Test Preview

Text: Calculus. Early Transcendental Version by C.H. Edwards and D.E. Penney, 6th Edition, 2003.

General information:

Closed-texts & closed-notes event. Calculators are not allowed.

Principal requirement for credit in B'03 MA1022:

Demonstration of an acceptable level of competence in the basic manipulative/computational skills of one-variable integral calculus.

How to satisfy the above requirement:

By achieving a passing grade on a Basic Skills exam.

Basic Skills - main features:

• Seven problems, 5 points each one, 35 points total
• No partical credit: answers are either correct (full credit), or incorrect (no credit).
• The minimum score to pass will be about 70% (i.e., probably 5 solved problems).

General topics to be covered on the Basic Skills part:

• Fundamental Theorem of Calculus
• Integrals of polynomials, exponentials, and trig functions
• Integration by substitution
• Integrations by parts

Concepts which should be under your unconditional control (for both parts of the Final Exam):

• An antiderivaite (indefinite integral)
• Definite Iitegral and its properties
• Fundamental Theorem of Calculus
• Area of curvilinear region and its computation
• Volume of solids of revolution
• Length of a plane curve (arclength)
• Mass, moments and centroid of plane laminae
• Natural logarithmic and exponential functions
• Logarithmic differentiation; differentiation of definite integrals
• Inverse trigonometric functions and their derivatives
• Basic integration rules (## 1-9, 14-19)
• Substitution method for evaluation of integrals
• Trigonometric (rationalizing) substitutions
• Evaluation of integrals by integration by parts method

Supportive B'02 material:

• MA1022 Sample Exam: Problems and Solutions (PDF)
• MA1022 Final Exam: Problems (PDF), Solutions (PDF)

General information:

Closed-text & closed-notes event. Calculators are allowed only for Problem 6 to compute ln(...) and e^(...).

Subjects:

Applications of the integral & Transcendental functions - the material considered in the second part of the course (after Test 1).

Concepts which should be under unconditional control::

• Area of a curvilinear region in the plane - slicing by vertical and horizontal approximating strips with integration x- and y-wise respectively.
• Volumes of solids of revolution - method of disks and method of washers.
• Generalized concept of a curve - parametric representation.
• Arc length (length of a plane curve)
• Area of a surface of revolution
• Work done by a varying force
• The center of mass and moments of the lamina
• The natural logarithmic and natural exponential functions; their differentiation and integration
• The inverse trigonometric functions; their differentiation and integration

Contents: Problems with Nos from 1 to 6:

1. Area of a plane region
2. Volume of a solid of revolution
3. Work
4. Center of mass of a plane region
5. Differentiation of expressions with transcendental functions
6. Process characterized by exponential growth or decay
7. Bonus.

Sample problems:

1. 6.1: 19, 23
2. 6.2: 10 (Answer: 6558Pi/7), 15
3. 6.5: 3; 6.7: 8 (Answer: (a) 16 in-lb; (b) 72 in-lb)
4. 6.6: 11, 12 (Answer: (0, -287/130)
5. 7.1: 9, 10 (Answer: - 1/x^3 - 3(lnx)^2/x)
6. 7.5: 11, 14 (Answer: about 5565 y. ago)

NB: Special arrangemnt: TA's office hours on Friday, December 5, 2003: Shawn Hallinan, SH204, 2 to 3 pm.

General information:

Closed-text & closed-notes event. Calculators are not allowed.

Subject:

Introduction to the integral - the material considered so far in the course.

Concepts which should be under unconditional control:

• Sum of a sequence; summation formulas.
• Area by inscribed/circumscribed polygons.
• Antidifferentiation; definite integral by definition; the Fundamental Theorem of Calculus; major properties of the definite integral.
• Techniques of integration: power rule, generalized power rule, method of substitution.

Contents: Problems with Nos from 1 to 4, and No 3 consists of 2 different tasks:

1. Evaluation of sum.
2. Area of curvilinear region by polygonal approximation.
3. (a) Indefinite integral by the method of substitution. (b) Definite integral by the method of substitution.
4. Derivative of the definite integral.
5. Bonus.

Sample problems:

1. 5.3: 27, 29
2. 5.4: 13, 15
3. (a) 5.8: 23, 25; (b) 5.8: 35, 49
4. 5.6: 15, 19

[ Back to Calc II Info Page ]

---

vadim@wpi.edu

Last modified: 11:55 am; Mon, Dec 15, 2003