IB Maths AA HL AA 1.4 Binomial theorem and counting questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 2, calculatorMedium12 marks

Let $S$ be a set of 9 distinct elements. Let $N$ be the number of subsets of $S$ that contain exactly 4 elements, and define

k=\left(1+\frac{1}{N}\right)^{1/2}.

(a)

Determine $N$

[2]

(b)

Find the first four non-zero terms, in descending powers of $N$ in the binomial expansion of $k$

[4]

(c)

Hence use the first three non-zero terms of this expansion to estimate $k$ Give your answer to 9 significant figures.

[2]

(d)

Use your GDC to determine $k$ and hence find the absolute difference between this value and your estimate in part (c), correct to 2 significant figures.

[3]

(e)

State whether your estimate in part (c) gives $k$ correctly to 3 decimal places.

[1]

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