4400 Higher November 2007 Paper 4 Q25
25
Diagram NOT accurately drawn
The diagram shows a shape.
All the corners are right angles.
The area of the shape is 11 cm2.
(a) Show that \(x^2 - 7x + 11 = 0\) (2)
(b) Solve \(y^2 - 7y + 11 = 0\)
Give your solutions correct to 3 significant figures. (3)
Give your solutions correct to 3 significant figures. (3)
(c)
(i) Use your answer to part (b) to find the value of \(x\) in the diagram.
(ii) Give a reason for your answer to (i). (2)
| Scheme | Marks |
|---|---|
| \(3x + x(4 - x) = 11\) or \(4x + x(3 - x) = 11\) or \((4 - x)(3 - x) = 1\) or \(12 - (4 - x)(3 - x) = 11\) | M1 |
| \(3x + 4x - x^2 = 11\) or \(4x + 3x - x^2 = 11\) or \(12 - 4x - 3x + x^2 = 1\) or \(12 - 12 + 4x + 3x - x^2 = 11\) | A1 |
| (2) |
Notes
Award M1 A1 for \(4x + 3x - x^2 = 11\)
| Scheme | Marks |
|---|---|
| \(\dfrac{7 \pm \sqrt{(-7)^2 - 4 \times 11}}{2}\) | M1 |
| \(\dfrac{7 \pm \sqrt{5}}{2}\) | M1 |
| 4.62, 2.38 | A1 |
| (3) |
Notes
M1: for correct substitution
Condone omission of brackets
M1: for correct simplification
A1: for 3 sf or better (4.61803... , 2.38196...)
| Scheme | Marks |
|---|---|
| (i) Answer: 2.38 | B1 |
| (ii) Answer: eg \(x \lt 3\) | B1 |
| (2) | |
| (7 marks) |
Notes
B1: for 2.38 or better