O-LevelAdditional MathematicsSeries4037/12 · Oct/Nov 2023 · Q47 Marks
It is given that the first four terms, in ascending powers of x, in the expansion of (1 - x/2)^n can be written in the form 1-8x+px²+qx³, where n, p and q are integers. Find the values of n, p and q.
- (a)It is given that the first four terms, in ascending powers of x, in the expansion of (1 - x/2)^n can be written in the form 1-8x+px²+qx³, where n, p and q are integers. Find the values of n, p and q.[5]
- (b)Find the term independent of x in the expansion of (2x² + 1/3x)^6, giving your answer as a rational number.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [5] (a) B1 n=16
- [5] (a) M1 for attempt at third term allow unsimplified in terms of n or their n, but not just as part of an expansion unless used to find p
- [5] (a) A1 for p.
- [5] (a) M1 for attempt at fourth term, allow unsimplified in terms of n or their n, but not just as part of an expansion unless used to find q
- [5] (a) A1 for q.
- [2] (b) B1 For identifying the correct term and attempting to evaluate.
- [2] (b) B1
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