Page 3. MathsWatch Clip 3 Rounding to the Nearest 10, 100, 1000 Grade E, F and G questions

Transcription

1 MathsWatch Clip Rounding to the Nearest 0, 00, 000 Grade E, F and G questions ) Round these numbers to the nearest 0: a) 6 b) 6 c) 75 d) e) 797 f) 5 84 g) h) 758 ) Round these numbers to the nearest 00: a) 78 b) c) 549 d) 450 e) 8 f) 4 57 g) 9 9 h) 7 65 ) Round these numbers to the nearest 000: a) 850 b) 455 c) 0 d) e) f) g) 90 h) 8 90 Page

2 MathsWatch Clip 5 Multiply and Divide by Powers of 0 Grade E, F and G questions ) Multiply the following numbers by 0, 00 and 000: e.g ) Divide the following numbers by 0, 00 and 000: e.g ) Work out the following: 00 = 65 0 = 7 0 = 59 0 = =. 000 = 4 00 = = = = = = Page 5

3 MathsWatch Clip 8 Grade E, F and G questions Fraction of an Amount ) Work out the following: a) of 0 b) of 9 c) 5 of 5 d) of 4kg e) 4 of 6cm f) 6 of 4kg g) 8 of 48kg h) of 66 i) 9 of 90km j) 7 of 8 k) 5 of 5kg l) 6 of 40km ) Work out the following: a) 4 of 0 b) 4 of 0 c) of d) of e) 4 of 44 f) of 4 g) 5 of 5 h) 4 of 6 i) 7 9 of 8 j) 5 7 of 56 k) 0 of 50 l) 6 of m) 4 of 4 n) 4 of 4 o) 8 of 0 ) The highest possible mark for a Maths test was 64. Dora got 7 8 of the full marks. How many marks did she get? 4) At MathsWatch School there are 500 students. 7 of these students are male. 5 a) What fraction of students are female? b) How many are male? c) How many are female? Page 8

4 MathsWatch Clip Grade E, F and G questions Money Questions ) Bill buys melons at.09 each. a) How much does he spend? b) How much change does he get from 5? ) Jenny is taking her family to the cinema. Jenny pays for adult and children. a) How much does she spend? b) How much change does she get from 0? Cinema Adult: 6.50 Child: 4.00 ) Bob is paid 7 per hour. a) Last monday Bob worked for 8 hours Work out his pay for that day. b) Yesterday Bob was paid 4. Work out how many hours Bob worked. 4) Complete this bill. ½ kg of carrots at 40p per kg =... kg of potatoes at 5p per kg = boxes of tea bags at 90p each =.80 4 packs of yogurts at... each = 4.80 Total =... Page

5 MathsWatch Clip 0 Grade E, F and G questions Rounding to Decimal Places ) Round the following numbers to decimal place a).68 b) c) 0.76 ) Round the following numbers to decimal places a) b) 4.7 c) ) Round the following numbers to decimal place a) b) c) ) Round the following numbers to decimal places a) b) 8.99 c) ) Work out the answer to and give your answer correct to decimal places. 6) Work out the answer to and give your answer correct to decimal place. 7) Work out the answer to 4.74 giving your answer correct to decimal places. 8) Find the answer to 7. giving your answer correct to decimal place. Page 0

6 MathsWatch Clip Grade E, F and G questions Proportion ) 8 bananas cost 4 Work out the cost of 5 bananas. ) Emily bought 4 identical pairs of sock for.60 Work out the cost of 9 pairs of these socks. ) The price of 6 chocolates is 7.0 Work out the cost of 8 chocolates. 4) Theresa bought 5 theatre tickets for 60 Work out the cost of 9 theatre tickets. 5) Jenny buys 4 folders. The total cost of these 4 folders is 6.40 Work out the total cost of 7 of these folders. 6) The cost of 5 litres of petrol is Work out the cost of 0 litres of petrol. 7) maths books cost 7.47 Work out the cost of 5 of these. 8) Five litre tins of paint cost a total of Work out the cost of seven of these litre tins of paint. 9) William earns 9.0 for hours of work. Work out how much he would earn for: a) 0 minutes b) 5 hours 0) It took hours for Emyr to lay 450 bricks. He always works at the same speed. How long will it take Emyr to lay 750 bricks? Page

7 MathsWatch Clip 4 Grade E, F and G questions Distance Tables ) The table shows the distances in kilometres between some cities in the USA. San Francisco 487 New York 4990 Miami Los Angeles Chicago a) Write down the distance between San Francisco and Miami. One of the cities in the table is 454 km from Los Angeles. b) Write down the name of this city. c) Write down the name of the city which is furthest from Chicago. ) The table shows the distances in miles between four cities. London 55 Cardiff 45 York Edinburgh a) Write down the distance between London and York. b) Write down the distance between Edinburgh and Cardiff. c) Which two cities are the furthest apart? Tom travels from London to York. He then travels from York to Edinburgh. He finally travels back to London from Edinburgh. d) Work out the total distance travelled by Tom. Peter and Jessica both drive to York. Peter travels from London whilst Jessica travels from Cardiff. e) Who travels the furthest out of Peter and Jessica and by how much? Page 4

8 MathsWatch Clip 5 Grade E, F and G questions Timetables ) Change the following to the 4 hour clock a) 4.0 pm d) 7.5 pm b) 5 am e) Quarter past midnight c) 0.6 am f) Half past noon ) Change the following to the hour clock a) 06 5 d) 9 5 b) 4 0 e) c) 45 f) Half past midnight ) What is the difference in hours and minutes between the following a) 0.5 pm and.0 pm? b) 4 0 and 7 0? c).50 pm and.0 am? d) 45 and 0 00? 4) Here is part of a train timetable Manchester Stockport Macclesfield Stoke Stafford Euston a) Tim catches the train from Manchester. At what time should he expect to arrive at Euston? b) Jenny arrives at the Stockport train station at (i) How long should she expect to wait for a train to Stoke? (ii) How long should her train journey take? c) Sarah needs to travel to Euston from Macclesfield. She has to arrive at Euston before What is the departure time of the latest train she can catch to get there on time? Page 5

9 MathsWatch Clip 7 Grade E, F and G questions Line Graphs ) The graph shows the number of ice creams sold each day during one week. 00 Number of ice creams sold Sun Mon Tue Wed Thu Fri Sat Day a) How many more ice creams were sold on Sunday than on Friday? b) Explain what might have happened on Monday. c) On Saturday, 50 ice creams were sold. Update the graph with this information. d) About how many ice creams were sold on Wednesday? ) The average temperature, in degrees Centigrade, was recorded for each month. The results are as follows: January 5 C February C March 8 C April C May 5 C June C July 4 C August 9 C September 0 C October C November 8 C December 6 C Draw a line graph to show these results. 0 Temperature in C 0 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Page 7

10 MathsWatch Clip 8 Grade E, F and G questions ) Write down the coordinates of the points A to H. Coordinates y B A C E 4 D F H O G x ) a) Write down the coordinates of: (i) A (ii) B b) Write down the coordinates of the midpoint of the line AB. y B A ) Using the pair of axes, a) Plot the points A(, 0), B(4, 0), C(5, ) and D(, ). b) Join the points in order, to form a shape and name the shape. M is the midpoint of the line segment AC. c) Find the coordinates of M. O y 5 4 x 4) Using the same pair of axes, a) Plot the points R(-, -), S(, ) and T(-, ). b) Join R to S and S to T. RSTU is a kite. c) Write the coordinates of point U O Page 8 x

11 MathsWatch Clip Grade E, F and G questions Angles ) a) One of these angles is an acute angle. Which one? b) Write the names of the other three angles next to them. A B C D ) a) Sketch a triangle which has three internal (inside) acute angles. b) Sketch a right-angled triangle. c) Sketch a triangle with one internal obtuse angle. ) Debbie says she is going to draw a triangle with two internal obtuse angles. Harry says that this is impossible. Is Harry correct? Explain why. 4) Draw a quadrilateral with a) Two internal acute angles, one reflex angle and one obtuse angle. b) Three internal acute angles and one reflex angle. Page

12 MathsWatch Clip Grade E, F and G questions Congruent and Similar Shapes Shape A B C D E F G H I J Congruent to Similar to Fill in the table on the left where possible. You are allowed to use tracing paper to help get the correct answers. A B C D E F H G I J Page

13 MathsWatch Clip Grade E, F and G questions Perimeters and Areas ) Find the perimeter of the following rectangle and pentagon: 4 cm 4 cm 4 cm 6 cm 4.5 cm 4.5 cm ) A rectangle has a perimeter of 40 cm. The length of the longest side is cm. Sketch the rectangle, and find the length of the shorter side. cm ) Find the area of the following rectangles: 4 cm 8 cm. cm 6. cm 7 cm.5 cm 4) A rectangle has an area of 40cm and a length of 8 cm. Sketch the rectangle and find the width. 5) Why can t we find the area of this parallelogram? 5 cm 8 cm 6) What is the area of the parallelogram, below? 4 cm 9 cm 7) Find the area of the following triangles: 6 cm 8 cm 0 cm 0 cm 6.4 cm 4 cm 8) The area of a triangle is 60 cm The base of the triangle is cm long. Sketch a triangle with this area and base and work out the height of the triangle. Page

14 MathsWatch Clip 4 Grade E, F and G questions Volume of Cuboids ) Find the volume of this cuboid. 5 cm 0 cm 6 cm ) Find the volume of this cuboid. 0.8 m.7 m. m ) The volume of this cuboid is 480 cm. Find the length of the side marked x. 6 cm x 8 cm 4) Boxes A and B are both cuboids. How many of box B could be packed into box A? 50 cm 60 cm A 0 cm 5 cm B 0 cm 80 cm Page 4

15 MathsWatch Clip 5 Grade E, F and G questions Converting Metric Measures ) Complete this table by writing down a sensible unit for each measurement. Four have been done for you. The distance between London and Manchester The length of a pen The weight of your Maths Teacher The amount of petrol in a car The length of an ant Metric cm Imperial miles pounds gallons ) Change the following measurements: a) 4 cm to mm d) 0 cm to mm g) km to m b) 7 m to cm e) 5 m to mm h) km to cm c) 5 m to mm f) 4 m to cm i) km to m ) Change the following measurements: a) 00 cm to m d) 6 cm to m g) 486 cm to m b) 4 mm to cm e) 4 cm to m h) 549 mm to cm c) 745 mm to m f) 500 m to km i) 0. km to m 4) Change the following measurements: a) 5 m to cm d) 8. m to cm g) 5. m to cm b) 8 cm to mm e) 70 mm to cm h) 5478 mm to cm c) 50 cm to m f) 8 m to cm i) 8000 cm to m Page 5

16 MathsWatch Clip 7 Grade E, F and G questions Names of Solids ) Draw a sketch of each of the following solids: a) A cube. b) A cylinder. ) Write down the mathematical name of each of these -D shapes. a) b) c) ) Look at this solid. a) What is its name? b) How many vertices does it have? c) How many edges are there? d) How many faces does it have? 4) This is a picture of a pentagonal prism. a) How many faces does it have? b) How many edges does it have? c) How many vertices does it have? Page 7

17 MathsWatch Clip 8 Grade E, F and G questions Tessellations ) On the grid below, show how the shaded shape will tessellate. You should draw at least six shapes. ) On the grid below, show how the shaded shape will tessellate. You should draw at least six shapes. ) On the grid below, show how the shaded shape will tessellate. You should draw at least six shapes. Page 8

18 MathsWatch Clip 9 Grade E, F and G questions Isometric Drawing ) Copy the shape below onto the isometric grid. 4 cm cm 5 cm ) The shape below is made out of cm by cm by cm cubes. Copy the shape onto the isometric grid. 4 cm 6 cm cm Page 9

19 MathsWatch Clip 40 Grade E, F and G questions The Probability Scale ) a) On the probability scale below, mark with a cross ( ) the probability that it will snow in Birmingham in July. 0 b) On the probability scale below, mark with a cross ( ) the probability that it will rain in Wales next year. 0 c) On the probability scale below, mark with a cross ( ) the probability that you will get a tail when you flip a fair coin. 0 d) On the probability scale below, mark with a cross ( ) the probability that you will get a number bigger than 4 when you roll an ordinary dice. 0 ) 4 jelly babies are in a bag. are red, is green and is black. Without looking in the bag, a jelly baby is taken out. a) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is green. 0 b) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is green or black. 0 c) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is red or black. 0 Page 40

20 MathsWatch Clip 50 Grade D questions Value for Money ) Which of the following offer better value for money? Working must be shown a) 00ml of toothpaste for 50p or 400ml of toothpaste for 90p b) 600g of bananas for 70p or 00g of bananas for p c) litres of paint for.60 or 5 litres of paint for.50 d) 60 teabags for.6 or 40 teabags for 0.96 ) Which of these is the best buy? 0 exercise books for exercise books for 7.80 ) Hamza needs to buy litres of paint. At the shop he gets two choices: 500ml for.55 or litre for a) Work out which of these would be the best buy for Hamza. b) How much does he save if he buys the best buy rather than the worst buy? You must show all your working. 4) Honey pots are sold in two sizes. A small pot costs 45p and weighs 450g. A large pot costs 80p and weighs 850g. Which pot of honey is better value for money? You must show all your working. Page 50

21 MathsWatch Clip 5 Grade D questions Find a Percentage with a Calculator ) Work out: a) % of 40 b) 64% of 080 c) 6% of 800 d) 98% of ) Work out: a) 7.5% of 58 b) 0% of 5.40 c) 6.7% of 000 d) 7.5% of ) A computer costs 406 plus VAT at 0%. Work out the total cost of the computer. 4) A car is usually priced at 9800 but now has a discount of 8%. What is the new price of the car? 5) 9500 people attend a festival and % of them are children. How many children are at the festival? 6) 65% of a car, by weight, is steel and iron. If a car weighs 00 kg, what is the weight of steel and iron in the car? 7) Tony earns 7800 per year and receives a.8% pay rise. How much does he now earn? Page 5

22 MathsWatch Clip 5 Grade D questions Change to a Percentage with a Calculator ) Write the following as percentages, giving all your answers to decimal place. a) out of 4 b) 6 out of 85 c) out of 5 d) 50 out of 45 ) Sarah sat a Science test and got a score of 64 marks out of possible marks. What was her mark as a percentage? Give your answer to decimal place. ) In a class of students, 8 of them are boys. What percentage of the class are boys? Give your answer to decimal place. 4) In a French class there are girls and 6 boys. What percentage of the class are girls? Give your answer to decimal place. 5) A new car usually costs Henry gets a discount of 000. What is the discount as a percentage of the usual cost? Give your answer to decimal place. 6) Write out 48 as a percentage of 600. Give your answer to decimal place. 7) In a wood there are 00 oak trees, 650 silver birch trees and 400 wild cherry trees. What percentage of the trees are oak trees? 8) In England in 00 there were 6880 deaths caused by cancer. Of these deaths, 7500 were caused by smoking. What percentage of deaths due to cancer were caused by smoking? Give your answer to decimal place. Page 5

23 MathsWatch Clip 55 Grade D questions Finding a Fraction of an Amount ) Work out these amounts. a) 4 of 0 b) of 60 kg c) 8 4 d) 50 e) 9 of 80 cm f) g) 60 4 h) 5 8 of 48 i) ) There are 600 apples on a tree and there are maggots in 5 of them. How many apples have maggots in them? ) Liz and Lee are travelling in a car from Glasgow to Poole (770 km). At midday they had already travelled 5 7 of the total distance. What distance, in km, had they travelled by midday? 4) A digital camera that cost 49 was sold on ebay for 7 of the original price. What was the selling price? 5) Yesterday Thomas travelled a total of 75 miles. He travelled 5 of this distance in the morning. How many miles did he travel during the rest of the day? 6) Debra received her 5 pocket money on Saturday. She spent of her pocket money on magazines. She spent 5 of her pocket money on a necklace. How much of the 5 did she have left? Page 55

24 MathsWatch Clip 56 Grade D questions Addition and Subtraction of Fractions In all the questions on this page, please give your answers in their simplest form. ) Work out the following: a) b) ) Work out the following: a) b) c) d) ) Work out the following: a) b) c) d) ) Work out the following: 5) Work out the following: a) b) c) d) ) Work out the following: a) b) c) d) ) Ted received his pocket money on Friday. He spent of his pocket money on games. 5 He spent of his pocket money on magazines. 0 What fraction of his pocket money did he have left? a) b) c) d) ) Maisie buys a bag of flour. She uses 4 to bake a cake and to make a loaf. 5 a) What fraction of the bag of flour was used? b) What fraction of the bag of flour is left? 9) Work out the total length of this shape. Give your answer as a mixed number. 4 inches inches Page 56

25 MathsWatch Clip 57 Grade D questions Multiplication and Division of Fractions In all the questions on this page, please give your answers in their simplest form. ) Work out the following: 4) Work out the following: a) a) 5 4 b) b) 7 5 c) 5 7 c) 4 9 d) d) ) Work out the following: 5) Work out the following: a) a) b) 4 8 b) c) 9 4 c) 9 d) 4 5 d) 5 0 ) Work out the following: 6) Work out the following: a) a) 4 b) 5 b) 5 c) c) 5 d) 7 d) 4 Page 57

26 MathsWatch Clip 59 Grade D questions BODMAS Work out the following. for all questions. ) ) ) 5 4 4) 48 (4 ) 5) 7 ( + 6) 6) ) (9 + ) + 5 8) 4 ( + 4) 6 9) ) ) ) ) ) ) ) 4 7 7) 0 0 ( 5+ 4) 8) Page 59

27 MathsWatch Clip 6 Grade D questions Proportion Recipe Type Questions ) Here are the ingredients needed to make 8 pancakes. James makes 4 pancakes. Pancakes Ingredients to make 8 pancakes 50 ml milk egg 40 g flour 5 g butter a) Work out how much milk he needs. Kate makes pancakes. b) Work out how much flour she needs. ) Here are the ingredients for making fish pie for 6 people. Fish pie for 6 people 80 g flour 40 g fish 80 g butter 4 eggs 80 ml milk Jill makes a fish pie for people. a) Work out how much flour she needs. Tim makes a fish pie for 5 people. b) Work out how much milk he needs. ) Here are the ingredients for making pineapple sorbet for 6 people. Pineapple sorbet for 6 people 800 g of pineapple 4 egg whites ½ lemon 00 g caster sugar Trevor makes pineapple sorbet for 8 people. a) Work out how much caster sugar he uses. Sid makes a pineapple sorbet. He uses lemons. b) Work out how many people he makes pineapple sorbet for. Page 6

28 MathsWatch Clip 6 Grade D questions Hard Calculator Questions ) Use your calculator to work out Write down all the figures on your calculator display. ) Use your calculator to work out Write down all the figures on your calculator display. ) Work out Write down all the figures on your calculator display. 4) Use your calculator to work out the value of Write down all the digits from your calculator. Give your answer as a decimal. 5) Use your calculator to work out Write down all the figures on your calculator display. You must give your answer as a decimal. 6) Use your calculator to work out Write down all the figures on your calculator display. You must give your answer as a decimal. 7) Use a calculator to work out Write down all the figures on your calculator display. Page 6

29 MathsWatch Clip 64 Grade D questions Real-Life Money Questions ) Lance goes on holiday to France. The exchange rate is =.5 Euros. He changes 50 into Euros. a) How many Euros should he get? In France, Lance buys a digital camera for 5 Euros. b) Work out the cost of the camera in pounds. ) Whilst on holiday in Spain, Gemma bought a pair of sunglasses for 77 Euros. In England, an identical pair of sunglasses costs The exchange rate is =.40 Euros. In which country were the glasses the cheapest, and by how much? Show all your working. ) Luke buys a pair of trainers in Switzerland. He can pay either 86 Swiss Francs or 56 Euros. The exchange rates are: =.0 Swiss Francs =.40 Euros Which currency should he choose to get the best price, and how much would he save? Give your answer in pounds ( ). 4) The exchange rate in London is =.4 The exchange rate in Paris is = 0.86 Tony wants to change some pounds into euros. In which of these cities would Tony get the most euros? All working must be shown. 5) The total cost of 5 kg of potatoes and kg of carrots is kg of potatoes cost.98. Work out the cost of kg of carrots. Page 64A

30 MathsWatch Clip 64 Grade D questions Real-Life Money Questions ) The cost of 4 kg of bananas is The total cost of kg of bananas and.5 kg of pears is 5.6. Work out the cost of kg of pears. ) In July 007, Peter hired a car in Italy. The cost of hiring the car was 60 The exchange rate was =.5 a) Work out the cost of hiring the car in euros ( ). Peter bought some perfume in Italy. The cost of the perfume in Italy was 50 The cost of the same perfume in London was 4 The exchange rate was still =.5 b) Work out the difference between the cost of the perfume in Italy and the cost of the perfume in London. Give your answer in pounds ( ). ) Jill wants to work out how much tax she needs to pay. Last year she earned 9000 She does not pay Income tax on the first 6475 she earned. She pays tax of 0 pence for each pound she earned above She pays the tax in two equal half-yearly instalments. a) How much Income tax does Jill pay in her first half-yearly instalment? Jill wants to know what percentage of her earnings she pays in tax. b) Calculate the Income tax Jill has to pay as a percentage of her earnings last year. Give your answer correct to decimal place. Page 64B

31 MathsWatch Clip 66 Grade D questions ) y = 5x a) Work out the value of y when x = b) Work out the value of y when x = - ) y = x + 7 a) Work out the value of y when x = 4 b) Work out the value of y when x = - ) y = x + 4t x = 6 t = Work out the value of y. Substitution 9) v = u + 5as u = 6 a =.5 s = 9 0) Work out the value of v. y = p qx p = -0 q = x = -5 Work out the value of y. 4) y = a b a = 4 b = - Work out the value of y. ) v = u + as u = 6 a =.5 s = 9 Work out the value of v. 5) v = a + 5b a = 6 b = - Work out the value of v. 6) y = x a) Work out the value of y when x = 6 b) Work out the value of y when x = -4 7) y = x a) Work out the value of y when x = 5 b) Work out the value of y when x = - ) ) v = u + as u = a = 9.8 s = Work out the value of v. Give your answer correct to decimal place s = ut + 0.5at a = 9.8 t = 5 u = 7 Work out the value of s. 8) y = x + x a) Work out the value of y when x = b) Work out the value of y when x = -4 Page 66

32 Areas and circumferences on pages 7B to 7C MathsWatch Clip 7 Grade D questions Area of Circles Take to be.4 for all questions. ) Find the areas of the following shapes. a) b) c) cm 7m 8cm ) Work out the areas of the following shapes. a) mm b) 0cm ) The diagram shows a circular garden comprising a rectangular pond enclosed by grass. The circular garden has a diameter of 0 m. The rectangular pond measures 8 m by 6 m. Work out the area of the garden covered in grass. Give your answer to the nearest m grass m m grass grass grass 4) The radius of the top of a circular table is 60 cm. The table also has a circular base with diameter 0 cm. a) Work out the area of the top of the table. b) Work out the area of the base of the table. 5) The diagram shows a shape, made from a semi-circle and a rectangle. The diameter of the semi-circle is cm. The length of the rectangle is 7 cm. Calculate the area of the shape. Give your answer correct to significant figures. cm 7 cm Page 7

33 MathsWatch Clip 7 Grade D questions Circumference of Circles Take to be.4 for all questions. ) Find the circumference of the following shapes. a) b) c) cm 5 m 8 cm ) Work out the perimeter of the following shapes. a) mm b) 0 cm ) The radius of the top of a circular table is 60 cm. The table also has a circular base with diameter 0 cm. a) Work out the circumference of the top of the table. Let be.4 b) Work out the circumference of the base of the table. Let be.4 4) The diagram shows a shape, made from a semi-circle and a rectangle. The diameter of the semi-circle is cm. The length of the rectangle is 5 cm. Calculate the perimeter of the shape. Give your answer correct to significant figures. cm 5 cm Page 7A

34 MathsWatch Clips 7 & 7 Grade D questions Area and Circumference of Circles ) A circle has a radius of 5 cm. A square has sides of length cm. 5 cm cm cm Work out the difference between the area of the circle and the area of the square if you take to be. ) Here is a tile in the shape of a semi-circle. 9 cm The diameter of the semi-circle is 9 cm. Work out the perimeter of the tile. Give your answer correct to two decimal places. ) A circle has a radius of 7 cm. 7 cm Work out the area of the circle. Give your answer correct to three significant figures. 4) A circle has a diameter of 4 cm. 4 cm Work out the circumference of the circle. Give your answer correct to three significant figures. Page 7B

35 MathsWatch Clips 7 & 7 Grade D questions Area and Circumference of Circles ) The radius of a circle is 0 cm. 0 cm Work out the area of this circle. Take to be.4 ) The diagram shows a circular pond with a path around it. 6 m m The pond has a radius of 6 m. The path has a width of m. Work out the area of the path. Give your answer correct to significant figures. ) The diagram shows a CD which has a radius of 6 cm. a) Work out the circumference of the CD. Give your answer correct to significant figures. 6 cm CDs of this size are cut from rectangular sheets of plastic. Each sheet is metre long and 50 cm wide. b) Work out the greatest number of CDs which can be cut from one rectangular sheet. Page 7C

36 MathsWatch Clip 7 Grade D questions Area of Compound Shapes ) Find the area of each shape. a) b) 0 cm 0 cm 4 cm cm 8 cm 8 cm 5 cm 5 cm c) d) 4 m 6 m 6 mm 9 m 5 mm 9 mm 6 mm mm ) Find the shaded area of each shape. a) b) cm cm cm 6 cm 7 cm 7 cm 4 cm 0 cm c) d) 6 mm mm mm mm 4 mm m 0 mm m Page 7A

37 MathsWatch Clip 7 Grade D questions Area of Compound Shapes ) A D ABCD is a rectangle. X is the midpoint of AB. Y is the midpoint of BC. Z is the midpoint of CD. X Z B Y C What fraction of the total area of ABCD is shaded? Show clearly how you get your answer. ) D 8 cm C 6 cm A cm B The diagram shows a trapezium ABCD. The parallel sides of the trapezium are 8 cm and cm. The height of the trapezium is 6 cm. Find the area of the trapezium ABCD. Page 7B

38 MathsWatch Clip 8 Grade D questions Plans and Elevations ) The diagram shows a prism drawn on an isometric grid. Front a) On the grid below, draw the front elevation of the prism from the direction marked by the arrow. b) On the grid below draw a plan of the prism. Page 8A

39 MathsWatch Clip 8 Grade D questions Plans and Elevations ) Here is the plan and front elevation of a prism. The front elevation shows the cross section of the prism. Plan Front Elevation On the grid below, draw the side elevation of the prism. Page 8B

40 MathsWatch Clip 8 Grade D questions Plans and Elevations ) The diagram shows a solid prism made from centimetre cubes. a) On the centimetre square grid, draw the front elevation of the solid prism from the direction shown by the arrow. b) On the centimetre square grid below, draw the plan of the solid prism. Page 8C

41 MathsWatch Clip 8 Grade D questions Plans and Elevations ) The diagram shows a solid prism. cm cm cm 4 cm a) On the grid below, draw the front elevation of the prism from the direction of the arrow. b) On the grid below, draw the plan of the prism. Page 8D

42 MathsWatch Clip 8 Grade D questions Nets ) Sketch nets of these solids. a) b) ) On squared paper draw accurate nets of these solids. a) Cube b) Cuboid 4 cm 5 cm 4 cm 4 cm 8 cm 6 cm c) Right-angled triangular prism d) Triangular prism 5 cm cm 5 cm 4 cm 8 cm 7 cm 7 cm cm ) The two nets, below, are folded to make cubes. Two other vertices will meet at the the dot, A. Mark them with As. One other vertex will meet the dot B. Mark it with B. a) A b) B Page 8

43 MathsWatch Clip 90 Grade D questions Simple Probability ) A blue dice and a red dice are rolled. a) How many different outcomes are possible? b) List the possible outcomes. ) Three coins are flipped. One possible outcome is H, H, H List all the outcomes. ) If five coins are flipped, how many possible outcomes are there? 4) A dice is rolled and a coin is flipped. List all the possible outcomes. 5) A box contains grey counters and white counters. A counter is taken from the box at random. What is the probability of choosing a white counter? 6) There are blue counters, 5 red counters and 7 green counters in a bag. A counter is taken from the bag at random. a) What is the probability that a green counter will be chosen? b) What is the probability that a blue or red counter will be chosen? 7) In a class there are 0 boys and 5 girls. A teacher chooses a student at random from the class. Eric says that the probability a boy will be chosen is 0.5 because a student can be either a boy or a girl. Jenny says that Eric is wrong. Decide who is correct - Eric or Jenny - giving reasons for your answer. 8) Spinner A has numbers to 4 on it. Spinner B has numbers to on it. Both spinners are spun and the numbers on each are added together to give a score. What is the probability that the score will be a) 7? b) or 4? Page 90

44 MathsWatch Clip 9 Grade D questions Mutually Exclusive Events ) If the probability of passing a driving test is 0.54, what is the probability of failing it? ) The probability that a football team will win their next game is. The probability they will lose is. What is the probability the game will be a draw? ) On the school dinner menu there is only ever one of four options. Some of the options are more likely to be on the menu than others. The table shows the options available on any day, together with three of the probabilities. Food Curry Sausages Fish Casserole Probability a) Work out the probability of the dinner option being Fish. b) Which option is most likely? c) Work out the probability that it is a Curry or Sausages on any particular day. d) Work out the probability that it is not Casserole. 4) Julie buys a book every week. Her favourite types are Novel, Drama, Biography and Romance. The table shows the probability that Julie chooses a particular type of book. Type of book Novel Drama Biography Romance Probability x x a) Work out the probability that she will choose a Novel or a Drama. b) Work out the probability that she will choose a Biography or a Romance. The probability that she will choose a Biography is the same as the probability she will choose a Romance. c) Work out the probability that she will choose a Biography. Page 9

45 MathsWatch Clip 9 Grade C questions Overview of Percentages ) Find the following to the nearest penny: a) % of 670 b) % of 580 c) 48% of 64 d) % of 7.50 e) 87% of 44 f) 5.7% of 7000 g).8% of 980 h) 4% of 6.4 i) 48.6% of 97.6 j) 78.4% of.8 k) 4.5% of l) 0.57% of ) Change the following to percentages, giving all answers to decimal place: a) 6 out of 8 b) 8 out of 7 c) 4 out of 8 d) 4 out of 96 e) 7 out of 40 f) 4 out of 659 g) 87 out of 90 h) 4.7 out of i) 6.9 out of 79 j) 4.8 out of.6 k) 65.8 out of 0.7 5) A shop gives a discount of 0% on a magazine that usually sells for.80. Work out the discount in pence. 6) A television costs 596 plus VAT at 7.5%. Work out the cost of the television including VAT. 7) Peter has 8 trees in his garden. 6 of the trees are pear trees. What percentage of the trees in his garden are pear trees? ) Find the following: a) 0% of 700 b) 0% of 400 c) 0% of 50 d) 0% of 50 e) 0% of 68 f) 0% of 46 g) 0% of 6.50 h) 0% of.0 i) 0% of 600 j) 0% of 900 k) 60% of 800 l) 0% of 650 m) 40% of 0 n) 5% of 00 o) 5% of 60 p) 65% of 000 q) 45% of 64 r) 85% of 96 s) 7.5% of 800 t) 7.5% of 40 u) 7.5% of ) Change the following to percentages: a) 46 out of 00 b) 8 out of 50 c) 7 out of 5 d) out of 5 e) 9 out of 0 f) 6 out of 0 g) 7 out of 0 h) 9.5 out of 0 i) 0 out of 40 j) 6 out of 40 k) 0 out of 40 l) out of 40 m) 8 out of 80 n) out of 80 o) 60 out of 80 p) out of 5 q) 4 out of 5 r) 5 out of 75 s) 4 out of 75 t) 0 out of 75 8) Jane scored 7 out of 4 in a Maths test and 9 out of 6 in a Science test. What were her percentages in both subjects to decimal place? 9) 0) ) In class 9A there are 7 girls and 8 boys. What percentage of the class are girls? A shop decides to reduce all the prices by 5%. The original price of a pair of trainers was 70. How much are they after the reduction? VAT at 7.5% is added to the price of a car. Before the VAT is added it cost How much does it cost with the VAT? Page 9A

46 MathsWatch Clip 9 Grade C questions Overview of Percentages ) The normal price of a dog basket is 0. In a sale the price of the dog basket is reduced by 5%. Work out the sale price of the dog basket. ) Tony bought a car. The total cost of the car was 6000 plus VAT at 7½%. Tony paid 000 when he got the car. He paid the rest of the total cost of the car in 0 equal monthly payments. Work out the cost of each monthly payment. ) Jill bought a car. The total cost of the car was 8000 plus VAT at 7½%. Jill paid 400 when she got the car. She paid the rest of the total cost of the car in equal monthly payments. Work out the cost of each monthly payment. 4) The cost of a radio is the list price plus VAT at 7.5%. The list price of the radio is 0. Work out the cost of the radio. 5) A computer costs 460 plus 7.5% VAT. Calculate the total cost of the computer. 6) Work out 68 as a percentage of ) A car tyre costs 90 plus VAT at 7.5%. Work out the total cost of the tyre. 8) Kate got 9 out of 40 in a test. Write 9 out of 40 as a percentage. Page 9B

47 MathsWatch Clip 9 Grade C questions Increase/Decrease by a Percentage ) Increase: a) 500 by 0% c) 80 by 5% b) 0 by 0% d) 75 by 0% ) Decrease: a) 400 by 0% c) 40 by 5% b) 80 by 0% d) 5 by 0% ) The price of a laptop is increased by 5%. The old price of the laptop was 00. Work out the new price. 4) The price of a 6800 car is reduced by 0%. What is the new price? 5) Increase: a) 65 by % c) 600 by 7.5% b) 0 by % d) 70 by 7.5% 6) Decrease: a) 4 by 5% c) 5 by 8.5% b) 79 by % d) 8900 by 8% 7) The price of a mobile phone is plus VAT. VAT is charged at a rate of 7.5%. What is the total price of the mobile phone? 8) In a sale, normal prices are reduced by 7%. The normal price of a camera is 89. Work out the sale price of the camera. 9) A car dealer offers a discount of 0% off the normal price of a car, for cash. Peter intends to buy a car which usually costs He intends to pay by cash. Work out how much he will pay. 0) A month ago, John weighed 97.5 kg. He now weighs 4.5% more. Work out how much John now weighs. Give your answer to decimal place. Page 9

48 MathsWatch Clip 0 Grade C questions ) Simplify the following a) x + x b) x + x c) 5t t d) 7y 6y e) x + x + x f) g g + 6g g) x 7x + 8x h) y y y + 6y Algebraic Simplification 4) Simplify the following a) x x b) x x x x x c) y y y 5) Simplify the following a) x x 4 b) x x 5 c) y y d) x x x 4 e) y y y 4 ) Simplify the following a) xy + xy b) 5xy xy c) 4x y + x y d) xy xy e) x y + 4x y x y f) 6a bc 4 + 5a bc 4 a bc 4 ) Simplify the following a) x + y + x + y b) x + y + x + 4y c) a + 4b a + b d) x + 4y x y e) 6x y + x + 5y f) 4x y x 5y g) t + 4u + t 7u h) xy + t xy 4t 6) Simplify the following a) x x b) 4x x c) t t d) 4y y e) x x x 7) Simplify the following a) x y b) x y c) 5r s t d) 6x y z 8) Simplify the following a) x y b) 4x y x c) xy xy d) 6xy x y y e) x y 5x 4 y f) tu t u 4tu Page 0A

49 MathsWatch Clip 0 Grade C questions Algebraic Simplification ) a) Simplify 4p 6q b) Simplify d d d d c) Simplify t t 8) a) Simplify a + 5c a + c b) Simplify x x 4 c) Simplify 4x y 4 5xy ) a) Simplify 4a + c a + c b) Simplify x 6c x + c 9) Simplify 6x + 8y + x 0y 0) a) Simplify x x x x b) Simplify x y ) a) Simplify 5xt + xt 4xt b) Simplify 4x + y x + 4y c) Simplify m m m d) Simplify n t 4) Simplify x 4x 5 y 4 ) a) Simplify pq + pq b) Simplify 5x + y x 4y ) a) Simplify 6a + 5b b + a b) Simplify x 4 + x 4 5) Simplify 4x + y x + 6y ) a) Simplify x + y + x + y + x b) Simplify t + t + t 6) a) Simplify t 4 t 5 b) Simplify a a a 4) a) Simplify a a b) Simplify x y 4xy 7) a) Simplify x 6 x b) Simplify x y 4x 5 y 4 5) a) Simplify d + e d + 4e b) Simplify x x c) Simplify 5t + 8d t d d) Simplify 4t q Page 0B

50 MathsWatch Clip 0 Grade C questions Expanding and Simplifying Brackets ) Expand these brackets a) (x + ) b) (x + 4) c) 5(p q) d) 4(x + y ) e) 6(r r ) 5) Expand and simplify a) (x + y) + (x + y) b) (x + y) + (5x + y) c) 5(x + y) + (x + y) d) (c + d) + (c + d) e) 4(p + q) + (p + q) ) Expand these brackets a) x(x ) b) x(x + 5) c) p(p 7q) d) y(y + 6y ) e) x(r + r ) 6) Expand and simplify a) (x + y) + (x y) b) 5(x + y) + (x y) c) 4(x y) + (x + y) d) 6(c d) + (c d) e) (5p q) + (p q) ) Expand these brackets a) x(x 5) b) 4x(x + ) c) 5p(4p q) d) y(y + 4x ) e) x(x + r ) 7) Expand and simplify a) (x + y) (x y) b) 5(x y) (x y) c) 7(x y) (x + y) d) 6(x y) (x + y) e) (5p q) (p q) 4) Expand these brackets a) x(x ) b) x(x + ) c) 5p (4p ) d) y (y + 4y) e) xy(x + y ) Page 0A

51 MathsWatch Clip 0 Grade C questions Expanding and Simplifying Brackets ) Expand and simplify a) (x + )(x + ) b) (x + 5)(x + ) c) (x + )(x + 4) d) (x + 6)(x + 4) e) (x + 5)(x + 7) 4) Expand and simplify a) (x 7)(x + ) b) (p 6)(p + 4) c) (e )(e 7) d) (x + 8)(x + ) e) (x 5)(x 5) ) Expand and simplify a) (x + 5)(x ) b) (x 7)(x + ) c) (x )(x + ) d) (x + 4)(x ) e) (x 5)(x + 5) 5) Expand and simplify a) (x + )(x + ) b) (p 4)(p + 5) c) (e )(e 4) d) (4x 6)(x + ) e) (x )(x + ) ) Expand and simplify a) (x )(x 4) b) (x )(x 6) c) (x )(x ) d) (x 7)(x ) e) (x 4)(x 5) 6) Expand and simplify a) (x + y)(x + y) b) (p q)(4p + 5q) c) (4e f )(e f ) d) (6x y)(6x + y) e) (x y)(x 5y) Page 0B

52 MathsWatch Clip 04 Grade C questions Factorisation ) Factorise a) x + 4 b) y + 0 c) x + d) x 6 e) 5x 5 ) Factorise a) p + 7p b) x + 4x c) y y d) p 5p e) x + x ) Factorise a) x + 6x b) y 8y c) 5p + 0p d) 7c c e) 6x + 9x 4) Factorise a) x 4xy b) t + 0tu c) 6x 8xy d) x y + 9xy Page 04

53 MathsWatch Clip 0 Grade C questions Trial and Improvement ) The equation x x = 9 has a solution between and 4 Use a trial and improvement method to find this solution. Give your answer correct to decimal place. You must show all your working. ) The equation x 4x = 5 has a solution between and 4 Use a trial and improvement method to find this solution. Give your answer correct to decimal place. You must show all your working. ) The equation x x = 68 has a solution between 4 and 5 Use a trial and improvement method to find this solution. Give your answer correct to decimal place. You must show all your working. 4) The equation x + 4x = 0 has one solution which is a positive number. Use a trial and improvement method to find this solution. Give your answer correct to decimal place. You must show all your working. Page 0

54 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) Complete the table of values for y = x 4x + x y On the grid, draw the graph of y = x 4x y - O x - - Page 6A

55 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) a) Complete the table of values for y = x x x y b) On the grid, draw the graph of y = x x y O 4 - x c) Use your graph to estimate the values of x when y = - Page 6B

56 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) a) Complete the table of values for y = x + x 4 x y b) On the grid, draw the graph of y = x + x 4 y O - x Page 6C

57 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) a) Complete the table of values for y = x x x y b) On the grid, draw the graph of y = x x for values of x from - to y O x c) Use the graph to find the value of y when x = -.5 d) Use the graph to find the values of x when y = 4-5 ) a) Complete the table of values for y = x x x y 8 0 b) On the grid, draw the graph of y = x x for values of x from - to y O x c) (i) On the same axes draw the straight line y =.5 (ii) Write down the values of x for which x x =.5-5 Page 6D

58 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) The diagram shows the graph of y = x 5x y O x a) Use the graph to find estimates for the solutions of (i) x 5x = 0 (ii) x 5x = 6 b) Use the graph to find estimates for the solutions of the simultaneous equations y = x 5x y = x 4 Page 6E

59 MathsWatch Clip 7 Grade C questions Real-Life Graphs 5 ) Sarah travelled 0 km from home to her friend s house. She stayed at her friend s house for some time before returning home. Here is the travel graph for part of Sarah s journey. 0 Distance from home (km) Time of day a) At what time did Sarah leave home? b) How far was Sarah from home at 0 0? Sarah left her friend s house at 0 to return home. c) Work out the time in minutes Sarah spent at her friend s house. Sarah returned home at a steady speed. She arrived home at 50 d) Complete the travel graph. e) Work out Sarah s average speed on her journey from her home to her friend s house. Give your answer in kilometres per hour. f) Work out Sarah s average speed on her journey home from her friend s house. Give your answer in kilometres per hour. Page 7

60 MathsWatch Clip 8 Grade C questions Pythagoras Theorem ) Find the length of side a. Give your answer to decimal place. cm a 4 cm ) Find the length of side b. Give your answer to decimal place. b 5 cm 8 cm ) Find the length of side c. Give your answer to decimal place. 0 cm cm c 4) Find the length of side d. Give your answer to decimal place. d 8 cm 5 cm 5) Find the length of the diagonal of this rectangle. Give your answer to decimal place. 9 cm 6 cm Page 8A

61 MathsWatch Clip 8 Grade C questions ) Find the length of side AC. Give your answer to decimal place. A Pythagoras Theorem 4) Below is a picture of a doorway. Find the size of the diagonal of the doorway. Give your answer to decimal place. cm.m 0.8m B 7cm ) Find the length of side QR Give your answer to decimal place. Q 4.8cm P C 5) In the sketch of the rectangular field, below, James wants to walk from B to D. A B 60m R 7.6cm D 50m Which of the following routes is shorter and by how much? From B to C to D or straight across the field from B to D. Give your answer to the nearest metre. C ) Find the length of side SU Give your answer to decimal place. T 4cm cm S 6) Fiona keeps her pencils in a cylindrical beaker as shown below. The beaker has a diameter of 8cm and a height of 7cm. Will a pencil of length 9cm fit in the beaker without poking out of the top? All workings must be shown. U Page 8B

62 MathsWatch Clip 9 Grade C questions Pythagoras - Line on a Graph ) Points P and Q have coordinates (, 4) and (5, ). Calculate the shortest distance between P and Q. Give your answer correct to decimal place. 6 y 5 4 P Q O x ) Points A and B have coordinates (-4, ) and (, -). Calculate the shortest distance between A and B. Give your answer correct to decimal place. 5 y A O x - B Page 9

63 MathsWatch Clip 0 Grade C questions Surface Area of Cuboids ) A cube has sides of length 5 cm. Find the total surface area of the cube. 5 cm 5 cm 5 cm ) A cuboid has sides of length 0 cm, 6cm and 7 cm. Find the total surface area of the cuboid. 6 cm 0 cm 7 cm ) A cuboid has sides of length cm, 4.5cm and 6 cm. Find the total surface area of the cuboid. 4.5 cm cm 6 cm Page 0

64 MathsWatch Clip Grade C questions Surface Area of Triangular Prisms ) Find the surface area of this triangular prism. cm 5 cm 4 cm 6 cm ) Find the surface area of this triangular prism. cm cm cm 0 cm 5 cm ) With the aid of Pythagoras Theorem, find the surface area of this triangular prism. Give your answer correct to significant figures. 9. cm 4.6 cm. cm Page

65 MathsWatch Clip Grade C questions Volume of a Prism ) The diagram shows a cuboid. Work out the volume of the cuboid. 50 cm 5 cm 0 cm ) Calculate the volume of this triangular prism. 4 cm 5 cm cm 9 cm ) An ice hockey puck is in the shape of a cylinder with a radius of.8 cm and a thickness of.5 cm. Take to be.4.5 cm Work out the volume of the puck. Give your answer correct to significant figures..8 cm 4) A cuboid has: a volume of 80cm a length of 5 cm a width of cm Work out the height of the cuboid. 5) Work out the maximum number of boxes which can fit in the carton. 50 cm Box 0 cm 00 cm Carton 80 cm 0 cm 00 cm Page A

66 MathsWatch Clip Grade C questions Volume of a Prism ) Work out the volume of the prism. cm 4 cm 5 cm 0 cm ) A solid cylinder has a radius of 5 cm and a height of 0 cm. 0 cm Work out the volume of the cylinder. Take to be.4 Give your answer correct to significant figures. 5 cm ) 8 cm 6 cm 0 cm cm The diagram shows a solid prism made from metal. The cross-section of the prism is a trapezium. Find the volume of the prism. You must state your units. Page B

67 MathsWatch Clip Grade C questions Similar Shapes ) B 05 6 cm 8 A 0 cm D C P Q 05 8 cm 5 cm S R ABCD and PQRS are mathematically similar. a) Find the length of PQ. b) Find the length of AD. Q ) B 5 cm 4 cm A C 6 cm P 9 cm R Triangles ABC and PQR are mathematically similar. Angle A = angle P. Angle B = angle Q. Angle C = angle R. AC = 6 cm. BC = 4 cm. PR = 9 cm. PQ = 5 cm a) Work out the length of QR. b) Work out the length of AB. Page A

68 MathsWatch Clip Grade C questions ) Similar Shapes A 5 cm B.5 cm C Triangle ABC is similar to triangle ADE. AC = 5 cm. CE = 6 cm. BC =.5 cm. 6 cm Work out the length of DE. D E ) ABC and AED are straight lines. EB is parallel to DC. Angle ACD = 90 A AB = 0 cm BC = 5 cm EB = 6 cm 0 cm a) Work out the length of DC. b) Work out the area of the trapezium EBCD. E 6 cm B 5 cm D C Page B

69 MathsWatch Clip Grade C questions Similar Shapes ) The diagram shows two quadrilaterals that are mathematically similar. B P 8 cm Q A cm S 4 cm R D 4 cm C a) Calculate the length of AB b) Calculate the length of PS ) SV is parallel to TU. RST and RVU are straight lines. RS = 9 cm, ST = cm, TU = 7 cm, RV = 6 cm Calculate the length of VU. R 9 cm 6 cm cm S V T 7cm U ) BE is parallel to CD. ABC and AED are straight lines. AB = 4 cm, BC = 6 cm, BE = 5 cm, AE = 4.4 cm a) Calculate the length of CD. A b) Calculate the length of ED. 4 cm 4.4 cm B E 6 cm 5 cm C D Page C

70 MathsWatch Clip 4 Grade C questions Converting Metric Units ) Change 9 m into cm ) How many square metres are there in 5 square kilometres? ) Change 4 cm into mm 4) Convert 6.5 m into mm 5) Change m into cm 6) How many cubic millimetres are there in cubic centimetres? 7) Change 7 m into mm 8) A tiler wants to tile a rectangular wall which measures 4 m by.5 m. Each tile measures 6 cm by 0 cm. How many tiles will he need for the wall? Tile 0 cm.5 m 6 cm 4 m 9) A carpet-fitter is laying carpet tiles on a rectangular floor which measures 7.5 m by 4.5 m. Each carpet tile measures 50 cm by 50 cm. How many carpet tiles will he need for the floor? Carpet tile 4.5 m 50 cm 50 cm 7.5 m Page 4

71 MathsWatch Clip 5 Grade C questions Bounds ) A silver necklace has a mass of grams, correct to the nearest gram. a) Write down the least possible mass of the necklace. b) Write down the greatest possible mass of the necklace. ) Each of these measurements was made correct to one decimal place. Write the maximum and minimum possible measurement in each case. a) 4.6 cm b) 0.8 kg c).5 litres d) 5.0 km/h e) 0. s f) 6. m g) 6.7 m/s h) 0. g ) Each side of a regular octagon has a length of 0.6 cm, correct to the nearest millimetre. a) Write down the least possible length of each side. b) Write down the greatest possible length of each side. c) Write down the greatest possible perimeter of the octagon. 4) A girl has a pen that is of length cm, measured to the nearest centimetre. Her pencil case has a diagonal of length.5 cm, measured to the nearest millimetre. Explain why it might not be possible for her to fit the pen in the pencil case. 5) A square has sides of length 7 cm, correct to the nearest centimetre. a) Calculate the lower bound for the perimeter of the square. b) Calculate the upper bound for the area of the square. Page 5