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Midterm

# MATA32 Midterm Exam Analysis

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Department
Mathematics
Course
MATA32H3
Professor
Raymond Grinnell
Semester
Fall

Description
Exam Analysis: MATA32 – Calculus for Management I 1. TEST BREAKDOWN The MATA32 term test generally covers 3 main topics:  Financial Mathematics  Limits  Differentiation (derivatives & applications, excluding implicit & logarithmic differentiation, Newton’s Method, and higher-order derivatives) The test is usually 120 minutes (2 hours) in length, consisting of 2 parts as follows:  A) Multiple Choice Questions ousually 7-8 questions which test your understanding of key concepts and/or involve straight-forward calculations (e.g. direct calculations of limits or derivatives) ooften 3-4 of the questions are on Financial Mathematics (calculation- based)  B) Full Solution Problems ooften 5-6 questions, each of which have multiple parts (a, b, c, d, etc.) oalmost all the questions are calculation-based (both direct calculations and applications) 2. TEST STATISTICS Frequency of Term Test Topics 8 7 6 5 4 FinancialMathematics 3 2 Limits N1mberof Questions Differentiation 0 Winter Fall Winter Fall Winter Fall 2013 2012 2012 2011 2011 2010 TermTest 3. TOPIC SUMMARIES All sections and pages cited refer to the course textbook, Introductory Mathematical Analysis, 13 ed. by Haeussler, Paul, & Wood. < KNOWLEDGE SUMMARY > 1 Exam Analysis: MATA32 – Calculus for Management I FINANCIAL MATHEMATICS Compound Interest (§5.1) For an original principal of money P, the formula gives the compound (or accumulated) amount S at the end of n interest periods at the periodic rate of ; APR: annual percentage rate (or nominal rate), N: number of interest periods per year. Remarks: 1. : time in years 2. Compound interest: The effective rate is given by: Present Value (§5.2) If we know the future value of an investment (accumulated amount), we may need to find its present value (principal amount). Equations of Value: (sum of present values of future payments) Net Present Value: (cash flows minus initial investment) Interest Compounded Continuously (§5.3) Let . We have the following equations: Compound Amount under Continuous Interest: Effective Rate under Continuous Interest: Annuities (§5.4) & (§5.5, p. 228) Annuity: any finite sequence of payments made at fixed periods of time over a given interval (called the term). We only consider fixed periods of time that are of equal length, and refer to that length of time as the payment period. If n payments (each of amount R) occur at times , we speak of an ordinary annuity. (Unless otherwise specified, we may assume an annuity is ordinary.) If they 2 Exam Analysis: MATA32 – Calculus for Management I occur at times , we speak of an annuity due. One main difference between these types of annuities is that an ordinary annuity’s payments are at the end of each payment period, while those of an annuity due are at the beginning. Present Value of Annuities:  Ordinary:  Annuity Due: Future Value of Annuities:  Ordinary:  Annuity Due: LIMITS Limits (§10.1-10.2) The (provisional) definition of a limit is given on p. 461. Limit Laws: Define functions . Basic Algebraic Limits 1. (Constant Law) 2. (Constant Multiple Law) 3. (Sum/Difference Law) 4. (Product Law) 5. (Quotient Law) 6. (Absolute Value Law) Consequent Limits 1. 2.  (Power Law) 3. (Root Law) 3 Exam Analysis: MATA32 – Calculus for Management I Basic Substitution Property: For all points in the domain of a polynomial or rational function , . Remarks: 1. 2. See p. 469 for a discussion of 1-sided and infinite limits. Relation between 1-sided and 2-sided limits: Limits at infinity are discussed on p. 471. N.B.: For , . Remarks: 1. Let . If , then DNE. 2. As
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