IB Maths AI HL Topic 1: Number and algebra 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.

Paper

Paper 1 Paper 2

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Question 1

Paper 2Hard6 marks

A comet lander collects dust during a $4.0$ -minute sampling pulse. Figure 1 shows the rate $R$ at which particles enter the collection chamber. Assume that $R$ varies linearly between consecutive readings. The mean mass of a particle is $2.4\times10^{-13}\,\text{kg}$

(a)

Determine the total mass of dust collected during the pulse. Give your answer in scientific notation to 2 significant figures.

[4]

(b)

A return canister has a maximum dust payload of $7.5\times10^{-3}\,\text{kg}$ Is it sufficient for the dust collected during the full pulse? Justify your answer with a numerical comparison.

[2]

Question 2

Paper 2Hard6 marks

Two accounts each receive a deposit of $10 000. The principal is returned in full by either account, so only interest and fees are compared.

Account A pays simple interest at $3\%$ per year and has no fees.

The annual interest payments observed for account B are shown below.

Year	1	2	3	4
Interest payment ($)	246	267	284	306

For a projection, an adviser models account B’s annual interest payments as an arithmetic sequence. The first term is the payment in year 1, and the common difference is the mean of the three consecutive changes shown in the table. Assume this model continues for $n$ years. Account B has a one-time opening fee of $200.

(a)

State the first term and common difference of the arithmetic model for account B.

[2]

(b)

Let $S_n$ be the total interest paid by account B during the first $n$ years. Show that

S_n=n(10n+236).

Hence determine the first whole number of years for which account B’s cumulative interest, after its opening fee, exceeds account A’s cumulative interest. Justify that this is the first such year.

[4]

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