Date | May 2021 | Marks available | 5 | Reference code | 21M.2.SL.TZ1.6 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 1 |
Command term | Find | Question number | 6 | Adapted from | N/A |
Question
Consider the expansion of (3+x2)n+1, where n∈ℤ+ .
Given that the coefficient of x4 is 20 412, find the value of n.
Markscheme
METHOD 1
product of a binomial coefficient, a power of 3 (and a power of x2) seen (M1)
evidence of correct term chosen (A1)
C2n+1×3n+1-2×(x2)2 (=n(n+1)2×3n-1×x4) OR n-r=1
equating their coefficient to 20412 or their term to 20412x4 (M1)
EITHER
C2n+1×3n-1=20412 (A1)
OR
Crr+2×3r=20412⇒r=6 (A1)
THEN
n=7 A1
METHOD 2
3n+1(1+x23)n+1
product of a binomial coefficient, and a power of x23 OR 13 seen (M1)
evidence of correct term chosen (A1)
3n+1×n(n+1)2!×(x23)2 (=3n-12n(n+1)x4)
equating their coefficient to 20412 or their term to 20412x4 (M1)
3n-1×n(n+1)2=20412 (A1)
n=7 A1
[5 marks]