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Mathematics

MATA30H3

Sophie Chrysostomou

Fall

Description

Exam Analysis: MATA30 - Calculus I for Biological & Physical
Sciences
1. TEST BREAKDOWN
The MATA30 term test generally covers 3 main topics:
Functions
Limits & Derivatives
Differentiation Rules
The test is usually 110 minutes (almost 2 hours) in length, consisting entirely of
problems requiring full solutions – not just quick calculations.
There are usually about 8-10 questions, some of which have multiple parts (a, b,
c, d, etc.).
All questions are calculation-based, with the exception of 1 or 2 questions
requiring a proof of a trig identity.
Some questions may ask you to state a certain definition or theorem
In studying for the term test, it is highly recommended that you thoroughly review your
lecture notes, although the presentation of concepts in the textbook is very good.
2. TEST STATISTICS
Frequency of Term Test Topics
4.5
4
3.5
3
2.5
2
Fall2012 Term Test
1.5 Fall2010 Term Test
Numberof Questions
0.5
0
Functions Limits Differentiation
Topic
3. TOPIC SUMMARIES
All sections and pages cited refer to the course textbook, Single Variable Calculus: Early
Transcendentals, 7E by James Stewart.
< KNOWLEDGE SUMMARY >
FUNCTIONS (CH. 1)
1 Exam Analysis: MATA30 - Calculus I for Biological & Physical
Sciences
Definition of a function, domain & range: see p. 10
Vertical Line Test: A curve in the -plane is the graph of a function of iff any vertical
line crosses the curve only once.
Absolute value of a number :
A function is increasing [decreasing] on an interval iff :
See pp. 27-32 for a “catalog” of important functions.
Recall that . An important property of sine and cosine functions
is that they are periodic (with period ). Periodic functions are s.t. ,
where is the period.
Combinations of functions:
Exponential functions are discussed in §1.5. A simple way to remember exponent laws
(p. 53) is by using the mnemonic “MADSEEM” – Multiplying exponentials? Add the
exponents. Dividing exponentials? Subtract the exponents. Exponent to Exponent:
Multiply them.
A function is 1-1 if . In fact, is 1-1 iff any horizontal line
crosses its graph only once. (Horizontal Line Test)
Inverse functions are discussed on pp. 60-62.
Logarithmic (i.e. inverse exponential) functions in particular are discussed on pp.
62-65. Note that and .
Inverse trigonometric functions are discussed on pp. 67-69.
LIMITS & DERIVATIVES (CH. 2)
The (provisional) definition of a limit is given on p. 87. The similar definition of a 1-sided
limit is given on p. 92.
Relation between 1-sided and 2-sided limits:
2 Exam Analysis: MATA30 - Calculus I for Biological & Physical
Sciences
The definition of an infinite limit is given on pp. 93-94. One-sided infinite limits indicate
vertical asymptotes of a function (see p. 94). Note that .
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)
Direct Substitution Property: For all points in the domain of a polynomial or rational
function , .
Remarks:
1. (In fact, this statement
with “=” replaced by “≤” also holds.)
2.
Squeeze Thm.:
Li

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