O-LevelAdditional MathematicsIndices and surds4037/22 · Oct/Nov 2016 · Q25 Marks
Without using a calculator, find the integers a and b such that a/(√3+1) + b/(√3-1) = √3-3.
- Without using a calculator, find the integers a and b such that a/(√3+1) + b/(√3-1) = √3-3.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [M1] a(√3-1)+b(√3+1) Common denominator or x(√3-1)(√3+1)
- =(√3-3)(√3-1)(√3+1)
- = 2(√3-3) oe
- [DM1] a+b=2 equate constant terms and √3 terms. both correct
- [A1] -a+b=-6
- [DM1] solve two linear equations to obtain a = or b=
- [A1] b=-2 and a = 4 both correct
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