IB Maths AI HL AI 1.1 Number and approximation 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.

Question 1

Paper 2Easy6 marks

A circular inspection window has a radius recorded as 6.4 cm6.4\text{ cm} correct to the nearest 0.1 cm0.1\text{ cm}

For this question, percentage error is

∣estimated value−actual value∣actual value×100%.\frac{|\text{estimated value}-\text{actual value}|}{\text{actual value}}\times 100\%.
(a)

Write down the lower and upper bounds for the radius.

[2]
(b)

Calculate the estimated area of the window, giving your answer to three significant figures.

[2]
(c)

Determine the greatest possible percentage error in this estimated area. Use unrounded values in your calculations and give your answer to three significant figures.

[2]

Question 2

Paper 2Hard6 marks

A comet lander collects dust during a 4.04.0-minute sampling pulse. Figure 1 shows the rate RR at which particles enter the collection chamber. Assume that RR varies linearly between consecutive readings. The mean mass of a particle is 2.4×10−13 kg2.4\times10^{-13}\,\text{kg}

0123400.20.40.60.811.21.41.61.82t (min)R (108 particles s-1)
(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 7.5×10−3 kg7.5\times10^{-3}\,\text{kg} Is it sufficient for the dust collected during the full pulse? Justify your answer with a numerical comparison.

[2]

Question 3

Paper 1Hard6 marks

A remote-sensing archive receives data from two instruments. Instrument A records 4.8×10124.8\times10^{12} observations, each requiring 2.7×1032.7\times10^3 bytes. Instrument B produces 2.24×10152.24\times10^{15} bytes of data. The archive has 4.1×10154.1\times10^{15} bytes of free space. Each additional storage module can hold at most 3.6×10143.6\times10^{14} bytes.

(a)

Show that the data from Instrument A require 1.296×10161.296\times10^{16} bytes. Give your answer in scientific notation.

[2]
(b)

Determine the least number of additional storage modules required to store all the data from both instruments. Justify that this number is least.

[4]

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