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Date May 2018 Marks available 3 Reference code 18M.2.AHL.TZ2.H_5
Level Additional Higher Level Paper Paper 2 Time zone Time zone 2
Command term Express Question number H_5 Adapted from N/A

Question

Express the binomial coefficient  ( 3 n + 1 3 n 2 )  as a polynomial in n .

[3]
a.

Hence find the least value of n for which ( 3 n + 1 3 n 2 ) > 10 6 .

[3]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

( 3 n + 1 3 n 2 ) = ( 3 n + 1 ) ! ( 3 n 2 ) ! 3 !      (M1)

= ( 3 n + 1 ) 3 n ( 3 n 1 ) 3 !      A1

= 9 2 n 3 1 2 n  or equivalent     A1

[3 marks]

a.

attempt to solve  = 9 2 n 3 1 2 n > 10 6      (M1)

n > 60.57      (A1)

Note: Allow equality.

n = 61      A1

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 1—Number and algebra » SL 1.9—Binomial theorem where n is an integer
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Topic 1—Number and algebra » AHL 1.10—Perms and combs, binomial with negative and fractional indices
Topic 1—Number and algebra

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