





Final Exam: April 12th 2018
Topics: Riemann Sums, the Definite Integral, the Fundamental Theorem of Calculus, Techniques of Integration, Areas
between curves, Volumes, Improper Integrals, Work, Probability Density Functions, Centre of Mass,
Modelling with Differentian Equations, Convergence of
Sequences and Series, Power Series and Taylor Series.
2017 April exam
2016 April exam
List of practice problems from the CLP Problem Book
 The Definitive Integral
 see list for midterm exam
 Techniques of Integration
 see list for midterm exam
 Improper Integrals
 see list for midterm exam
 Applications of Integration
 Areas and Volumes
 see list for midterm exam
 Probability
 Chapter 8 (from Math 103 Notes): 8.2, 8.4, 8.5, 8.6, 8.8, 8.9, 8.10, 8.14, 8.15, 8.18, 8.19, 8.22, 8.25, 8.26, 8.31ab, 8.33.
 Work
 2.1: 7, 8, 10, 11, 13, 14, 15, 20, 21, 22, 24, 26, 28
 Centre of Mass
 2.3: 13, 14, 16, 17, 18, 19, 20, 24, 25, 26.
 Modelling with ODEs
 2.4: 6, 7, 15, 21, 27, 28, 32
 Series and Sequences
 3.1: 10, 11, 12, 14, 17, 18
 3.2: 15, 16, 17, 20, 21, 25
 3.3: 1, 2, 4, 5, 6, 10, 13, 14, 15, any one of 16 to 41, 48, 49, 51
 3.4: 3, 4, 5, 6, 8, 9, 10, 12.
 3.5: 2, 3, 4, 6, 7, 10, 12, 13, 16, 17, 18, 19a, 20, 21, 22, 25
 3.6: 4, 7, 8, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23
25, 32, 33, 38, 40a, 43a, 44a, 47, 49a
Here is a list of practice problems on Applications of Integration and Series
from the Stewart (8th edition) textbook:
 Work
 6.4: 4, 8, 9, 14, 17, 20, 21, 23, 24
 Chap 6 Review: 28, 29
 Chap 7 Review: 80
 Centre of Mass
 8.3: 2533 are all appropriate, 39, 42.
 Probability
 8.5: 2, 3, 4, 6, 8, 10, 12, 13.
 Chap 8 Review: 9, 21.
 Differential Equations
 9.1: 14, 16
 9.3: 118 are all appropriate, 24, 34, 38, 39, 40, 41, 43, 44, 45, 46, 48, 49, 50.
 9.4: 15 are all appropriate, 10, 17, 18, 21(a).
 Chap 9 Review: 17, 19, 21.
 Sequences
 11.1: 38, 1318, 2355, 7278 are all appropriate.
 Series
 11.2: 1, 914 are all appropriate, 15, 1748 are all appropriate, so are 5763, 67, 69, 75, 84, 87.
 11.3: 328 are all appropriate, 31, 33, 34, 45.
 11.4: 1, 2, 332 are all appropriate, 39, 44, 45.
 11.5: 230 are all appropriate, 33, 36, 37, 44.
 11.8: 1, 2, 328 are all appropriate, 29, 32, 33, 41, 42.
 11.9: 310 are all appropriate, 13, 14, 1520 are all appropriate, 2528, 38, 40, 41.
 11.10: 1, 2, 3, 518 are all appropriate, 3540 are all appropriate, 54, 55, 56, 6163, 65, 66, 75, 76, 84.
 11.11: 32, 33, 36.





February Midterm Exam: February 13th 2018
Topics: Riemann Sums, the Definite Integral, the Fundamental Theorem of Calculus, Techniques of Integration, Areas
between curves, Volumes, Improper Integrals.
Midterm exam solutions.
2016 February midterm exam.
2017 February midterm exam, 2017 February midterm exam solutions.
List of practice problems from the CLP textbook:
 Riemann Sums
 1.1: 4, 11, 12, 13, 15, 21, 24, 29, 32, 33, 39.
 The Definitive Integral
 1.2: 3, 5, 6, 9, 10
 1.3: 1, 3, 6, 7, 12, 13, 21, 22, 25, 27, 29, 34, 35, 36, 38, 40, 41, 42, 44, 45, 48, 49, 50, 51.
 Areas and Volumes
 1.5.2: 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 17, 18.
 1.6.2: 2, 3, 4, 5, 7, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 23.
 Techniques of Integration
 1.4.2: 2, 3, 4, 7, 8, any question from 9 to 14, any from 18 to 22.
 1.7.2: 4, any question from 6 to 21, 23, 25, 27.
 1.8.4: 2, 4, 5, 7, 8, 9, 10, 12, 13, 15, 24, 27, 29.
 1.9.2: 1, 2, 4, 6, 7, 8, 9, 12, 14, 17, 19, 20, 24.
 1.10.4: 4a, 7, 9, 11, 12, 13, 24, 26, 27.
 Improper Integrals
 1.12: 4, 6, 7, 9, 11, 13, 14, 15, 18, 19, 22, 23, 24, 26, 27.





Final Exam: December 18th 2017
Topics: Limits, Continuity and the Intermediate Value Theorem,
the Derivative (definition and differentiation rules),
Implicit differentiation, Linear approximation and Taylor polynomials,
Rates problems, Tangent line
problems,
Related rates problems, Exponential growth/decay models, Differential Equations, the Mean Value Theorem,
Shape of a curve and Curve Sketching, Optimization.
Learning Goals: This is a
complete list of concepts and techniques we discussed since the start of
term. Not all of the skills and concepts in this list will be tested on the
exam.
2015 December Exam
2016 December Exam. There is a typo in Q11a: the given Taylor polynomial is
for ln(1+x) at x=0 and the question should ask for the 100th derivative of ln(1+x) at x=0.
Practice Questions from the CLP Problem Book
 Limits and continuity
 We covered all material in sections 1.1 to 1.6. We also
discussed material in section 1.7 (formal definitions of a limit), but this
material will not be tested.
 Any problem in section 1.3, 1.4, 1.5, 1.6, especially problems with asterisk and stage 3 problems.
 Derivatives
 We covered all the material in section 2.1 to 2.14.
 Section 2.2: 11, 13, 16, 19, 22, 26, 27.
 Section 2.4: 14, 15, 17, 18.
 Section 2.6: 16, 18 (without using L'Hopital's rule)
 Section 2.8: 18, 21, 23, 24, 25, 26, 27.
 Section 2.9: any Stage 1 and 2 problem, 31, 32.
 Section 2.10: any Stage 2 problem.
 Section 2.11: 3, any Stage 2 and 3 problem.
 Section 2.12: any stage 2 problem.
 Section 2.13: see Mean Value Theorem below.
 Section 2.14: 2, 3, any stage 2 problem, 16, 17, 18, 20, 22.
 Differential Equations
The problems listed below are from the Active Calculus Textbook. Ignore any
questions asking for direction fields and stability of equilibrium solutions.
 section 7.1.5: Exercise 4, 6
 section 7.1.6: Activity 7.2.2
 section 7.2.2: Activity 7.2.3
 section 7.2.4: Exercise 5, 6, 7, 8
 section 7.3.1: Activity 7.3.2 (ignore c), 7.3.3 (ignore a).
 section 7.3.4 Exercise 1, 2, 3, 4.
 section 7.4.2: Activity 7.4.2, 7.4.3, 7.4.4.
 Section 7.4.3: Exercise 1, 2, 3, 4, 5, 6, 7, 8, 9
 Section 7.5.3: Activity 7.5.3
 Section 7.5.3: Exercise 3, 4, 7, 8.
 Section 7.6.1: Activity 7.6.2
 Section 7.6.2: Activity 7.6.3
 Section 7.6.4: Exercise 2, 3, 5, 7.
 Mean Value Theorem, Extrema, Concavity, L'Hopital's Rule, and Curve Sketching
 We covered all the material in sections 2.13, 3.5.1, 3.5.2, 3.6, 3.7.
 Section 2.13: 4, 5, 6, 7, 8, 13, 14, 15, 18, 21, 22.
 Section 3.5.1: 7.
 Section 3.6.1: 1, 3, 4.
 Section 3.6.2: any Stage 2 problem.
 Section 3.6.3: 2, 3, 4, 6, 7.
 Section 3.6.6: 1, 3, 5, 6, 7, 8, 11, 13, 14.
 Section 3.7: any Stage 1 and 2 problem.
 Optimization
 We covered all the material in section 3.5.3.
 Section 3.5.2: 4, 5.
 Section 3.5.3: 6, 7, 9, 10, 12, 15.
 Antiderivatives
 We covered section 4.1.
 4.1: 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 23, 24.
 Taylor Polynomials
 any problem in section 3.4.2, 3.4.3 (ignore Q7, 8, 11), 3.4.4 (ignore 2, 5), 3.4.5 (ignore 8, 9, 10, 11),
3.4.8, 3.4.9.






Midterm Exam: October 24th 2017,
Midterm exam solutions
Topics: Limits, Continuity and the Intermediate Value Theorem,
Differentiation rules, Antiderivatives,
Implicit differentiation, Linear approximation, Euler's method,
Rates problems, Tangent line
problems,
Related rates problems, Growth models.
Learning Goals: This is a
complete list of concepts and techniques we discussed since the start of
term. Not all of the skills and concepts in this list will be tested on the
midterm exam.
2016 Midterm Exam and Solutions.
The exam will test conceptual understanding and applications
of all topics covered in the course so far. Computational fluency is also expected.
This is a list of suggested practice problems from the Problem Book.
 1.1: 2, 3.
 1.2: 5, 6, 7.
 1.3: 1, 3, 4, 5, 6, 7, 8, 9, 11, 14, 15, 17.
 1.4: 1, 2, 3, 5, 9, 10, 16, 25, 27, 32, 35, 38, 39, 44.
 1.6: 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 17, 19, 24.
 2.2: 4, 5, 6, 7, 10, 11, 16, 19, 21, 26, 27.
 2.3: 1, 3, 6, 7.
 2.4: 11, 12, 14, 15, 17.
 2.6: 12, 15, 16, 17, 19, 20.
 2.7: 13, 14.
 2.8: 14, 15, 17, 18, 20, 24, 25, 26
 2.9: 1, 8, 10, 26, 27, 28, 35
 2.10: 3, 11, 12, 13, 16, 17, 18, 31.
 2.11: 2, 4, 6, 8, 11, 12, 14, 15.
 2.12: 4, 9, 18, 23, 28.
 2.14: 4, 8, 12, 16, 18
 3.1: 13, 17.
 3.2: 2, 4, 8, 9, 10, 13, 17, 20, 22
 3.3.1: 4, 6, 7, 8, 9, 10
 3.3.3: 2, 5, 6.
 3.4.2: 1, 2, 4, 6, 7, 9.
 4.1: 2, 5, 7, 8, 13, 14, 15.






Quiz on Limits and Derivatives: solutions
 