E-Maths

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.

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

$1105 = 5\times 13\times 17$

Step 3: I find the HCF of these two numbers

HCF $=5 \times 17=85cm=0.85m$

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.

mensuration-formula-sheet

2015 GCE O-Level Elementary Maths 4016 Paper 1 (Post Mortem not Solutions)

I have just completed the 2015 GCE O-Level Elementary Maths 4016 Paper 1 and found it to be more applications based.

Some questions are indirect and required more analysis. Some of the questions I enjoyed doing were:

Mode, median and mean
Mean and standard deviation
HCF and LCM
Coordinate geometry linked to vectors
Matrix

Once again, just like last year, there are about 2-3 questions which are 5 marks. (If I remembered correctly)

Based on what were tested, we are logically make some guesses of what we are expecting in Paper 2. The following topics are what I'm suggesting and they are for reference only:

Indices
Proportion
Quadratic equations & graphs (Skill: completing the square)
General shapes of graphs
Everyday Maths (Compound interest, simple interest, hire purchase, exchange rate, taxation, utilities, profit and loss)
Proving of congruency and similarity
Angle & symmetry properties of circles
Trigonometry (sin rule, trigo ratio of obtuse angle, angle of elevation or depression, shortest distance, area of triangle formula)
Vectors
Cumulative frequency (includes frequency table), box & whisker, stem & leaf, dot diagram (Concept on lower quartile, upper quartile)
Kinematics
Mensuration

Regardless of how you think you have fared for Paper 1, continue to work hard for Paper 2 which is 2 days away. Practice daily!

All the best!

O-Level Maths December 2014 Revision Workshops

How will our Year End Revision Workshops benefit your child ?

The Year End Revision Workshops will get your child to gain the momentum and confidence to:

Revise comprehensively on key essential concepts on a topic – by – topic basis.
Gain a better understanding of the topics.
Apply concepts on application examination questions

We know it isn’t easy for students to accomplish all the mentioned by themselves, with distractions from Internet, handphones, TV, friends, going out, no interest in subject, almost totally giving up on the subject…

Basic Essential Concepts Workshop 2013

Here’s what we have to help your child:

Annual Year End Revision Workshops for GCE O-Level Additional + Elementary Mathematics:

Designed into workshops with a focused topic(s) coverage, including key essential concepts, application strategies, relationship linkage, easy-to-remember analogies for understanding abstracts.

Our lessons are delivered in an interactive manner: participants are encouraged to take part in questioning and answering in every workshop. This ensures your child learns effectively within the shortest period of time.

Mole Calculations Revision

How can we be sure that our Year End Revision Workshops will help your child?

She is also the invited book author for the latest GCE O-Level Ten Years Series (2004-2013) for Additional and Elementary Maths, Mentor Series for Secondary 3 and 4 Elementary Maths.
She is also a full-time professional trainer who has over 15+ years of teaching experience.
Ai Ling has also worked with thousands and thousands of students (& parents) from more than 160 schools.
Ai Ling is writer for popular academic website widely read by almost ten thousands of local and international readers every month. She also produces Math videos which are viewed almost 220,000 times.
Proven track record: In 2013, the average O-Level grade for Elementary Maths and Additional Maths is A2!
Ai Ling & his colleague Sean had been invited by CDAC , SINDA and Mendaki to conduct revision programmes and public talks for O-Levels.

O-Level Elementary Maths Ten Years Series Book Topical Ai Ling Ong 300 O-Level Additional Maths Ten Years Series Book Topical Ai Ling Ong 300 Elementary Maths Mentor 3 Cover Elementary Maths Mentor 4 Cover

"I especially enjoyed the functions and graphs workshop as I learnt many different ways to remember the shapes of curves. The workshop allowed me to gain confidence in handling the graph questions in the future. Besides, recaps in basics Trigonometry in E Math also allowed me to be more aware of concepts taught in school that I have get to grasp. I’d recommend anyone who’s unable to cope with studies to join Winners Education. Thank you Ai Ling!" Doreen Gan | Commonwealth Secondary

" The workshop explained challenging concepts in simple ways. Along with examples and a variety of questions that tested our understanding of the topic, this workshop helped me better understand the more complex chapters of math! " Nicholas Lam | St. Gabriel’s Secondary

Schedule for O-Level Revision Workshops

Maths Schedule

2014 GCE O-Level Elementary Maths 4016 Paper 1 (Post Mortem)

After completing this year O-Level E-Maths Paper 1, I personally find that the difficulty level has increased compared to the last 3 years.

I was slightly shocked to see question 1 as a arrangement question.Quite a handful of students commented that there are questions which aren't even Maths questions.

One of the questions is "Questionnaire on how much time does student spoil on Internet". It was probably what the question is asking for which brought some surprises to the candidates.
I found the cuboid, cube and the equal area of rectangles questions well crafted.
The train leaving tunnel was sneaky. It reminded me of PSLE Math.
I like the number pattern question as it has a twist to it. Instead of listing down the first few terms, they skipped some terms. It was very refreshing.
One of the observations I have: 2014 Paper 1 has a few questions which are 3-5 marks for a single part. It seems to deviate from the usual short questions of 1 to 3 marks in the past few years.

Based on what were tested, we are logically make some guesses of what we are expecting in Paper 2. The following topics are what I'm suggesting and they are for reference only:

Standard form
Scales & Maps
Factorisation
Solving simultaneous equations
Solving fractional equations
Inequality
Subject formula
General shapes of graphs
Functions & Graphs
Quadratic equations & Graphs
Distance, speed and acceleration graphs
Construction of bisectors
Congruent & Similar Figures
Angle & Symmetry Properties of circles
Arc length, area of sector and radian measure
Pythagoras’ theorem and Trigonometry
Mensuration
Coordinate Geometry
Mean & SD
Cumulative frequency
Vectors (ratio of areas, magnitude, linked to coordinate geometry)

Regardless of how you think you have fared for Paper 1, continue to work hard for Paper 2 which is 9 days away. Practice daily!

All the best!

Edit: My view on O-Level exam answers as reported in 4 November 2013 TODAY papers.

Source: http://www.todayonline.com/singapore/exam-answer-fever-heats-web

E-Maths: Probability in everyday life

Recently, during the Chinese New Year period, I saw many people queuing up at Singapore Pools. For readers from other countries, Singapore Pools is like a betting station for lottery and sports. It was around the same period in which I was preparing to start teaching Probability to my Secondary 4 Elementary Maths students.

I decided to share with them on the probability of winning a number as a teaser to the topic. I did a poster and shared it on my Facebook. I was humbled by the response - the poster was shared 29 times!

I believe the 'truth of winning' relates well to many people.

Details of a 4D game:

There are a total of 23 winning numbers which consist of 1st, 2nd, 3rd prizes, 10 starter prizes and 10 consolation prizes.
You may choose any 4 digit numbers from 0000 to 9999.
The following poster shows that to win any prize, the chance is a mere 0.23%

How often do we fall into the trap of greed, thinking that we can be lucky one day and win some money? In the end, who is the big winner? I'm sure you have the answer.

Whether you are a parent or student, I hope this blog post has shed some light on winning 4D game through the application of Maths in everyday life.