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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 n3 and nZ.

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)×2n2 ; coefficient of x3:(n3)×2n3         A1A1

Note: Condone terms given rather than coefficients. Terms may be seen in an equation such as that below.

(n3)×2n3=4(n2)×2n2       (A1)

attempt to solve equation using GDC or algebraically       (M1)

(n3)=8(n2)

n!3!(n3)!=8n!2!(n2)!

13=8n2

n=26       A1

[6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » SL 1.9—Binomial theorem where n is an integer
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