### On time

The one thing many students overlook in A-level is Time. A lot of students I see lack the ability to finish the full paper on time, that is, in 2.5h, not 3h. We all need to check on the presentation and for silly careless mistakes.

The solution to this is old-school. You just have to sit down and train yourself to endure the full paper. This is very important as some students can’t even sit still for 2h without checking their handphone for updates. If you can, find a friend who is decently your standard and do the paper with him/her. Pace both of yourself together. But make sure you guys don’t cheat and consult each other. Some of my students know I simply do the paper alongside with them, analyse the paper alongside while doing it with them, highlighting the keywords that strike me when I read the questions. The worst was when I simply challenge them to do as fast as me.

### Vectors: Cross vs Dot Product

Many students have asked me why is there a difference between cross(vector) and dot(scalar) product, after all it is like multiplying. For starters, the former produces a resultant vector while the latter produces a scale quantity, as its name suggests. So is there an intuitive explanation?

If you know a bit of physics, it will be quite easy. Simply consider electromagnetic induction, there is a resultant work done and a resultant force. The resultant work done is our scalar product here while the resultant force (Fleming’s left hand rule) is our vector product here. I hope this helps your understanding!

### How I encourage students to study Math in JC

A couple of weeks ago, I met up with friend of mine who is still teaching in a renowned JC. He was lamenting how students today don’t study for the sake of learning. So I thought of sharing a learning (teaching) method which I adopt with my students: Meta-Cognition Approach. This approach starts with the students being aware and understanding his/ her own thought process while learning.

Mathematical problem solving is often best treated with meta-cognition methods. So instead of doing the same type of question 10 times and secretly pray that it comes out in exam, I often encourage my students to think about what they’ve learnt. When they meet a question, be it a new type, they will then be able to have somewhat a starting point. Through this, they think more and most questions can be solved then. If a student is able to learn how to think properly with any question, that shows they exhibit stronger foundations too.

In the 2014 A-level, we saw a handful of questions asking students such as:

• “what can be said”,
• “what do you think”

These are qualitative questions which test students on how much understanding they have of the topics.

At the same time, I strongly encourage students to see the 24 topics in A-level as one subject and not segregate the learning of the topics. Topics such as complex numbers and vectors can easily be tested together, so can Complex Numbers and Maclaurin’s. And only if students learn the topics as a whole subject can they tackle these surprise questions effectively.

If you want to learn more, check out my Math class schedule.

This is an interesting probability problem (paradox). And no, this isn’t about the Cheryl’s Birthday Problem.

In probability theory, the birthday problem or birthday paradox[1] concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. -Wikipedia

The above graph shows how many people you need to approach to find someone who has the same birthday with you!

This shows how counter-intuitive probability is! And like what I always tell my students, don’t use intuition for probability but formulas.

### A-level vs IB Mathematics

I’ve been giving several JC Talk at various tuition centres, students mostly ask me the difference between A-level vs IB. I’ll simply share my opinions on Mathematics.

### Difference between A-level Math and IB Math

For A-level, there are two categories namely H1 and H2. Content wise, H1 is 50% of H2. H1 students sit for a 3H paper while H2 students sit for two sets of 3H paper. Students without A’Math background will be more comfortable with H1, though I do have a few students doing H2 without A’math background; they really shed blood and sweat for their A. H2 is definitely more helpful with your university transition. The sad truth is that Math is quite hard to avoid in University.

For IB, there are three categories namely, Math Studies (MS), Standard level (SL) & Higher level (HL). They are of increasing difficulty as their name suggests.

My favourite way of explaining their difference is that A-level is deeper and more narrower while IB is wider but less deep. It will be unfair to compare HL to H2 as they are exposed to different amounts of content. Students should google the content and see if the topics interest them. Pre-University education needs sufficient amount of interest to excel, and as 17 years old, they should be learn to take the responsibility of such decisions.

### Vectors: to draw or not to draw?

When I teach vectors, I notice how students love to draw the diagrams of their own diagrams and then depend on them to solve question.

Firstly, there is nothing wrong with drawing. But I always remind my students to take their image with a pinch of salt. Why? Cos you’re attempting to draw a 3-D diagram on a 2-D space! Half the time, you probably overlook some minor description

Next, the diagrams have no marks. Examiners don’t mark your diagrams so is it worth to spend 10mins drawing out something nice.

So what do we do then? I always advice my students, ask my a piece of foolscap paper and start folding if you need planes, then poke your pen through if you need a line. I had a student bringing in satay stick for A-level haha. He looked funny in exam, but he got his A.

Even better, try visualising it!

The above contains all permutations of 3 planes interactions and their results. Hope it helps. For more tricks on dealing with vectors questions, contact KS @ 98156827 or check out my Math class schedule.

### Scary complex numbers

Many JC1 heard fearsome tales of Complex number from their seniors. But how scary is it? Is this imaginary thing so bad.

Having taught so many batches of students, many fear complex numbers as it seem to be out of the comfort zone. After all, the secondary and primary school teachers used to say the you can never square root a negative number, so what is the deal with complex number.

Firstly, complex numbers allow us to explore more dimensions and possibility. But this is probably talk for the advanced. I’ll discuss how to overcome this fear. Complex numbers is algebra, with the introduction of an addition constant, $i$. There isn’t much to fear. Techniques like rationalising, completing the square, substitution of simultaneous equations will come into good use.

I notice that once students overcome that fear and treat it as a simple algebra topic, they have not much problems handling the topic. You can always set up consultations with me!

### Why is 0! = 1?

This question is probably very baffling to several students. Many students will exclaim $0!=0$ to me, but this is incorrect. To understand why $0!=1$, we need to first look at what $n!$ means; $n!$ is the number of ways to arrange $n$ objects in a row. And we all know that $n!=1 \times 2 \times 3 \ ... \times n$. So shouldn’t $0!=0$?

Think about this, the number of ways to arrange 1 object is 1, that is, put the object there by itself. However, the number of ways to arrange $0$ object is one! Cos there is nothing to arrange so we still have one way to do it.

Give it some thought and feel free to discuss with me!

Related video by Dr James Grime

### Importance of Prelims

Many students have the mentality that now they are in JC2, what matters is just how you do in A-levels since its what you get into University. I thought I should share some pros of doing well in Prelims.

Firstly, doing well in prelims allow students to obtain early admission into universities. I know a handful of students getting placements prior to receiving results.

Secondly, students that are aiming for scholarships, your teachers’ testimonials are very crucial to your application. And doing well in prelims, usually allows you to receive good testimonials from them.

Lastly, who doesn’t want some confidence booster going to A-levels!

If you’re having problems getting ready for A-levels, consider getting help soon! The 20H Crash Course information can be found here!