O-LevelMathematicsGeometry4024/21 · May/June 2022 · Q67 Marks
The diagram shows a field, ABCD, drawn to a scale of 1 cm to 50 m. [Figure showing irregular quadrilateral ABCD]
- (a)The field has a straight path from D to the midpoint of AB. Draw the path and measure the angle the path makes with DC.[2]
- (b)Grass is to be planted on an area of the field. The area to be planted is to be • less than 325 m from B • nearer to CB than CD and • can only be on one side of the path. By drawing appropriate loci, find and shade the largest possible area for the grass to be planted.[4]
- (c)Find the actual length of the part of the path that forms a boundary for the grass.[1]
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 (May/June 2022). The mark or mark type is shown in brackets.
- [2] 44 to 48 with correct ruled line drawn
- B1 for correct ruled line drawn or their angle measured from a ruled line from D to AB.
- [4] Arc 6.5 cm centre B, angle bisector of angle BCD and correct region shaded
- FT their path from D to AB
- B1 for angle bisector of angle BCD
- B2 for arc 6.5 cm centre B or B1 for arc centre B
- [1] 130 to 150 nfww
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