#### Tuition Timetable

Check the latest timetable of my tuition classes.

#### Resources

Complete Resources about past year questions are here.

#### Ai Tuition

Visit Ai Tuition Website for more subjects tuition.

VIEW ALL SERVICES

Discussion –

9

Discussion –

9

# STPM 2016 Mathematics (M) Term 1 Assignment

## Introduction

The binomial theorem is a quick way of expanding a binomial expression that is raised to some power. When the binomial expressions are expanded, is there any type of pattern developing which might help us expand more quickly? It is fun to investigate how it works out in a pattern.

## Sample Question

Question 1

(a) Expand  $(a+ b)^n$  for  $n=0, 1, 2, \ldots, 6$.
(b) What observations can we make about the terms in the expansion of  $(a + b)^n$?
(c) Write down the general formula for the binomial expansion of  $(a + b)^n$.
(d) Obtain the general formula for binomial expansion of  $(1 + x)^n$ where $n$ is a rational number, and state the condition for the validity of the binomial expansion with a negative integral exponent or a rational exponent.

Question 2

Deduce the value of

(a)  ${n \choose 0}+{n \choose 1}+{n \choose 2}+\ldots+{n \choose n}$

(b) ${n \choose 0}-{n \choose 1}+{n \choose 2}-\ldots+(-1)^n{n \choose n}$

Question 3

The number $e$ may be defined by $e=\lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n$. Determine the approximate value for $e$.

##### Sample Solution
Scroll down for solution 🙂

## Question 1 (b)

• There are $n+1$ terms in the expansion.
• The first term’s powers start at $n$ and go down.
• The second term’s powers start at 0 and go up.
• The coefficients are from Pascal’s triangle or ${n \choose r}=\frac{n!}{(n-r)!r!}$.

## Question 1 (c)

The general term of the expansion  $(a+b)^n$$(r+1)$-th term is  ${n \choose r}a^{n-r} b^r$.

## Question 1 (d)

In short, $(1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2+\frac{n(n-1)(n-2)}{3!}x^3+\ldots+\frac{n(n-1)(n-2)(n-3)\ldots(n-r+1)}{r!}x^r+\ldots$. And the expansion is valid for  $|x|<1$.

## Question 3

Here are our most recent updates posts

- Feel free to check it out -

## STPM 2021 Term 2 Exam Timetable

View the exam timetable for STPM 2021 Term 2. Countdown to STPM 2021 Examination. Join my tuition to help you achieve better results in the exam. Contact (60) 018-2016992 or kklee@kkleemaths.com for more information.

## Integration of cos^3 x

There are many methods to integrate . 1. Use trigonometric identity Given that  , -Here are our most recent updates posts- Feel free to...

## STPM 2018 Term 3 Mathematics (T) Coursework Sample Answer

STPM 2018 term 3 mathematics (T) Coursework sample Guideline for solving STPM 2018 Term 3 Mathematics (T) PBS coursework assignment methodology   Hint: Binomial Theorem   Chi-Squared tests   tabulate Thanks for helping in doing the survey. You can find...

## STPM 2018 Term 2 Mathematics (T) Coursework Sample Solution

STPM 2018 term 2 mathematics (T) Coursework sample Guideline for solving STPM 2018 Term 2 Mathematics (T) PBS coursework assignment methodology Hint: limits L' Hopital rule Rationalisation Indeterminate Form Existance of limitsThanks the two students who sent me the...

## Integration Booklet Page 10 Page 11 Solution

Here are our most recent updates posts- Feel free to check it out -

## STPM 2018 Term 1 Mathematics (T) Coursework Sample

Question A complex number is an extension of a real number and it can be represented in Cartesian and polar forms. In this assignment, you are required to explore the powers and roots of complex numbers. 1 (a) Let z =1+i. Find z^n, where n = 2, 3, 4, …, and represent...

#### KK LEE

KK LEE has been a STPM Mathematics tuition teacher since June 2006, but his love of Maths dates back to at least 1999 when he was Form 4. KK LEE started teaching in 2006 at Pusat Tuisyen Kasturi. He was known as "LK" when he was teaching in PTK. After teaching STPM Mathematics for 8 years in PTK, he joined Ai Tuition Centre in 2014. Over the years he has taught Mathematics (T), Mathematics (S), Mathematics (M), Additional Mathematics.

1. THX…

2. Sir, can u explain question 2

• To get the equation, you need to substitute x=1 and x=-1

3. hi, may i know how to write the methodology? i have no idea. QAQ

• For methodology, try to write about the methods/theorem/ways you used to solve the questions.

4. sir, may i know how to write about “communication”? and what is “viva”

• It depends on your teacher.

5. How about term 2 methodology?

• Hi. Are you referring to Mathematics (M)? I havent receive the question paper. T.T

This site uses Akismet to reduce spam. Learn how your comment data is processed.

## STPM 2017 Mathematics (M) Term 1 Assignment

Sample solution of STPM 2017 Term 1 Mathematics (M) PBS coursework assignment

## STPM 2017 Mathematics (T) Term 1 Assignment

Sample solution of STPM 2017 Mathematics (T) PBS coursework assignment

## STPM Mathematics (T) Term 3 Assignment

Sample Question of STPM 2016 Term 3 Maths (T) Assignment Coursework