June 2024 Paper 1 Q13
13 A garden patio is made from two rectangles.
All lengths are in metres.
The area of the patio is less than 51 m\(^2\)
Work out the range of possible values of \(x\).
Give your answer in the form \(\quad a \lt x \lt b \quad\) where \(a\) and \(b\) are both integers.
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(7x + 8(x - 3)\) | M1 | oe eg \(7 \times 3 + 15(x - 3)\) or \((8 + 7)x - 8 \times 3\) |
| A correct inequality formed for \(x\) | M1dep | eg. \(7x + 8x - 24 \lt 51\) or \(7x + 8(x - 3) \lt 51\) or \(15x \lt 75\) or \(21 + 15x - 45 \lt 51\) |
| \(x \lt 5\) | A1 | |
| \(3 \lt x\ (\lt k)\) | B1 | \(k\) greater than 3 or blank on answer line |
Additional guidance
| \(3 \lt x \lt 5\) with no or incorrect working can only score the B1 | |
| Trial and Improvement: stop marking once this begins (may have scored M2 and may go on to score B1) | |
| Ignore any units stated | |
| Inequalities replaced with \(=\) or other inequalities are penalised unless recovered |