O-LevelAdditional MathematicsPermutations and combinations4037/12 · Oct/Nov 2022 · Q129 Marks
The first three terms, in descending powers of x, of the expansion of (ax+3)(1-b/x)⁵ can be written as 32x⁵-160x⁴+cx³, where a, b and c are constants. Find the exact values of a, b and c.
- The first three terms, in descending powers of x, of the expansion of (ax+3)(1-b/x)⁵ can be written as 32x⁵-160x⁴+cx³, where a, b and c are constants. Find the exact values of a, b and c.[9]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [1] a=2 (from a³=32, implying a relation for the coefficient of x⁵)
- [1] -2ba⁴ + 2a⁴ = -160 (seen or implied, for the coefficient of x⁴ using a=2)
- [1] b=3
- [1] 8/5 a³ - 4a²b + ab² = c (seen or implied, for the coefficient of x³ using a=2 and b=3)
- [1] c = 64/5 - 192 + 288 (correct substitution)
- [1] c = 544/5 or equivalent
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