# Author Archives: Ai Ling Ong

### 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:

### A-Maths: Differentiation Application - Stationary Value [Video]

I received this question on finding minimum gradient of a curve and it is confusing for many students as they probably lack the flexibility in seeing gradient beyond dy/dx.

I have presented this question in a slightly different manner by reducing the usage of  first derivative (dy/dx) and second derivative (d^2y/dx^2).

Check the 3 minutes video by clicking on the video to find out the step-by-step solutions and the explanations.

Video URL: https://youtu.be/K5-LaQUXo94