4MA0 Higher June 2013 Paper 3 Q5
5
Diagram NOT accurately drawn
The shape in the diagram is made from a rectangle and a right-angled triangle.
The diagram shows, in terms of \(x\) and \(y\), the lengths, in centimetres, of the sides of the rectangle and of the triangle.
The perimeter, \(P\) cm, of the shape is given by the formula
\[P = 12x + 2y\](a) Work out the value of \(x\) when \(P = 43\) and \(y = 6.5\) (3)
(b) Find, in terms of \(x\) and \(y\), a formula for the area, \(A\) cm2, of the shape.
Give your answer as simply as possible. (2)
Give your answer as simply as possible. (2)
| Scheme | Marks |
|---|---|
| \(43 = 12x + 2 \times 6.5\) or \(43 = 12x + 13\) or \(P - 2y = 12x\) (oe with \(\pm 12x\) or \(\pm x\) as the subject) | M1 |
| \(12x = 43 - 13\) or \(12x = 30\) or \(-12x = 13 - 43\) or \(-12x = -30\) | M1 |
| 2.5 oe | A1 |
| (3) |
Notes
M1: for correct rearrangement of original equation or substitution
M1: for correct rearrangement and substitution
A1: Correct answer scores full marks
M2 for 43 − 2×6.5 (= \(12x\)) or 30 (=\(12x\))
| Scheme | Marks |
|---|---|
\(4xy + \dfrac{1}{2} \times 3x \times 4x\) or \(\dfrac{3x + y + y}{2} \times 4x\) | M1 |
| \(4xy + 6x^2\) etc | A1 |
| (2) |
Notes
M1: for any one correct area
eg \(4xy\) oe or \(\dfrac{1}{2} \times 3x \times 4x\) oe or \(4x(3x + y)\)
A1: for \(4xy + 6x^2\) or \(4yx + 6x^2\) or \(2x(3x + 2y)\) or \(2(3x^2 + 2xy)\) or \(x(6x + 4y)\) (No fractions or uncollected terms but could be multiplication signs and/or brackets present)