The diagram shows two circles with equal radii. A, E and C are points on the circle, centre B. B, E, D and F are points on the circle, centre C. ABCD is a straight line. [Figure of two overlapping circles]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

1. [3] (a)(i) EC = BE or AC = FE and ∠AEC = ∠FBE or ∠ECA = ∠BEF Two correct reasons for their choices
2. [3] (a)(i) B1 B1 B1 Statements and reasons: EC = BE; radii AC = FE; diameters ∠AEC = ∠FBE [= 90°]; angle in semicircle ∠ECA = ∠BEF [= 60°]; equilateral triangle Third statement, leading to correct congruence condition i.e. RHS, SAS, SSA
3. [1] (a)(ii) BFD
4. [2] (a)(iii) ∠EBF = ∠DFB = 90° Cointerior/interior/supplementary/allied angles [sum to 180]
5. [2] (a)(iii) 1 Both 90° could be marked on diagram 1dep
6. [2] (a)(iii) OR ∠BEF = ∠EFD = 60° Alternate angles [are equal]
7. [2] (a)(iii) OR 1 Both 60° could be marked on diagram 1dep
8. [1] (a)(iv) 120°
9. [1] (a)(iv) 120° could be marked on diagram
10. [2] (b)(i) 6.126 to 6.13
11. [2] (b)(i) M1 for 1/2 × 4 × 4 × sin 130 Or 1/2 PQ x perpendicular height (numerical)
12. [3] (b)(ii) 38.2 to 38.3
13. [3] (b)(ii) M1 for ((360-130) / 360) × π × 4² soi by 32.11 or (130 / 360) × π × 4² soi by 18.15 And M1 for 'their major sector area' + 'their triangle area' Or for 'their circle area' - 'their minor sector area' + 'their triangle area'