Date | May 2022 | Marks available | 5 | Reference code | 22M.1.AHL.TZ1.6 |
Level | Additional Higher Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 1 |
Command term | Determine | Question number | 6 | Adapted from | N/A |
Question
Consider the expansion of (8x3-12x)n where n∈ℤ+. Determine all possible values of n for which the expansion has a non-zero constant term.
Markscheme
EITHER
attempt to obtain the general term of the expansion
Tr+1=Crn(8x3)n-r(-12x)r OR Tr+1=Cn-rn(8x3)r(-12x)n-r (M1)
OR
recognize power of x starts at 3n and goes down by 4 each time (M1)
THEN
recognizing the constant term when the power of x is zero (or equivalent) (M1)
r=3n4 or n=43r or 3n-4r=0 OR 3r-(n-r)=0 (or equivalent) A1
r is a multiple of 3 (r=3,6,9,…) or one correct value of n (seen anywhere) (A1)
n=4k, k∈ℤ+ A1
Note: Accept n is a (positive) multiple of 4 or n=4,8,12,…
Do not accept n=4,8,12
Note: Award full marks for a correct answer using trial and error approach
showing n=4,8,12,… and for recognizing that this pattern continues.
[5 marks]
Examiners report
There was a mixed response to this question. Candidates who used a trial and error approach were more successful in obtaining completely correct answers than those who tried to solve algebraically by finding the general term to form an equation relating n and r . Poor explanations were often noted in the trial and error approach. Candidates often failed to make progress after obtaining n=43r in the algebraic approach. Some candidates did not attempt this question.