Prove that (1 – cosX) / sinX = sinX / (1 + cosX)
Good luck!
Rgds,
Ilyasa
Do not drop a subject if you still have interest in it.
This is the time of the year when your school may ask you to drop certain subjects that you are weak in, using the lame excuse that even if you work hard, you will at most obtain a B4 or a C5. In reality, your school is more concerned about its own academic reputation, not about you. Schools are worried that if weak students continue to sit for certain exams, their national exam results (percentage passes or distinctions) will worsen. Yes, it’s not about you or your future; it’s about the school’s image.
Thus you must be wary when any of your school teachers call you in to give you hints to drop a subject. The teacher will say that if you drop one subject, you will have more time to study for the other subjects. While this may be true, what about the months that you have spent learning that subject? And the extra hours that you create by dropping a subject, will it all go into learning the other subjects? Having less subjects also mean that you will be taking a bigger risk should the unexpected happen to your remaining subjects, as you would be relying on a narrower band of subjects.
Two subjects that schools like to ask students to drop are Physics and Additional Math, the two most conceptually difficult subjects to master, in my opinion. So should you drop any of these subjects if you are asked to?
For Physics, the answer depends on whether you still like learning about Physics. If you still do, then continue doing it and take the exam, even if you have hardly ever passed Physics before. Why? The reason is, Physics has always been a difficult subject for most people. Thus the minimum mark to obtain the A1 grade for Physics may still be in the 75 to 79 range, significantly below that for Math (which is probably around 88 to 91). Hence you still stand a good chance of getting a B3 or above for Physics if you are willing to spend enough time practising Physics questions. This is only possible if you don’t mind studying Physics.
I have a tuition student who is very weak in Physics, and true enough, his teacher has been pestering him to drop Physics. So his mum turned to me for advice. Since he still likes Physics, I told the mum not to give in to the teacher. The boy finally passed Physics for his recent SA1 exam, and is now doing exam papers to get a better grade for his upcoming Prelim exam. The boy is mentally slow, but since he likes Physics, the school should have helped him improve instead. Isn’t it the purpose of schools to develop each student to his maximum potential?
The boy had also been asked to drop A. Math. But like I’ve said elsewhere, NEVER EVER drop A. Math, as knowledge of it is useful for many future courses such as Business, Engineering or Science. Although he still failed in his SA1 A. Math, he has been making significant progress as he still likes doing Math. Where there is a will there is a way. Let children and young people learn what they want to learn, even if it means getting poor exam results for the short term. A school should not be telling students to stop learning this or that, or to stop making effort, or to give up on something good that they have started.
If you need more advice (or even tuition, see below) on Math, A.Math, Physics or Chemistry or Combined Science, do whatsapp me at 97860411.
Ilyasa
An NIE-trained Teacher, Mr Ilyasa has been coaching students in O-Level & IP Chemistry, Physics and Math for more than 12 years. An alumnus of Raffles Institution, Mr Ilyasa holds a a Bachelor of Science degree from the NUS as well as a Master of Education (Curriculum & Teaching) degree from the National Institute of Education. Mr Ilyasa’s thinking and metacognitive approaches to problem solving has helped many students of varying abilities to excel in Math and the Sciences. He has coached students from many different schools and streams, including IP, SAP, and IB.
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If you wish to visit us, kindly call or sms first. Thank you.
‘O’-Level Elementary Math
For students to master each topic in ‘O’-Level Elementary Math, I would recommend the following series of books:
1. ‘O’ Level Elementary Mathematics Companion
Publisher: Casco Publications Pte Ltd; Author: Lee-Ann Goh
It comes in two volumes. Book 1 provides notes, examples and practice questions for Arithmetic, Algebra, Coordinate Geometry and Graphs. Book 2 provides notes, examples and practice questions for Geometry, Trigonometry, Sets, Matrices, Vectors and Statistics. Each book comes with fully worked-out solutions to all the practice questions.
How to use these books?
Use the two books to learn or revise the theories of each topic and analyse the examples to understand and remember how different types of problems are solved.
Then attempt to answer as many questions as you can in the Revision Exercises provided and after that, mark your own solutions by comparing them with the worked solutions. If your answers are incorrect, seek to understand where, how and why you got them wrong.
If you often find yourself not understanding some parts of the worked solutions, then, yes, you’d probably need to consult a tutor. But you can first try asking your school teachers or friends first.
If you have mastered most of the topics in ‘O’-Level and you need practice papers, then I would recommend that you complete the papers in the following book:
2. G.C.E. ‘O’ Level Mathematics Paper 1 and Paper 2
Publisher: Casco Publications Pte Ltd; Author: Lee-Ann Goh
It has 10 ‘Trial Exam’ papers, with fully worked-out solutions for each paper. You should attempt each paper in the time allocated (2hrs for Paper 1 and 2.5hrs for Paper 2). Then mark your own solutions and reflect on your errors and learn from them.
3. Pass With Distinction, Elementary Mathematics (By Topic) with Solutions
Publisher: Shinglee Publishers Pte Ltd; Author: Teh Keng Seng, Loh Cheng Yee
‘O’-Level Additional Mathematics
For students to master each topic in A. Math, I would recommend the following series of books:
- Pass With Distinction, Additional Mathematics (By Topic) with Solutions
Publisher: Shinglee Publishers Pte Ltd; Author: L. K. Lee
- O–Level Additional Mathematics Revision Guide 3 and 4
Publisher: Pearson Longman; Author: Aven Choo
How to use these books?
Use the two books to learn or revise the theories of each topic and analyse the examples to understand and remember how different types of problems are solved.
Then attempt to answer as many questions as you can in the Practice Exercises provided and after that, mark your own answers. If your answers are incorrect, seek to understand where, how and why you got them wrong.
If you have mastered most of the topics and you need practice papers, then I would recommend that you complete the papers in the following book:
- ‘O’ Level Additional Mathematics Revision Guide Paper 1 and 2
Publisher: Dolphin Publications
It has 14 challenging ’Revision Exam’ papers, with fully worked-out solutions for each paper. You should attempt each paper in the time allocated (2hrs for Paper 1 and 2.5hrs for Paper 2). Then mark your own solutions and reflect on your errors and learn from them.
‘O’ Level Chemistry
For students to master each topic in ‘O’-Level Chemistry, I would recommend the following series of books:
- Understanding Chemistry ‘O’ Level
Publisher: GLM Pte Ltd; Author: Li Geok Jin
- Pass With Distinction: Chemistry (By Topic)
Publisher: Shinglee Publications; Author: Sean Chua
- ‘O’ Level Chemistry Workout (Structured and Free-Response Questions)
Publisher: Pearson Longman; Author: Lim Eng Wah, JGR Briggs
- Effective Guide to ‘O’ ‘Level Chemistry (2nd Edition)
Publisher: Pearson Longman; Author: Lim Eng Wah
‘O’ Level Physics
For students to master each topic in ‘O’-Level Physics, I would recommend the following series of books:
- ‘O’ Level Challenging Drill Questions Physics
Publisher: Cosmic Services; Authors/Compilers: Thomas Bond, Chris Hughes
- Pass With Distinction: Physics (By Topic)
Publisher: Shinglee Publications; Author: Tan Kim Seng
- ‘O’ Level Physics Workout (Structured and Free-Response Questions)
Publisher: Pearson Longman; Author: Gabriel Lionel Morris
- 1001 Physics MCQs for ‘O’ Level
Publisher: Pearson Longman; Author: Tan Peng Yeon
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CALL 65694897.
Yay, my Sec 4 student topped her class in Math. : )
Congrats to Ameerah from Clementi Town Sec who obtained 24/25 for her most recent Math test. It’s my fourth good news in two weeks (before this, Daniel Lam from BPGHS topped his class in A Math, Peng Wee from CTSS did the same in Physics and Hanaa from Hillgrove Sec missed the top spot in her class for Math by just one mark).
Over the years, many of my tutees topped their classes, in Math and/or Physics. Is there a secret to their accomplishments? No, and Yes. It’s not a secret that they all worked hard and smart. The secret is, and I intend to keep it as a trade secret, is what I tell them in class, at the crucial moments. The power of words, truly amazing.
In case you don’t believe, let me tell you of another student, Victoria, formerly from Nan Hua High, now in RI year 6. Her math results were very inconsistent, but she obtained A1 for both in the O-levels. She didn’t attend my lessons in the last month before the O-levels because I kind of scolded her badly, and she decided to study by herself. When she called to inform me of her O-level results, I asked her what caused the change, and she said, “It’s something you said.”
The lesson for teachers and tutors is, be careful of what you say to your students. I’ve made mistakes in this area before, in my first few years of teaching. If you are a parent, please be even more careful of what you say to your children. Words have power beyond our comprehension.
Rgds,
Ilyasa
Yay, my sec 3 NA student topped his class in A. Math.
Congratulations to Daniel Lam, from BPGHS, who obtained 39 out of 40 marks for his recent A. Math class test on Quadratic Equations.
I’m still not used to publishing testimonials from current or past students for my teaching or tutoring. In fact, I hardly record or remember their pre-tuition and post-tuition marks. It is sufficient for me that my students have stayed with me for as long as they have needed my guidance (or nagging), and that they continue to do well all the way to university.
Yes, I’m not good at marketing. Even my website is not dazzling enough. It’s ok for now, as I still get a sufficient number of students every year. I don’t even produce my own materials (but I know where to get the good ones).
So without aggressive marketing, testimonials and “own materials”, how have I been able to attract students to come and learn? And in what ways do I add value to a student’s learning? Well, you have to attend my tutorial sessions to know what thinking looks like. : )
Rgds,
Ilyasa
S4 A. Math O-Level Conceptual Revision: Exam Prep beginning 2nd week of April
For our latest timetable, click here => 
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ORIGINAL POST(OUTDATED):
Conceptual Revision classes are for Sec 4 students to revise their Sec 3 work in preparation for their SA1 or Prelim exams. Details as follows (sms or call 97860411 to register):
Level/Subject: S4 Additional Math
Days/Times: (1) Sundays, 5.30 pm to 7.00 pm.
Location: Blk 627 Bukit Batok Central #07-640
Topics: Sec 3 A. Math topics such as Polynomials, Binomial Theorem, Logarithms etc.
Target Group: This series of revision workshops is suitable for low to medium ability Sec 4 A. Math students who need to revise their A. Math in a systematic and effective way. High ability Sec 3 students may also attend these sessions to revise or have a headstart in their A. Math.
Focus: Conceptual Understanding, Solving Challenging or Tricky A. Math Problems, Exam-Answering Techniques.
Format: Lecture + Worksheets + Discussions
Fees: $200 per month
Class Size: 2 to 6 students.
Tutor: Mr Ilyasa; M.Ed (NIE), PGDE (NIE), BSc (NUS), Ex-RI/RJC; ex-sch teacher, full-time tutor of PSLE, O and A Level Math and Physics. (h/p: 97860411)
A former secondary school Physics teacher, Mr Ilyasa has been coaching students in ‘A’ Level (H2/H1) Physics and (H2/H1) Mathematics for more than 7 years, as well as ‘O’ Level Physics, Additional Math, Math and PSLE Math for more than 10 years. An alumnus of RI and RJC, Mr Ilyasa holds a Bachelor of Science degree with Merit from the National University of Singapore, a Postgraduate Diploma in Education with Credit from the National Institute of Education, Singapore, and a Master of Education (Curriculum & Teaching) degree also from the NIE, Singapore.
To register, kindly call or send an sms to 97860411.
A-Level & O-Level 2013 Preparation (morning classes, mainly for those re-taking)
We do provide coaching for students who are free to attend classes in the mornings or early afternoons. Such students are typically those who are re-taking their A-levels or O-levels. The levels and subjects offered are:
A-Level: General Paper, (H2/H1) Economics, (H2/H1) Math, (H2) Management of Business. (H2/H1) Physics (upon request)
O-Level: English, Math, Additional Math, Science (Physics/Chemistry), Pure Physics, Pure Chemistry, Economics, Business Studies.
Class type: Small group or Individual
Location: 3-min walk from Bukit Batok MRT station.
For other details, such as timings and fees, kindly call or sms to 97860411, or send an email to ilyasa@conceptlearning.sg.
The Tutors:
Mr Ilyasa: A former MOE school teacher, Mr Ilyasa has been coaching students in ‘A’ Level Physics, Mathematics and Economics for more than 7 years, as well as ‘O’ Level Physics, Additional Math and Math for more than 10 years. An alumnus of RI and RJC, Mr Ilyasa holds a Bachelor of Science degree with Merit from the National University of Singapore, a Postgraduate Diploma in Education with Credit from the National Institute of Education, Singapore, and a Master of Education (Curriculum & Teaching) degree also from the NIE, Singapore.
Mr Jay Lim: An experienced full-time tutor, Mr Lim holds a Master of International Management (USA), B.Sc (USA) majoring in Finance & Retail Management, Higher Stage Certificate in Economics, The London Chamber of Commerce & Industry. He was formerly a financial services consultant and an ex-bank officer. Mr Lim has been teaching English at various levels in an Integrated Programme school for about 5 years. He will be focusing on General Paper, Management of Business and Economics in Singapore Learner.
For details, such as timings and fees, kindly call or sms to 97860411.
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For our latest timetable, click here => 
Sec 4 A. Math & Math Tuition By Ex-Sch Teacher
For our latest timetable, click here =>
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ORIGINAL POST(OUTDATED):
Sec 4 A. Math (Investment amt: $180 per mth):
Fri 5.45 – 7.15 pm;
Sat 2.15 pm – 3.45 pm;
Sec 4 E. Math (Investment amt: $180 per mth):
Tues 7.45 – 9.15 pm;
Tutor: Mr Ilyasa; M.Ed (NIE), PGDE (NIE), BSc (NUS), Ex-RI/RJC; ex-sch teacher, full-time tutor of PSLE, O and A Level Math and Physics. (h/p: 97860411)
A former secondary school teacher, Mr Ilyasa has been coaching students in ‘A’ Level (H2/H1) Physics and (H2/H1) Mathematics for more than 6 years, as well as ‘O’ Level Physics, Additional Math, Math and PSLE Math for more than 10 years. An alumnus of RI and RJC, Mr Ilyasa holds a Bachelor of Science degree with Merit from the National University of Singapore, a Postgraduate Diploma in Education with Credit from the National Institute of Education, Singapore, and a Master of Education (Curriculum & Teaching) degree also from the NIE, Singapore.
DETAILS:
Location: Blk 627 Bukit Batok Central #07-640
Average Class Size: 2-6 students
To register, kindly call or send an sms to 97860411, indicating the Student Name, the Subject and Level.
Sec 3 A. Math & Math Tuition By Ex-Sch Teacher
For our latest timetable, click here =>
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ORIGINAL POST(OUTDATED):
Sec 3 A. Math: (Investment amt: $180 per mth):
Thurs 5.45 to 7.15 pm;
Sun 2.15pm to 3.45 pm;
Sec 3 E. Math: (Investment amt: $180 per mth):
Tues 5.45 to 7.15 pm;
Tutor: Mr Ilyasa; M.Ed (NIE), PGDE (NIE), BSc (NUS), Ex-RI/RJC; ex-sch teacher, full-time tutor of PSLE, O and A Level Math and Physics. (h/p: 97860411)
A former secondary school teacher, Mr Ilyasa has been coaching students in ‘A’ Level (H2/H1) Physics and (H2/H1) Mathematics for more than 6 years, as well as ‘O’ Level Physics, Additional Math, Math and PSLE Math for more than 10 years. An alumnus of RI and RJC, Mr Ilyasa holds a Bachelor of Science degree with Merit from the National University of Singapore, a Postgraduate Diploma in Education with Credit from the National Institute of Education, Singapore, and a Master of Education (Curriculum & Teaching) degree also from the NIE, Singapore.
DETAILS:
Location: Blk 627 Bukit Batok Central #07-640
Average Class Size: 2-6 students
To register, kindly call or send an sms to 97860411, indicating the Student Name, the Subject and Level.
Improvement in a student’s math result …
Daniel, one of A. Math tutees, showed me his class test result yesterday: 34/40. The test was on Indices and Surds, Wow, excellent, I said to him. Daniel is from the N(A) stream, and usually fails his Math tests. That he could obtain 34/40 and top his class in just a few weeks of tuition was phenomenal. So I started reflecting on what went right, because there are many students, even those from top schools, who do not make such a giant leap in such a short amount of time.
So what was the major factor contributing to Daniel’s significant improvement? Well, it’s not some secret special technique. In fact, it’s a well-known technique that some students just don’t want to use – ask many, many questions, even “silly” ones, about the same topic until one is satisfied that understanding has been achieved. Daniel even questions me when he doesn’t understand the steps I show him, whereas many students simply copy or write down my solution. Daniel sometimes takes a while to process the information I give to him; he will pause and ponder, and then sheepishly asks a basic question. He will even ask questions periodically to affirm that his steps are correct.
Students need to make meaning out of what they hear or see; it’s not enough to just listen to teachers or observe what they do in class. And you make meaning when you have a dissonance in your mind; some pieces of the jigsaw puzzle don’t fit and you have the courage to ask and then ponder again.
Regarding asking questions, I have one advice though: you must attempt to answer your own questions first, for the struggle to answer your own questions will make it easier for you to understand another person’s explanation. : )
Good luck!
Rgds,
Ilyasa