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Further Mathematics Paper 2, May/June. 2008  
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Questions: 1 2 3 4 5 6 7 8 9 10111213 14 15 16 17 18 Main
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Question 12

(a)   The point P (3 -5) is rotated through an angle 60 degrees anticlockwise about the orign.

(i)   Obtain the matrix for the rotation.
(ii) Find the image pl of the point P under the rotation.
(b) A linear transformation is given by N: (x/y) ~(2x + 3y, 3x - y).
              (i)             Write down the matrix N of the transformation.
             (ii)         If N2 + aN + bI = 0, where a, b E R, I is the 2 x 2 unit matrix and 0 is the 2 x 2 null matrix, find the values of a and b.

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Observation

This question was not meant for Nigerian candidates but a few candidates attempted it. Some of the candidates wrote N2 =(22 32'1 instead Of[2 3/ (2 3J Le. N x N. They were also not able
                                                          1221-0)                               3 -~ L3-1
to neither substitute correctly in the equation nor equate corresponding entries. Teachers are encouraged to spend more time in the study of matrices.

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