Foundation June 2017 Paper 1 Q13
13.
(a)
The area of a rectangle is \(100\,\text{cm}^2\).
The length of the rectangle is 4 times its width.
Work out the width of this rectangle. [2]
(b)
A square has sides of length \(x\) cm.
The length of a rectangle is equal to the perimeter of this square.
The perimeter of this rectangle is \(14x\) cm.
Find an expression for the width of this rectangle.
Give your answer in terms of \(x\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| Correctly evaluated trial(s) using the product(s) of a pair of numbers where one is 4 times the other and comparing to 100 eg stating 4 × 16 = 64 and 64 < 100 or stating 5 × 20 = 100 or 100 ÷ 5 = 20 as final answer or with final answer 5 or 20 or Trial(s) using the product(s) of factors of 100 and comparing/testing the factors to check if one is 4 times the other eg stating 50 × 2 and 2 × 4 \(\neq\) 50 or stating 5 × 20 and 5 × 4 = 20 or stating 100 ÷ 5 = 20 and 20 ÷ 4 = 5 | M1 | or for at least two calculations of the form \(w \times 4w\) or for \(w \times 4w = 100\) Allow eg a rectangle with 20 and 5 marked as dimensions but 20 given as the answer to imply M1 |
| 5 (cm) | A1 | CAO; implies M1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(3x\) (cm) | B2 | B1 for \(14x - 4x - 4x\) (\(= 6x\)) or for ‘their \(6x\)’ ÷ 2 or for a rectangle with the correct dimensions marked |
| (4) |