Worksheets · Foundation and Higher

Estimation and sense checks

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 4 marks
Round each number to 1 significant figure to estimate each answer.
(a) Estimate the value of $612 \times 4.87$ (2)
(b) Tickets for a show cost £11.95 each. Estimate the cost of 38 tickets. (2)
Question 2Non-calculator · 3 marks
Petrol costs £1.89 per litre. A driver buys 38.7 litres.
(a) Estimate the cost by rounding each number to one significant figure. (2)
(b) Is your estimate greater or less than the exact cost? Give a reason. (1)
Question 3Non-calculator · 4 marks
A lorry can carry at most $12$ tonnes. It needs to carry $385$ boxes, and each box has a mass of $29.7$ kg. $1$ tonne $= 1000$ kg.
(a) Estimate the total mass of the boxes, in tonnes. (3)
(b) The driver says, "My estimate is 12 tonnes, exactly the limit, so I cannot tell whether one trip is enough." Is the driver right? Give a reason. (1)
1. The driver is right
2. The driver is wrong: one trip is enough

Answers and marks

(a) $3000$

(b) £400

M1 Rounding both numbers to 1 significant figure and multiplying: $40 \times 10$ .
A1 The correct answer, £400.

(a) £ $80$

(b) Greater: both numbers were rounded up, so their product is larger than the exact cost.

C1 Correct conclusion with supporting reasoning: Greater: both numbers were rounded up, so their product is larger than the exact cost.

(a) $12$ tonnes

(b) No: both numbers were rounded up, so the real mass is less than 12 tonnes and one trip is enough.

C1 Stating one trip is enough because both numbers were rounded up, so the estimate is an overestimate.

Estimation and sense checks

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