There comes the time when Mathematics is more alphabets than numbers, more Greek than English, and more comprehension than counting. Once when I was revising for my H2 Mathematics Common Test earlier this year, I encountered a question which goes like this:
[HCI 2018/BT1/Q4]
(ii) Find the first three non-zero terms in the Maclaurin series for ecx sin dx, where c and d are non-zero real numbers.
*taken from 2021 C1/2022 C2 H2 HCI Lecture Notes, Chapter 8: Maclaurin Series
I felt like I was playing Scrabble. But the notoriety of Mathematics questions does not stop there. Here’s another example, which left me more confused than ever:
[SRJC 2015/BT2/P1/Q10]
Five hundred litres of salt solution is kept in a huge tank.
A man turns on a tap to allow salt solution containing 250 g of salt per litre of water to be poured into this tank at a rate of 4 litres/min. At the same time…
[omitted]
*taken from 2021 C1/2022 C2 H2 HCI Lecture Notes, Chapter 9: Differential Equations
What’s this, GP comprehension? In the end, I opted to stare blankly at the question and gave up (though, I did come back to it later on).
This is the reality of the Mathematics we are studying. In a way, we are being tested, aside from what is constituted in the syllabus, our linguistic skills and ability to not be confused when being flooded with the constant stream of constants a, b, c, k, m, n, x, y, and z and their capital counterparts.
After all this talk about the woes of Mathematics, this might be the part where you are most interested in: how to study and do well in Mathematics. In this article, I will share some tips on how to channel your inner Pythagoras and Pascal in Hwa Chong.
1 Power of the answer key
There is no point in lingering on a practice question for hours. Rather, I would suggest referring to the answer key immediately after struggling for quite a long while. Sounds like heresy, right?
However, remember this: as much as you want to solve that particular question with your own effort, time is of the essence. Yes, in exam conditions, there will be no answer key to accompany you, and yes, many teachers will vehemently disagree with me. But isn’t it better to analyze and understand the answer key instead of wasting time pining for a question? The opportunity cost of time trying to solve the question is really not worth it, when the time you spent can be used to revise other materials.
Imagine you have been stuck in solving a particular question for, say, half an hour, this is the course of action you should take:
Open the Math Google site and access the answer key (if it is already released).
Skim through the document. Take note of the relevant mathematical concepts required for the question. Read through, if any, the teacher’s comments.
Do NOT copy the answer. Move on to other questions first.
Come back to the question, and try solving it without referring to the answer key.
If you are still not able to solve the question, repeat steps 1 to 4 until you are able to do so.
Mark this question with, for example, an asterisk. This allows you to pay more attention to this question the next time you revise.
In an event that the answer key has not been released yet, fret not––your tutors will guide you. Leave the question blank, then ask away in class.
2 Mugging makes better
When you have done something a hundred times, you would be more experienced in it. This applies to studies as well. As you do more practice questions, you will be more acclimated to typical exam questions and their requirements. Mugging makes, though not perfect, better.
In each of our Mathematics lecture notes, there is a ‘supplementary exercise’ segment. Questions from this segment come from past school-based and official tests (A levels), which are suited to hone your skills for an exam. I suggest you do them close to the date of ungraded tests (e.g. Common Test).
Revision packages are also given before major exams (e.g. Promotional Exams). In them, there are tables of summary listing skill sets needed to answer various question archetypes that are helpful during revision. There are also (many) questions, similar to the supplementary questions, which you can do. But don’t be too ambitious to go through every question in this package; try out just a handful from each topic. The most important thing is, after all, your basics. You should spend more time constructing a firm foundation, lest you crumble from the slightest tremors.
During your revision period, below shows the resources you can look into, in order of importance:
Lecture exercises to consolidate your basic understanding.
Summaries from revision packages to be fully aware of the skill sets needed.
Tutorial questions to explore how you can solve problems.
Supplementary and revision package questions to get used to typical exam questions and their requirements.
At the very least, you should look through items 1 to 3 in the list above if you don’t have much time for revision. Also, remember to apply what I have discussed in the first section when attempting questions.
3 Don’t fight the question
Words of questions are absolute. All questions have a set of conditions and command words we need to heed in order to obtain the full marks assigned to them. If a question dictates to use X to find Y, then you MUST use X to find Y. Simple as that. In this question below, a specific condition for answering the question is given:
[HCI 2022/C2 CT1/Q2]
(i) Using a suitable scalar product, find the value of a.b.
[3]
In this situation, you can only derive the value of a.b using a ‘suitable scalar product’. Any other way would not yield you marks.
Another common condition is ‘hence’. It is illustrated below:
Find the total number of terms in the first n sets.
(i) Hence find the sum of numbers in the first n sets.
*taken from 2021 C1/2022 C2 H2 HCI Lecture Notes, Chapter 1: Series and Sequences
Here, your answer for the first question must appear in your attempts to derive the answer for (i).
There are many other conditions which you will get more used to as you attempt more questions. In any case, always scrutinize the questions for any specific conditions that they require. You can underline important parts of the question so that you constantly take note of it.
Written by: Warren Tanaka (21S70)
Edited by: Uyen Tran (21A15)
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