O-LevelAdditional MathematicsSeries4037/11 · May/June 2019 · Q47 Marks
The first 3 terms, in ascending powers of x, in the expansion of (2+bx)^8 can be written as a + 256x + cx². Find the value of each of the constants a, b and c.
- (i)The first 3 terms, in ascending powers of x, in the expansion of (2+bx)^8 can be written as a + 256x + cx². Find the value of each of the constants a, b and c.[4]
- (ii)Using the values found in part (i), find the term independent of x in the expansion of (2+bx)^8 (2x-3/x)².[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] a = 256
- [M1] 8 × 2^7 × bx [= 256x] oe or 8 × 7 × 2^6 × (bx)² / 2 [= cx²] oe
- [A2] A1 for each b = 1/4 oe, c = 112
- [B1] for (256+256x+112x²)(4x²-12+9/x²)
- [M1] adding and selecting (their256×their(-12))+(their112×their9)
- [A1] = -2064
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