IB Maths AI HL AI 1.2 Sequences and financial mathematics 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 1Medium7 marks

A town records the annual grants it gives to a park. The recorded grants are not exactly arithmetic, so an arithmetic model is to be used for estimating future grants. Use the values for years 1 and 5 to estimate the common difference.

Recorded annual grants$5200$5480$5750$6030$6310YearYear 1Year 2Year 3Year 4Year 5
(a)

Write down the first term of the arithmetic model.

[1]
(b)

Estimate the common difference and hence write an expression for the estimated grant, GnG_n in year nn

[2]
(c)

Write, in sigma notation, an expression for the total estimated grants in years 1 to 6, and calculate this total.

[2]
(d)

Using the model, determine the first year in which the estimated grant exceeds $7000.

[2]

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