O-LevelMathematicsGeometry4024/11 · Oct/Nov 2015 · Q246 Marks
P, Q, R, S and T are points on the circumference of a circle. PQ = QR. ∠PQR = 118° and ∠QRS = 99°. Find PTS. Show all your working. [Figure of a cyclic pentagon PQRST with chords PQ=QR indicated, angles PQR=118° and QRS=99° shown.]
- (a)Find PTS. Show all your working.[2]
- (b)(i)A, B, C, D and E are points on the circumference of a circle, centre O. AE = ED = DC = CB and AÔB = 60°. Find ECD. Show all your working. [Figure: A circle with center O, points A, B, C, D, E on circumference, chords AE, ED, DC, CB are equal, angle AOB=60 shown.][2]
- (b)(ii)The radius of the circle is 12 cm. Calculate the length of the minor arc AB. Use π = 3.14.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [2] (a) 112°
- [2] B1 for PRQ = 31° ; or for PRS = 68°; or for PTS = 180° – their PRS
- [2] (b) (i) 37.5° WWW
- [2] M1 for EÔD, or other angle at the centre, (360-60) / 4 (= 75°)
- [2] (b) (ii) 12.56
- [2] M1 for 60/360 × 2 × 3.14 × 12 or better
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