Higher June 2025 Paper 1 Q15
15 \(A\), \(C\) and \(D\) are points on a circle, diameter \(AC\).
\(ABC\) is an isosceles triangle with \(AC = BC\)
\(BCD\) is a straight line.
Not drawn accurately
Work out the size of angle \(x\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: from triangle ADC | ||
| \(CAB = 20\) | M1 | |
| \(ACB = 180 - 20 - 20\) or \(ACB = 140\) or \(ACD = 40\) | M1dep | oe |
| \(ADC = 90\) or \(ADB = 90\) | M1 | |
| 50 | A1 | |
| Alternative method 2: from triangle ADB | ||
| \(ADC = 90\) or \(ADB = 90\) | M1 | |
| \(DAB = 180 - 90 - 20\) or \(DAB = 70\) | M1dep | oe |
| \(CAB = 20\) | M1 | |
| 50 | A1 | |
Additional guidance
Angles may be seen on the diagram throughout
For an incomplete method, for angles not marked in the correct position on the diagram the correct 3-letter codes must be given, but condone \(D\) for \(ADC\) or \(ADB\)
\(ADC = 90\) or \(ADB = 90\) may be designated by a square at the angle