O-LevelAdditional MathematicsIndices and surds4037/12 · May/June 2011 · Q46 Marks
You must not use a calculator in Question 4. In the triangle ABC, angle B = 90°, AB = 4+ 2√2 and BC = 1 + √2 .
- (i)Find tan C, giving your answer in the form k√2.[2]
- (ii)Find the area of the triangle ABC, giving your answer in the form p + q √2, where p and q are integers.[2]
- (iii)Find the area of the square whose side is of length AC, giving your answer in the form s + t √2, where s and t are integers.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- (i) (4+2√2) / (1+√2) = 2√2; M1 for attempt to rationalise and attempt to expand; A1
- (ii) Area = ½(4+2√2)×(1+√2) = 4+3√2; M1 for attempt at area using surd form and attempt to expand; A1
- (iii) Area = AC² =(4+2√2)²+(1+√2)² = 27+18√2; M1 for attempt at AC² or AC in surd form, with attempt to expand; A1
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