June 2025 Paper 2 Q16
16 \(A\), \(B\), \(C\) and \(D\) are points on a circle.
\(EBF\) is a tangent.
Work out the value of \(x\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Correct expression for angle \(BDC\) eg \(\dfrac{1}{2}x + 60\) | M1 | eg \(180 - (x + 20) - [180 - (4x - 15)]\) or \(3x - 35\) may be on the diagram implied by a correct equation |
| Correct expression for angle \(BCD\) or angle \(EBD\) eg \(180 - (4x - 15)\) or \(180 - \left(\dfrac{1}{2}x + 60\right) - (x + 20)\) | M1 | eg \(195 - 4x\) or \(100 - \dfrac{3}{2}x\) may be on the diagram implied by a correct equation |
| Equation from correct geometrical reasoning eg \(\dfrac{1}{2}x + 60 + x + 20 + 180 - (4x - 15) = 180\) | M1dep | eg \(275 - \dfrac{5}{2}x = 180\) dep on M2 |
| 38 | A1 | SC2 two different correct expressions for one of angle \(BDC\) or angle \(BCD\) or angle \(EBD\) SC2 two different correct expressions, one for angle \(BCD\), one for angle \(EBD\) |
Additional guidance
| Up to M2 or SC2 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| A correct expression with no indication of which angle it represents cannot be awarded M marks or SC marks eg \(100 - \dfrac{3}{2}x\) not labelled as angle \(BCD\) or angle \(EBD\) in working or not shown in correct position on diagram (may be implied by a correct equation which will be awarded M3) | 2nd M0 |
| Other equations which are awarded M3 include \(4x - 15 + 100 - \dfrac{3}{2}x = 180\) or \(\dfrac{1}{2}x + 60 + x + 20 = 4x - 15\) or \(180 - (4x - 15) = 180 - \left(\dfrac{1}{2}x + 60\right) - (x + 20)\) or \(195 - 4x = 100 - \dfrac{3}{2}x\) | |
| If an angle is written correctly, ignore any subsequent processing errors (3rd M1 may also be awarded) eg angle \(BDC = \dfrac{1}{2}x + 60\) angle \(BCD = 180 - (4x - 15) = 165 - 4x\) (should be \(195 - 4x\)) \(\dfrac{1}{2}x + 60 + x + 20 + 165 - 4x = 180\) | M1 M1 M1A0 |
| Missing brackets must be recovered | |
| Ignore reasons |