O-LevelAdditional MathematicsSeries4037/22 · May/June 2014 · Q56 Marks
Find and simplify the first three terms of the expansion, in ascending powers of x, of (1 – 4x)5.
- (i)Find and simplify the first three terms of the expansion, in ascending powers of x, of (1 – 4x)5.[2]
- (ii)The first three terms in the expansion of (1 – 4x)⁵(1 + ax + bx²) are 1-23x + 222x². Find the value of each of the constants a and b.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [B2, 1, 0] 1-20x+160x² -1 each error if B0 then M1 for 3 correct terms seen; may be unsimplified e.g. 1, 5(-4x), 5x4(-4x)²/2
- [M1] a + (their – 20) = -23 soi condone sign errors only; must be their -20 from (i)
- [A1] a =-3 validly obtained
- [M1] b + (their – 20)a + (their160) = 222 soi condone sign errors only ; must be their -20 and their160 from (i) and their a if used
- [A1] b=2 validly obtained
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