Maths Extension 1 Year 11 - Module 2 - Lesson 14

Applications of Polynomials

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

Applications of polynomials. Translate dimensions or constraints into polynomial expressions, then retain only values that make every physical dimension valid.

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. An open box is made by cutting squares of side x from a 20 cm by 14 cm sheet. Write its volume.

2. State the physically valid domain for x in that box model.

3. Find the volume when x=2 cm.

3. Challenge

Expand the box volume polynomial.

4. Multiple choice

A cut-out square of side x leaves which box height?

A. 2x

B. x

C. 14−2x

D. 20−x

Worked answer key

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

1. An open box is made by cutting squares of side x from a 20 cm by 14 cm sheet. Write its volume.

Base dimensions are 20−2x and 14−2x, height x; V(x)=x(20−2x)(14−2x) cm³.

2. State the physically valid domain for x in that box model.

x>0 and 14−2x>0, so 0<x<7.

3. Find the volume when x=2 cm.

V(2)=2(16)(10)=320 cm³.

Challenge. Expand the box volume polynomial.

V=x(280−68x+4x²)=4x³−68x²+280x.

Multiple choice. A cut-out square of side x leaves which box height?

Correct answer: B. The cut square folds upward, so its side length x becomes the box height.

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