4u hsc questions by topics 1990 to 2006 and summary
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HOW I CAN KICK BUTT IN THE HSC IN 4U MATHS!!!
By : Khiet Hoang – World’s craziest teacher
WARNING
This book may be considered by some as offensive, insensitive and politically incorrect ……..and if you do then go and tell someone who cares!
……..uhh and it also contains lots of speling and grematical erors……and the odd maths error!
Footnote: (should really be at the bottom of the page but who cares…….) The author of this book has about 500808 different split personalities so sometimes he (she/it/they/we) uses the first person (often “I”) to refer to himself. Other times he uses third person such as “the author”. I believe he uses perpendicular pronouns too…..so if you are confused already before you even read the rest of this book then he has succeeded! I can tell you that one of the author’s favourite sayings to his students is “are you scarred for life yet?” and then laugh very loudly in an infectious manner! You’d have to be one of my students to understand the joke! The man is crazy!!!!
Acknowledgements:
I would like to thank my Mum, my Dad for bringing me into this world, my wife, my kids, my dog……
No seriously, I’d like to thank all of my students and ex-students at Kellyville High and at the various coaching institutions in Sydney. By teaching you I have learnt a great deal about how the NSW 4U syllabus should be taught. Thank you for putting up with me and my eccentricities.
I’d also like to thank my colleagues and friends who have read this and have given feed back and support. This humble grass hopper owes you.
Most of all I must thank my wife, Vanessa for being so understanding about me writing this during the wee hours of the mornings in my “spare” time……….
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Content
Page
Why I wrote this book ----------------------- 4
Most Important Procedure for HSC ----------------------- 7
4U course overview ----------------------- 8
4U syllabus content ----------------------- 9
Chapter 1 – GRAPHS :Sketch a curve ----------------------- 35
Chapter 2 – GRAPHS :Do something to a curve ----------------------- 39
Chapter 3 – COMPLEX NO: locus ----------------------- 50
Chapter 4 - COMPLEX NO: Geometry ----------------------- 55
Chapter 5 - COMPLEX NO: nth Roots and proofs ----------------------- 65
Chapter 6 – CONICS - Rectangular Hyperbolas ----------------------- 86
Chapter 7 – CONICS - Ellipse ----------------------- 92
Chapter 6 – CONICS - Hyperbolas ----------------------- 100
Chapter 6 – INTEGRATION - Special properties ----------------------- 107
Chapter 14 – INTEGRATION - partial fractions ----------------------- 113
Chapter 8 – INTEGRATION - reduction/recurrence formulas -------------------- 117
Chapter 9 – INTEGRATION - By Parts ----------------------- 124
Chapter 10 – INTEGRATION -subs, complete sq and integration table ------- 126
Chapter 11 – VOLUMES - Slice ----------------------- 133
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Chapter 12 – VOLUMES - cross-section ----------------------- 137
Chapter 13 – VOLUMES - shell ----------------------- 148
Chapter 15 – MECHANICS – Projectile and SHM ----------------------- 154
Chapter 15 – MECHANICS – Resisted Motion ----------------------- 159
Chapter 15 – MECHANICS – Circular Motion ----------------------- 166
Chapter 16 – POLYNOMIALS – transformation + roots and coeffs ------------ 180
Chapter 16 – POLYNOMIALS – Solve and factorise ----------------------- 185
Chapter 16 – POLYNOMIALS – Multiple Roots ----------------------- 188
Chapter 18 – HARDER 3U – Permutation and Combination ---------------------- 191
Chapter 18 – HARDER 3U – Inequality ---------------------- 202
Chapter 18 – HARDER 3U – Circle Geometry ---------------------- 210
Chapter 18 – HARDER 3U – Induction ---------------------- 227
Chapter 18 – HARDER 3U – Other ---------------------- 235
Chapter 23 – Integration Table ----------------------- 253
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Why I wrote this book.
This book was compiled by an experienced teacher who has taught this course from as early as 1989. He was NOT a terribly good student at 2U/3U/4U maths (….who also refuses to recognise the new course names as the names are the only things that changed. The syllabus content has NOT) and had to teach himself these courses again during 1990-1991 using this book below. This book was written with the 1982 syllabus in mind and is only good until 2010 because the syllabus is due to be changed then and who knows what will become of the new syllabus. If there are only cosmetic changes then this book will still be useful. Else, if you’re ever short on toilet paper then……….
This book explains the whole 4U course in easy to understand language and it is intended to be used as a self help guide for students as well as teachers.
90% of 2U/3U and especially 4U is about following certain procedures to obtain the answers. This book is just that. You can easily get over 90% for 2, 3 and 4U maths just by following the procedures in this book alone.
Students often find 3U/4U (and even 2U) hard. This is the case NOT because the content is hard. I can teach my 10 year old son (in 2007) some 4U maths concepts! Will he be able to remember it is another story?!!! Will he want to learn?!!!!
Maths IS hard though for the following reasons:
1) There is TOO MUCH to REMEMBER.
From the formula perspective alone, can you REMEMBER about 15 pages of typed up formulas, let alone know which one to use? If you cannot remember, then do General maths because 90% of the formulas are given to you. Somewhere in this book you’ll find all the formulas you’ll need to know.
2) People fear and RESIST any CHANGE in their lives
………..and hence they do NOT REMEMBER new definitions or concepts given to them.
When a new theory or formula is given to students the first thing they often ask is why? Or say “That’s too hard. How am I going to remember that” (cast your mind back to the quadratic formula…..Oh sorry you don’t remember that one? ………my point exactly. For those who do remember, that’s the one with a, b and c in it. How about the distance formula from a point to a line……..what you didn’t know there was such a formula? ......... Uhh yeah there is and that one is not even 3U maths. It is 2U maths !!!!!).
3) Students DON’T UNDERSTAND the CONCEPTS
……..and hence do NOT REMEMBER them.
Unfortunately maths is often typically taught by teachers putting a few QUESTIONS on the board, showing how the QUESTIONS ARE TO BE SOLVED. They then ask the students to do a million (or thereabout) questions for homework which the students, of course, find difficult to
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do because they didn’t understand the CONCEPTS of the topic. Then the teacher puts some more questions on the board the next day, again showing the students how to solve those questions and again ask the students to do another million (or more) questions for homework ………..and the vicious cycle goes on…………meanwhile the students fall behind.
And the text book also “teaches” the same way. They show how two or three questions are done and hardly show the concepts behind it, or if they do it is not explicitly shown. One of the text books I’ve seen shows a couple of questions with solutions in one chapter and then the concepts are shown in the NEXT chapter. I think the rationale there was to show “Oh do you see how hard it is for you to do the question this way but with this formula it is so much easier!!!”
Well, why wasn’t it shown in the same chapter at the beginning of the chapter in the first place?
4) Students PONDER upon the beauty of THE QUESTION.
This is the biggest problem of all. This happens in not only maths but in all subjects. This is the main reason why HSC students do not do as well as they should in the HSC.
What is the problem? Simply put, students, when sitting an exam, spend far too much time on questions they CAN’T do and very little or no time on questions they CAN do and hence run out of time. Many of my students often say “Oh, I didn’t have time to do the last question and it was the easiest question of the exam!!!”
My response is always: “Well then why didn’t you do that question first?” which is often met with another of the student’s question: “Oh can you do that?”
“Uhh……yeah you can….”
I often say to my 4U maths students that you can suck at 4U maths but the idea is to make others suck at it worse than you. That is unfortunately how the UAI works. It simply ranks you in order from highest to lowest. The aim of any HSC exam is NOT to finish the paper but to finish AS MUCH AS YOU CAN. So if you ponder upon the beauty of the questions that you could not do and “accidentally” ignore questions that you can do, than you will suck worse then your HSC peers.
The rule of thumb is if you read the question and you do not understand or have a mental blank you count to 3 and if you still do not know then go onto the next question. Don’t sit there and ponder upon its beauty. That is the real secret behind the HSC!!! There is an actual procedure on how to attack an HSC paper also somewhere in this book……
I’ll give you two actual real life everyday situations and one of my personal experiences where people ponder upon the beauty of the questions:
Situation 12 DAY FM (and other radio stations) often has a contest where they ask the contestants 10 questions in a minute. You answer all 10 correctly you get $1000 otherwise you get $10 (or $100 depending on the radio station) per question. If the contestant does not know the answer they are allowed to say “pass” and the next question is asked. All questions are always asked until they answer all the questions correctly or run out of time.
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Not many contestants get $1000!!!
Most often get $50 or even $60. A lot get $30 - $40. Some even get $10 or nothing!!!This is NOT because they do not know a lot of the answers. It’s simply because they ponder upon the beauty of one or two questions and before you know it, the minute is up.
Instead of saying “pass” STRAIGHT AWAY when they do not know the answer, typical contestants say “Uhh can you read the question again?” or “Uhhh…… I read that in Cosmopolitan the other day…..what was his name again?......Uhh, what was the question again?” Of course I am exaggerating here a little but you get the idea.
Situation 2Students often claim that they study 3-4 hours some say even 6 hours a day after school and still their marks do not reflect their efforts!!! Why is this so? It’s because they ponder upon the beauty of the questions!!! This happens for ALL subjects not just for maths.
When students come across a difficult question or concept or theme or theory or a certain place in their essay etc they often sit and ponder sometimes for hours (sometimes on just one question - I know because I myself have done it!!!!) because if they leave the question then it means in their mind that they have failed and so they must do that particular question before they can do the next one. It’s quite a funny psychological thing! The right thing to do is of course to move onto something else or ask your teacher or friend or tutor etc the next day so that you can carry on your study in a productive and effective manner.
If you ponder upon the beauty of one or two questions then you will never finish the million or so question for maths that were set for homework.
Remember the teacher asked you to do the million questions but they did not say that you have to do them in any order. That means that you finish as many as you can in the time set.
This approach of “skipping” questions should be done not just for homework but for class work and particularly for exams (especially HSC exams). Make sure you come back to the ones you skipped and attempt them when you have done all the others that you can do.
One of my own personal experiences.
In writing this book the author pondered upon the beauty of this section alone ……..sitting there thinking and thinking some more and so far for the last 2 pages spent 3 hours pondering what to write. What he should have done is he should have stood up. Go and make a cup of coffee and write it the next day……But no, he must finish this section otherwise he cannot write the next section……..that funny psychological bs…remember?
………Sorry got to go….got other things I must write for this book…..the pages of formulas for example which is much easier to write then the pages above…....
I think I made my point………..NEVER PONDER UPON THE BEAUTY OF THE QUESTION!
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Most Important Procedure for HSC.Out of all of the procedures in this book this is by far the most important one. Here it is:
0) Take a few (10) deep breaths so you can relax and also get some brain food (oxygen) into the brain. 1) Read the whole paper in 2 minutes (you WILL be given at least 5 minutes reading time in the HSC regardless of how crappy your school is in NOT giving you reading time in the trials or in any test. I give reading time for EVERY single exam I give to my students from year 7 to year 12 even if it’s just for a minute or 10 seconds – for my one minute exam!). Of course you are not to read word for word question for question in the 2 minutes (you just don’t have time for that unless you are a very good speed reader). Instead you glance at the whole paper to see what you can do and plan to do those first. Trust me, this is the most productive 2 minutes of the exam.
2) Write down the formulas next to each question when you are asked to start writing since your mind is still fresh at the start of the exam. There’s nothing worse then you not remembering the formulas mid-way through the exam even though you know the topic. And don’t stress if you don’t remember at the start. You’ll dig it out later out of that brain of yours during the exam. The idea is not to stress your self but to remain calm…easier said then done. Remember it’s just a STUPID test (all tests are stupid believe me and you’ll unfortunately go through a lot of tests in your lifetime). It does not change the fact that you are a wonderful person! (pay me later for that one later!!!)
3) Do the exam in the order that you can skipping the ones that you can’t. If question 1 is the hardest question for you then skip it straight away and go to question 2. If question 2 is also not obvious to you then go to Q3. I often deliberately put question 1 as the hardest question in my exams to train my students to skip. Remember if you have read the question and for some reason it’s not obvious to you then don’t sit there and ponder upon its beauty. Go onto the next question straight away. Don’t be afraid to do this because even though you consciously leave the question your mind subconsciously works at the solution to try and find the answer.
Your mind is a wonderful machine for that very reason. And I can prove it to you.
All of us have problems of our own. But how often do we CONSCIOUSLY think about our problems during the course of the day. We still carry on with our busy lives but our brain continues to work on the problem and then somehow the solution presents itself!!!
Just make sure though that you make a marking on the questions that you skipped so you can come back to do them later.
4) When you get to the end of the paper go back to the beginning of the exam and repeat steps 2 to 4 until you finish every question in the exam or when time is up, whichever is sooner.
5) Check the exam for silly mistakes or check whether you have answered what they asked for. They may have asked you to factorise for example and you gave them the roots instead! If you do finish the whole paper then don’t just sit there and show off “oh look at me I’m a smart ar…I finished the paper first before yous all!!!”
Remember the idea of any HSC paper is NOT to finish the whole paper but to FINISH CORRECTLY AS MUCH AS YOU CAN.
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Graphs: sketch a curve usual do something to a curve including composite curves
Complex: Roots and proofs geometry locus
Integration: By parts reduction/recurrence partial fractions substitution special property
Volumes: slice shell cross section
Conics: Ellipse tangents and normals etc and the 4 proofs
Hyperbola tangents and normals etc and the 4 proofs
Rectangular Hyperbola tangents and normals etc locus and the 2 proofs
Mechanics: Projectile and SHMotion Resisted motion circular motion
Polynimials: multiple roots transformation of roots solve + factorise
Harder 3 U: perm and comb inequality circle geo induction other
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Topic1 GRAPHS – sketch a curveYear question marks comment1990 Q1/Q1
1991 Q2
1992 Q4/Q3
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GRAPHS – sketch a curve1992 Q4
1993 Q5
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GRAPHS – sketch a curve1994 Q6
19951996 Q4/Q7
Q6/Q8
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GRAPHS – sketch a curve1997 Q3/Q9
19981999 Q4/Q10
200020032004 Q3/Q11
2005 Q3/Q12
200620072010
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Topic1 GRAPHS- do something to a curve including compositeYear question marks comment19901991 Q13
1992199319941995 Q3/Q14
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GRAPHS- do something to a curve including composite1996 Q3/Q15
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1997 GRAPHS- do something to a curve including composite1998 Q3/Q16
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GRAPHS- do something to a curve including composite1999 Q3/Q17
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GRAPHS- do something to a curve including composite2000 Q3/Q18
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GRAPHS- do something to a curve including composite2001 Q4/Q19
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GRAPHS- do something to a curve including composite2002 Q3/Q20
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GRAPHS- do something to a curve including composite2003 Q3/Q21
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GRAPHS- do something to a curve including composite2004 Q3/Q22
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GRAPHS- do something to a curve including composite2005 Q3/Q23
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GRAPHS- do something to a curve including composite2006 Q3/Q24
20072010
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Topic2 COMPLEX NUMBERS – locusYear question marks comment199019911992 Q2/Q25
1993 Q26
1994 Q2/Q27
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COMPLEX NUMBERS – locus1995 5 Q2/Q28
1996 Q2/Q29
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COMPLEX NUMBERS – locus1996 Q2/Q30
1997 Q2/Q31
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COMPLEX NUMBERS – locus1998 Q2/Q32
1999 Q2/Q33
2000 Q2/Q34
2001 Q2/Q35
2002 Q2/Q36
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COMPLEX NUMBERS – locus2003 Q2/Q37
2004 Q2/Q38
2005 Q2/Q39
2006 Q2/Q40
20072010
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Topic2 COMPLEX NUMBERS – geometry rotate vectors etcYear question marks Comment1990 Q1/Q41
1991 Q2/Q42
1992 Q43
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COMPLEX NUMBERS – geometry rotate vectors etc1993 Q2/Q44
Q45
1994
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COMPLEX NUMBERS – geometry rotate vectors etc1995 Q46
1996
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COMPLEX NUMBERS – geometry rotate vectors etc1997 Q8/Q47
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COMPLEX NUMBERS – geometry rotate vectors etc1998 Q2/Q48
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COMPLEX NUMBERS – geometry rotate vectors etc1999 Q2/Q49
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COMPLEX NUMBERS – geometry rotate vectors etc2000 Q2/Q5
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COMPLEX NUMBERS – geometry rotate vectors etc2001 Q2/Q51
20022003
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COMPLEX NUMBERS – geometry rotate vectors etc2004 Q2/Q52
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COMPLEX NUMBERS – geometry rotate vectors etc2005 Q2/Q53
200620072010
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Topic2 COMPLEX NUMBERS – nth roots of unity and their proofs Year question marks comment199019911992 Q7/Q54
1993 Q55
1994 Q56
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COMPLEX NUMBERS – nth roots of unity and their proofs1995 Q4/Q57
1996 Q8/Q58
19971998 Q2/Q59
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COMPLEX NUMBERS – nth roots of unity and their proofs1999 Q8/Q60
2000 Q2/Q61
2001 Q2/Q62
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COMPLEX NUMBERS – nth roots of unity and their proofs2002 Q7/Q63
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COMPLEX NUMBERS – nth roots of unity and their proofs2003 Q8/Q64
2004
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COMPLEX NUMBERS – nth roots of unity and their proofs2005 Q6/Q65
2006 2 Q2/Q66
20072010
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Topic2 COMPLEX NUMBERS – algebra including square roots Year question marks comment1990 Q67
1991 Q68
1992 Q2/Q69
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COMPLEX NUMBERS – algebra including square roots1993 Q2/Q70
1994 Q71 a
Q71b
19951
3
Q2/Q72
Q73
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COMPLEX NUMBERS – algebra including square roots1996 2 Q2/Q74
1997 Q2/Q75
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COMPLEX NUMBERS – algebra including square roots1998 Q2/Q76
1999 Q2/Q77
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COMPLEX NUMBERS – algebra including square roots2000 Q2/Q78
Q8/Q79
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COMPLEX NUMBERS – algebra including square roots2001 Q2/Q80
Q7/Q81
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COMPLEX NUMBERS – algebra including square roots2002 Q2/Q82
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COMPLEX NUMBERS – algebra including square roots2002 Q8/Q83
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COMPLEX NUMBERS – algebra including square roots2003 Q2/Q84
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COMPLEX NUMBERS – algebra including square roots2004 Q2/Q85
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COMPLEX NUMBERS – algebra including square roots
2004 Q7/Q86
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COMPLEX NUMBERS – algebra including square roots2005 Q2/Q87
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COMPLEX NUMBERS – algebra including square roots2006 Q2/Q88
20072010
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Topic2 COMPLEX NUMBERS – complex conjugate root theorem and proofsYear question marks comment199019911992 Q89
1993199419951996 Q90
19971998
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COMPLEX NUMBERS – complex conjugate root theorem and proofs1999 Q2/Q91
200020012002 Q2/Q92
20032006 Q3/Q93
20072010
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Topic3 CONICS- rectangular hyperbolaYear question marks comment19901991 Q94
19921993 Q95
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1994 CONICS- rectangular hyperbola19951996 Q5/Q96
199719981999
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CONICS- rectangular hyperbola2000 Q4/Q97
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2001 CONICS- rectangular hyperbola2002 Q3/Q98
2003
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2004 CONICS- rectangular hyperbola2005 Q8/Q99
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CONICS- rectangular hyperbola2006 Q4/Q100
20072010
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Topic3 CONICS EllipseYear question marks comment19901991 Q3/Q101
1992 Q102
19931994
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CONICS Ellipse1995 Q8/Q103
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1996 CONICS Ellipse199719981999 Q3/Q104
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CONICS Ellipse2000 Q7/Q105
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CONICS Ellipse2001 Q5/Q106
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CONICS Ellipse2002 Q5/Q107
2003 Q3/Q108
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CONICS Ellipse2004 Q4/Q109
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CONICS Ellipse2005 Q4/Q110
200620072010
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Topic3 CONICS HyperbolaYear question marks Comment1990 Q111
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Topic3 CONICS - Hyperbola1991199219931994 Q112
19951996
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CONICS Hyperbola1997 Q4/Q113
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CONICS Hyperbola1998 Q6/Q114
1999
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2000 CONICS Hyperbola2001 Q3/Q115
2002 Q4/Q116
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CONICS Hyperbola2003 Q8/Q117
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2004 CONICS Hyperbola20052006 Q118
20072010
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Topic4 INTEGRATION – special propertiesYear question marks comment1990
19911992 Q119
19931994 Q120
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INTEGRATION – special properties1995 7 Q4/Q121
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INTEGRATION – special properties1996 Q3/Q122
Q7/Q123
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1997 INTEGRATION – special properties1998 Q7/Q124
1999 Q7/Q125
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INTEGRATION – special properties2000 6 Q6/Q126
200120022003 Q6/Q127
2004 Q6/Q128
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INTEGRATION – special properties2005 Q5/Q129
200620072010
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Topic4 INTEGRATION – partial fractionsYear question marks Comment1990
Q1/Q130
1991 Q1/Q131
1992 Q1/Q132
1993 Q1/Q133
1994 Q1/Q134
1995 4 Q1/Q135
1996 3 Q1/Q136
1997 4 Q1/Q137
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INTEGRATION – partial fractions1998 Q1/Q138
1999 4 Q1/Q139
2000 Q1/Q140
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INTEGRATION – partial fractions2001 Q1/Q141
2002 3 Q1/Q142
2003 Q1/Q143
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INTEGRATION – partial fractions2004 Q1/Q144
2005 Q1/Q145
2006 Q1/Q146
20072010
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Topic4 INTEGRATION – reduction formulaYear question marks comment1990 Q2/Q147
1991Q1c/Q148
199219931994
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INTEGRATION – reduction formula1995 Q7/Q149
199619971998 Q3/Q150
1999
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2000 INTEGRATION – reduction formula20012002 Q6/Q151
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INTEGRATION – reduction formula2003 Q8/Q152
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INTEGRATION – reduction formula2004 Q8/Q153
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INTEGRATION – reduction formula2005 Q6/Q154
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INTEGRATION – reduction formula2006 Q7/Q155
20072010
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Topic4 INTEGRATION – by partsYear question marks comment1990
19911992 Q1/Q156
1993 Q1/Q157
1994 Q1/Q158
1995 2 Q1/Q159
1996 3 Q1/Q160
1997 4 Q1/Q161
1998 3 Q1/Q162
1999 4 Q1/Q163
2000 3 Q1/Q164
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INTEGRATION – by parts2001 3 Q1/Q165
2002 4 Q1/Q166
2003 3 Q1/Q167
2004 2 Q1/Q168
2005 3 Q1/Q169
2006 3 Q1/Q170
20072010
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Topic4 INTEGRATION – substitution, complete the square or using integration tableYear question marks comment1990 Q2a/Q171
Q2b/Q172
1991Q1a/Q173
Q1b/Q174
1992 Q175
1993 Q176
1994
Q177
1995 2 Q1/Q178
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INTEGRATION – substitution, complete the square or using integration table1995 3 Q1/Q179
19962
2
Q1/Q180
19972
3
2
Q1/Q181
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INTEGRATION – substitution, complete the square or using integration table1998 2 Q1/Q182
1999 Q1/Q183
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INTEGRATION – substitution, complete the square or using integration table2000
2
2
4
Q1/Q184
20012
2
4
Q1/Q185
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INTEGRATION – substitution, complete the square or using integration table2002
2
2
4
Q1/Q186
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INTEGRATION – substitution, complete the square or using integration table2003 2
2
4
Q1/Q187
2004
3
2
4
Q1/Q188
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INTEGRATION – substitution, complete the square or using integration table2005
2
2
Q1/Q189
2006 2
2
3
Q1/Q190
20072010
document.doc - 132 - K Hoang 2007
Topic5 VOLUMES - sliceYear question marks comment199019911992199319941995 Q3/Q191
document.doc - 133 - K Hoang 2007
VOLUMES - slice1996 Q3/Q192
document.doc - 134 - K Hoang 2007
VOLUMES - slice1997 Q3/Q193
19981999200020012002
document.doc - 135 - K Hoang 2007
VOLUMES - slice2003 Q3/Q194
20042005200620072010
document.doc - 136 - K Hoang 2007
Topic5 VOLUMES – cross-sectionYear question marks comment19901991 Q5/Q195
document.doc - 137 - K Hoang 2007
VOLUMES – cross-section1991 Q5
cont’/Q195
document.doc - 138 - K Hoang 2007
VOLUMES – cross-section1992 Q196
document.doc - 139 - K Hoang 2007
VOLUMES – cross-section1993 Q197
19941995
document.doc - 140 - K Hoang 2007
1996 VOLUMES – cross-section19971998 Q5/Q198
1999
document.doc - 141 - K Hoang 2007
VOLUMES – cross-section2000 Q3/Q199
document.doc - 142 - K Hoang 2007
VOLUMES – cross-section2001 Q4/Q200
document.doc - 143 - K Hoang 2007
VOLUMES – cross-section2002 Q8/Q201
document.doc - 144 - K Hoang 2007
2003 VOLUMES – cross-section2004 Q3/Q202
document.doc - 145 - K Hoang 2007
VOLUMES – cross-section2005 Q5/Q203
document.doc - 146 - K Hoang 2007
VOLUMES – cross-section2006 Q4/Q204
20072010
document.doc - 147 - K Hoang 2007
Topic5 VOLUMES - shellYear question marks Comment1990 Q205
199119921993
document.doc - 148 - K Hoang 2007
VOLUMES - shell1994 Q3/Q206
199519961997 Q5/Q207
1998
document.doc - 149 - K Hoang 2007
VOLUMES - shell1999 Q4/Q208
20002001 Q3/Q209
document.doc - 150 - K Hoang 2007
VOLUMES - shell2002 Q4/Q210
document.doc - 151 - K Hoang 2007
VOLUMES - shell2003 Q7/Q211
2004 Q5/Q212
document.doc - 152 - K Hoang 2007
VOLUMES - shell2005 Q4/Q213
2006 Q5/Q214
20072010
document.doc - 153 - K Hoang 2007
Topic6 MECHANICS – Motion including projectile and SHMYear question marks Comment199019911992 Q5/Q215
199319941995
document.doc - 154 - K Hoang 2007
MECHANICS – Motion including projectile and SHM1996 Q7/Q216
1997
document.doc - 155 - K Hoang 2007
MECHANICS – Motion including projectile and SHM1998 Q7/Q217
19992000
document.doc - 156 - K Hoang 2007
2001 MECHANICS – Motion including projectile and SHM2002200320042005 Q7/Q218
document.doc - 157 - K Hoang 2007
MECHANICS – Motion including projectile and SHM2006 Q6/Q219
20072010
document.doc - 158 - K Hoang 2007
Topic6 MECHANICS – Resisted motionYear question marks comment1990 Q220
1991 Q6/Q221
1992
document.doc - 159 - K Hoang 2007
1993 MECHANICS – Resisted motion1994 Q4/Q222
19951996
document.doc - 160 - K Hoang 2007
MECHANICS – Resisted motion1997 Q6/Q223
1998
document.doc - 161 - K Hoang 2007
MECHANICS – Resisted motion1999 Q6/Q224
2000
document.doc - 162 - K Hoang 2007
MECHANICS – Resisted motion2001 Q5/Q225
2002
document.doc - 163 - K Hoang 2007
MECHANICS – Resisted motion2003 Q5/Q226
document.doc - 164 - K Hoang 2007
MECHANICS – Resisted motion2004
Q6/Q227
20052010
document.doc - 165 - K Hoang 2007
Topic6 MECHANICS – circular motionYear question marks comment199019911992 Q228
document.doc - 166 - K Hoang 2007
MECHANICS – circular motion1993 Q229
1994
document.doc - 167 - K Hoang 2007
MECHANICS – circular motion1995 Q8/Q230
document.doc - 168 - K Hoang 2007
MECHANICS – circular motion1996 Q6/Q231
document.doc - 169 - K Hoang 2007
MECHANICS – circular motion1997 Q5/Q232
document.doc - 170 - K Hoang 2007
MECHANICS – circular motion1998 Q4/Q233
document.doc - 171 - K Hoang 2007
MECHANICS – circular motion1999 Q5/Q234
document.doc - 172 - K Hoang 2007
MECHANICS – circular motion2000 Q5/Q235
document.doc - 173 - K Hoang 2007
MECHANICS – circular motion2001 Q6/Q236
document.doc - 174 - K Hoang 2007
MECHANICS – circular motion2002 Q6/Q237
document.doc - 175 - K Hoang 2007
MECHANICS – circular motion2003 Q4/Q238
document.doc - 176 - K Hoang 2007
MECHANICS – circular motion2004 Q5/Q239
document.doc - 177 - K Hoang 2007
MECHANICS – circular motion2005 Q3/Q240
document.doc - 178 - K Hoang 2007
MECHANICS – circular motion2006 Q5/Q241
20072010
document.doc - 179 - K Hoang 2007
Topic7 POLYNOMIALS – transformation + relationship bwt roots and coefficients +othersYear question marks Comment1990 Q242
19911992199319941995 Q5/Q243
19961997
document.doc - 180 - K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others1998 Q6/Q244
1999 Q5/Q245
2000
document.doc - 181 - K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others2001 Q3/Q246
2002 Q5/Q247
document.doc - 182 - K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others2003 Q5/Q248
2004 Q4/Q249
document.doc - 183 - K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others2005 Q4/Q250
200620072010
document.doc - 184 - K Hoang 2007
Topic7 POLYNOMIALS – solve and factorise Year question marks comment19901991 Q251
199219931994 Q8/Q252
document.doc - 185 - K Hoang 2007
POLYNOMIALS – solve and factorise1995199619971998 Q7/Q253
19992000 Q5/Q254
document.doc - 186 - K Hoang 2007
POLYNOMIALS – solve and factorise2001 Q7/Q255
20022003200620072010
document.doc - 187 - K Hoang 2007
Topic7 POLYNOMIALS – multiple rootsYear question marks comment19901991
Q7/Q256
19921993 Q257
1994 Q258
19951996
document.doc - 188 - K Hoang 2007
POLYNOMIALS – multiple roots1997 Q5/Q259
document.doc - 189 - K Hoang 2007
POLYNOMIALS – multiple roots1998 Q4/Q260
1999 Q4/Q261
200020012002 Q5/Q262
2003200420052006 Q4/Q263
20072010
document.doc - 190 - K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probabilityYear Question marks comment1990 Q5/Q264
1991 Q265
document.doc - 191 - K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probability
1992 Q266
1993 Q267
document.doc - 192 - K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probability
1994 Q5/Q268
document.doc - 193 - K Hoang 2007
HARDER 3U- permutation and combination and probability1995 Q7/Q269
document.doc - 194 - K Hoang 2007
HARDER 3U- permutation and combination and probability1996 Q4/Q270
document.doc - 195 - K Hoang 2007
HARDER 3U- permutation and combination and probability1997 Q3/Q271
1998 Q4/Q272
document.doc - 196 - K Hoang 2007
HARDER 3U- permutation and combination and probability
1998 Q6/Q273
document.doc - 197 - K Hoang 2007
HARDER 3U- permutation and combination and probability1999 Q7/Q274
document.doc - 198 - K Hoang 2007
HARDER 3U- permutation and combination and probability2000 Q8/Q275
2001 Q5/Q276
document.doc - 199 - K Hoang 2007
HARDER 3U- permutation and combination and probability2002 Q4/Q277
2003 Q4/Q278
2004 Q5/Q279
document.doc - 200 - K Hoang 2007
HARDER 3U- permutation and combination and probability2005 Q5/Q280
2006 Q5/Q281
20072010
document.doc - 201 - K Hoang 2007
Topic8 HARDER 3U - inequalitiesYear question marks comment199019911992 Q8/Q282
1993 Q8/Q283
document.doc - 202 - K Hoang 2007
HARDER 3U - inequalities1994 Q284
19951996
document.doc - 203 - K Hoang 2007
HARDER 3U - inequalities1997 Q6/Q285
document.doc - 204 - K Hoang 2007
HARDER 3U - inequalities1998 Q8/Q286
19992000
document.doc - 205 - K Hoang 2007
HARDER 3U - inequalities2001 Q8/Q287
20022003 Q6/Q288
document.doc - 206 - K Hoang 2007
HARDER 3U - inequalities
2003 Q7/Q289
2004
document.doc - 207 - K Hoang 2007
HARDER 3U - inequalities2005 Q8/Q290
document.doc - 208 - K Hoang 2007
HARDER 3U - inequalities2006 Q8/Q291
20072010
document.doc - 209 - K Hoang 2007
Topic8 HARDER 3U- circle geometryYear question marks comment1990
Q6/Q292
1991 Q293
document.doc - 210 - K Hoang 2007
Topic8 HARDER 3U- circle geometry1992 Q3/Q294
1993 Q6/Q295
document.doc - 211 - K Hoang 2007
HARDER 3U- circle geometry1994 Q6/Q296
document.doc - 212 - K Hoang 2007
HARDER 3U- circle geometry
1995 Q6/Q297
document.doc - 213 - K Hoang 2007
HARDER 3U- circle geometry1996 Q8/Q298
document.doc - 214 - K Hoang 2007
HARDER 3U- circle geometry
1997 Q7/Q299
document.doc - 215 - K Hoang 2007
HARDER 3U- circle geometry1997 Q7/Q300
document.doc - 216 - K Hoang 2007
HARDER 3U- circle geometry1997 Q8/Q301
document.doc - 217 - K Hoang 2007
HARDER 3U- circle geometry1998 Q8/Q302
document.doc - 218 - K Hoang 2007
HARDER 3U- circle geometry1999 Q8/Q303
document.doc - 219 - K Hoang 2007
HARDER 3U- circle geometry2000 Q6/Q304
document.doc - 220 - K Hoang 2007
HARDER 3U- circle geometry2001 Q6/Q305
document.doc - 221 - K Hoang 2007
HARDER 3U- circle geometry2002 Q4/Q306
document.doc - 222 - K Hoang 2007
HARDER 3U- circle geometry2003 Q7/Q307
document.doc - 223 - K Hoang 2007
HARDER 3U- circle geometry2004 Q4/Q308
document.doc - 224 - K Hoang 2007
HARDER 3U- circle geometry2005 Q7/Q309
document.doc - 225 - K Hoang 2007
HARDER 3U- circle geometry2006 Q4/Q310
20072010
document.doc - 226 - K Hoang 2007
Topic8 HARDER 3U- inductionYear question marks Comment1990
Q7/Q311
document.doc - 227 - K Hoang 2007
HARDER 3U- induction1991 Q8/Q312
1992 Q6/Q313
1993 Q7/Q314
document.doc - 228 - K Hoang 2007
document.doc - 229 - K Hoang 2007
HARDER 3U- induction1994 Q7/Q315
document.doc - 230 - K Hoang 2007
HARDER 3U- induction1995 Q4/Q316
1996199719981999 Q6/Q317
2000
document.doc - 231 - K Hoang 2007
HARDER 3U- induction2001 Q8/Q318
2002 Q2/Q319
document.doc - 232 - K Hoang 2007
HARDER 3U- induction2003 Q6/Q320
2004 Q7/Q321
2005
document.doc - 233 - K Hoang 2007
HARDER 3U- induction2006 Q7/Q312
20072010
document.doc - 234 - K Hoang 2007
Topic8 HARDER 3U - otherYear question marks comment1990 Q313
document.doc - 235 - K Hoang 2007
Topic8 HARDER 3U - other1990 Q314
19911992
document.doc - 236 - K Hoang 2007
HARDER 3U - other1993 Q3/Q315
19941995 4 Q5/Q316
document.doc - 237 - K Hoang 2007
HARDER 3U - other1995 Q5/Q317
document.doc - 238 - K Hoang 2007
HARDER 3U - other1995 Q6/Q318
1996 Q4/Q319
document.doc - 239 - K Hoang 2007
HARDER 3U - other1996 Q6/Q320
document.doc - 240 - K Hoang 2007
HARDER 3U - other1997 Q4/Q321
1998 Q3/Q322
document.doc - 241 - K Hoang 2007
HARDER 3U - other
1998 Q5/Q323
document.doc - 242 - K Hoang 2007
HARDER 3U - other1999 Q5/Q324
document.doc - 243 - K Hoang 2007
HARDER 3U - other2000 Q3/Q325
document.doc - 244 - K Hoang 2007
HARDER 3U - other2000 Q4/Q326
document.doc - 245 - K Hoang 2007
HARDER 3U - other2000 Q7/Q327
2001 Q4/Q328
document.doc - 246 - K Hoang 2007
HARDER 3U - other2002 Q7/Q329
document.doc - 247 - K Hoang 2007
2003 HARDER 3U - other20042005 Q5/Q330
document.doc - 248 - K Hoang 2007
HARDER 3U - other2006 Q5/Q331
Q6/Q332
document.doc - 249 - K Hoang 2007
HARDER 3U - other
2006 Q7/Q333
document.doc - 250 - K Hoang 2007
document.doc - 251 - K Hoang 2007
HARDER 3U - other2006 Q8/
Q334
20072010
document.doc - 252 - K Hoang 2007
document.doc - 253 - K Hoang 2007
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