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4024/12 Oct/Nov 2021, Question 11: Locus

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Using the scale drawing of a garden with trees P and Q at 1 cm to 6 m, construct a path equidistant from P and Q, then shade regions for a third tree nearer Q than P and over 18 m from Q.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

With straight edge and compasses only, construct the locus of points equidistant from P and Q on the scale drawing.

  1. 1Compasses at P, radius more than half of PQ: draw arcs above and below PQ
  2. 2Same radius from Q: arcs cross the first arcs at two points
  3. 3Rule a line through the two crossing points: the perpendicular bisector of PQ is the path

AnswerAcceptable perpendicular bisector of PQ with correct arcs

Part (b) · 3 marks

Shade the region inside the garden that is closer to Q than P and more than 18 m from Q.

  1. 118 m ÷ 6 = 3 cm on the drawing
  2. 2Draw an arc, centre Q, radius 3 cm, reaching the sides of the garden
  3. 3Nearer to Q: the side of the bisector containing Q
  4. 4Shade the parts on Q's side of the bisector that are outside the 3 cm arc and inside the garden

AnswerCorrect shaded regions

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Also searched as: 4024/12/O/N/21 · 4024_w21_qp_12 · 4024 w21 12 · question 11.
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