MAV REVISION LECTURE. MATHEMATICAL METHODS UNITS 3 AND 4. Presenter: MICHAEL SWANBOROUGH Flinders Christian Community College. EXAMINATION 1. Short-answer questions (40 marks) Questions are to be answered without the use of technology and without the use of notes Time Limit:

Download Presentation

MAV REVISION LECTURE

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

MAV REVISION LECTURE MATHEMATICAL METHODS UNITS 3 AND 4 Presenter: MICHAEL SWANBOROUGH Flinders Christian Community College

EXAMINATION 1 • Short-answer questions (40 marks) • Questions are to be answered without the use of technology and without the use of notes • Time Limit: • 15 minutes reading time • 60 minutes writing time

EXAMINATION 2 • Part I: Multiple-choice questions • 22 questions (22 marks) • Part II: Extended response questions: • 58 marks • Time limit: • 15 minutes reading time • 120 minutes writing time

Examination Advice General Advice • Answer questions to the required degree of accuracy. • If a question asks for an exact answer then a decimal approximation is not acceptable. • When an exact answer is required, appropriate workingmust be shown.

Examination Advice General Advice • When an instruction to use calculus is stated for a question, an appropriate derivative or antiderivative must be shown. • Label graphs carefully – coordinates for intercepts and stationary points; equations for asymptotes. • Pay attention to detail when sketching graphs.

Examination Advice General Advice • Marks will not be awarded for questions worth more than one mark if appropriate working is not shown.

Examination Advice Notes Pages • Well-prepared and organised into topic areas. • Prepare general notes for each topic. • Prepare specific notes for each section of Examination 2. • Include processsteps as well as specific examples of questions.

Examination Advice Notes Pages • Include key steps for using your graphic calculator for specific purposes. • Be sure that you know the syntax to use with your calculator (CtlgHelp is a useful APP for the TI-84+)

Examination Advice Strategy - Examination 1 • Use the reading time to carefully plan an approach for the paper. • Momentum can be built early in the exam by completing the questions for which you feel the most confident. • Read each question carefully and look for key words and constraints.

Examination Advice Strategy - Examination 2 • Use the reading time to plan an approach for the paper. • Make sure that you answer each question in the Multiple Choice section. There is no penalty for an incorrect answer. • It may be sensible to obtain the “working marks” in the extended answer section before tackling the multiple choice questions.

Examination Advice Strategy - Examination 2 • Some questions require you to work through every multiple-choice option – when this happens don’t panic!! • Eliminate responses that you think are incorrect and focus on the remaining ones. • Multiple Choice questions generally require only one or two steps – however, you should still expect to do some calculations.

Examination Advice Strategy - Examination 2 • If you find you are spending too much time on a question, leave it and move on to the next. • When a question says to “show” that a certain result is true, you can use this information to progress through to the next stage of the question.

is the sum of the For the equation solutions on the interval Question 4 a) b) E c) d) e)

Question 5 What does V.C.A.A. stand for? a) Vice-Chancellors Assessment Authority b) Victorian Curriculum and Assessment Authority c) Victorian Combined Academic Authority d) Victorian Certificate of Academic Aptitude e) None of the above B

Functions and Their Graphs Vertical line test - to determine whether a relation is a function A represents the DOMAIN B represents the CODOMAIN (not the range!)

Maximal (or implied) Domain The largest possible domain for which the function is defined • A function is undefined when: • a) The denominator is equal to zero • The square root of a negative number is present. • The expression in a logarithm results in a negative number.

Using Transformations When identifying the type of transformation that has been applied to a function it is essential to state each of the following: NATURE– Reflection, Dilation, Translation MAGNITUDE(or size) DIRECTION

1. Translations a) Parallel to the x-axis – horizontal translation. b) Parallel to the y-axis – vertical translation. To avoid mistakes, let the bracket containing x equal zero and then solve for x. If the solution for x is positive – move the graph x units to the RIGHT. If the solution for x is negative – move the graph x units to the LEFT.

Note: A dilation of a parallel to the y-axis is the same as a dilation of parallel to the x-axis. • 2. Dilations • a) Parallel to the y-axis – the dilation factor is the number outside the brackets. This can also be described as a dilation from the x-axis. • Parallel to the x-axis – the dilation factor is the reciprocal of the coefficient of x. This can also be described as a dilation from the y-axis.

a) Reflection about the x-axis b) Reflection about the y-axis c) Reflection about both axes d) Reflection about the line 3. Reflections

Square Root Functions • The graph is: • translated 2 units in the positive x direction • translated 1 unit in the positive y direction

Question 9 The rule of the graph shown could be ANSWER: D

Vertical: Horizontal: Graphs of Rational Functions Question 10 The equations of the horizontal and vertical asymptotes of the graph with equation ANSWER: E

a) b) c) d) e) Question 12 The graph shown could be that of the function f whose rule is ANSWER: A

Step 4: Remember that: Investigating Composite Functions Step 1: Complete a Function, Domain, Range (FDR) table. Step 2: Check that the range of g is contained in the domain of f . Step 3: Substitute the function g(x) into the function f (x).

Inverse Functions Key features: The original function must be one-to-one Reflection about the line y = x Domain and range are interchanged Intersections between the graph of the function and its inverse occur on the line y = x

To find the equation of an inverse function Step 1: Complete a Function, Domain, Range (FDR) table. Step 2: Interchange x and y in the given equation. Step 3: Transpose this equation to make y the subject. Step 4: Express the answer clearly stating the rule and the domain.