Specimen 2020 Paper 2 Q12
12 This shape is made from two rectangles.
All dimensions are in centimetres.
Not drawn accurately
(a) The perimeter of the shape is 252 cm
Show that \(\quad y = 126 - 45x\) [2 marks]
(b) The area of the shape is \(A\) cm\(^2\)
Show that \(\quad A = 2520x - 450x^2\) [2 marks]
(c) Use differentiation to work out the maximum value of \(A\) as \(x\) varies. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(30x + 20x + 15x + 10x + 15x + y + y = 252\) or \(90x + 2y = 252\) | M1 | oe |
| \(y = \dfrac{252 - 90x}{2}\) and \(y = 126 - 45x\) | A1 | must see working for M1 |
| Answer | Mark | Comments |
|---|---|---|
| \(30x \times 15x + 20x \times (126 - 45x)\) or \(15x \times 10x + 20x \times (126 - 45x + 15x)\) or \(15x \times 10x + 20x \times (126 - 30x)\) | M1 | oe |
| \(450x^2 + 2520x - 900x^2 = 2520x - 450x^2\) or \(150x^2 + 2520x - 900x^2 + 300x^2\) \(= 2520x - 450x^2\) or \(150x^2 + 2520x - 600x^2 = 2520x - 450x^2\) | A1 | must see correct expansion of brackets |
| Answer | Mark | Comments |
|---|---|---|
| \(2520 - 900x\) | M1 | |
| their \((2520 - 900x) = 0\) or \(x = 2.8\) | M1dep | oe |
| 3528 | A1 |