Preparing for the 2011 HSC MATHEMATICS EXAM

Acknowledgements Cath Whalan, Mathematics Head Teacher Hornsby Girls High School for her contributions to this PowerPoint. NSW Curriculum and Learning Innovation Centre 2

Overview The Syllabus Draft Performance Bands Useful resources for mathematics Exam instructions and equipment Overview of the marking process Examiners’ comments How to study for mathematics Using the Standards Package NSW Curriculum and Learning Innovation Centre 3

THE SYLLABUS Curriculum and Learning Innovation Centre 4

The Syllabus A complete copy of the syllabus is available from the Board of Studies website: Up to 20% of the HSC examination paper may be based on the Preliminary course so you need to revise the whole course NSW Curriculum and Learning Innovation Centre 5

(accessed 9/8/2011) NSW Curriculum and Learning Innovation Centre6 To access the HSC mathematics syllabus click here

Curriculum and Learning Innovation Centre, Mathematics & Numeracy7 Click on M for Mathematics Click here

NSW Curriculum and Learning Innovation Centre 8 Access the syllabus and other materials here for (accessed 28/9/2011)

Syllabus Outline NSW Curriculum and Learning Innovation Centre 9

PERFORMANCE BANDS Curriculum and Learning Innovation Centre 10

accessed 27/9/2011 NSW Curriculum and Learning Innovation Centre 11 Access the Mathematics performance band descriptions here

DRAFT PERFORMANCE BANDS MATHEMATICS The typical performance in this band: NSW Curriculum and Learning Innovation Centre 12

Draft Performance Descriptors Which band best describes your performance now? Which band are you aiming to achieve in the HSC? What do you need to do to achieve this? NSW Curriculum and Learning Innovation Centre 13

Table of Standard Integrals Make sure you are confident with using the table of Standard Integrals NSW Curriculum and Learning Innovation Centre 14

RESOURCES Curriculum and Learning Innovation Centre 15

Useful resources for Mathematics Your mathematics teacher, any mathematics teacher, your friends, older brothers or sisters. School assessment task exams. Your own class notes and summaries. NSW Mathematics Stage 6 Syllabus Outline HELP EACH OTHER – you learn the most when you can teach it to someone else NSW Curriculum and Learning Innovation Centre 16

Useful resources for Mathematics Board of Studies website HSC exam paper & Notes from the Marking Centre s/papers.html s/papers.html 2010 HSC exam paper, Notes from the Marking Centre, Marking guidelines & sample answers s/hsc2010exams/#m s/hsc2010exams/#m Curriculum and Learning Innovation Centre17

Useful resources for Mathematics NSW BOS HSC Exam Workbook - Mathematics This workbook is designed to help you prepare for the HSC Mathematics exam. The workbook consists of the 2010 exam and study resources, including: marking guidelines marker feedback top-scoring student answers. Available from the eBOS Shop Online for $15.40eBOS Shop Online Curriculum and Learning Innovation Centre, Mathematics & Numeracy18

Useful resources for Mathematics HSC examination timetable In 2011, the Mathematics exam is on Monday 24 October 9.25 am to pm Curriculum and Learning Innovation Centre, Mathematics & Numeracy accessed 27/9/11

Useful resources for Mathematics NSW HSC Online website This website provides study strategies, tutorials in more than 40 HSC subjects, references, links to useful websites and other important materials for HSC students and teachers. It is hosted by Charles Sturt University and maintained by the NSW Department of Education and Communities. NSW Curriculum and Learning Innovation Centre 20

Curriculum and Learning Innovation Centre 21 Accessed 2/9/2011 Click on this link.

NSW Curriculum and Learning Innovation Centre 22 Accessed 2/9/2011 Click on this link.

NSW Curriculum and Learning Innovation Centre 23

Curriculum and Learning Innovation Centre 24

Curriculum and Learning Innovation Centre 25 (accessed 28/9/2011)

Curriculum and Learning Innovation Centre 26 KEY WORDS MATHEMATICS APPLYCALCULATEDEDUCEEVALUATEFINDJUSTIFYSOLVEPROVESHOWSTATESKETCH

NSW Curriculum and Learning Innovation Centre 27 Useful resources for Mathematics (accessed 28/9/2011)

Useful resources for Mathematics HSC Advice Line (Phone: ). HSC Advice Line  A telephone information service for students preparing for the HSC examinations.  Provides an after-hours and weekend service leading up to and during the examination period.  The cost is a local call.  Check dates and operating times closer to the end of term 3. NSW Curriculum and Learning Innovation Centre 28

Useful resources for Mathematics MANSW - Mathematical Association of NSW (Ask you teacher if they order copies through your school) MANSW - Mathematical Association of NSW  Red book of Past HSC (Mathematics 2/3 Unit common), 2001— 2009 (Mathematics) exam papers with worked solutions T (02) E NSW Curriculum and Learning Innovation Centre 29

EXAM INSTRUCTIONS AND EQUIPMENT NSW Curriculum and Learning Innovation Centre 30

HSC Mathematics exam instructions TOTAL MARKS = Questions each worth 12 marks. Reading Time - 5 minutes (work out your plan of attack!) Working time = 3 hours (i.e. 18 minutes per question!) Write using black or blue pen. Board-approved calculators may be used. A table of standard integrals is provided at the back of the paper. NSW Curriculum and Learning Innovation Centre 31

HSC Mathematics exam equipment You may only take the equipment listed in the next slide into the examination room. No other equipment is allowed. Any equipment brought into the examination room may be subject to inspection before the examination commences. It is the student’s responsibility to supply equipment that is in good working order. This includes calculators. Curriculum and Learning Innovation Centre, Mathematics & Numeracy32 (taken from HSC Examination Timetable 2011, NSW BOS, page 3)

HSC Mathematics exam equipment Students are expected to provide pens (black is recommended), pencils and erasers, and a ruler marked in millimetres and centimetres, for ALL EXAMINATIONS. Students may use a pencil sharpener and/or highlighter pen. For the Mathematics exam: A Board approved calculator (see slide 31 for details)slide 31 A pair of compasses A protractor Set squares (optional) a curve drawing template (see slide 32 for details)slide 32 Curriculum and Learning Innovation Centre, Mathematics & Numeracy33 (taken from HSC Examination Timetable 2011, NSW BOS, page 3)

HSC Mathematics exam calculator In the Mathematics HSC examination students are permitted to use Board-approved calculators. Curriculum and Learning Innovation Centre, Mathematics & Numeracy34 A Board-approved calculator is one that appears on the Board’s 2011 HSC list of approved scientific calculators. This list can be found at: s/calculators.html s/calculators.html

HSC Mathematics exam curve drawing template Students may take into the HSC mathematics examination templates for drawing curves and geometrical figures, measuring, constructing etc. Such templates may contain equations of simple curves (eg y=x², y=sin x, y=1/x) that can be drawn using the template, and decimal approximations (eg for pi, e), but no other printed formulae (eg sine rule, cosine rule, quadratic formulae, area and volume formulae). Acceptable templates include Mathomat, Mathomat Senior and Mathaid (Non Formulae).Mathomat Mathomat SeniorMathaid (Non Formulae). (taken from HSC Examination Timetable 2011, NSW BOS, page 2) Curriculum and Learning Innovation Centre, Mathematics & Numeracy35

HSC MARKING PROCESS NSW Curriculum and Learning Innovation Centre 36

An overview of the marking process for the HSC Mathematics exam Each of the TEN questions is marked by a team of ten experienced maths teachers - two Senior Markers and eight markers. NSW Curriculum and Learning Innovation Centre 37

An overview of the marking process for the HSC Mathematics exam MARKING GUIDELINES, developed by the examination committee, are given for all questions – these guidelines indicate the process for which marks will be allocated. PART MARKS for each question are awarded according to the guidelines. NSW Curriculum and Learning Innovation Centre 38

An overview of the marking process for the HSC Mathematics exam HALF MARKS are never used –full marks may be awarded before the correct numerical answer is reached TRANSCRIPTION ERRORS (which do not make the question easier) are not penalised. (incorrect substitution into a formula is NOT a transcription error) NSW Curriculum and Learning Innovation Centre 39

EXAMINER’S COMMENTS NSW Curriculum and Learning Innovation Centre 40

Examiners’ comments HSC Mathematics SHOW substitutions and working out clearly— marks are allocated for the PROCESS and the answer, not just the answer. Watch the number of MARKS allocated to each part of the question — don’t write half a page of explanation for 1 mark! NSW Curriculum and Learning Innovation Centre 41

Examiners’ comments HSC Mathematics Take CARE—make sure you recall the FORMULA correctly — marks lost from careless errors are as ‘expensive’ as marks lost by not doing the more difficult questions. You have to WRITE the CORRECT FORMULA and SUBSTITUTE correctly into it in order to be awarded a mark. NSW Curriculum and Learning Innovation Centre 42

Examiners’ comments HSC Mathematics When PROVING or SHOWING a given result, check that your answer is the SAME as the result given in the paper! CORRECT answers from INCORRECT working are not awarded marks - if you have made a mistake, fix the error in EVERY line of working - don’t fudge! NSW Curriculum and Learning Innovation Centre 43

Examiners’ comments HSC Mathematics LINK parts of a question—If (a) has parts (i) and (ii), often using the result in (i) makes answering (ii) easier. If a question has multiple parts, check that you have answered the question in the CORRECT part. NSW Curriculum and Learning Innovation Centre 44

Examiners’ comments HSC Mathematics Draw large, clear DIAGRAMS in pencil—about 1/3 a page is a good size and mark on it all given information. Use your diagram to PLAN your response (if you think it, write it on your diagram) If drawing axes, use a RULER, start the horizontal axis on a line and mark off points EVENLY. NSW Curriculum and Learning Innovation Centre 45

Examiners’ comments HSC Mathematics READ the question carefully and UNDERLINE key points. Check at the end of each part that you have ANSWERED THE QUESTION THAT WAS ASKED. NSW Curriculum and Learning Innovation Centre 46

Examiners’ comments HSC Mathematics Write working out CLEARLY—some students can’t read their own writing, so markers have some difficulty awarding marks. (i.e. ‘r’ & ‘n’ & ‘x’ often look similar, as do 5 & 8 and 4 & 9) Read the question carefully — watch for KEYWORDS e.g. 3 significant figures. NSW Curriculum and Learning Innovation Centre 47

Examiners’ comments HSC Mathematics Use NOTATION and TERMINOLOGY correctly. Some syllabus outcomes: H9 - communicates using mathematical language, notation, diagrams and graphs HE7 - evaluates mathematical solutions to problems and communicates them in an appropriate form E9 - communicates abstract ideas and relationships using appropriate notation and logical argument NSW Curriculum and Learning Innovation Centre 48

Examiners’ comments HSC Mathematics Keep an eye on the TIME—don’t spend so long on the early questions you don’t get to Q10! Remember Q2 is not as difficult as Q10 — don’t look for trouble! NSW Curriculum and Learning Innovation Centre 49

When using a CALCULATOR, don’t round off too early and watch for radians/degrees. Check that your answer is REASONABLE. Examiners’ comments HSC Mathematics NSW Curriculum and Learning Innovation Centre 50

If you make a mistake, just put a LINE THROUGH it—NEVER use liquid paper. A note on multiple attempts of a question... YOU GET TO ATTEMPT A QUESTION ONCE!!!!!!!!!!!!!! Examiners’ comments HSC Mathematics NSW Curriculum and Learning Innovation Centre 51

CORRECT INCORRECT More than one attempt on a question worth 2 marks Award 2Award 0 Subtract 1 mark for multiple attempt Award 1 NSW Curriculum and Learning Innovation Centre 52

CORRECT INCORRECT More than one attempt on a question worth 2 marks Award 2Award 0 Ignore incorrect as it is crossed out......Award 2 NSW Curriculum and Learning Innovation Centre 53

CORRECT INCORRECT More than one attempt on a question worth 2 marks Award 2Award 0 Subtract 1 mark for crossing out correct response Award 1 NSW Curriculum and Learning Innovation Centre 54

When showing maximum/minimum/concavity, NO FUDGING is allowed. Examiners’ comments HSC Mathematics X You must indicate these You must SHOW substitutions, not just write: >, < etc. NSW Curriculum and Learning Innovation Centre 55

HOW TO STUDY NSW Curriculum and Learning Innovation Centre 56

How to study for Mathematics Practise doing questions from textbooks, study guides, other schools’ Trial HSC’s Learn your formulas Do past HSC papers – the more the better! Correct your work – ask for help Just Do It !!! NSW Curriculum and Learning Innovation Centre 57

2002 HSC Mathematics exam question practice Do the solutions for Question 1 – we will then have a look at the marking guidelines and see how you went! NSW Curriculum and Learning Innovation Centre 58

2002 HSC Mathematics Question 1 NSW Curriculum and Learning Innovation Centre 59

Using the 2002 Standards Package Exemplar solutions are given in the 2002 Standards Package Use them to mark your solutions for Question 1 NSW Curriculum and Learning Innovation Centre 60

Exemplar sample Question 1(a), (b) and (c). NSW Curriculum and Learning Innovation Centre 61

Using the Marking Guidelines Marking Guidelines are given on the BOS website for all past HSCs These guidelines are used by HSC markers NSW Curriculum and Learning Innovation Centre 62

2002 HSC Mathematics Marking Guidelines NSW Curriculum and Learning Innovation Centre 63

2002 HSC Mathematics Marking Guidelines NSW Curriculum and Learning Innovation Centre 64

Exemplar sample Question 1(d), (e) NSW Curriculum and Learning Innovation Centre 65

2002 HSC Mathematics Marking Guidelines NSW Curriculum and Learning Innovation Centre 66

Exemplar sample for Question 1(f) NSW Curriculum and Learning Innovation Centre 67

Notes from the Marking Centre The markers comments for the past HSCs are available on the BOS website are Let’s look at the comments for 2002 Question 1 NSW Curriculum and Learning Innovation Centre 68

2002 HSC Notes from the Marking Centre - Mathematics NSW Curriculum and Learning Innovation Centre 69

Using the 2002 Standards Package The following are student work samples for students at the band cut offs for parts of Q1 on the 2002 HSC. What do you notice? NSW Curriculum and Learning Innovation Centre 70

2002 HSC Mathematics Band 5 / 6 Cut-off Question 1 (a), (b) & (c) NSW Curriculum and Learning Innovation Centre 71

2002 HSC Mathematics Band 5 / 6 Cut-off Question 1 (d) & (e) NSW Curriculum and Learning Innovation Centre 72

2002 HSC Mathematics Band 5 / 6 Cut-off Question 1 (f) NSW Curriculum and Learning Innovation Centre 73

2002 HSC Mathematics Band 3 / 4 Cut-off Question 1 (a), (b) & (c) NSW Curriculum and Learning Innovation Centre 74

2002 HSC Mathematics Band 3 / 4 Cut-off Question 1 (d) & (e) NSW Curriculum and Learning Innovation Centre 75

2002 HSC Mathematics Band 3 / 4 Cut-off Question 1 (f) NSW Curriculum and Learning Innovation Centre 76

2002 HSC Mathematics Band 1 / 2 Cut-off Question 1 (a), (b) & (c) NSW Curriculum and Learning Innovation Centre 77

2002 HSC Mathematics Band 1 / 2 Cut-off Question 1 (d) & (e) NSW Curriculum and Learning Innovation Centre 78

2002 HSC Mathematics Band 1 / 2 Cut-off Question 1 (f) NSW Curriculum and Learning Innovation Centre 79

2002 HSC Mathematics Exam Do the solutions for Question 6 – we will then have a look at the marking guidelines and see how you went! NSW Curriculum and Learning Innovation Centre 80

2002 HSC Mathematics Question 6 NSW Curriculum and Learning Innovation Centre 81

2002 HSC Mathematics Question 6 NSW Curriculum and Learning Innovation Centre 82

Using the Marking Guidelines Marking Guidelines are given on the BOS website for all past HSCs These guidelines are used by HSC markers NSW Curriculum and Learning Innovation Centre 83

2002 HSC Mathematics Marking Guidelines NSW Curriculum and Learning Innovation Centre 84

2002 HSC Mathematics Marking Guidelines NSW Curriculum and Learning Innovation Centre 85

2002 HSC Mathematics Marking Guidelines NSW Curriculum and Learning Innovation Centre 86

Using the 2002 Standards Package Exemplar solutions are given in the 2002 Standard Package Use them to mark your solutions for Question 6 To see samples of the band cut-offs, check the standards package at your school NSW Curriculum and Learning Innovation Centre 87

Exemplar Sample Question 6(a) NSW Curriculum and Learning Innovation Centre 88

Exemplar Sample Question 6(b)(i) NSW Curriculum and Learning Innovation Centre 89

Exemplar Sample Question 6(b)(ii) NSW Curriculum and Learning Innovation Centre 90

Exemplar Sample Question 6(b)(ii) & (iii) NSW Curriculum and Learning Innovation Centre 91

Exemplar Sample Question 6(c) NSW Curriculum and Learning Innovation Centre 92

2002 Notes from the Marking Centre The markers comments for the past HSCs are available on the BOS website Let’s look at the comments for Question NSW Curriculum and Learning Innovation Centre 93

2002 HSC Notes from the Marking Centre - Mathematics NSW Curriculum and Learning Innovation Centre 94

2011 HSC Mathematics Exam ENJOY!! May You Get the Marks You Deserve!! NSW Curriculum and Learning Innovation Centre 95