O-LevelMathematicsGeometry4024/21 · May/June 2021 · Q89 Marks
P, Q and R are points on the circumference of a circle, centre O. Angle POQ = 8x°, angle RPO = x° and angle OQR = 24°. Calculate angle PQO. [Figure 8.1]
- (a)P, Q and R are points on the circumference of a circle, centre O. Angle POQ = 8x°, angle RPO = x° and angle OQR = 24°. Calculate angle PQO. [Figure 8.1][4]
- (b)Triangle KLM is similar to triangle KNJ. JKM and NKL are straight lines. KÎM = KNJ_and LKM = y°. KL = 6cm, KM = 10.5 cm and KN = 10cm. The area of triangle JKN is 75 cm². Calculate y. [Figure 8.2][5]
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Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [4] 58°
- [4] B2 for x=8
- [4] or B1 for PRQ = 4x or for PÔR = 180-2x
- [4] M1 for a correct equation involving PQO
- [5] 58.99... to 59[.0]
- [5] B2 for JK = 17.5
- [5] or M1 for 6/10 = 10.5/JK oe
- [5] M2 for sin y = 75/(0.5×10×their 17.5) oe
- [5] or M1 for 0.5 × 10 × their 17.5 × sin y = 75 oe
- [5] Alternative: B2 for area MKL = 27
- [5] or M1 for (6/10)² or (6/10)²
- [5] M2 for sin y = (75×their (6/10)²)/(0.5×6×10.5) oe
- [5] or M1 for 0.5 × 6 × 10.5 × sin y = 75 × their (6/10)² oe
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