Date | November 2019 | Marks available | 6 | Reference code | 19N.2.AHL.TZ0.H_5 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | H_5 | Adapted from | N/A |
Question
Consider the expansion of (2+x)n, where n⩾3 and n∈Z.
The coefficient of x3 is four times the coefficient of x2. Find the value of n.
Markscheme
attempt to find coefficients in binomial expansion (M1)
coefficient of x2:(n2)×2n−2 ; coefficient of x3:(n3)×2n−3 A1A1
Note: Condone terms given rather than coefficients. Terms may be seen in an equation such as that below.
(n3)×2n−3=4(n2)×2n−2 (A1)
attempt to solve equation using GDC or algebraically (M1)
(n3)=8(n2)
n!3!(n−3)!=8n!2!(n−2)!
13=8n−2
n=26 A1
[6 marks]
Examiners report
[N/A]