MATA30 Midterm Exam Analysis

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Sophie Chrysostomou

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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