Why I share suggested solutions for free

JC Mathematics

Many of my ex-students know that I send them this link post A-level. Prior to 2012, it was a link to a shared pdf that contains the suggested solutions that I rushed out, for both paper 1 and 2, in like an hour. In 2013 & 2014, I shared them on another site, Singapore Learner. I also rushed the suggested solutions out in an hour to put in up online.

I just want to clarify, I am not sadistic and want students to feel bad or torture them mentally by sharing my solutions. Furthermore, I do make a handful of mistakes while rushing them and I learn from them too. My main objective is to also collect different responses and provide a simple platform for discussion. Alternative methods by other tutors or students were being able to be shared there too. This helps me to improve. 🙂

Last but not least, having done the paper also allows me to respond and discuss with my students about it actively. At the same time, I can better prepare them for Paper 2.

Statistics before calculus!

JC Mathematics

This is an interesting opinion which I do agree with. Statistics is very much more applicable in today’s world, and important too. It helps students to think better and be more critical! So do pay extra attention in your statistics classes!

Ice Cream Week

Ice Cream Week

JC Mathematics

Last week, I treated all my students to Ice Cream as a reward for their hardwork, or effort for their Midyears in June. I had the opportunity to chat with a handful of them and some of them are really stress about their upcoming A-level or promotional exams. Here is a little advice from experience.

J1s, I strongly encourage you to seek help if you have problems now. Promoting with straight E’s will not give you confidence in year 2. Junior College is only two years and things happen in a blink of eye. So do get ready and exhibit consistency.

J2s, by now most of my JC2 are half-way through their topical revision. I hope others out there are too as A-level is to each his own.

To the secondary school students who were jealous of the ice cream in the tuition centre, do know what you are signing up for in JC. We will have post O-levels talk in Jan – Feb to advise students on their options. It is free. So do look forward to it!:)

Upcoming Preliminary Exams 2015

JC Mathematics

One of my Anglo Chinese Junior College (ACJC) student just told me he got 99th percentile for the recent Math Midyears but is still worried for Prelims. This is partly because they were only tested on half the syllabus. For AC Students, your prelims are just round the corner, probably another 5 weeks. I have a handful of AC students too, most of them are currently doing topical revision already and in August, I plan to have them get ready to do 3H papers in 2.5H and t brush up on their answering techniques.

Over the years, I have taught ACJC students numerous times and my advice to you guys is to try your best to be disciplined for the upcoming A-levels.

And I understand from the JC1 that they are worried seeing that their seniors have yet finish the tutorials in class but are taking the exams really soon, and wonder if they are safe next year. Typically, ACJC prepares their students really well as post-prelims, you have a few mock exams. Not forgetting many delicious catered meals haha. For year 5s in ACJC, I know that you’re worried as your peers in other schools seem to finish more topics than you guys. But quantity never correlates to quality. 🙂

The General Paper – An Overview

JC General Paper

What is General Paper (GP)?

In essence, GP is academic writing and analyses on anything and everything, hence the term ‘general’. Topics covered in GP include:

  • History
  • Economics
  • Law and Politics
  • Education
  • Sports and leisure
  • Culture and Society
  • Philosophy
  • Science and Technology
  • Environmental issues
  • Music and the Arts
  • Language and Literature

In the A Levels, the GP paper consists of an essay part and a comprehension passage part. For the essay part, students are required to write between 500-800 words on a chosen question. For the comprehension passage part, students will need to attempt all comprehension questions, write a summary and do an application question (AQ). The AQ is a mini-essay where one is required to discuss the ideas presented in the comprehension passage and apply it to other contexts, usually local i.e. Singapore.

Why do we need to take GP?

This was a question even I asked myself when I was in junior college (JC). If you are currently in JC, you might not appreciate GP now but trust me –coming from a person who loathes GP— it does prepare you for university because GP trains you to:

  • understand and think critically about a piece of information or data
  • apply the knowledge learnt to other contexts
  • form and communicate ideas or opinions in a coherent manner

Continue reading “The General Paper – An Overview”

About H2 Math classes

JC Mathematics

Some Singapore parents and students have called, telling me they want to know more about the class structures.

Most of my private classes range from one student to four students, preferably held at their residences. These classes can be ad-hoc, long term of short term.

For group classes in tuition centres, the class size is not more that 8.

My notes and worksheet are prepared by myself. I don’t like to be long-winded with notes so they are really concise. Questions mostly seek to teach and mentor students.

In general, I utilise the class timing to impart my knowledge and understanding to students. I don’t like to see my students do work in front of me unless necessary.

Most of the times, I can finish a topic in a 2H lesson. There was a student who was doing really badly, took tuition daily just two weeks prior to A-levels and I saw her to an A. So it is possible; but I do not generally like such methods of teaching as I wasn’t teaching but just telling her what to do in A-levels.

Deriving the polar form for complex number

JC Mathematics

I always stress to students the importance of the basics of complex numbers, that is

z
=x+iy
=re^{i \theta}
=r(cos{\theta}+isin{\theta})

The three forms of the complex numbers. I have shown how to derive from the cartesian (x+iy) to trigonometric form (r(cos{\theta}+isin{\theta})) form. But I seldom show students how to derive the polar form due to the rigor. So here we go. Lets first identify a few formulas from MF15.

e^{x}=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\frac{x^5}{5!}+...

cosx=1-\frac{x^2}{2!}+\frac{x^4}{4!}+...

sinx=x-\frac{x^3}{3!}+\frac{x^5}{5!}+...

Let us consider the polar form then.

e^{i\theta}=1+{i\theta}+\frac{{i\theta}^2}{2!}+\frac{{i\theta}^3}{3!}+\frac{{i\theta}^4}{4!}+\frac{{i\theta}^5}{5!}+...

Resolving the i's

e^{i\theta}=1+{i\theta}-\frac{{\theta}^2}{2!}-\frac{i{\theta}^3}{3!}+\frac{{\theta}^4}{4!}+\frac{i{\theta}^5}{5!}+...

Rearranging them

e^{i\theta}=1-\frac{{\theta}^2}{2!}+\frac{{\theta}^4}{4!}+...+{i\theta}-\frac{i{\theta}^3}{3!}+\frac{i{\theta}^5}{5!}+...

Notice if we factorise i out

e^{i\theta}=1-\frac{{\theta}^2}{2!}+\frac{{\theta}^4}{4!}+...+i[{\theta}-\frac{{\theta}^3}{3!}+\frac{{\theta}^5}{5!}]+...

Then with the formula we started with,

e^{i\theta}=cos{\theta}+isin{\theta}

Voila! We are done and we have successfully derive our trigonometric form.

Simpson’s Rule

JC Mathematics

With regards to a recent post on The Simpson’s triangles. We know that Simpson’s is quite a witty show. So is there a rule?

Yes! And this rule is called Simpson’s Rule! But what does it do?

Simpson’s Rule lets us estimate the area under a curve, this is akin to drawing rectangles at the curve and finding the area. The trick is that we require the values of an odd number of coordinates, including the those at both ends.

Simpson’s rule can be derived by approximating the integrand f (x) (in blue) by the quadratic interpolant P(x) (in red). From Wikipedia.

A sigh of relief

JC Mathematics

A J1 (Junior College Year 1) recently told me she was very impressed by what I did for her Mid years.

Lets rewind a bit. Many J1s actually was worried about Mid years and wanted to have extra lessons. But I was tight down with many J2s as many of them were doing last minute sprint in June. So I only manage to stick to the regular four lessons monthly. I assured them that following my method will work and the extra tuition lessons were not necessary.

So this J1 told me (just two days ago), “my classmate went for crash courses and 12 lessons in June with ___ then only get D, while I still get A with just 4 lesson.”

To be honest, I even canceled lessons during the Mid Year Exam week as I see no need (well, I was overseas too). So many students were quite thankful it worked out.

I feel that all these boils down to methodology and how the student gets ready for exam. The tutor’s job should be to get the student ready, by direct and simple means, not massive thick notes as this is no difference from the school.

What is a regression line?

JC Mathematics

When we do correlation & regression as a topic, we know correlation is talking about the relationship between two variables, but what exactly is “regression”?

So this is a bit of English. To regress something is to reduce, and what do you think we are regressing here? For most regression questions, we start off with a bunch of sample data points and somehow, into the GC it goes and out comes a regression line. The GC did regress (reduce) something, the errors between the data points, one can consider it as the distance between the fitted values and collected data values. So the regression line, in layman terms, is really just the best fit line that students always attempt to draw during their science SPA haha. Just that we got an even more accurate one, I describe to students that this is the “best of the best” best fit line. 🙂