O-LevelAdditional MathematicsSeries4037/12 · May/June 2018 · Q56 Marks
The first three terms in the expansion of (3 - 1/(9x))⁵ can be written as a + b/x + c/x². Find the value of each of the constants a, b and c.
- (i)The first three terms in the expansion of (3 - 1/(9x))⁵ can be written as a + b/x + c/x². Find the value of each of the constants a, b and c.[3]
- (ii)Use your values of a, b and c to find the term independent of x in the expansion of (3 - 1/(9x))⁵ (2+9x)².[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- B1 for each coefficient, must be simplified a = 243, b = -45, c = 10/3
- B1 For (4+36x+81x²)
- M1 for having 3 terms independent of x
- A1 Independent term is 972 - 1620 + 270 = -378
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