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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.

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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
Correct answer: quadratics
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
Correct answer: x(x+3)
Q3.
A square is cut out of the rectangle. Give an expression for the area.
An image in a quiz
Option 1
Correct answer: Option 2
Option 3
Option 4
Q4.
A square is cut out of the rectangle. What is the maximum area?
An image in a quiz
60 cm²
62 cm²
Correct answer: 64 cm²
80 cm²
Q5.
A square is cut out of the rectangle. What is the minimum area?
An image in a quiz
0 cm²
16 cm²
4 cm²
Correct answer: 48 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?
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?
Correct answer: 2x²
4x²
5x
5x²
Q4.
The length and width of a rectangle add to 14 cm. Which expression gives the area?
14 - x²
14x - 4x²
Correct answer: 14x - x²
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
Correct answer: 49 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
Correct answer: 50 cm²
There is not an upper bound.