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Science One Mathematics

Exams



       

       

   

   

       
       

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, 8.31a-b, 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: 25-33 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: 1-18 are all appropriate, 24, 34, 38, 39, 40, 41, 43, 44, 45, 46, 48, 49, 50.
    • 9.4: 1-5 are all appropriate, 10, 17, 18, 21(a).
    • Chap 9 Review: 17, 19, 21.
  • Sequences
    • 11.1: 3-8, 13-18, 23-55, 72-78 are all appropriate.
  • Series
    • 11.2: 1, 9-14 are all appropriate, 15, 17-48 are all appropriate, so are 57-63, 67, 69, 75, 84, 87.
    • 11.3: 3-28 are all appropriate, 31, 33, 34, 45.
    • 11.4: 1, 2, 3-32 are all appropriate, 39, 44, 45.
    • 11.5: 2-30 are all appropriate, 33, 36, 37, 44.
    • 11.8: 1, 2, 3-28 are all appropriate, 29, 32, 33, 41, 42.
    • 11.9: 3-10 are all appropriate, 13, 14, 15-20 are all appropriate, 25-28, 38, 40, 41.
    • 11.10: 1, 2, 3, 5-18 are all appropriate, 35-40 are all appropriate, 54, 55, 56, 61-63, 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 100-th 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