O-LevelAdditional MathematicsSeries4037/12 · May/June 2022 · Q58 Marks
The first three terms, in ascending powers of x, in the expansion of (1 + x/6)^12 (2−3x)^3 can be written in the form 8+px+qx², where p and q are constants. Find the values of p and q.
- The first three terms, in ascending powers of x, in the expansion of (1 + x/6)^12 (2−3x)^3 can be written in the form 8+px+qx², where p and q are constants. Find the values of p and q.[8]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [2] B2 for (1 + x/6)^12 = 1 + 2x + (11/6)x² (3 correct terms)
- [1] B1 for (1 + x/6)^12 (2 correct terms)
- [2] B2 for (2-3x)³ = 8 - 36x + 54x²... (3 correct terms)
- [1] B1 for (2-3x)³ (2 correct terms)
- [M1] A correct method using their terms or coefficients, must be considering 2 terms (for p)
- [A1] p = -20 soi
- [M1] A correct method using their terms or coefficients, must be considering 3 terms (for q)
- [A1] q = -10/3 soi
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