A-Maths Tuition

The Exclamation Mark ! in Binomial Theorem

factorial-sign-binomial Binomial Theorem came out as a 9 marks question in 2009 GCE 'O' Level Additional Mathematics Paper (Subject Code: 4038) so you know as well as I do the importance of Binomial.

Read about other useful posts on Binomial Theorems:

Binomial Expansion Teaches how to choose the RIGHT partner (:

A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method

Exam Question : Usage of Binomial Formula

I'm looking at the question now. It is testing on the usage of the Binomial formula, including the 'n choose r' formula. Many students call this sign: '!' 'exclamation mark' which is known correctly as factorial.

I will be using the following question to illustrate how to simplify the 'n choose r' formula without memorizing. (I understand some schools want students to memorize)

Let's begin by understanding what's 'n choose r' all about:

n-choose-r-binomial — Click on image for larger view

Do you know how to simplify 'n choose 3'?

Here's the question which requires us to apply what we have discussed. I would suggest you attempt it on your own before clicking here for the solution.

Differentiation & Integration Mastery Workshop (Includes Kinematics too!)

Update: Click here for early bird registration.

Dear Students,

Do you know that Differentiation & Integration are 2 very important sections for O Level A-Math? Based on 2008 GCE O Level Additional Mathematics Papers, the weightage of Differentiation & Integration is almost 30%!

We received feedback from students and parents that due to time constraint, many schools rush through these 2 very important topics, leaving many students totally lost in their understanding. This coupled with the fact that Differentiation & Integration are totally new concepts for all A-Math students, made matter worst.
So with less than 7 weeks to GCE O Levels are you equipped with the tools and strategies to score in Differentiation & Integration or are you facing problems in understanding the concepts?

4 Days Differentiation & Integration Mastery Workshop

5, 12, 19, 26 Sep 2009, 2 - 6pm, YMCA Orchard (Tentative venue)

(Click on image for clearer view)

In this workshop, you will learn:

Comprehensive 100% coverage of Differentiation & Integration
Understand abstract concepts in an easy to relate manner
Learn and Apply strategies ('approved' short-cuts) on real examination questions
Time management enforced during every workshop
Pre & Post review assessment for checking level of understanding

Scope of the workshop:
Skills In Differentiation:

Basic Techniques of Differentiation
Differentiation involving trigonometrical functions
Differentiation involving exponential & ln functions

Applications In Differentiation:

Equations of Tangent & Normal
Connected Rate of Changes
Increasing & Decreasing Functions
Maxima & Minima Problems

Skills In Integration:

Basic Techniques of Integration
Integration involving trigonometrical functions
Integration involving exponential & ln functions

Applications In Integration:

Hence question (reversed differentiation)
Equation of curve
Area under the curve
Kinematics

Registration will open on 21st Aug 2009.(Update: Click here for early bird registration.)
This is the last workshop for O level students.

(Click on image for clearer view)

A-Math: Kinematics Step by Step Solution (Strategy To Answer Distance Question Correctly)

In the previous post on the typical questions on Kinematics, I am going to show up the step by step solution to answer a typical Kinematics exam question taken from my A-Math TREQ Book.

Things to take note:

How to get the acceleration equation?
What does it mean by 'momentarily at rest' ?
How to find greatest velocity?
*How to find distance accurately (using a diagram, I called it DD-Diagram; Displacement Distance Diagram)

Every year and in almost every paper, you will be asked to find Distance. The examiners are testing on your understanding of displacement, displacement, momentarily at rest. You must learn how to find it accurately and within the shortest period of time.

Learn from this example well!

(click on the image for a bigger view)

A-Math: Differentiation & Integration Application : Examples of Typical Kinematics Questions

I was looking through 2008 GCE O Level Additional Mathematics Exam Papers (Subject Code: 4038) and as expected, there was a Kinematics question (worth 6 marks) in Paper 1.

Kinematics is a application topic for Differentiation and Integration. To master this topic, you do not necessarily need to bring in your physics knowledge though it could be useful at times.

Instead, how I get my students to be a master in this topic is to be familiarize with a KINEMATICS VOCABULARY LIST.

Here's some of the vocabulary words that are useful and common:

Momentarily at rest, instantaneously at rest, changes direction of motion, stationary
Initial displacement, initial velocity, initial acceleration
Greatest displacement, greatest velocity, greatest acceleration
Distance travelled in the 4th second VS Distance travelled in the first 4 seconds
Maximum distance from Point O
Particle returns to Point O
Constant Velocity

I would say for Kinematics, it is one of the few topics in A-Math which uses extensive vocabulary. This is also the reason for you to decipher the meaning behind these words.

So do you know the meaning behind these words? I would love to hear about it in the comments section.

I have also taken a few questions from my A-Math TREQ book (Topical Real Exam Questions) to illustrate some common exam questions on Kinematics, further highlighting the importance of knowing your Kinematics well. (Click on the image for bigger view)

I would be sharing the step by step solutions for Question 8 in the next post. Subscribe to my blog to be updated again!

O Level A-Math Trigonometry Basics : How Do We Know Which Formula To Use?

For the past month, other than being busy with the June Intensive Revision Programmes, I was also packed with Mid Year Exam Papers Review for my group of students.

I am pleased to announce that almost all see an improvement in their Mid Year Results (One boy has his grades jump from F9 to A2! Congrats, B!)

I was reviewing the school a-Math exam papers with one of my students during my A-Math Ultimate Leap Programme when she posted me a good question.

Let's take a look at her Trigonometry question first:

This was her solution for the question:

There is one misconception in her thoughts, can you spot it?

sin 3x is not equal to sin x + sin 2x!

In fact, the correct formula to choose for this question is

sin 3x = sin (2x + x)

= sin2xcosx + cos2xsinx

Her question was: how do you know which formula to use?

TIP: When the angle involved is ODD, we usually use addition formula (just like in this question).

When angle is EVEN, double angle formula is perhaps the correct one to choose.

Are you confused just like my student, which formula should be use? Leave me a comment.

I hope this post has made your understanding clearer :-)

Below is a list of useful posts on A-Math Trigonometry:

PS: I will be re-running A-Math Trigonometry Mastery Workshop in July as some students miss out the one in June due to other commitments. Registration is open! Click here for more details

Your Questions on O level A/E-Math & Chemistry June Intensive Revision Programme Answered

We thank you for the many email questions regarding our O level A/E-Math & Chemistry June Intensive Revision Programme.

In this video, I have personally answered the following commonly asked questions by students (Secondary 3 & 4 + IP + IGCSE Programme) & parents:

Scope of programme
Benefits of attending our programme
Fees
Proven track record (on the effectiveness of our coaching)

If you can't view this video, please click here to the direct video link:

Leave me a comment below or any other questions you have.

I look forward in making a difference in your child's academic success!