Maths Extension 1 Year 11 - Module 4 - Lesson 11

Applications of the Binomial Theorem

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name

Date

Class

1. Lesson focus

Binomial theorem applications. Choose a term by its exponent, use a nearby binomial expansion for approximations, and track the domain/sign in numerical applications.

Success criteria

Apply the lesson method accurately in a routine example.
Show each algebraic or domain step and check the result.
Explain why the method and restrictions fit the question.

2. Worked practice

1. Find the coefficient of x² in (1−2x)^5.

2. Use the first three terms of (1+x)^6 to approximate 1.01^6.

3. Find the coefficient of x³ in (2+x)^5.

3. Challenge

Use the first four terms of (1+x)^5 to estimate 0.98^5.

4. Multiple choice

The coefficient of x² in (1−3x)^4 is?

A. −54

B. 36

C. −36

D. 54

Worked answer key

Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.

1. Find the coefficient of x² in (1−2x)^5.

r=2: 5C2(−2)²=10·4=40.

2. Use the first three terms of (1+x)^6 to approximate 1.01^6.

With x=0.01: 1+6(0.01)+15(0.01)²=1.0615 (truncated approximation).

3. Find the coefficient of x³ in (2+x)^5.

Choose x³: 5C3·2²=10·4=40.

Challenge. Use the first four terms of (1+x)^5 to estimate 0.98^5.

Set x=−0.02: 1+5x+10x²+10x³=1−0.1+0.004−0.00008=0.90392.

Multiple choice. The coefficient of x² in (1−3x)^4 is?

Correct answer: D. Choose r=2: 4C2(−3)²=6·9=54.

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