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O-LevelAdditional MathematicsStraight line graphs4037/12 · Oct/Nov 2012 · Q78 Marks

Solutions to this question by accurate drawing will not be accepted. [Figure 7.1] The vertices of the trapezium ABCD are the points A(−5, 4), B(8, 4), C(6, 8) and D. The line AB is parallel to the line DC. The lines AD and BC are extended to meet at E and angle AEB = 90°.

  1. (i)Find the coordinates of D and of E.[6]
  2. (ii)Find the area of the trapezium ABCD.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [M1] M1 for attempt to obtain the equation of BC, BE, EC, (gives y = 20 – 2x)
  2. [M1] M1 for attempt to obtain the equation of AD, AE, (gives 2y = x + 13)
  3. [B1, A1] B1 for y = 8, allow anywhere A1 for x = 3
  4. [M1] M1 for attempt at the point of intersection of BE with AD, not dependent.
  5. [A1] A1 for both
  6. [M1] M1 for a correct attempt at the area – allow odd arithmetic slip
  7. [A1]

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About this question

Topic
Straight line graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2012 Paper 1 Variant 2, question 7.

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