O-LevelAdditional MathematicsIndices and surds4037/22 · May/June 2017 · Q25 Marks
Without using a calculator, express ( (1 + √5) / (3 - √5) ) ^-2 in the form a + b√5, where a and b are integers.
- Without using a calculator, express ( (1 + √5) / (3 - √5) ) ^-2 in the form a + b√5, where a and b are integers.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] dealing with the negative index soi
- [B1] correctly squaring with at least 3 terms in the numerator and denominator (3-√5)² / (1+√5)² = (9-6√5+5) / (1+2√5+5) oe
- [M1] rationalising their (14-6√5) / (6+2√5) oe
- [A1] multiplying out correctly; at least 3 terms in the numerator but condone a single value for the denominator (84-64√5+60) / (36-20) oe
- [A1] 9-4√5 cao
- [M1] [3-√5 = (c+d√5)(1+√5) leading to]
- [A1] c=-2 and d=1
- [A1] (-2+√5)² = 4-4√5+5
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