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  1. Copyright S-cool

    In the diagram A and B are the midpoints of OC and OD respectively.

    Copyright S-cool

    a) Write down Copyright S-cool in terms of a and b.

    (1 mark)

    b) (i) Write down Copyright S-cool in terms of a.

    (1 mark)

    (ii) Use a vector method to prove that CD is parallel to AB.

    (3 marks)

    (iii) What other conclusions can you make about AB and CD?

    (1 mark)

    E is the midpoint of CD.

    c) Use a vector method to prove that OAEB is a parallelogram.

    (2 marks)

    (Marks available: 8)

    Answer

    Answer outline and marking scheme for question: 1

    a) 2a

    (1 mark)

    b) (i) b - a

    (1 mark)

    (ii) 2b - 2a

    (3 marks)

    (iii) CD is twice as long as AB.

    (2 marks)

    c) AE = AC + ½ CD = b

    (1 mark)

    (Marks available: 8)

  2. Copyright S-cool

    The diagram shows the positions of points A, B, C and D.

    A is due North of C. The straight line BCD is perpendicular to AC.

    A is 12.4 kilometres from B and 8.5 kilometres from C.

    a) Calculate the distance BC.

    (3 marks)

    b) The bearing of D from A is 138°.

    Calculate the distance DC.

    (3 marks)

    (Marks available: 6)

    Answer

    Answer outline and marking scheme for question: 2

    a) 8.9 to 8.94

    (3 marks)

    b) 7.7 to 7.75

    (3 marks)

    (Marks available: 6)

  3. Copyright S-cool

    a) The diagram shows a kite ABCD with measurements in metres.

    BD bisects AC at right angles.

    Calculate the size of angle ABC.

    (4 marks)

    b)

    Copyright S-cool

    PQRS is similar to ABCD.

    PR is of length 1m.

    Calculate the length of the side PS.

    (2 marks)

    (Marks available: 6)

    Answer

    Answer outline and marking scheme for question: 3

    a) 83.6° to 84°

    (4 marks)

    b) 1.125

    (2 marks)

    (Marks available: 6)

  4. O is the centre of a circle through A, B, C and D.

    Angle DOC is 110° and angle OCB is 65°.

    a)

    Copyright S-cool

    (i) Find angle DBC.

    (1 mark)

    (ii) Fnd angle DCO.

    (1 mark)

    (iii) Find angle DAB.

    (1 mark)

    b)

    Copyright S-cool

    (i) Find angle PXZ.

    (1 mark)

    (ii) Find angle OTY.

    (2 marks)

    (Marks available: 6)

    Answer

    Answer outline and marking scheme for question: 4

    a) (i) 55

    (1 mark)

    (ii) 35

    (1 mark)

    (iii) 80

    (1 mark)

    b) (i) 54°

    (1 mark)

    (ii) 22°

    (2 marks)

    (Marks available: 6)