Higher June 2025 Paper 3 Q24
24 Triangles \(ABC\) and \(DEF\) are similar.
Not drawn accurately
The area of \(ABC\) is 26.355 cm\(^2\)
Work out the area of \(DEF\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(0.5 \times 6 \times x \times \sin 127 = 26.355\) or \(26.355 \div 6 \div \sin 127 \times 2\) or \(26.355 \div 6 \div [0.7986, 0.8] \times 2\) or [10.98, 11.001] | M1 | length BC oe any letter |
| their \([10.98, 11.001] \div 4.4\) or [2.495, 2.50023] or \(4.4 \div\) their [10.98, 11.001] or [0.39996, 0.40073] | M1dep | length scale factor oe implied by [2.3997, 2.405] for length of DF |
| \(6 \div\) their [2.495, 2.50023] or \(6 \times\) their [0.39996, 0.40073] or [2.3997, 2.405] and \(0.5 \times 4.4 \times\) their [2.3997, 2.405] \(\times \sin 127\) or \(0.5 \times 4.4 \times\) their [2.3997, 2.405] \(\times\) [0.7986, 0.8] or \(26.355 \div (\text{their } [2.495, 2.50023])^2\) or \(26.355 \times (\text{their } [0.39996, 0.40073])^2\) | M1dep | length DF and area oe area ratio and area \(26.355 \div \dfrac{[10.98, 11.001]^2}{4.4^2}\) or \(26.355 \times \dfrac{4.4^2}{[10.98, 11.001]^2}\) scores M3 |
| [4.2, 4.234] | A1 | SC2 [16.8, 16.94] |
Additional guidance
SC2 is for omitting the 0.5 in the area formula