IGCSE · Practice questions · Limits of accuracy: upper and lower bounds

Halve the unit, then add and subtract.

Six original Cambridge-style questions on upper and lower bounds, error intervals and (Extended) bounds of calculations.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Unit, half unit, bounds, then combine.

Unit: read it from the accuracy (nearest 5 kg, 1 d.p., 2 s.f.).
Bounds: value \(\pm\) half a unit.
Interval: lower \(\le x <\) upper.
Add, multiply (Extended): max with max, min with min.
Subtract, divide (Extended): max with the OTHER value's min, and vice versa.

Recall

[2 marks]

The length of a pencil is 23 cm, correct to the nearest centimetre. Write down the lower and upper bounds of the length.

Lower bound 22.5 cm ✓
Upper bound 23.5 cm ✓

Recall

[2 marks]

The mass \(m\) kg of a melon is 0.8 kg, correct to 1 decimal place. Write down the error interval for \(m\).

Half of 0.1 is 0.05 ✓
\(0.75 \le m < 0.85\) ✓

Recall

[2 marks]

The population of a town is 45 000, correct to the nearest thousand. Write down the lower and upper bounds.

Lower bound 44 500 ✓
Upper bound 45 500 ✓

Calculation

[2 marks]

A sprinter's time \(t\) seconds is 9.8 s, correct to the nearest 0.1 s.

(a) Write down the error interval for \(t\). (b) Could the actual time have been 9.85 s? Explain.

(a) \(9.75 \le t < 9.85\) ✓
(b) No: 9.85 s would round to 9.9 s, so it is outside the interval. ✓

Calculation

[3 marks]

(Extended) A rectangle measures 12 cm by 7 cm, each correct to the nearest centimetre.

Calculate (a) the upper bound of the area (b) the lower bound of the perimeter.

(a) \(12.5 \times 7.5 = 93.75\) cm² ✓
(b) \(2 \times (11.5 + 6.5) = 36\) cm ✓

Analysis

[4 marks]

(Extended) A car travels 250 km, correct to the nearest 10 km, in 3.2 hours, correct to the nearest 0.1 hour.

(a) Calculate the upper bound and the lower bound of the average speed. Give your answers correct to 3 significant figures.

(b) The driver says her average speed was definitely below 80 km/h. Is she right? Explain.

Distance bounds 245 and 255 km; time bounds 3.15 and 3.25 h. ✓
(a) Upper bound: \(255 \div 3.15 = 80.95\dots = 81.0\) km/h ✓
Lower bound: \(245 \div 3.25 = 75.38\dots = 75.4\) km/h ✓
(b) No: the upper bound is above 80 km/h, so the speed could have been over 80 km/h. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.