Further Mathematics Paper 2, Nov/Dec. 2012
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength
Question 5

I

Two sides of a triangle are represented by the vectors
p =   and  q = .

1.        Show that they are perpendicular to each other
2.        Find the:
3. area;
4. angles of the triangle.
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Observation

IThis question was also reported to be poorly attempted by majority of the candidates.  According to the report, candidates displayed poor knowledge of vectors.  Candidates were advised to work harder at learning this topic.  If p and q  are perpendicular, then     p . q  = 0 i.e.  = 0. p . q  = (3 x 2 + (-2)(3)) = 6 – 6 = 0.  This implied that they are perpendicular. ‌‌‌│p│=   =   │q│=   =  .  Since they are perpendicular, then area of triangle =  =  = 6  or 6.5 square units.  Candidates should also know that one of the angles is 90o since they were perpendicular.  If q is one of the remaining angles, then tanq =  = 1 Þ q = 45o.  Therefore, the angles of the triangle were 90o, 45o and 45o which also implied that the triangle is isosceles.

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