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Approximations and errors — KCSE Mathematics

KCSE Mathematics · 106 practice questions · 3 syllabus objectives

36 easy35 medium35 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Define absolute, relative, percentage, round-off and truncation errors

Determine possible errors from computations and find maximum and minimum errors

Express values to a given number of significant figures and make reasonable approximations

Sample Questions

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1
easySHORT ANSWER4 marks

A thermometer reads 37.0 °C to one decimal place. (a) State the maximum and minimum possible temperatures. (2 marks) (b) If the actual temperature is 36.8 °C, determine the percentage error. (2 marks)

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Part (a) — 2 marks
Minimum possible temperature = 36.95 °C (1 mk)
Maximum possible temperature = 37.05 °C (1 mk)
Part (b) — 2 marks
Absolute error = |37.0 - 36.8| = 0.2 °C (1 mk)
Percentage error = (0.2 / 37.0) × 100 = 0.5405% (to 4 decimal places) (1 mk)
2
easySHORT ANSWER3 marks

A student measures the length of a table as 1.25 m accurate to two decimal places. (a) State the range of possible lengths for the table. (2 marks) (b) If the actual length is 1.23 m, calculate the absolute error. (1 mark)

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Part (a) — 2 marks
Minimum possible length = 1.245 m (1 mk)
Maximum possible length = 1.255 m (1 mk)
Part (b) — 1 mark
Absolute error = |1.25 - 1.23| = 0.02 m (1 mk)
3
easySHORT ANSWER2 marks

A round table's diameter is recorded as 1.2 m, accurate to the nearest 0.1 m. Identify the absolute error in the measurement. (2 marks)

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Part (a) — 2 marks
Absolute error = 0.05 m (1 mk)
This is half of the precision of the measurement (1 mk)
4

A piece of wood is measured to be 2.5 m long, accurate to the nearest 0.1 m. Identify the maximum and minimum possible lengths of the wood. (2 marks)

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Why Practise Approximations and errors?

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