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 1Medium6 marks

A laboratory receives microscopic particles in sealed deliveries. Figure 1 shows the mass of one particle and the numbers of particles and cartridges in a cartridge and a delivery, respectively. The diagram is not to scale.

one particlemass = 3.8×10−18 g6.4×1013 particlesper cartridge1.5×103 cartridgesper delivery

(a) Calculate the mass of particles in one cartridge. Give your answer in standard form, correct to 2 significant figures. [2]

(b) Calculate the total mass of particles in one delivery. Give your answer in standard form, correct to 2 significant figures. [2]

(c) A laboratory requires at least 1.0 g1.0\,\text{g} of particles. Find the minimum whole number of deliveries required. [2]

(a)

Calculate the mass of particles in one cartridge. Give your answer in standard form, correct to 2 significant figures.

[2]
(b)

Calculate the total mass of particles in one delivery. Give your answer in standard form, correct to 2 significant figures.

[2]
(c)

A laboratory requires at least 1.0 g1.0\,\text{g} of particles. Find the minimum whole number of deliveries required.

[2]

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