(1) Simultaneous Equations
Generally an easy topic, but beware of certain kinds of questions such as:
(a) Questions involving reciprocals of x and y, such as
Solve 3(1/x) + 1/y = 1; 1/(x^2) + 1/(y^2) = 5
Ans: x = 1, y = -1/2 or x = -5/2, y = 5/11
Do not make common denominators and cross-multiply; the better technique is to let p = 1/x and q = 1/y.
(b) Questions involving coefficient matrices that are singular (determinant = 0), such as
Given that x and y satisfy the simultaneous equations mx + (m-1)y = 10 and (m-2)x + 3my = 20,
(i) if the equations have no unique solution, find the values of m; (ans: 1/2, -2)
(ii) if the equations have no solution, find the value of m.(ans: 1/2)
(adapted from Additional Math, EPB Panpac, p. 13)
(2) Indices, Surds & Logarithms
Generally an easy topic, except for students who do not understand or memorize the laws of indices and logarithms properly. I find that quite a number of weak students do not know the meaning of logarithm, thus not appreciating and enjoying the topic. Weak students do not realize that while Indices is concerned with the answer or expression obtained when a power is applied to a base number, Logarithms is about the power itself; the power that is needed to be applied to a base to give a certain number.
For eg, why is lg1000 = 3? ‘Evaluate lg1000’ or ‘What is lg1000?’ is the same as asking, “What is the Power that must be applied to the number 10 (the base) to obtain 1000?” Since 10^3 = 1000, therefore the answer is 3.
Weak students almost always make one or more of the following mistakes, thinking that (i) logA x logB = logA + logB, (ii) log(A + B) = logA + logB, (iii) logAB = logA x logB, (iv) (logA)^n = nlogA, (v) logAB^n = nlogAB, (vi) (a^m)^n = a^(m+n). All these are wrong.
How to be good in Indices and Logarithms? READ AND UNDERSTAND THE LAWS OF INDICES AND LOGARITHMS CAREFULLY. Yes, there is such a thing as READING MATH, not just practising Math.
(3) Quadratic Functions & Equations
Some of the points to note are:
(1) Understand that alpha and beta by themselves also satisfy the quadratic eqn because they are the roots of the equation! So it’s not just abt finding the sum and product of roots;
You must be able to solve questions like:
If α is the root of the equation x^2 = 2x – 1, show that α^4 – α^2 = 2α – 2.
(2) Understand that the discriminant (b^2 – 4ac) is less than or equal to zero when the question involves the phrase “for which the function is never positive or never negative”;
(3) Understand that sometimes you are required to solve an inequality involving the discriminant but at other times the inequality involves the function itself;
(4) Understand how to complete the square to determine the maximum or minimum value of a quadratic function;
(5) Recognise that “real and distinct roots”, “real and equal roots”, and “no real roots” have other names that express the same meaning.
TO BE CONTINUED ……….. (by Mr Ilyasa)
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Sec 4 Physics Nov/Dec 2012 Headstart Programme – Electricity
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ORIGINAL POST(OUTDATED):
The details of the 2-day, 6-hr programme are as follows:
Date/Time (choose one pair of sessions only):
(1) Sat 24 Nov (10 am to 1 pm) and Sun 25 Nov (10 am to 1 pm);
(2) Sat 8 Dec (10 am to 1 pm) and Sun 9 Dec (10 am to 1 pm);
Location: Blk 627, Bukit Batok Central, 07-640.
Class size: Max 6 students.
Investment amt: $150 total for both days (6 hrs).
Topics: Electrostatics, Current Electricity
Tutor: Mr Ilyasa; M.Ed (NIE), PGDE (NIE), BSc (NUS), A-Level (RJC); ex-sch teacher, full-time tutor (8 years) of PSLE, O and A Level Math and Physics.
To book a place in the programme, sms to or call Mr Ilyasa at 97860411.
Sec 4 Physics, A. Maths One-to-One Tuition
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ORIGINAL POST (OUTDATED):
Objective: Intensive Revision or Crash Course for O-Levels 2013
Focus: Understanding Key Concepts, Problem-Solving Techniques, Difficult Topics
DETAILS:
Available Time Slots:
Mon 4pm – 7pm
Thur 1.30pm – 4.30pm, 8pm – 10pm
Fri 6pm – 8pm
Sat 9am – 11am
Investment Amt: $80 per hr
Tutor: Mr Ilyasa; M.Ed (NIE), PGDE (NIE), BSc (NUS), A-Level (RJC); ex-sch teacher, full-time tutor (8 years) of PSLE, O and A Level Math and Physics.
Location: Blk 627 Bukit Batok Central #07-640
Average Class Size: 2-6 students
For appointment, call or sms to 97860411. Thank you.
What subject combination to choose for Sec 3 or O-levels …
Based on my experience as a secondary school teacher, if you are now in Sec 2, here are the subjects I think you should choose for Sec 3 which will ultimately become your all-important O-Level subjects:
Other than (1) English, (2) Mother Tongue and (3) Mathematics, your other subjects should be:
(4) Additional Mathematics (A. Math is important for all higher level courses in Business and Science, including Engineering, and it will help you tremendously in JC Math (H1 or H2), as well as in math modules in the Polytechnics or ITE. Even a fail in A. Math is given some recognition for the purpose of application to some poly courses. Many university courses which do not require a pass in A-Level Math still require a pass in O-Level Additional Math. And NEVER, EVER drop A. Math even if your school asks you to; schools only care about their overall percentage passes and image, not about you. A school cannot force you to drop A. Math)
(5) Pure Chemistry or Combined Science with Chemistry (Chemistry is the central science. Without any O-level Chemistry, most likely you will not be allowed to do Chemistry in JC which in turn will bar you from taking any unversity courses related to the life sciences, such as medicine, dentistry, pharmacy etc.)
(6) Whether you take Geography, History or Literature depends on your inclinations. If you are unsure, take History if you intend to go to a JC for it will train you in argumentative or discursive essay writing skills necessary for the General Paper (I took history last time, got an A1 for it and my GP grades were always B3 and above. If you intend to do Law, getting good grades in History and GP helps)
(7) If you want to be in Engineering or Aviation, you must take Physics. If you intend to work in the life or ecological sciences field, you should do Biology.
(8)(added on 21/10/2016) You may also need to consider your overall workload. By taking “triple science”, you may end up taking 8 or 9 subjects when you only need 6 to go to a JC and only 5 to go to a polytechnic. Bear in mind that you may also be more involved in CCA as Sec 3 students will soon become CCA leaders. For example, even though my daughter can do “triple science”, but because she is in the Art Elective Programme and also actively involved in the school band, she has decided to opt for double science instead and I’m happy for her.
Please be very serious in choosing the above subjects because they may actually determine your career in Singapore.
If you need more info on the above, or about choosing JCs or JC subjects, or simply on how to effectively study Math, Physics or Chemistry, do drop by my centre in Bt Batok for a frank, no-obligations discussion. But do msg me (hp no: 9786 0411) first as I may have classes or meetings. Whether you are a parent or a student, if you are serious about education, I look forward to seeing you.
Rgds,
Ilyas
If you need academic help, kindly click on any of the following programs:
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For enquiries on the above, you may contact the tutor directly at 97860411.
SCIENCE PRACTICAL TRAINING:
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Beware the critical years in math education in Singapore.
TUITION FOR INTEGRATED PROGRAMME (IP) STUDENTS
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By EX-MOE TEACHERS & EXPERIENCED TUTORS
@ BLK 644, BUKIT BATOK CENTRAL, #01-68. S(650644).
CALL 65694897 OR SMS 98530744 OR 97860411.
Sec 4 Pure Physics Intensive Revision for O-Level @ Bt Batok by qualified and exp. tutor
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ORIGINAL POST (OUTDATED):
If you need Topical Intensive Revision for Pure Physics for the coming O-Levels, the following programme is suitable for you:
Day/Time: Every Monday, Wednesday and Friday, 6 pm to 7.30 pm (each slot is a different topic according to the Physics syllabus)
Start Date: Monday, 27 August.
Location: Blk 627, Bukit Batok Central.
Class size: 2 to 5 students.
Investment amt: $50 per session.
Tutor: Mr Ilyasa; M.Ed (NIE), PGDE (NIE), BSc (NUS), A-Level (RJC); ex-sec teacher (3 years); full-time tutor of O and A Level Math and Physics (8 years). To see his detailed resume, click here.
To book a tuition slot, sms to or call Mr Ilyasa at 97860411.
Sec 4 Physics, Chemistry, Math revision classes …
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A. Math Chap 2 – Quadratic Functions & Equations
I was teaching this topic in sch the other day and as expected, students encountered quite a number of problems with this topic. Many of my tuition students over the years also reported the same problems in handling issues related to Quadratic Functions.
Some of these problems are:
(1) not understanding that alpha and beta by themselves also satisfy the quadratic eqn because they are the roots of the equation! So it’s not just abt finding the sum and product of roots;
(2) not knowing the condition for the discriminant (b^2 – 4ac) when the question involves the phrase “for which the function is never positive or never negative”;
(3) not being sure whether one is required to solve an inequality involving the discriminant or the function itself;
(4) not knowing how to complete the square to determine the maximum or minimum value of a quadratic function (even those who can do it do not understand why it works!);
(5) not recognising that “real and distinct roots”, “real and equal roots”, and “no real roots” have other names that express the same meaning.
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New Sec 4 A. Math class Fri 7.45 pm …
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ORIGINAL POST (OUTDATED):
Sec 4 A. Math (Investment amt: $150 per mth):
Fri 7.45 pm – 9.15 pm; Course Code: s4amfri745. ( 3 vacancies) *NEW
Sat 10.45 am – 12.15 pm; Course Code: s4amsat1045. (1 vacancy)
Sun 10.00 am – 12.00 pm; Course Code: s4amsun10. (IP Programme – $200 per mth) (2 vacancies)
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SINGAPORE LEARNER
Singapore Learner provides Group Tuition, Individual Tuition, Intensive Revision, Enrichment Workshops, Headstart Classes, Holiday Classes and Crash Courses at the Primary, Secondary and Junior College levels in the areas of Math, Pure Physics, Pure Chemistry, Science, Economics, and General Paper for the Singapore A-Levels, O-Levels and PSLE.
I think the O-Level results will be released on ….
Well, some say on the 9th of January, which is a Monday. Personally, I think it will be on the 11th or 12th. I may be completely wrong of course. But what you do with the results is more important. The soon-to-be O-Level graduates right now need to do some serious thinking, and even soul-searching, about what they want to do as a career, what they are good at, and what they are passionate about. It is a scary yet exciting part of life.
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Singapore Learner provides Group Tuition, Individual Tuition, Intensive Revision, Enrichment Workshops, Headstart Classes, Holiday Classes and Crash Courses at the Primary, Secondary and Junior College levels in the areas of Math, Pure Physics, Pure Chemistry, Science, Economics, and General Paper for the Singapore A-Levels, O-Levels and PSLE.