GCSE Maths Estimation & bounds questions by topic

Rounding practice.

1. (a)Round 12.378 to 1 decimal place.[1]
2. (b)Round 12.378 to 2 decimal places.[1]
3. (c)Round 4852 to 2 significant figures.[1]
4. (d)Round 0.0716 to 1 significant figure.[1]

Estimate each calculation by rounding every number to 1 significant figure.

1. (a)Estimate 21.6 × 4.8.[2]
2. (b)Estimate 63.4 ÷ 7.9.[2]

Units and decimals.

1. (a)Write 350 g in kilograms.[1]
2. (b)Write £2.35 in pence.[1]
3. (c)A bus journey takes 50 minutes. Write 50 minutes in hours as a decimal.[2]

A shopping receipt is checked by estimation.

1. (a)3 books cost £14.85 each. Estimate the total cost.[2]
2. (b)The till shows £52.40. Use your estimate to explain whether the till is likely to be correct.[2]

A poster is printed for a school event.

1. (a)The poster is 48.6 cm wide and 29.5 cm high. Work out its exact area.[2]
2. (b)Estimate the area by rounding each measurement to 1 significant figure.[2]

A cyclist trains on a flat road.

1. (a)The ride lasts 90 minutes. Write this time in hours.[1]
2. (b)The cyclist rides 27 km in this time. Work out the average speed in km/h.[2]
3. (c)Convert your answer to metres per minute.[1]

Error intervals.

1. (a)A mass m is 6.4 kg to 1 d.p. Write an error interval for m.[2]
2. (b)A number n is 4800 to 2 significant figures. Write an error interval for n.[2]
3. (c)State which end of your interval in part (b) is excluded, and why.[1]

Estimating a harder calculation.

1. (a)Estimate the value of (31.6 × 9.8) ÷ 0.48.[3]
2. (b)A calculator gives 645.17. Use your estimate to explain whether this answer is sensible.[1]

Truncation.

1. (a)A number t is 3.72 by truncation to 2 d.p. Write an error interval for t.[2]
2. (b)Explain how the interval would differ if 3.72 had been rounded instead.[2]

A fuel gauge reads 12 litres to the nearest litre.

1. (a)Write an error interval for the fuel in the tank, f litres.[2]
2. (b)The car uses 0.08 litres per km. Work out the greatest possible distance the car can travel on the fuel shown.[2]

A bridge is measured twice.

1. (a)The first measurement is 12.4 m, rounded to 1 d.p. Write down the error interval for the true length.[2]
2. (b)The second measurement, 12.4 m, was truncated to 1 d.p. instead. Write down the error interval this implies.[2]

A calculation is estimated, then checked.

1. (a)Use 1-significant-figure rounding to estimate (61.3 − 19.8) ÷ 4.05.[3]
2. (b)Show that the calculator value is 10.2 correct to 1 decimal place, and state whether your estimate is an over-estimate or an under-estimate.[2]

Bounds of a calculation. (Higher)

1. (a)x = 8.7 and y = 2.4, both to 1 d.p. Write down the upper and lower bounds of x and y.[2]
2. (b)Find the bounds of xy.[2]
3. (c)Find the bounds of x ÷ y, giving your answers to 3 significant figures.[2]

Bounds in context. (Higher)

1. (a)A sprinter runs 100 m (to the nearest metre) in 11.8 s (to 1 d.p.). Write down the bounds of the distance and the time.[2]
2. (b)Calculate the upper and lower bounds of the sprinter’s speed in m/s, giving your answers to 3 significant figures.[3]
3. (c)The world-record pace for the drill is 9.2 m/s. Can the coach claim the sprinter “may have exceeded” it? Justify with your bounds.[1]

Bounds of a difference and a decision. (Higher)

1. (a)A recipe needs 550 g of flour (to 2 s.f.) and Ali has 600 g (to 2 s.f.). Write down the bounds of both masses.[2]
2. (b)Find the bounds of the amount of flour left over, r = 600 − 550.[3]
3. (c)Can Ali be certain at least 25 g will be left over? Justify your answer.[1]

A mixed bounds investigation. (Higher)

1. (a)A rectangular garden is 7.4 m long and 5.6 m wide, both to 1 d.p. Find the bounds of its area.[3]
2. (b)A gardener buys exactly 43 m² of turf. Can the gardener be certain the turf will cover the garden? Justify your answer.[2]
3. (c)State one assumption behind your answer to part (b).[2]

A circle is drawn for a metal disc. (Higher)

1. (a)The radius is 6.2 cm to 1 d.p. Write down the upper bound of the radius.[1]
2. (b)Work out the upper bound of the circumference, giving your answer correct to 1 decimal place.[2]
3. (c)Work out the lower bound of the area, giving your answer correct to 1 decimal place.[2]

A goods lift has a maximum safe load of 480 kg.

1. (a)Three crates are weighed as 96 kg, 88 kg and 104 kg, each to the nearest kg. Work out the upper bound of their combined mass.[2]
2. (b)A fourth crate of 190 kg (to the nearest kg) is proposed. Explain why the lift cannot be guaranteed to carry all four crates safely.[2]
3. (c)Crates are weighed to the nearest kg. Work out the greatest mass the fourth crate could state so that safety is guaranteed.[2]