Higher November 2023 Paper 1 Q8
8 In the diagrams, all lengths are in centimetres.
Not drawn accurately
The two shapes have equal areas.
Work out \(\quad k : m\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: using algebra | ||
| \(\dfrac{1}{2} \times k \times 12\) or \(6k\) or \(2 \times k + 3 \times m\) or \(2k + 3m\) | M1 | oe correct expression for either area eg \(2(k - 3) + 3(m + 2)\) or \(k(m + 2) - m(k - 3)\) |
| \(\dfrac{1}{2} \times k \times 12 = 2 \times k + 3 \times m\) or \(4k = 3m\) | M1dep | oe equation |
| 3 : 4 | A1 | oe ratio |
| Alternative method 2: substituting a value for \(k\) | ||
| Substitutes a value for \(k\) and gives correct method or value for area of triangle or correct area in \(m\) for L-shape | M1 | eg \(k = 5\) and area of triangle is 30 or \(k = 5\) and area of L-shape is \(10 + 3m\) |
| Correct equation connecting the two areas or correct value of \(m\) for their \(k\) | M1dep | eg \(k = 5\) and \(30 = 10 + 3m\) or \(k = 6\) and \(m = 8\) |
| 3 : 4 | A1 | oe ratio |