GCSEMathsOCRExam Questions4. Approximation & EstimationRounding, Estimation & Bounds

Rounding, Estimation & Bounds (OCR GCSE Maths)

Exam Questions

3 hours58 questions
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Hard
Very Hard
1
Sme Calculator2 marks

A number, n, is rounded to 2 decimal places.
The result is 4.76

Using inequalities, write down the error interval for n.

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2
Sme Calculator2 marks

The length, L cm, of a line is measured as 13 cm correct to the nearest centimetre.

Complete the following statement to show the range of possible values of L


................. ≤ L < .................

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3a
Sme Calculator1 mark

Find the value of the reciprocal of 1.6
Give your answer as a decimal.

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3b
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Jess rounds a number, x, to one decimal place.
The result is 9.8

Write down the error interval for x.

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4
Sme Calculator2 marks

Jim rounds a number, x, to one decimal place.
The result is 7.2

Write down the error interval for x.

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5
Sme Calculator3 marks

By writing each number correct to 1 significant figure, find an estimate for this calculation.

fraction numerator 606.3 space cross times space 0.312 over denominator 19.93 end fraction

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6
Sme Calculator2 marks

Use the symbols less than space comma less-than or slanted equal to space comma equals space comma greater than space comma greater-than or slanted equal to or to complete this statement.

If x = 4.7, truncated to 1 decimal place, then 4.7 ............... x ............... 4.8

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7
Sme Calculator2 marks

The length, d, of Jamal’s car is 4.72 m, correct to 2 decimal places.

Complete the error interval for the length, d.

....................... less-than or slanted equal to space d space less than ........................ 

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8
Sme Calculator3 marks

Asha worked out fraction numerator 326.8 space cross times open parentheses 6.94 space minus space 3.4 close parentheses over denominator 59.4 end fraction

She got an answer of 19.5, correct to 3 significant figures.

Write each number correct to 1 significant figure to decide if Asha’s answer is reasonable.

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9
Sme Calculator2 marks

The length, L, of a steel rod is 8.3 m, correct to 1 decimal place.

Complete the error interval for length L.

............................ less-than or slanted equal to L less than ............................

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10
Sme Calculator1 mark

When rounded to 3 significant figures, x space equals space 6.37

Circle the correct error interval.

6.365 space less-than or slanted equal to space x space less than space 6.375 6.36 space less-than or slanted equal to space x space less than space 6.38
6.369 space less-than or slanted equal to space x space less than space 6.379 6.365 space less-than or slanted equal to space x space less than space 6.3749

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11
Sme Calculator1 mark

The height of a tree is 12 metres, correct to the nearest metre.

Circle the error interval.

11.5 m ⩽ height < 12.5 m 11.5 m ⩽ height ⩽ 12.5 m
11.5 m < height ⩽ 12.5 m 11.5 m < height < 12.5 m

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12
Sme Calculator2 marks

To the nearest 1000, there are 18 000 people at a festival.

i)

Write down the minimum possible number of people at the festival.

[1]

ii)

Write down the maximum possible number of people at the festival.

[1]

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13
Sme Calculator2 marks

The length of a table is 110 cm to the nearest cm

Complete the error interval.

.................cm ⩽ length < .................cm

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14a
Sme Calculator2 marks

The length of each side of a regular pentagon is 8.4 cm to 1 decimal place.

Complete the error interval for the length of one side.

....................cm ⩽ length < ....................cm

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14b
Sme Calculator1 mark

Complete the error interval for the perimeter.

....................cm ⩽ perimeter < ....................cm

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15
Sme Calculator2 marks

Each side of a regular octagon has a length of 18 mm, correct to the nearest 0.5 mm

q4-4ma1-2h-qp-jan22-paper2-igcse-maths

i)
Write down the lower bound of the length of each side of the octagon.
[1]

ii)
Write down the upper bound of the length of each side of the octagon.
[1]

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16
Sme Calculator2 marks

The mass of a cat is 4.3 kg correct to 2 significant figures.

i)

Write down the upper bound of the weight of the cat.
 

........................... kg [1]

ii)

Write down the lower bound of the weight of the cat.
 

........................... kg [1]

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17
Sme Calculator2 marks

The length of a book is 33.8 cm, correct to one decimal place.

i)
Write down the lower bound of the length of the book.

.............................................. cm [1]

ii)
Write down the upper bound of the length of the book.

.............................................. cm [1]

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1a
Sme Calculator1 mark

The value of p is 4.3
The value of q is 0.4

Both p and q are given correct to the nearest 0.1

Write down the lower bound for p.

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1b
Sme Calculator3 marks

      r space equals space p space plus 1 over q

Work out the upper bound for r.
You must show all your working.

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2
Sme Calculator3 marks

I equals space 5 left parenthesis v space long dash space u right parenthesis


v space equals space 14 space correct space to space 2 space significant space figures u space equals space 8.7 space correct space to space 2 space significant space figures


Work out the upper bound for the value of I.
You must show your working.

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3
Sme Calculator3 marks

a space equals space fraction numerator v minus u over denominator t end fraction

table attributes columnalign right center left columnspacing 0px end attributes row cell v space end cell equals cell space 37.6 space correct space to space 3 space significant space figures. end cell row cell u space end cell equals cell space 11.3 space correct space to space 3 space significant space figures. end cell row cell t space end cell equals cell space 8.4 space correct space to space 2 space significant space figures. end cell end table


Work out the upper bound for the value of a.
Show your working clearly.

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4
Sme Calculator3 marks

D space equals space x over y

x space equals space 99.7 space correct space to space 1 space decimal space place. space y space equals space 67 space correct space to space 2 space significant space figures.

Work out an upper bound for D.

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5
Sme Calculator2 marks

There are space 892 spacelitres of oil in Mr Aston's oil tank.
He uses space 18.7 spacelitres of oil each day.

Estimate the number of days it will take him to use all the oil in the tank.

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6
Sme Calculator3 marks

Work out an estimate for fraction numerator 31 space cross times space 9.87 over denominator 0.509 end fraction

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7a
Sme Calculator2 marks

Work out an estimate for the value of  square root of 63.5 cross times 101.7 end root.

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7b
Sme Calculator1 mark

left parenthesis 2.3 right parenthesis to the power of 6 space equals space 148 spacecorrect to 3 significant figures.

Find the value of left parenthesis 0.23 right parenthesis to the power of 6 correct to 3 significant figures.

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7c
Sme Calculator1 mark

Find the value of space 5 to the power of negative 2 end exponent.

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8
Sme Calculator2 marks

Sally used her calculator to work out the value of a number y.
The answer on her calculator display began

8.3

Complete the error interval for y.

............................less-than or slanted equal to y space less than ....................

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9
Sme Calculator3 marks

By writing each number correct to 1 significant figure, use estimation to show that

fraction numerator 39.6 cross times 20.2 over denominator square root of 99.2 end root end fraction almost equal to 80

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10
Sme Calculator3 marks

Last year, Katie earned £16200.
Her total loan repayments were £6400.
Katie estimates that the ratio of her loan repayments to her earnings is approximately 3 : 8.

Is she correct?
Show your reasoning.

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11
Sme Calculator3 marks

Safety rules on a campsite require Sarah to set up her barbecue at least 4 m from her tent.
She decides to measure this distance using her stride length.
Sarah knows that her stride length is 0.8 m, rounded to the nearest 0.1 m.

Find the minimum number of strides Sarah will need to take to guarantee that her barbecue is a safe distance from her tent.

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12
Sme Calculator3 marks

To the nearest pound, Jon has £9

To the nearest 50p, Ellie has £6.50

Work out the maximum possible total amount of money.

£........................................ 

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13
Sme Calculator3 marks

Use approximations to estimate the answer to   fraction numerator square root of 97 plus 2.014 cubed over denominator 0.49 end fraction

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14a
Sme Calculator2 marks

The length of a pipe is 6 metres to the nearest metre.

Complete the error interval for the length of the pipe.

...........................m ⩽ length < ...........................m

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14b
Sme Calculator2 marks

The length of a different pipe is 4 metres to the nearest metre.

Olly says,

“The total length of the two pipes is 11 metres to the nearest metre.”

Give an example to show that he could be correct.

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15
Sme Calculator3 marks

k equals fraction numerator t over denominator a minus h end fraction

t space= 14 correct to 2 significant figures
a = 7.8 correct to 2 significant figures
h = 3.4 correct to 2 significant figures

Work out the lower bound for the value of k.
Show your working clearly.

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16
Sme Calculator2 marks

Nav has worked out fraction numerator 68.3 space cross times space 42.8 over denominator 0.021 end fraction on his calculator.

His answer is 139 space 201.9048

Without using a calculator and using suitable approximations, check that his answer is sensible.
Show your working clearly.

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17a
Sme Calculator2 marks

P space equals space e f

table row cell e space end cell equals cell space 4.8 space correct space to space 2 space significant space figures. space end cell row cell f space end cell equals cell space 0.26 space correct space to space 2 space significant space figures. end cell end table

Work out the lower bound for the value of P.
Show your working clearly.
Give your answer correct to 3 significant figures.

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17b
Sme Calculator2 marks

Q space equals space t over w
table row cell t space end cell equals cell space 2.73 space correct space to space 3 space significant space figures. space end cell row cell w space end cell equals cell space 0.04 space correct space to space 1 space significant space figure. end cell end table

Work out the upper bound for the value of Q.
Show your working clearly.
Give your answer correct to 2 significant figures.

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1
Sme Calculator4 marks

Dan does an experiment to find the value of pi.
He measures the circumference and the diameter of a circle.

He measures the circumference, C , as 170 mm to the nearest millimetre.
He measures the diameter, d, as 54 mm to the nearest millimetre.

Dan uses pi space equals space C over d to find the value of pi.
Calculate the upper bound and the lower bound for Dan's value of pi .

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2
Sme Calculator4 marks

Steve travelled from Ashton to Barnfield.

   He travelled space 235 spacemiles, correct to the nearest 5 miles.
   The journey took him 200 minutes, correct to the nearest 5 minutes.

   Calculate the lower bound for the average speed of the journey.
   Give your answer in miles per hour, correct to 3 significant figures.
   You must show all your working.

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3
Sme Calculator3 marks

Jarek uses the formula

Area space equals 1 half a b space sin C


to work out the area of a triangle.

For this triangle,

    a space equals space 7.8 space cm space correct space to space the space nearest space mm. space b space equals space 5.2 space cm space correct space to space the space nearest space mm. space C space equals space 63 to the power of ring operator space correct space to space the space nearest space degree.

Calculate the lower bound for the area of the triangle.

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4
Sme Calculator4 marks

q4-hard-1-8-roundingest-and-bound-edexcel-gcse-maths

a is 8.3 cm correct to the nearest mm
b is 6.1 cm correct to the nearest mm

Calculate the upper bound for c.
You must show your working.

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5a
Sme Calculator4 marks

A train travelled along a track in 110 minutes, correct to the nearest 5 minutes.

Jake finds out that the track is 270 km long.
He assumes that the track has been measured correct to the nearest 10 km.

Could the average speed of the train have been greater than 160 km/h?
You must show how you get your answer.

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5b
Sme Calculator1 mark

Jake's assumption was wrong.
The track was measured correct to the nearest 5 km.

Explain how this could affect your decision in part (a).

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6
Sme Calculator3 marks

The petrol consumption of a car, in litres per 100 kilometres, is given by the formula

         Petrol space consumption space equals space fraction numerator 100 space cross times space Number space of space litres space of space petrol space used space over denominator Number space of space kilometres space travelled end fraction

Nathan's car travelled 148 kilometres, correct to 3 significant figures.
The car used 11.8 litres of petrol, correct to 3 significant figures.


Nathan says,

   "My car used less than 8 litres of petrol per 100 kilometres."

Could Nathan be wrong?
You must show how you get your answer.

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7a
Sme Calculator3 marks

A cone has a volume of 98 cm3.
The radius of the cone is 5.13 cm.

q7a-hard-1-8-roundingest-and-bound-edexcel-gcse-maths

Work out an estimate for the height of the cone.

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7b
Sme Calculator1 mark

John uses a calculator to work out the height of the cone to 2 decimal places.

Will your estimate be more than John's answer or less than John's answer?
Give reasons for your answer.

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8
Sme Calculator3 marks

Work out an estimate for square root of 4.98 plus 2.16 cross times 7.35 end root

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9
Sme Calculator3 marks

Margaret has some goats.
The goats produce an average total of 21.7 litres of milk per day for 280 days.
Margaret sells the milk in 1 half litre bottles.

Work out an estimate for the total number of bottles that Margaret will be able to fill with the milk.
You must show clearly how you got your estimate.

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10
Sme Calculator4 marks
Competition

a prize every 2014 seconds

In a competition, a prize is won every 2014 seconds.

Work out an estimate for the number of prizes won in 24 hours.
You must show your working.

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11a
Sme Calculator3 marks

The mass of Jupiter is 1.899 x 1027 kg.
The mass of Saturn is 0.3 times the mass of Jupiter.

Work out an estimate for the mass of Saturn.
Give your answer in standard form.

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11b
Sme Calculator1 mark

Give evidence to show whether your answer to (a) is an underestimate or an overestimate.

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12a
Sme Calculator3 marks

D space equals space fraction numerator u squared over denominator 2 a end fraction

table attributes columnalign right center left columnspacing 0px end attributes row cell u space end cell equals cell space 26.2 space correct space to space 3 space significant space figures space end cell row cell a space end cell equals cell space 4.3 space correct space to space 2 space significant space figures end cell end table

Calculate the upper bound for the value of D.
Give your answer correct to space 6 space significant figures.
You must show all your working.

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12b
Sme Calculator2 marks

The lower bound for the value of D is 78.6003 correct to 6 significant figures.

By considering bounds, write down the value of D to a suitable degree of accuracy.
You must give a reason for your answer.

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13
Sme Calculator6 marks

Claudine cycled a distance of 53 km in 2.7 hours.
The distance is measured correct to the nearest km.
The time is given correct to 1 decimal place.

Calculate the lower and upper bounds of her average speed.

Give your answers correct to 2 decimal places.

Lower bound = ................................ km/h
Upper bound = ................................ km/h

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14
Sme Calculator4 marks

Sunil makes 7.5 litres of soup, correct to the nearest 0.5 litre.
He serves the soup in 300 ml portions, correct to the nearest 10 ml.
24 people order this soup.

Does Sunil definitely have enough soup to serve the 24 people?
Show how you decide.

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15
Sme Calculator4 marks

Edith’s van can safely carry a maximum load of 920 kilograms.

She wants to use her van to carry

30 sacks of potatoes, each of mass 25 kilograms to the nearest kilogram

and

20 sacks of carrots, each of mass 7.5 kilograms to 1 decimal place.

Can she definitely use her van safely in one journey?

You must show your working.

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16
Sme Calculator3 marks

The length of a roll of ribbon is 30 metres, correct to the nearest half-metre.

A piece of length 5.8 metres, correct to the nearest 10 centimetres, is cut from the roll.

Work out the maximum possible length of ribbon left on the roll.

...................metres

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1
Sme Calculator5 marks

m equals fraction numerator square root of s over denominator t end fraction

s equals space 3.47 space correct space to space 2 space decimal space places space t space equals space 8.132 space correct space to space 3 space decimal space places

By considering bounds, work out the value of m to a suitable degree of accuracy.
You must show all your working and give a reason for your final answer.

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2
Sme Calculator5 marks

A road is 4530 m long, correct to the nearest 10 metres.
   Kirsty drove along the road in 205 seconds, correct to the nearest 5 seconds.

   The average speed limit for the road is 80 km/h.

   Could Kirsty's average speed have been greater than 80 km/h?
   You must show your working.

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3
Sme Calculator5 marks

Jackson is trying to find the density, in g/cm3, of a block of wood.
The block of wood is in the shape of a cuboid.

He measures
   the length as 13.2 cm, correct to the nearest mm
   the width as 16.0 cm, correct to the nearest mm
   the height as 21.7 cm, correct to the nearest mm

He measures the mass as 1970 g, correct to the nearest 5 g.

By considering bounds, work out the density of the wood.
Give your answer to a suitable degree of accuracy.

You must show all your working and give a reason for your final answer.

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4
Sme Calculator3 marks

Sanders has a water tank for storing rainwater.

q4-veryhard-1-8-roundingest-and-bound-edexcel-gcse-maths

The tank is in the shape of a cylinder.
The radius of the cylinder is 31 cm.
The height of the cylinder is 97.5 cm.

The tank is full of water.

Work out an estimate for the volume of water in the tank.
Give your answer in litres.
You must show your working.

Use 1000 cm3 = 1 litre.

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5a
Sme Calculator3 marks

A cycle race across America is 3069.25 miles in length.

Juan knows his average speed for his previous races is 15.12 miles per hour.
For the next race across America he will cycle for 8 hours per day.

Estimate how many days Juan will take to complete the race.

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5b
Sme Calculator1 mark

Juan trains for the race.
The average speed he can cycle at increases.
It is now 16.27 miles per hour.

How does this affect your answer to part (a)?

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6a
Sme Calculator3 marks

One uranium atom has a mass of 3.95 x 10-22 grams.

Work out an estimate for the number of uranium atoms in 1 kg of uranium.

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6b
Sme Calculator1 mark

Is your answer to (a) an underestimate or an overestimate?
Give a reason for your answer.

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7
Sme Calculator3 marks

A £1 coin weighs 8.75 g, correct to the nearest 0.01 g.
Mitul weighs the contents of a large bag of £1 coins.
The coins weigh 2.63 kg, correct to the nearest 10 g.

Mitul says

   I am sure that the bag contains exactly £300 because, using bounds,
   2625 ÷ 8.755 = 299.8 to 1 decimal place.

Show that Mitul may not be correct.

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8
Sme Calculator5 marks


The dimensions of a rectangular floor are to the nearest 0.1 metres.

q25-paper2h-nov2017-aqa-gcse-maths

A force of 345 Newtons is applied to the floor.
The force is to the nearest 5 Newtons.

pressure space equals space force over area

Work out the upper bound of the pressure.
Give your answer to 4 significant figures.
You must show your working.

........................N/m2 

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