O-LevelMathematicsGeometry4024/21 · Oct/Nov 2024 · Q910 Marks
ABD is a triangle. C is a point on BD and E is a point on AD. AB is parallel to EC and CD = DE. Find the value of x and the value of y. [Figure showing triangle ABD with line EC parallel to AB, and angles 54°, 28°, x°, y°]
- (a)ABD is a triangle. C is a point on BD and E is a point on AD. AB is parallel to EC and CD = DE. Find the value of x and the value of y. [Figure showing triangle ABD with line EC parallel to AB, and angles 54°, 28°, x°, y°][4]
- (b)PQR is a triangle. P and R are points on a circle, centre O. O is a point on PQ. QR is a tangent to the circle at R. QR = 12 cm and angle RPQ = 35°. Calculate the area of triangle PQR. [Figure showing a circle with points P, R on circumference, O on PQ, and tangent QR][6]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [4] B2 [x =] 98
- [4] B2 [y =] 72
- [4] B1 for ∠ABE = 28 or ∠AEC = 126 or M1 for 180-54-28 oe
- [4] B1 for ∠CED = 54 or ∠ECD = 54 or ∠CED = 180-28 – their x oe
- [6] B1 for ∠ORQ = 90 soi
- [6] B1 for ∠OQR = 20 or ∠ROQ = 70
- [6] M2 for [radius =] 12 / tan(their 70) oe
- [6] or [6] M1 for tan(their 20) = R/12 oe
- [6] M1 for 1/2 × PQ × QR × sin(∠PQR)
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