Prove that (1 – cosX) / sinX = sinX / (1 + cosX)
Good luck!
Rgds,
Ilyasa
Category: A. Math
A good Indices question for you to try (answer given)
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.
If you need academic help, kindly click on any of the following programs:
REVISION AND RE-LEARNING (NOV-DEC)
HEAD START (NOV-DEC)
STANDARD WEEKLY TUITION (JAN-OCT)
INDIVIDUAL TUITION
SCIENCE PRACTICAL TRAINING
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 =>
==========================================================
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
“Models (drawing of) destroyed my life.” – Sec 3 Math student
I laughed when he said it. But it’s a significant statement by my Sec 3 Math student made two days ago. It’s something I’ve been warning parents and students about, in my earlier article Beware the Critical Years in Math.
This Sec 3 Math tutee is from a top government secondary school in the west. Being mathematically intelligent, he had found it easy to use models-drawing to solve PSLE Math problems. But he had a hard time coping with Algebra in Sec 1 and Sec 2, and it’s affecting both his Math and A. Math performance now. This situation is not unique to him.
The best years of learning by your brain is probably from the time you were born to just before your teenagehood. Singaporeans around my age or older were taught to use algebraic equations to solve math problems at the PSLE back then. I remember using simultaneous equations in 1984 to solve today’s “guess & check” problems in the PSLE. Thus our algebraic skills were good and it helped us, even those who didn’t do well at the PSLE, in doing O-Level and A-Level Math.
Algebra is SO important for Math at O-level and A-level, yet our dear MOE chooses not to introduce it for problem-solving in today’s PSLE. I still don’t understand why.
It is true that some young students may not be able to understand Algebra, due to it being very abstract. But it is also true that some young students are not visually or spatially intelligent enough to draw, cut and move rectangles to solve problems. For eg, what has rectangles got to do with mass or age? (you know, those problems involving age relationships between persons or mass relationships between objects). Using rectangles or boxes to represent age or mass is just as ridiculous or abstract as using letters such as ‘x’ and ‘y’ as in algebra.
The least the MOE should do is to allow the teaching of BOTH methods to solve problems. Since those boxes start appearing in P2 or P3, algebraic expressions should also be introduced at P2 or P3, algebraic expansion in P4, algebraic factorisation in P5, and algebraic equations in P6. Sec 1 students can straightaway start on algebraic fractions etc. Do we lose anything by introducing algebra earlier in our math curriculum?
I’m glad I started my Sec 1 Algebra course for post-PSLE students in Nov and Dec last year (see Sec 1 Algebra Headstart Holiday Enrichment Programme for post-PSLE students). I think students still don’t realise how ill-prepared they are for math in sec school and JC. I dare say that if you are weak in your S1 and S2 algebra, you don’t have to take Math anymore.
Good Luck.
Rgds,
Ilyasa
(M.Ed., PGDE, B.Sc, ex-teacher, full-time tutor: 97860411)
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