Foundation November 2024 Paper 2 Q26
26 The diagram shows triangle \(ABC\).
In the diagram, all measurements are in centimetres.
\(AC = BC\)
The perimeter of the triangle is 72 cm.
Work out the area of the triangle. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 240 | P1 | for forming an appropriate equation, eg \(2x + 11 = 4x - 4\) or \(2x + 11 + 4x - 4 + 2x + 5 = 72\) or \(8x + 12 = 72\) |
| P1 | (dep P1) for process to correctly isolate terms in \(x\), eg \(4x - 2x = 11 + 4\) or \(2x + 4x + 2x = 72 - 11 + 4 - 5\) or \(x = 7.5\) oe | |
| P1 | for correct application of Pythagoras, eg \((\text{``}26\text{''})^2 - \left(\dfrac{\text{``}20\text{''}}{2}\right)^2\) or \([AC]^2 - \left(\dfrac{[AB]}{2}\right)^2\) or height = 24 or a complete method to find the height or for a correct trig statement to find \(CAB\) or \(CBA\) or \(ACB\), eg \(\cos CAB = \cos CBA = \dfrac{\text{``}20\text{''} \div 2}{\text{``}26\text{''}}\) or \(\cos CAB = \cos CBA = \dfrac{20^2 + 26^2 - 26^2}{2 \times 20 \times 26}\) or \(\cos ACB = \dfrac{26^2 + 26^2 - 20^2}{2 \times 26 \times 26}\) or \(CAB = 67.3\ldots\) or \(CBA = 67.3\ldots\) or \(ACB = 45.2\ldots\) | |
| P1 | for process to find area of triangle, eg \(\text{``}20\text{''} \times \text{``}24\text{''} \div 2\) or \([AB] \times [\text{height}] \div 2\) or for process to find area of triangle, eg \(\dfrac{1}{2} \times \text{``}26\text{''} \times \text{``}20\text{''} \times \sin \text{``}67.3\ldots\text{''}\) or \(\dfrac{1}{2} \times \text{``}26\text{''} \times \text{``}26\text{''} \times \sin \text{``}45.2\ldots\text{''}\) or \(\dfrac{1}{2} \times [AB] \times [AC] \times \sin [BAC]\) or \(\dfrac{1}{2} \times [BC] \times [AC] \times \sin [ACB]\) | |
| A1 | cao |
Additional guidance
\(8x = 60\) or \(2x = 15\) implies P2
A correct length stated or shown on diagram implies P2,
eg \(AB = 20\), \(AC = 26\), \(CB = 26\)
\([AC]\) \([BC]\) \([AB]\) \([ACB]\) \([CAB]\) and \([BAC]\) must be clearly identified if incorrect. May be on diagram.
\(AB = 2 \times \text{``}7.5\text{''} + 5\ (= 20)\)
\(AC = 2 \times \text{``}7.5\text{''} + 11\ (= 26)\)
\(CB = 4 \times \text{``}7.5\text{''} - 4\ (= 26)\)
Alternative scheme not expected on Foundation tier but may be seen.
ft incorrect figures providing at least one previous P1 awarded.
[height] is what they clearly think is the height of the triangle but not 26 or 20 or 10