, 409, 411, 413, 419, 421, 427, 429

5.5 Substitution Rule                                                 5.5Substitution                                                                                      257, 267, 275, 279, 283, 285, 291, 295, 299, 302, 311

2020 Spring Class Recordings about some extra exercises: 

Chapter 3    3/20 office hour recording    Notes

                    3/27 office hour recording    Notes

                    4/3 office hours recording   Notes 

Chapter 4    4/10 office hours recording   Notes 

                    4/17 office hours recording   Notes 

Chapter 5    4/24 office hours recording   Notes 

                    5/1 office hours recording   Notes 

Kahoot game:  K1  K2  K3  K4    

Tactivity:  T1a  T1b  T2  T3  T4

Exam Wrapper

Acknowledgement: The examples in the worksheets are taken from the book (Briggs & Cochran, Calculus: Early Transcendentals, Pearson,   2011, ISBN: 9780321570567) and Kiryl Tsishchanka's notes. The formula sheets are taken from Paul Dawkins' online math notes. If you find some useful online resources which may be beneficial to the whole class, please let me know. Thank you!!! :-)