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……….
106763489
-1-
K Hoang 2007
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
Chapter 9 – INTEGRATION
- By Parts
--------------------
----------------------- 124
Chapter 10 – INTEGRATION -subs, complete sq and integration table
Chapter 11 – VOLUMES - Slice
106763489
-2-
117
------- 126
-----------------------
K Hoang 2007
133
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
106763489
----------------------- 253
-3-
K Hoang 2007
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
106763489
-4-
K Hoang 2007
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 1
2 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.
106763489
-5-
K Hoang 2007
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 2
Students 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!
106763489
-6-
K Hoang 2007
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.
106763489
-7-
K Hoang 2007
106763489
-8-
K Hoang 2007
106763489
-9-
K Hoang 2007
106763489
- 10 -
K Hoang 2007
106763489
- 11 -
K Hoang 2007
106763489
- 12 -
K Hoang 2007
106763489
- 13 -
K Hoang 2007
106763489
- 14 -
K Hoang 2007
106763489
- 15 -
K Hoang 2007
106763489
- 16 -
K Hoang 2007
106763489
- 17 -
K Hoang 2007
106763489
- 18 -
K Hoang 2007
106763489
- 19 -
K Hoang 2007
106763489
- 20 -
K Hoang 2007
106763489
- 21 -
K Hoang 2007
106763489
- 22 -
K Hoang 2007
106763489
- 23 -
K Hoang 2007
106763489
- 24 -
K Hoang 2007
106763489
- 25 -
K Hoang 2007
106763489
- 26 -
K Hoang 2007
106763489
- 27 -
K Hoang 2007
106763489
- 28 -
K Hoang 2007
106763489
- 29 -
K Hoang 2007
106763489
- 30 -
K Hoang 2007
106763489
- 31 -
K Hoang 2007
106763489
- 32 -
K Hoang 2007
106763489
- 33 -
K Hoang 2007
Graphs:
sketch a curve
usual do something to a curve including composite curves
Complex:
Roots and proofs
geometry
Integration:
By parts
reduction/recurrence
Volumes:
slice
shell
Conics:
Ellipse tangents and normals etc and the 4 proofs
locus
partial fractions
substitution
special
property
cross section
Hyperbola tangents and normals etc and the 4 proofs
Rectangular Hyperbola tangents and normals etc
Mechanics:
Projectile and SHMotion
Polynimials: multiple roots
Harder 3 U:
106763489
perm and comb
locus
Resisted motion
transformation of roots
inequality
circle geo
- 34 -
induction
and the 2 proofs
circular motion
solve + factorise
other
K Hoang 2007
Topic1 GRAPHS – sketch a curve
Year
question
1990
marks comment
Q1/Q1
1991
Q2
1992
Q4/Q3
106763489
- 35 -
K Hoang 2007
GRAPHS – sketch a curve
1992
Q4
1993
Q5
106763489
- 36 -
K Hoang 2007
GRAPHS – sketch a curve
1994
Q6
1995
1996
Q4/Q7
Q6/Q8
106763489
- 37 -
K Hoang 2007
GRAPHS – sketch a curve
1997
Q3/Q9
1998
1999
Q4/Q10
2000
2003
2004
Q3/Q11
2005
Q3/Q12
2006
2007
2010
106763489
- 38 -
K Hoang 2007
Topic1 GRAPHS- do something to a curve including composite
Year
question
1990
1991
marks comment
Q13
1992
1993
1994
1995
106763489
Q3/Q14
- 39 -
K Hoang 2007
GRAPHS- do something to a curve including composite
1996
106763489
Q3/Q15
- 40 -
K Hoang 2007
1997
1998
106763489
GRAPHS- do something to a curve including composite
Q3/Q16
- 41 -
K Hoang 2007
GRAPHS- do something to a curve including composite
1999
106763489
- 42 -
Q3/Q17
K Hoang 2007
GRAPHS- do something to a curve including composite
2000
106763489
- 43 -
Q3/Q18
K Hoang 2007
GRAPHS- do something to a curve including composite
2001
106763489
- 44 -
Q4/Q19
K Hoang 2007
GRAPHS- do something to a curve including composite
2002
106763489
- 45 -
Q3/Q20
K Hoang 2007
GRAPHS- do something to a curve including composite
2003
106763489
- 46 -
Q3/Q21
K Hoang 2007
GRAPHS- do something to a curve including composite
2004
106763489
- 47 -
Q3/Q22
K Hoang 2007
GRAPHS- do something to a curve including composite
2005
106763489
- 48 -
Q3/Q23
K Hoang 2007
GRAPHS- do something to a curve including composite
2006
Q3/Q24
2007
2010
106763489
- 49 -
K Hoang 2007
Topic2 COMPLEX NUMBERS – locus
Year
question
1990
1991
1992
marks comment
Q2/Q25
1993
Q26
1994
Q2/Q27
106763489
- 50 -
K Hoang 2007
COMPLEX NUMBERS – locus
1995
5
1996
106763489
Q2/Q28
Q2/Q29
- 51 -
K Hoang 2007
COMPLEX NUMBERS – locus
1996
Q2/Q30
1997
Q2/Q31
106763489
- 52 -
K Hoang 2007
COMPLEX NUMBERS – locus
1998
Q2/Q32
1999
Q2/Q33
2000
Q2/Q34
2001
Q2/Q35
2002
Q2/Q36
106763489
- 53 -
K Hoang 2007
COMPLEX NUMBERS – locus
2003
Q2/Q37
2004
Q2/Q38
2005
Q2/Q39
2006
Q2/Q40
2007
2010
106763489
- 54 -
K Hoang 2007
Topic2 COMPLEX NUMBERS – geometry rotate vectors etc
Year
question
1990
marks Comment
Q1/Q41
1991
Q2/Q42
1992
Q43
106763489
- 55 -
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
1993
Q2/Q44
Q45
1994
106763489
- 56 -
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
1995
Q46
1996
106763489
- 57 -
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
1997
106763489
- 58 -
Q8/Q47
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
1998
106763489
- 59 -
Q2/Q48
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
1999
106763489
- 60 -
Q2/Q49
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
2000
106763489
- 61 -
Q2/Q5
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
2001
Q2/Q51
2002
2003
106763489
- 62 -
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
2004
106763489
- 63 -
Q2/Q52
K Hoang 2007
COMPLEX NUMBERS – geometry rotate vectors etc
2005
Q2/Q53
2006
2007
2010
106763489
- 64 -
K Hoang 2007
Topic2 COMPLEX NUMBERS – nth roots of unity and their proofs
Year
question
1990
1991
1992
marks comment
Q7/Q54
1993
Q55
1994
Q56
106763489
- 65 -
K Hoang 2007
COMPLEX NUMBERS – nth roots of unity and their proofs
1995
Q4/Q57
1996
Q8/Q58
1997
1998
Q2/Q59
106763489
- 66 -
K Hoang 2007
COMPLEX NUMBERS – nth roots of unity and their proofs
1999
Q8/Q60
2000
Q2/Q61
2001
Q2/Q62
106763489
- 67 -
K Hoang 2007
COMPLEX NUMBERS – nth roots of unity and their proofs
2002
106763489
- 68 -
Q7/Q63
K Hoang 2007
COMPLEX NUMBERS – nth roots of unity and their proofs
2003
Q8/Q64
2004
106763489
- 69 -
K Hoang 2007
COMPLEX NUMBERS – nth roots of unity and their proofs
2005
Q6/Q65
2006
2
2007
2010
106763489
- 70 -
K Hoang 2007
Q2/Q66
Topic2 COMPLEX NUMBERS – algebra including square roots
Year
question
1990
marks comment
Q67
1991
Q68
1992
Q2/Q69
106763489
- 71 -
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
1993
Q2/Q70
1994
Q71 a
Q71b
1995
Q2/Q72
1
3
106763489
- 72 -
K Hoang 2007
Q73
COMPLEX NUMBERS – algebra including square roots
1996
2
1997
106763489
Q2/Q74
Q2/Q75
- 73 -
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
1998
Q2/Q76
1999
Q2/Q77
106763489
- 74 -
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2000
Q2/Q78
Q8/Q79
106763489
- 75 -
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2001
Q2/Q80
Q7/Q81
106763489
- 76 -
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2002
106763489
- 77 -
Q2/Q82
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2002
106763489
- 78 -
Q8/Q83
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2003
106763489
- 79 -
Q2/Q84
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2004
106763489
- 80 -
Q2/Q85
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2004
106763489
Q7/Q86
- 81 -
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2005
106763489
- 82 -
Q2/Q87
K Hoang 2007
COMPLEX NUMBERS – algebra including square roots
2006
Q2/Q88
2007
2010
106763489
- 83 -
K Hoang 2007
Topic2 COMPLEX NUMBERS – complex conjugate root theorem and proofs
Year
question
1990
1991
1992
marks comment
Q89
1993
1994
1995
1996
Q90
1997
1998
106763489
- 84 -
K Hoang 2007
COMPLEX NUMBERS – complex conjugate root theorem and proofs
1999
Q2/Q91
2000
2001
2002
Q2/Q92
2003
2006
Q3/Q93
2007
2010
106763489
- 85 -
K Hoang 2007
Topic3 CONICS- rectangular hyperbola
Year
question
1990
1991
marks comment
Q94
1992
1993
106763489
Q95
- 86 -
K Hoang 2007
1994
1995
1996
CONICS- rectangular hyperbola
Q5/Q96
1997
1998
1999
106763489
- 87 -
K Hoang 2007
CONICS- rectangular hyperbola
2000
106763489
Q4/Q97
- 88 -
K Hoang 2007
2001
2002
CONICS- rectangular hyperbola
Q3/Q98
2003
106763489
- 89 -
K Hoang 2007
2004
2005
106763489
CONICS- rectangular hyperbola
Q8/Q99
- 90 -
K Hoang 2007
CONICS- rectangular hyperbola
2006
Q4/Q100
2007
2010
106763489
- 91 -
K Hoang 2007
Topic3 CONICS Ellipse
Year
question
1990
1991
marks comment
Q3/Q101
1992
Q102
1993
1994
106763489
- 92 -
K Hoang 2007
CONICS Ellipse
1995
106763489
Q8/Q103
- 93 -
K Hoang 2007
1996
1997
1998
1999
106763489
CONICS Ellipse
Q3/Q104
- 94 -
K Hoang 2007
CONICS Ellipse
2000
106763489
Q7/Q105
- 95 -
K Hoang 2007
CONICS Ellipse
2001
106763489
Q5/Q106
- 96 -
K Hoang 2007
CONICS Ellipse
2002
Q5/Q107
2003
Q3/Q108
106763489
- 97 -
K Hoang 2007
CONICS Ellipse
2004
106763489
Q4/Q109
- 98 -
K Hoang 2007
CONICS Ellipse
2005
Q4/Q110
2006
2007
2010
106763489
- 99 -
K Hoang 2007
Topic3 CONICS Hyperbola
Year
question
1990
106763489
marks Comment
Q111
- 100 -
K Hoang 2007
Topic3 CONICS - Hyperbola
1991
1992
1993
1994
Q112
1995
1996
106763489
- 101 -
K Hoang 2007
CONICS Hyperbola
1997
106763489
Q4/Q113
- 102 -
K Hoang 2007
CONICS Hyperbola
1998
Q6/Q114
1999
106763489
- 103 -
K Hoang 2007
2000
2001
CONICS Hyperbola
Q3/Q115
2002
106763489
Q4/Q116
- 104 -
K Hoang 2007
CONICS Hyperbola
2003
106763489
Q8/Q117
- 105 -
K Hoang 2007
2004
2005
2006
CONICS Hyperbola
Q118
2007
2010
106763489
- 106 -
K Hoang 2007
Topic4 INTEGRATION – special properties
Year
question
1990
marks comment
1991
1992
Q119
1993
1994
Q120
106763489
- 107 -
K Hoang 2007
INTEGRATION – special properties
1995
106763489
7
- 108 -
K Hoang 2007
Q4/Q121
INTEGRATION – special properties
1996
Q3/Q122
Q7/Q123
106763489
- 109 -
K Hoang 2007
1997
1998
INTEGRATION – special properties
Q7/Q124
1999
106763489
Q7/Q125
- 110 -
K Hoang 2007
INTEGRATION – special properties
2000
6
Q6/Q126
2001
2002
2003
Q6/Q127
2004
Q6/Q128
106763489
- 111 -
K Hoang 2007
INTEGRATION – special properties
2005
Q5/Q129
2006
2007
2010
106763489
- 112 -
K Hoang 2007
Topic4 INTEGRATION – partial fractions
Year
question
1990
marks Comment
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
106763489
- 113 -
K Hoang 2007
INTEGRATION – partial fractions
1998
Q1/Q138
1999
4
2000
106763489
Q1/Q139
Q1/Q140
- 114 -
K Hoang 2007
INTEGRATION – partial fractions
2001
Q1/Q141
2002
3
2003
106763489
Q1/Q142
Q1/Q143
- 115 -
K Hoang 2007
INTEGRATION – partial fractions
2004
Q1/Q144
2005
Q1/Q145
2006
Q1/Q146
2007
2010
106763489
- 116 -
K Hoang 2007
Topic4 INTEGRATION – reduction formula
Year
question
1990
marks comment
Q2/Q147
1991
Q1c/Q148
1992
1993
1994
106763489
- 117 -
K Hoang 2007
INTEGRATION – reduction formula
1995
Q7/Q149
1996
1997
1998
Q3/Q150
1999
106763489
- 118 -
K Hoang 2007
2000
2001
2002
106763489
INTEGRATION – reduction formula
Q6/Q151
- 119 -
K Hoang 2007
INTEGRATION – reduction formula
2003
106763489
Q8/Q152
- 120 -
K Hoang 2007
INTEGRATION – reduction formula
2004
106763489
Q8/Q153
- 121 -
K Hoang 2007
INTEGRATION – reduction formula
2005
106763489
Q6/Q154
- 122 -
K Hoang 2007
INTEGRATION – reduction formula
2006
Q7/Q155
2007
2010
106763489
- 123 -
K Hoang 2007
Topic4 INTEGRATION – by parts
Year
question
1990
marks comment
1991
1992
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
106763489
- 124 -
K Hoang 2007
INTEGRATION – by parts
2001
3
Q1/Q165
2002
4
Q1/Q166
2003
3
Q1/Q167
2004
2
Q1/Q168
2005
3
Q1/Q169
2006
3
Q1/Q170
2007
2010
106763489
- 125 -
K Hoang 2007
Topic4 INTEGRATION – substitution, complete the square or using integration table
Year
question
1990
marks comment
Q2a/Q171
Q2b/Q172
1991
Q1a/Q173
Q1b/Q174
1992
Q175
1993
Q176
1994
Q177
1995
106763489
2
- 126 -
K Hoang 2007
Q1/Q178
INTEGRATION – substitution, complete the square or using integration table
1995
3
1996
Q1/Q179
Q1/Q180
2
2
1997
Q1/Q181
2
3
2
106763489
- 127 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table
1998
2
1999
106763489
Q1/Q182
Q1/Q183
- 128 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table
2000
Q1/Q184
2
2
4
2001
Q1/Q185
2
2
4
106763489
- 129 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table
2002
Q1/Q186
2
2
4
106763489
- 130 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table
2003
2
Q1/Q187
2
4
2004
Q1/Q188
3
2
4
106763489
- 131 -
K Hoang 2007
INTEGRATION – substitution, complete the square or using integration table
2005
Q1/Q189
2
2
2006
2
2
3
2007
2010
106763489
- 132 -
K Hoang 2007
Q1/Q190
Topic5 VOLUMES - slice
Year
question
1990
1991
1992
1993
1994
1995
106763489
marks comment
Q3/Q191
- 133 -
K Hoang 2007
VOLUMES - slice
1996
106763489
Q3/Q192
- 134 -
K Hoang 2007
VOLUMES - slice
1997
Q3/Q193
1998
1999
2000
2001
2002
106763489
- 135 -
K Hoang 2007
VOLUMES - slice
2003
Q3/Q194
2004
2005
2006
2007
2010
106763489
- 136 -
K Hoang 2007
Topic5 VOLUMES – cross-section
Year
question
1990
1991
106763489
marks comment
Q5/Q195
- 137 -
K Hoang 2007
VOLUMES – cross-section
1991
106763489
Q5
cont’/Q195
- 138 -
K Hoang 2007
VOLUMES – cross-section
1992
106763489
Q196
- 139 -
K Hoang 2007
VOLUMES – cross-section
1993
Q197
1994
1995
106763489
- 140 -
K Hoang 2007
1996
1997
1998
VOLUMES – cross-section
Q5/Q198
1999
106763489
- 141 -
K Hoang 2007
VOLUMES – cross-section
2000
106763489
Q3/Q199
- 142 -
K Hoang 2007
VOLUMES – cross-section
2001
106763489
Q4/Q200
- 143 -
K Hoang 2007
VOLUMES – cross-section
2002
106763489
Q8/Q201
- 144 -
K Hoang 2007
2003
2004
106763489
VOLUMES – cross-section
Q3/Q202
- 145 -
K Hoang 2007
VOLUMES – cross-section
2005
106763489
Q5/Q203
- 146 -
K Hoang 2007
VOLUMES – cross-section
2006
Q4/Q204
2007
2010
106763489
- 147 -
K Hoang 2007
Topic5 VOLUMES - shell
Year
question
1990
marks Comment
Q205
1991
1992
1993
106763489
- 148 -
K Hoang 2007
VOLUMES - shell
1994
Q3/Q206
1995
1996
1997
Q5/Q207
1998
106763489
- 149 -
K Hoang 2007
VOLUMES - shell
1999
Q4/Q208
2000
2001
Q3/Q209
106763489
- 150 -
K Hoang 2007
VOLUMES - shell
2002
106763489
Q4/Q210
- 151 -
K Hoang 2007
VOLUMES - shell
2003
Q7/Q211
2004
Q5/Q212
106763489
- 152 -
K Hoang 2007
VOLUMES - shell
2005
Q4/Q213
2006
Q5/Q214
2007
2010
106763489
- 153 -
K Hoang 2007
Topic6 MECHANICS – Motion including projectile and SHM
Year
question
1990
1991
1992
marks Comment
Q5/Q215
1993
1994
1995
106763489
- 154 -
K Hoang 2007
MECHANICS – Motion including projectile and SHM
1996
Q7/Q216
1997
106763489
- 155 -
K Hoang 2007
MECHANICS – Motion including projectile and SHM
1998
Q7/Q217
1999
2000
106763489
- 156 -
K Hoang 2007
2001
2002
2003
2004
2005
106763489
MECHANICS – Motion including projectile and SHM
Q7/Q218
- 157 -
K Hoang 2007
MECHANICS – Motion including projectile and SHM
2006
Q6/Q219
2007
2010
106763489
- 158 -
K Hoang 2007
Topic6 MECHANICS – Resisted motion
Year
question
1990
marks comment
Q220
1991
Q6/Q221
1992
106763489
- 159 -
K Hoang 2007
1993
1994
MECHANICS – Resisted motion
Q4/Q222
1995
1996
106763489
- 160 -
K Hoang 2007
MECHANICS – Resisted motion
1997
Q6/Q223
1998
106763489
- 161 -
K Hoang 2007
MECHANICS – Resisted motion
1999
Q6/Q224
2000
106763489
- 162 -
K Hoang 2007
MECHANICS – Resisted motion
2001
Q5/Q225
2002
106763489
- 163 -
K Hoang 2007
MECHANICS – Resisted motion
2003
106763489
Q5/Q226
- 164 -
K Hoang 2007
MECHANICS – Resisted motion
2004
Q6/Q227
2005
2010
106763489
- 165 -
K Hoang 2007
Topic6 MECHANICS – circular motion
Year
question
1990
1991
1992
106763489
marks comment
Q228
- 166 -
K Hoang 2007
MECHANICS – circular motion
1993
Q229
1994
106763489
- 167 -
K Hoang 2007
MECHANICS – circular motion
1995
106763489
Q8/Q230
- 168 -
K Hoang 2007
MECHANICS – circular motion
1996
106763489
Q6/Q231
- 169 -
K Hoang 2007
MECHANICS – circular motion
1997
106763489
Q5/Q232
- 170 -
K Hoang 2007
MECHANICS – circular motion
1998
106763489
Q4/Q233
- 171 -
K Hoang 2007
MECHANICS – circular motion
1999
106763489
Q5/Q234
- 172 -
K Hoang 2007
MECHANICS – circular motion
2000
106763489
Q5/Q235
- 173 -
K Hoang 2007
MECHANICS – circular motion
2001
106763489
Q6/Q236
- 174 -
K Hoang 2007
MECHANICS – circular motion
2002
106763489
Q6/Q237
- 175 -
K Hoang 2007
MECHANICS – circular motion
2003
106763489
Q4/Q238
- 176 -
K Hoang 2007
MECHANICS – circular motion
2004
106763489
Q5/Q239
- 177 -
K Hoang 2007
MECHANICS – circular motion
2005
106763489
Q3/Q240
- 178 -
K Hoang 2007
MECHANICS – circular motion
2006
Q5/Q241
2007
2010
106763489
- 179 -
K Hoang 2007
Topic7 POLYNOMIALS – transformation + relationship bwt roots and coefficients +others
Year
question
1990
1991
1992
1993
1994
1995
Q5/Q243
1996
1997
106763489
marks Comment
Q242
- 180 -
K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others
1998
Q6/Q244
1999
Q5/Q245
2000
106763489
- 181 -
K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others
2001
Q3/Q246
2002
Q5/Q247
106763489
- 182 -
K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others
2003
Q5/Q248
2004
Q4/Q249
106763489
- 183 -
K Hoang 2007
POLYNOMIALS – transformation + relationship bwt roots and coefficients +others
2005
2006
2007
2010
106763489
- 184 -
K Hoang 2007
Q4/Q250
Topic7 POLYNOMIALS – solve and factorise
Year
question
1990
1991
marks comment
Q251
1992
1993
1994
106763489
Q8/Q252
- 185 -
K Hoang 2007
POLYNOMIALS – solve and factorise
1995
1996
1997
1998
Q7/Q253
1999
2000
Q5/Q254
106763489
- 186 -
K Hoang 2007
POLYNOMIALS – solve and factorise
2001
Q7/Q255
2002
2003
2006
2007
2010
106763489
- 187 -
K Hoang 2007
Topic7 POLYNOMIALS – multiple roots
Year
question
1990
1991
marks comment
Q7/Q256
1992
1993
Q257
1994
Q258
1995
1996
106763489
- 188 -
K Hoang 2007
POLYNOMIALS – multiple roots
1997
106763489
Q5/Q259
- 189 -
K Hoang 2007
POLYNOMIALS – multiple roots
1998
Q4/Q260
1999
Q4/Q261
2000
2001
2002
Q5/Q262
2003
2004
2005
2006
Q4/Q263
2007
2010
106763489
- 190 -
K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probability
Year
Question
1990
marks comment
Q5/Q264
1991
106763489
Q265
- 191 -
K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probability
1992
Q266
1993
Q267
106763489
- 192 -
K Hoang 2007
Topic8 HARDER 3U- permutation and combination and probability
1994
106763489
Q5/Q268
- 193 -
K Hoang 2007
HARDER 3U- permutation and combination and probability
1995
106763489
- 194 -
Q7/Q269
K Hoang 2007
HARDER 3U- permutation and combination and probability
1996
106763489
- 195 -
Q4/Q270
K Hoang 2007
HARDER 3U- permutation and combination and probability
1997
Q3/Q271
1998
Q4/Q272
106763489
- 196 -
K Hoang 2007
HARDER 3U- permutation and combination and probability
1998
106763489
Q6/Q273
- 197 -
K Hoang 2007
HARDER 3U- permutation and combination and probability
1999
106763489
- 198 -
Q7/Q274
K Hoang 2007
HARDER 3U- permutation and combination and probability
2000
Q8/Q275
2001
Q5/Q276
106763489
- 199 -
K Hoang 2007
HARDER 3U- permutation and combination and probability
2002
Q4/Q277
2003
Q4/Q278
2004
Q5/Q279
106763489
- 200 -
K Hoang 2007
HARDER 3U- permutation and combination and probability
2005
Q5/Q280
2006
Q5/Q281
2007
2010
106763489
- 201 -
K Hoang 2007
Topic8 HARDER 3U - inequalities
Year
question
1990
1991
1992
marks comment
Q8/Q282
1993
106763489
Q8/Q283
- 202 -
K Hoang 2007
HARDER 3U - inequalities
1994
Q284
1995
1996
106763489
- 203 -
K Hoang 2007
HARDER 3U - inequalities
1997
106763489
Q6/Q285
- 204 -
K Hoang 2007
HARDER 3U - inequalities
1998
Q8/Q286
1999
2000
106763489
- 205 -
K Hoang 2007
HARDER 3U - inequalities
2001
Q8/Q287
2002
2003
Q6/Q288
106763489
- 206 -
K Hoang 2007
HARDER 3U - inequalities
2003
Q7/Q289
2004
106763489
- 207 -
K Hoang 2007
HARDER 3U - inequalities
2005
106763489
Q8/Q290
- 208 -
K Hoang 2007
HARDER 3U - inequalities
2006
Q8/Q291
2007
2010
106763489
- 209 -
K Hoang 2007
Topic8 HARDER 3U- circle geometry
Year
question
1990
marks comment
Q6/Q292
1991
106763489
Q293
- 210 -
K Hoang 2007
Topic8 HARDER 3U- circle geometry
1992
Q3/Q294
1993
Q6/Q295
106763489
- 211 -
K Hoang 2007
HARDER 3U- circle geometry
1994
106763489
Q6/Q296
- 212 -
K Hoang 2007
HARDER 3U- circle geometry
1995
106763489
Q6/Q297
- 213 -
K Hoang 2007
HARDER 3U- circle geometry
1996
106763489
Q8/Q298
- 214 -
K Hoang 2007
HARDER 3U- circle geometry
1997
106763489
Q7/Q299
- 215 -
K Hoang 2007
HARDER 3U- circle geometry
1997
106763489
Q7/Q300
- 216 -
K Hoang 2007
HARDER 3U- circle geometry
1997
106763489
Q8/Q301
- 217 -
K Hoang 2007
HARDER 3U- circle geometry
1998
106763489
Q8/Q302
- 218 -
K Hoang 2007
HARDER 3U- circle geometry
1999
106763489
Q8/Q303
- 219 -
K Hoang 2007
HARDER 3U- circle geometry
2000
106763489
Q6/Q304
- 220 -
K Hoang 2007
HARDER 3U- circle geometry
2001
106763489
Q6/Q305
- 221 -
K Hoang 2007
HARDER 3U- circle geometry
2002
106763489
Q4/Q306
- 222 -
K Hoang 2007
HARDER 3U- circle geometry
2003
106763489
Q7/Q307
- 223 -
K Hoang 2007
HARDER 3U- circle geometry
2004
106763489
Q4/Q308
- 224 -
K Hoang 2007
HARDER 3U- circle geometry
2005
106763489
Q7/Q309
- 225 -
K Hoang 2007
HARDER 3U- circle geometry
2006
Q4/Q310
2007
2010
106763489
- 226 -
K Hoang 2007
Topic8 HARDER 3U- induction
Year
question
1990
marks Comment
Q7/Q311
106763489
- 227 -
K Hoang 2007
HARDER 3U- induction
1991
Q8/Q312
1992
Q6/Q313
1993
Q7/Q314
106763489
- 228 -
K Hoang 2007
106763489
- 229 -
K Hoang 2007
HARDER 3U- induction
1994
106763489
Q7/Q315
- 230 -
K Hoang 2007
HARDER 3U- induction
1995
Q4/Q316
1996
1997
1998
1999
Q6/Q317
2000
106763489
- 231 -
K Hoang 2007
HARDER 3U- induction
2001
Q8/Q318
2002
Q2/Q319
106763489
- 232 -
K Hoang 2007
HARDER 3U- induction
2003
Q6/Q320
2004
Q7/Q321
2005
106763489
- 233 -
K Hoang 2007
HARDER 3U- induction
2006
Q7/Q312
2007
2010
106763489
- 234 -
K Hoang 2007
Topic8 HARDER 3U - other
Year
question
1990
106763489
marks comment
Q313
- 235 -
K Hoang 2007
Topic8 HARDER 3U - other
1990
Q314
1991
1992
106763489
- 236 -
K Hoang 2007
HARDER 3U - other
1993
Q3/Q315
1994
1995
106763489
4
- 237 -
K Hoang 2007
Q5/Q316
HARDER 3U - other
1995
106763489
Q5/Q317
- 238 -
K Hoang 2007
HARDER 3U - other
1995
Q6/Q318
1996
Q4/Q319
106763489
- 239 -
K Hoang 2007
HARDER 3U - other
1996
106763489
Q6/Q320
- 240 -
K Hoang 2007
HARDER 3U - other
1997
Q4/Q321
1998
Q3/Q322
106763489
- 241 -
K Hoang 2007
HARDER 3U - other
1998
106763489
Q5/Q323
- 242 -
K Hoang 2007
HARDER 3U - other
1999
106763489
Q5/Q324
- 243 -
K Hoang 2007
HARDER 3U - other
2000
106763489
Q3/Q325
- 244 -
K Hoang 2007
HARDER 3U - other
2000
106763489
Q4/Q326
- 245 -
K Hoang 2007
HARDER 3U - other
2000
Q7/Q327
2001
Q4/Q328
106763489
- 246 -
K Hoang 2007
HARDER 3U - other
2002
106763489
Q7/Q329
- 247 -
K Hoang 2007
2003
2004
2005
106763489
HARDER 3U - other
Q5/Q330
- 248 -
K Hoang 2007
HARDER 3U - other
2006
Q5/Q331
Q6/Q332
106763489
- 249 -
K Hoang 2007
HARDER 3U - other
2006
106763489
Q7/Q333
- 250 -
K Hoang 2007
106763489
- 251 -
K Hoang 2007
HARDER 3U - other
2006
Q8/Q334
2007
2010
106763489
- 252 -
K Hoang 2007
106763489
- 253 -
K Hoang 2007