A-LevelMathematicsSeries9709/31 · May/June 2022 · Q25 Marks
Expand (2-x²)⁻² in ascending powers of x, up to and including the term in x⁴, simplifying the coefficients.
- (a)Expand (2-x²)⁻² in ascending powers of x, up to and including the term in x⁴, simplifying the coefficients.[4]
- (b)State the set of values of x for which the expansion is valid.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [M1] State a correct unsimplified version of the x² or the x⁴ term of the expansion of (2-x²)⁻² or (1-x²/2)⁻² Symbolic binomial coefficients are not sufficient for the M1.
- [B1] State correct first term 1/4 Accept 2⁻².
- [A1 A1] Obtain the next two terms – x²/4 + 3x⁴/16 A1 for each one correct ISW. Full marks for 1/4(1 + x² + 3x⁴/4) ISW.
- SC allow M1 A1 A1 for 1/4 and 1+x²+x⁴ SOI.
- SC allow M1 A1 for 1+x²+x⁴
- [B1] State answer |x|<√2 Or -√2 < x < √2.
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