# Maximum and minimum area

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## Lesson details

### Key learning points

- In this lesson, we will explore how we can use quadratic graphs to solve maximum and minimum problems.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 5 Questions

Q1.

Select the word that best fills in the gap: Sometimes ___________ can be used to model situations.

expanding

factorisation

mathematical contexts

Q2.

"I think of two numbers with a difference of 3 and multiply them together." Which expression bests represents the statement?

3x

3x + 3

x - 3

Q3.

A square is cut out of the rectangle. Give an expression for the area.

Option 1

Option 3

Option 4

Q4.

A square is cut out of the rectangle. What is the maximum area?

60 cm²

62 cm²

80 cm²

Q5.

A square is cut out of the rectangle. What is the minimum area?

0 cm²

16 cm²

4 cm²

64 cm²

### 6 Questions

Q1.

The length and width of a rectangle add to 4cm. Stacey thinks only 2 different rectangles are possible. Do you agree?

No, Stacey is incorrect, there is only 1 possible rectangle.

Yes, Stacey is correct.

Q2.

A rectangle's length is 2cm greater than its width. Which expression gives the area?

2x + 4

2x cm²

x² + 2

Q3.

A triangle's height is 4 times greater than its base. Which expression gives the area?

4x²

5x

5x²

Q4.

The length and width of a rectangle add to 14 cm. Which expression gives the area?

14 - x²

14x - 4x²

14x²

Q5.

The length and width of a rectangle add to 14 cm. What is the largest possible area?

14 cm²

196 cm²

40 cm²

56 cm²

Q6.

A triangle has a base and height that sum to 20cm. What is the upper bound of the triangle's area?

10 cm²

100 cm²

There is not an upper bound.