# MATA32 Final Exam Analysis

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University of Toronto Scarborough

Mathematics

MATA32H3

Raymond Grinnell

Fall

Description

Final Exam Analysis: MATA32 – Calculus for Management I
1. TEST BREAKDOWN
The MATA32 final exam is generally cumulative, covering 5 main topics: the 3 main
topics covered on the midterm test, an expansion of the differentiation topic, and the
new topic of integration. These are listed below.
Financial Mathematics
Limits
Differentiation
Derivatives & Applications (includes implicit & logarithmic differentiation,
Newton’s Method, higher-order derivatives, and curve sketching)
Integrals & Applications
The test is usually 180 minutes (3 hours) in length, and the format is very similar to that
of the midterm test:
A) Multiple Choice Questions (usually 10-12 total)
B) Full Solution Problems (usually 7-10 total)
2. TEST STATISTICS
Winter 2013 Fall2012
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Content 45% Content 47%
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Winter 2012 Fall2011
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Winter 2011 Fall2010
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Content 44% Content
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1 Final Exam Analysis: MATA32 – Calculus for Management I
3. TOPIC SUMMARIES
All sectionthand pages cited refer to the course textbook, Introductory Mathematical
Analysis, 13 ed. by Haeussler, Paul, & Wood.
< KNOWLEDGE SUMMARY >
FINANCIAL MATHEMATICS See Midterm Exam
LIMITS Analysis
DIFFERENTIATION
DERIVATIVES & APPLICATIONS
Implicit & Logarithmic Differentiation (§12.4-12.5)
An equation of the form (e.g. ) does not express
explicitly as a function of . That is to say, in such equationis expressed implicitly as
a function of . To find , we use the technique of implicit differentiation
(described on p. 557).
Logarithmic differentiation (described on p. 561) is a technique used to ease the process
of differentiating functions involving products, quotients, or powers – especially those
of the form , where and are both functions of , and thus variable as opposed to
constant.
Newton’s Method (§12.6)
Finding the roots of a non-polynomial function or even a polynomial function of degree
>2, can often prove to be a tedious (or impossible) task by standard methods. Hence, we
may settle for approximate roots. Newton’s method (discussed on pp. 564-565) is often
useful in this regard.
Given an initial approximation (or “seed”) , successive approximations of roots of the
equation are given by the following iteration formula, provided that is
differentiable:
where
Higher-Order Derivatives (§12.7)
See p. 568. Convenient notation for derivatives:
2 Final Exam Analysis: MATA32 – Calculus for Management I
(“ th derivative of ”, particularly handy for derivatives of order higher than 3)
Curve Sketching (Ch. 13)
A nice chapter summary can be found on pp. 620-621.
A function is increasing [decreasing] on an interval iff :
Extrema are maxima and minima.
Relative (or local) extrema and the 1 -derivative test are discussed in §13.1.
Extreme Value Thm. (EVT): If a function is continuous
on , then s.t. . (I.e., has both an
absolute/global maximum and minimum value over .)
The closed-interval method

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