O-LevelAdditional MathematicsIndices and surds4037/12 · May/June 2012 · Q66 Marks
You must not use a calculator in this question.
- (i)Express 8 / (√3+1) in the form a(√3 – 1), where a is an integer.[2]
- (ii)An equilateral triangle has sides of length 8 / (√3+1). Show that the height of the triangle is 6 – 2√3.[2]
- (iii)Hence, or otherwise, find the area of the triangle in the form p√3 – q, where p and q are integers.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [M1] M1 for rationalisation or attempt to form equation
- [A1] a = 4
- [M1] M1 for use of sine or tangent and their value of a from (i) or 8 / (√3+1)
- [A1] A1 for rearranging and simplifying correctly to obtain given answer.
- [M1] M1 for valid method for area using their a from (i) or 8 / (√3+1)
- [A1] A1 working must be seen
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