IGCSE Maths Estimation and bounds topical questions

Round as instructed.

1. (a)Round 27.483 correct to 1 decimal place.[1]
2. (b)Round 27.483 correct to 2 significant figures.[1]
3. (c)Round 0.005392 correct to 2 significant figures.[2]

A table is 7 metres long, correct to the nearest metre.

1. (a)Write down the lower bound of the length.[1]
2. (b)Write down the upper bound of the length.[1]
3. (c)Write the two bounds as an inequality.[1]

Estimate (392 × 8.1) ÷ 1.97 by rounding each number to 1 significant figure. Show the values you use.

1. (a)Write the rounded values.[1]
2. (b)Calculate the estimate.[2]

Round each number as instructed.

1. (a)Round 7.863 to 2 decimal places.[1]
2. (b)Round 0.04729 to 1 significant figure.[1]
3. (c)Round 639.7 to the nearest ten.[1]
4. (d)Round 3.999 to 2 significant figures.[1]
5. (e)Explain why your answer to part (d) must keep its zero.[1]

A cinema admits 486 people for a screening, with tickets at 7.95 each.

1. (a)Estimate the total takings by rounding each value to 1 significant figure.[3]
2. (b)Is your estimate larger or smaller than the exact takings? Explain your answer.[2]

A rectangle measures 8.4 cm by 3.6 cm, each correct to the nearest centimetre. (Extended)

1. (a)Write down the upper and lower bounds of each side.[2]
2. (b)Calculate the upper bound of the perimeter.[1]
3. (c)Calculate the upper and lower bounds of the area, correct to 3 significant figures.[3]

p = 47.2 and q = 2.06, both correct to 3 significant figures. (Extended)

1. (a)Write down the bounds of p and of q.[2]
2. (b)Find the upper bound of p ÷ q, correct to 4 significant figures.[2]
3. (c)Explain, without calculating, how to find the lower bound of p ÷ q.[1]

Estimate √98 × 21.4 ÷ 0.473.

1. (a)Write each number correct to 1 significant figure.[2]
2. (b)Hence find the estimate.[2]

A swimming pool measures 25 m by 10 m, each correct to the nearest metre. (Extended)

1. (a)Find the upper and lower bounds of the perimeter of the pool.[2]
2. (b)Show that the greatest possible area of the pool is less than 270 m².[3]

A charity walk has three legs of 4.6 km, 11.8 km and 7.5 km, each correct to the nearest 0.1 km.

1. (a)Find the lower bound of the total distance.[2]
2. (b)Find the upper bound of the total distance.[2]
3. (c)The total time is 90 minutes, correct to the nearest 5 minutes. Find the upper bound of the average speed, in km/h, correct to 3 significant figures. (Extended)[2]

A sprinter runs 250 m, correct to the nearest metre, in a time of 34 s, correct to the nearest second. (Extended)

1. (a)Write down the bounds of the distance and of the time.[2]
2. (b)Calculate the upper bound of the speed, correct to 3 significant figures.[2]
3. (c)Calculate the lower bound of the speed, correct to 3 significant figures.[2]

The mass of a rock is 3.4 kg, correct to the nearest 0.1 kg, and its volume is 480 cm³, correct to the nearest 10 cm³. (Extended)

1. (a)Write down the bounds of the mass in grams.[2]
2. (b)Write down the bounds of the volume in cm³.[1]
3. (c)Find the upper and lower bounds of the density in g/cm³, correct to 3 significant figures.[4]

Answer this question without a calculator.

1. (a)Estimate √102 by choosing a sensible perfect square.[1]
2. (b)Estimate (60.3 − √99) ÷ 4.98, showing the values you use.[3]
3. (c)Explain why replacing √99 by 10 is sensible.[1]

A cylinder has radius r = 6.2 cm and height h = 14.5 cm, each correct to the nearest 0.1 cm. The volume is V = πr²h. (Extended)

1. (a)Write down the lower bounds of r and h.[1]
2. (b)Find the lower bound of the volume. Give your answer correct to 3 significant figures.[3]
3. (c)Explain why the lower bound of V uses the lower bound of each measurement.[1]