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Mathematical Methods CAS Units 3 and 4 Allason McNamara THE MAV REVISION LECTURE 2011

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Lecture Notes MAV Revision Lecture Series 2011.doc

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EXAMINATION 1 Structure of the paper Short answer questions 40 marks Time limit:60 minutes writing time 15 minutes reading time

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Added Content to Exam 1 General solutions to trigonometric equations Average value of a function Functional Equations Matrices transformations, transition matrices and steady state (Further Mathematics), solving simultaneous equations (up to 5 unknowns) (Compound and Double Angle formulae)

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Sample VCAA Questions and Frequently Asked Questions Solutions to VCAA 2010 Sample Questions.doc mmcasfaqs2011.pdf

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EXAMINATION 2 Structure of the paper Part I 22 multiple choice questions 22 marks Part II Extended answer questions 58 marks Time limit:120 minutes writing time 15 minutes reading time

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General Advice No calculator syntax Always give exact answers unless the question asks for an approximate answer. Draw graphs properly: scale axes, give coordinates if asked for For questions worth more than one mark show appropriate working. On Exam 2, this is the rule you are using and the answer. For show that questions show all the steps.

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Algebra

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E Dont forget to put the multiplication sign between a and x and the b and x on the calculator.

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No f is not exactly divisible by x + 1.

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There are 4 types of relations (Horizontal line: Vertical Line Test) many:many circle 1:manyinverse is a function many:1parabolafunction 1:1linefunctioninverse is a function

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If they ask for f give the domain and rule. If they ask for f(x) give the rule.

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Be careful if the square root is in the denominator.

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Solving Equations 2010 Exam 2 If the calculator does not give a solution, just solve the numerator equal to zero.

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Using transformations

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A

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B

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New to Exam 1 2010 A

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psandqs[1].doc n: even over odd >1n: odd over odd >1

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psandqs[1].doc

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n: odd over even less than 1

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n: odd over odd less than one

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D ab ce

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5

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Dont flick your graphs back show asymptotic behaviour Domain R\{b} Range R\{c} Give the equations of the asymptotes Scale the axes properly

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Domain R\{b} Range y > c

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D

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E

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Check the a value. A

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Note both curves go through the origin. Solve the determinant equal to zero. New to Exam 1 2010 By-hand B

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B

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D

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No solution

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Domain is the same as the domain of f(x).

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B Which one is a many:1 function?

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E Asymptotes of f Asymptotes of inverse Swap x and y and solve for y on the calculator.

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C

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B

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C

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C

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or CHECK ANSWERS

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D

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D

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The amplitude is 2. The graph has been translated 1 unit up. The period is about 0.4. A

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Change the domain. E Reflection in the x-axis Dilation from the y-axis (reciprocal)

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The first maximum, where x > 0, of f occurs at The graph of f has been shifted one unit to the right to get the graph of g.

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A

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A New to Exam 1 2010

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D

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E

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E

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C

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Can get directly from some calculators. at x = 2 D

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C

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Find the equation of the normal to the line.

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b = 4 Solve

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D Do 2010 Exam 1 last question. Using the y coordinate of the tangent line to f(x) to estimate the new f(x).

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Write down the rule. Put your units in.

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B

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D What is wrong with my calculator? Put your calculator in mode radians

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A

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A

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D

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D

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Top curve minus bottom curve

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D

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D

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D

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B

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Answer 0.49 OR

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598 Tea 102 coffee

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600 Tea 100 coffee New to Exam 1 2010 OR

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D

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C

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E

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Solve for a. a = 2.09 E

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D

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4.73.5 B

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7280 6472

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64

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D 200208

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130 D