4MA0 Foundation June 2015 Paper 1R Q21
21 The diagram shows a right-angled triangle and a rectangle.
Diagram NOT accurately drawn
The area of the triangle is twice the area of the rectangle.
(i) Write down an equation for \(x\).
(ii) Find the area of the rectangle.
Show clear algebraic working.
Show clear algebraic working.
(7)
| Scheme | Marks |
|---|---|
| M1 | |
| eg. \(9(8x + 4) = 28(10 - x)\) | A1 |
| (2) |
Notes
M1: for \(0.5 \times 9 \times (8x + 4)\) oe or \(7 \times (10 - x)\) oe (may be seen as part of an equation)
A1: for any correct equation
| Scheme | Marks |
|---|---|
| \(36x + 18 = 140 - 14x\) | M1 |
| \(50x = 122\) | M1 |
| \(x = 2.44\) or \(\dfrac{61}{25}\) oe | A1 |
| 7 × (10 – “2.44”) | M1 |
| 52.92 | A1 |
| (5) | |
| Total 7 marks |
Notes
M1: Correct removal of either bracket in an equation (ft providing equation is of form \(a(x + b) = c(x + d)\))
NB: This mark can be implied
M1: dep ft for getting to \(mx = k\) oe
A1: ft (at least 3 sig figs or a fraction)
M1: ft their value substituted (must be positive)
A1: cao
NB: Working for part (ii) may be seen in part (i)