O-LevelAdditional MathematicsCircular measure4037/12 · May/June 2017 · Q1011 Marks

The diagram shows a circle, centre O, radius 8 cm. The points A, B, C and D lie on the circumference of the circle such that AB is parallel to DC. The length of the arc AD is 4 cm and the length of the chord AB is 15 cm. [Figure 10.1 - A circle with center O and radius 8 cm. Points A, B, C, D are on the circumference. Chord AB is near the top, chord DC is near the bottom, and they are parallel. Arc AD is on the left side, arc BC on the right side. The region between the two parallel chords is shaded.]

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Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[B1] 0.5
[M1] use of cosine rule (or equivalent) to obtain angle AOB.
[M1] use of angle AOD and symmetry
[A1] Answer Given: need to have seen either 2.431 or better, or 1.431 or better in previous calculations
[M1] use of cosine rule or basic trigonometry to obtain DC
[A1] awrt 10.5, may be implied
[A1] awrt 33.5
[B1] area of one appropriate sector; allow unsimplified; may be implied by a correct segment
[B1] an appropriate segment, allow unsimplified
[B1] attempt at trapezium, must have a correct attempt at finding the distance between the parallel sides – allow unsimplified
[B1] final answer 42.8

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