## 2017 GCE O-Level A-Maths Paper 1 Question 3 Linear Law Discussion

I am selecting unique questions from 2017 GCE O-Level Additional Mathematics to discuss in my upcoming videos.

This first one is on linear law.

Basic concepts that you must know are:

• Equation of a line
• Understanding of coordinate system

In this video, I share with you a strategy I teach my student to make linear law easier to understand and reduce careless mistakes to a minimum. I called it "Capital Letter". I use capital letters to represent the complicated horizontal and vertical axes. Even my equation of line is in capital letters too.

Look at my video to understand my thinking process and apply it to yours when it's your turn to solve a linear law question.

This question is interesting as we do not have to draw the graph which is commonly asked in the past.

This question will cause your downfall if you are not absolutely clear on the concepts of linear law.

Get my copy of Ten Year Series in all Popular bookstores!

## E-Maths: Application of Highest Common Factor (HCF) Concept

Many students upon reading this question might not realise that it is testing our understanding of the concept on Highest Common Factor learnt in Secondary 1 Mathematics.

A floor 6.8m width and 11.05m length is to be paved with equal square tiles. Find the number of largest dimension square tiles that exactly fit the floor?

Step 1: I converted the metres into centimetres by multiplying with 100 (1m = 100cm) so that I can work with whole numbers instead of decimals.

6.8m = 680cm 11.05m = 1105cm

Step 2: I express each dimension in index notation by prime factorisation method.

$680=2^{3}\times&space;5\times&space;17$

$1105&space;=&space;5\times&space;13\times&space;17$

Step 3: I find the HCF of these two numbers

HCF $=5&space;\times&space;17=85cm=0.85m$

This means the largest dimension of square tile will be 0.85m by 0.85m

Number of largest dimension square tiles used

$=\frac{6.8}{0.85}\times\frac{11.05}{0.85}$

$=104$

Question of similar nature was asked in the recent year GCE O-Level examination in Paper 1 and many students did not know how to approach the question. I hope you find the explanation clear. It is always recommended to sketch a simple diagram to get your thinking started.

## E-Maths: Mensuration Formula Sheet

I have compiled a 'cheat sheet' to find volume and surface area of
• cube
• cuboid
• prism
• cylinder
• pyramid
• cone
• sphere
This will be a quick summary for all students taking their O-Level examinations and school examinations. This will be useful for E-Maths students as the new syllabus includes a real life application question which can be testing on concepts involving these figures. It will be helpful for A-Maths students as well especially in their Differentiation proving questions. On top of that, A-Level H1/H2 students will benefit from it as well since it could required in their calculus proving questions too.

## A-Maths: Forming a Polynomial Equation, Given its Roots

It is simple to follow the steps of solving a cubic equation which includes finding the linear factor by using calculator and the quadratic factor by long division or comparing coefficient. However, when the question is asked in another manner in which the solutions are given and the polynomial equation is to be formed. Some students might be at a lost of how to start the question. I share with you on how we approach this style of question below:

## The 2 Methods to Solve Exponential Equations

There are two methods to solve exponential equations:
1. Take ln on both sides
2. Substitution
Students must know which method to use when solving an equation. Generally, we take ln on both sides when there is just a single exponential function and we use substitution when there is a common term. Let's take a look at the examples: