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