Year 9

Year 9

# Maximum and minimum area

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## Lesson details

### Key learning points

1. 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.

## Video

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## Worksheet

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## Starter quiz

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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

## Exit quiz

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### 6 Questions

Q1.
The length and width of a rectangle add to 4cm. Stacey thinks only 2 different rectangles are possible. Do you agree?
Correct answer: No, Stacey is incorrect, there are more than 2 different rectangles.
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
Correct answer: x (x + 2)
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