Test Preview

Text: G.B. Thomas, Jr., M.D. Weir, and J. Hass, Thomas' Calculus. Early Transcendentals, 14th Edition, 2018.

Test Preview Help Session:

Wednesday, December 11, 3:00-4:00 pm, SH203

Calculus II Common Final Exam Review:

Wednesday, December 11, 6:00-7:00 pm, AK116

General information:

Closed-book & closed-notes event. Calculators are not allowed. The Exam consists of two parts (similarly to the Common Final in MA1021 in A'19):

(1) Basic Skills Component
(2) General Exam Component

In (1), there is no partial credit on the problems; only final answer is graded, and binary grades (solved/not solved = yes/no = 5/0) are used. On the general part, your work and your explanations are graded, not just the final answers.

Contents:

(1): 7 integral problems

(2):

• Area of curvilinear region
• Volume of the solid of revolution
• Arc length
• Center of mass (centroid)
• Techniques of integration (6 integrals)
• Definite integral through the Riemann sum

Sample problems:

• MA1022 Common Final, B Term 2018 (PDF)
• MA1022 Common Final, B Term 2017 (PDF)
• MA1022 Common Final, B Term 2016 (PDF)

General information:

"Simple" calculators are required for arithmetic calculations in Problem 6; however, no tablets, gadgets, laptops, smartphones, etc. Printouts of Slides 8-9 (Elementary Integrals, Part 1 & Part 2) of the PPT Class Notes are allowed.

Subjects:

Applications of the integral; natural exponential function and related functions - the material considered in the course after Test 1

Concepts which should be under unconditional control:

• Volumes by the method of cross-sections; solids of revolution; revolution about the x- and y-axes
• Length of a smooth curve
• Area of surface of revolution
• Center of mass (centroid) of a plane region; moments about the x- and y-axes
• Natural logarithmic function (NLF) and natural exponential function (NEF); general exponential function and general logarithmic function; differentiation and integration of these functions
• Applications involving exponential change (growth or decay)

Contents:

Problems with Nos from 1 to 6; No 5 consists of 2 problems:

1. Finding the volume of a solid of revolution
2. Finding the length of a smooth curve
3. Finding the surface area of revolution
4. Finding the centroid of a plane region
5. Evaluation of indefinite integrals (related to NLF and NEF)
6. Problem on a process involving exponential change
7. Bonus.

Sample problems - Recommended Exercises:

1. 6.1: 21 - 30
2. 6.3: 1 - 16
3. 6.4: 13 - 21
4. 6.6: 1 - 14
5. 7.1: 1 - 46
6. 7.2: 23 - 40

General information:

Printouts of Slides 8-9 (Elementary Integrals, Part 1 & Part 2) of the PPT Class Notes (downloadable from News page) are allowed. No calculators, tablets, gadgets, laptops, etc.

Subject:

The integral - the material considered so far in the course and covered by Chapter 5

Concepts which should be under unconditional control:

• Sums; Sigma notation; summation formulas.
• Definite integral as the limit of the Riemann sum.
• Antidifferentiation; definite integral by definition (as a limit of the Riemann sum); the Fundamental Theorem of Calculus; major properties of the definite integral.
• Techniques of integration: elementary integrals & u-substitution.
• Differentiation of definite integrals
• Area of a curvilinear region

Contents:

Questions with Nos from 1 to 6; No 5 consists of 2 problems:

1. Evaluation of a sum.
2. Evaluation of the definite integral through its definition.
3. Differentiation of the definite integral.
4. Evaluation of an indefinite integral.
5. Evaluation of the definite integral.
6. Finding the area of a region.
7. Bonus.

Sample problems - Recommended Exercises:

1. 5.2: 19 - 36
2. 5.3: 63 - 70
3. 5.4: 45 - 56
4. 5.5: 17 - 66
5. 5.6: 1 - 48
6. 5.6: 65 - 94

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Last modified: 14:30 pm; Wed, Dec 11, 2019