O-LevelAdditional MathematicsIndices and surds4037/11 · May/June 2015 · Q25 Marks
Do not use a calculator in this question. [Figure 2.1] The diagram shows the triangle ABC where angle B is a right angle, AB = (4 + 3√2) cm, BC = (8 + 5 √2) cm and angle BAC = θ radians. Showing all your working, find
- (i)tan θ in the form a + b√2, where a and b are integers,[2]
- (ii)sec² θ in the form c + d√2, where c and d are integers.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [M1] attempt to obtain tanθ and rationalise. Must be convinced that no calculators are being used
- [A1] =1+2√2 cao
- [M1] attempt to use sec² θ =1+ tan² θ, with their answer to (i)
- [DM1] attempt to simplify, must be convinced no calculators are being used.
- [A1] Need to expand (-1+2√2)² as 3 terms =10-4√2
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