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M.A.V. REVISION LECTURES. MATHEMATICAL METHODS UNITS 3 AND 4. Presenter: MICHAEL SWANBOROUGH Flinders Christian Community College. Examinations. EXAMINATION 1 - Facts, Skills and Applications Task Part A - Multiple-choice questions Part B - Short-answer questions I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
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1. M.A.V. REVISION LECTURES MATHEMATICAL METHODS UNITS 3 AND 4 Presenter: MICHAEL SWANBOROUGH Flinders Christian Community College

2. Examinations EXAMINATION 1 - Facts, Skills and Applications Task Part A - Multiple-choice questions Part B - Short-answer questions EXAMINATION 2 - Analysis Task

3. 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.

4. 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.

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

6. Examination Advice Notes Pages • Well-prepared and organised into topic areas. • Prepare two pages of general notes. • Prepare two separate pages for each of the two examinations. • Include processsteps rather than just specific examples of questions.

7. Examination Advice Notes Pages • Some worked examples can certainly be of benefit. • 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-83+)

8. Examination Advice Strategy - Examination 1 • Use the reading time to plan an approach for the paper. • Make sure that you answer each question. There is no penalty for incorrect answers. • It may be sensible to obtain the “working marks” in the short answer section before tackling the multiple choice questions.

9. Examination Advice Strategy - Examination 1 • 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. • Questions generally require only one or two steps – however, you should still expect to do some calculations.

10. Examination Advice Strategy - Examination 2 • 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.

11. 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.

12. Revision Quiz

13. Question 1 The derivative of is equal to a) b) c) e) d) A

14. a) b) c) d) e) Question 2 The range of the function with graph as shown is B

15. a) b) d) c) e) Question 3 Angie notes that 2 out of 10 peaches on her peach tree are spoilt by birds pecking at them. If she randomly picks 30 peaches the probability that exactly 10 of them are spoilt is equal to D

16. Question 4 The total area of the shaded region shown is given by a) b) c) d) D e)

17. 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

18. m < m s < s and a) 1 2 1 2 m > m s < s and b) 1 2 1 2 m < m s > s and c) 1 2 1 2 m > m s > s and d) 1 2 1 2 m > m s = s and e) 1 2 1 2 Question 6 Which one of the following sets of statements is true? A

19. Bonus Prize!!

20. where a, b and c are three different positive real numbers. The equation has exactly a) 1 real solution b) 2 distinct real solutions c) 3 distinct real solutions d) 4 distinct real solutions e) 5 distinct real solutions Question 8 B

21. is the sum of the For the equation solutions on the interval Question 9 a) b) E c) d) e)

22. EXAMINATION 1 - FACTS, SKILLS AND APPLICATIONS TASK • Part A • 27 multiple-choice questions (27 marks) • Part B • short-answer questions (23 marks) • Time limit: • 15 minutes reading time • 90 minutes writing time

23. EXAMINATION 2 - ANALYSIS TASK • Extended response questions • 4 questions (55 marks) • Time limit: • 15 minutes reading time • 90 minutes writing time

24. The linear factors of the polynomial are Question 1 ANSWER: B

25. Question 4 fully a) Expand

26. b) is exactly divisible by Find the value of a.

27. b)

28. Coefficient of Question 6 ANSWER: B

29. Coefficient of Question 7 ANSWER: D

30. Functions and Their Graphs Vertical line test - to determine whether a relation is a function A represents the DOMAIN

31. Interval Notation Square brackets [ ] – included Round brackets ( ) – excluded

32. a) b) c) d) e) Question 9 The range of the function with graph as shown is ANSWER: D

33. 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 b) The square root of a negative number is present.

34. So the maximal domain is: Consider the function

35. Question 10 This question requires EVERY option to be checked carefully. a) b) c) d) e)

36. ANSWER: E

37. a) b) c) d) e) Question 11 The graph shown could be that of the function f whose rule is ANSWER: A

38. 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- Translation, Dilation, Reflection MAGNITUDE(or size) DIRECTION

39. 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.

40. 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.

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

42. Reflection about the x-axis

43. Reflection about the y-axis

44. Reflection about both axes

45. Determine the graph of Question 13

46. Reflection about the x-axis

47. ANSWER: A Translation of 1 unit parallel to the y-axis

48. The graph of the function f is obtained from the graph of the function with equation by a reflection in the y-axis followed by a dilation of 2 units from the x-axis. The rule for f is: a) b) c) d) e) Reflection: Dilation: EXTRA QUESTION ANSWER: E