Limits of accuracy and bounds

The length of a ship is 142.8 m, correct to 1 decimal place.

Write down the lower bound of the length of the ship.

Write down the upper bound of the length of the ship.

Anna makes cups. Each cup costs 6 Swiss francs to make.

Anna puts the cups into boxes to sell. Each box contains 4 cups.

Anna sells 80 boxes of cups for a total of 2160 Swiss francs.

Work out the percentage profit Anna makes. Show your working clearly.

The height of each cup is 9 cm, correct to the nearest cm

Write down the lower bound of the height.

The weight of each cup is 120 g, correct to the nearest 10 g

Write down the upper bound of the weight.

The length of a ship is 142.8 m, correct to 1 decimal place.

Write down the lower bound of the length of the ship.

Write down the upper bound of the length of the ship.

Anna makes cups. Each cup costs 6 Swiss francs to make.

Anna puts the cups into boxes to sell. Each box contains 4 cups.

Anna sells 80 boxes of cups for a total of 2160 Swiss francs.

Work out the percentage profit Anna makes. Show your working clearly.

The height of each cup is 9 cm, correct to the nearest cm

Write down the lower bound of the height.

The weight of each cup is 120 g, correct to the nearest 10 g

Write down the upper bound of the weight.

The diagram shows a square inside rectangle ABCD

The total area of the region shown shaded in the diagram is Xcm²

AB 11 5. cm correct to the nearest 0.5cm BC 9 2. cm correct to 2 significant figures side of square 4 1.cm correct to 2 significant figures

By considering bounds, work out the value of X to a suitable degree of accuracy. Show your working clearly.

P a(c y)

a = 8.3 correct to 2 significant figures c = 2 correct to 1 significant figure y = 15 correct to the nearest 5

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

Diego builds a fence using fence panels.

The total length of the fence is 50 metres, correct to the nearest 5 metres. The length of each fence panel is 1.3 metres, correct to the nearest 10 cm.

The cost of each fence panel is £8.65

Diego may only buy complete fence panels. Diego only pays for the number of panels he needs to build the fence.

Work out the greatest difference in the possible amounts that Diego could pay to build the fence. Show your working clearly.

A solid sphere has a radius of 2.8 centimetres, correct to 1 decimal place. The sphere has a mass of M π grams, where M = 260 correct to 2 significant figures.

Work out the upper bound for the density of the sphere. Give your answer in g / cm³ correct to 2 decimal places. Show your working clearly.

_........ g / cm³

p = 0.51 correct to 2 significant figures. r = 6.3 correct to 2 significant figures.

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

The acceleration, a, of an object is given by

where

v = 45.23 correct to 2 decimal places u = 5.12 correct to 2 decimal places t = 8.5 correct to 2 significant figures

By considering bounds, work out the value of a to a suitable degree of accuracy. Show your working clearly and give a reason for your answer.

The weight of a cake is 2.75 kg, correct to 2 decimal places.

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

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

Her answer is 13 332.299 17

Penny’s answer is not sensible.

By rounding each number to one significant figure, work out a suitable estimate to show that her answer is not sensible. Show your working clearly.

The weight of a cake is 2.75 kg, correct to 2 decimal places.

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

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

Her answer is 13 332.299 17

Penny’s answer is not sensible.

By rounding each number to one significant figure, work out a suitable estimate to show that her answer is not sensible. Show your working clearly.

Kaidan and Sonja went on two different car journeys.

For Kaidan’s journey d istance = 80 km correct to the nearest 5 km time = 2.7 hours correct to 1 decimal place

For Sonja’s journey d istance = 33 km correct to 2 significant figures time = 1 hour correct to the nearest 0.1 hour

Kaidan says, “My average speed could have been greater than Sonja’s average speed.”

By considering bounds, show that Kaidan is correct. Show your working clearly.

w = 3.45 correct to 2 decimal places. x = 1.9 correct to 1 decimal place. y = 5 correct to the nearest whole number.

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

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

Write down the lower bound of the length of each side of the octagon.

Write down the upper bound of the length of each side of the octagon.

Here is a triangle XYZ.

The length XZ and the angles YXZ and XYZ are each given correct to 2 significant figures.

Calculate the upper bound for the length YZ. Give your answer correct to one decimal place. Show your working clearly.

15

v = 9.6 correct to 1 decimal place u = 3.8 correct to 1 decimal place t = 1.84 correct to 2 decimal places

Calculate the upper bound for the value of a. Give your answer as a decimal correct to 2 decimal places. Show your working clearly.

t = 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.

A metal block has a mass of 5 kg, correct to the nearest 50 grams. The block has a volume of (1.84 10^–3) m³, correct to 3 significant figures.

Work out the upper bound for the density of the block. Give your answer in kg/m³ correct to 1 decimal place. Show your working clearly.

The diagram shows rectangle ABCD with rectangle EFGH cut out to form the shaded region.

AD = 8.3 cm correct to one decimal place DC = 7.2 cm correct to one decimal place EH = 6.2 cm correct to one decimal place HG = 5.3 cm correct to one decimal place

Work out the upper bound of the area of the shaded region. Show your working clearly.

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

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

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

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

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

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

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

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

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

G=e−f

e= 17 correct to the nearest integer f= 9.4 correct to one decimal place

Work out the upper bound for the value of G.

a= 58.4 correct to 3 significant figures. c= 20 correct to 2 significant figures. d= 3.6 correct to 2 significant figures.

Work out the upper bound for the value of P. Show your working clearly. Give your answer correct to 2 decimal places.

C = ba

a = 6 correct to the nearest integer b = 15 correct to the nearest 5

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

20

a = 3.46 correct to 3 significant figures. b = 6.3 correct to 1 decimal place.

Work out the upper bound for the value of x. Give your answer as a decimal correct to 3 significant figures. Show your working clearly.

e = 8.31 correct to 2 decimal places f = 0.65 correct to 2 decimal places

Work out the lower bound for the value of e – f Show your working clearly.

p = 8.4 correct to 2 significant figures. q = 6.3 correct to 2 significant figures. t = 0.27 correct to 2 significant figures.

Work out the upper bound for the value of a. Show your working clearly. Give your answer correct to 1 decimal place.