KS3 Mathematics. Homework Pack E: Level 7. Stafford Burndred ISBN

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1 p KS3 Mathematics Homework Pack E: Level 7 Stafford Burndred ISBN Pearson Publishing, 998 Published by Pearson Publishing Limited, 998 A licence to copy the material in this pack is only granted to the purchaser strictly within their school, college or organisation. The material must not be reproduced in any other form without the express written permission of Pearson Publishing. Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel Fax Web site:

2 C = / x = Multiplication and division by numbers less than one 8 x x x x x x x x x x A B C D E 0 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

3 C = / x = Mental arithmetic shortcuts 36 x x x x x x x x x x A B C D E 0 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

4 C = / x = 3 Mental arithmetic shortcuts 6. x x x x x x x x x x A B C D E 0 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

5 C = / x = 4 Rounding numbers Write 38 correct to one significant figure.... Write 687 correct to two significant figures Write 3078 correct to three significant figures Write 73 correct to one significant figure Write 73.0 correct to three significant figures Write 6.83 correct to two significant figures Write 5.7 correct to one decimal place Write 3.67 correct to two decimal places Write correct to three decimal places Write correct to two significant figures Write 6.86 correct to one decimal place.... Write correct to three decimal places Write 779 correct to one significant figure Write 6008 correct to three significant figures Write.09 correct to one decimal place Write correct to two significant figures Write correct to three decimal places Write correct to one decimal place Write 7.37 correct to two significant figures Write correct to two decimal places A B C D E 0 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

6 C = / x = 5 Estimating Estimate the answers to the following questions by rounding each number to one significant figure. 936 x x x x x x x litres of water flow over a waterfall each second. Estimate how long 0 80 litres will take to flow over the waterfall A greengrocer sold 68. kg of potatoes at 9p per kilogram. Estimate the total value of the sale A lorry can carry 49 tonnes in one load. Estimate how many loads will be required to transport 0 3 tonnes of bricks A glass holds 0.98 l. Estimate how many glasses can be filled from a tank containing 89.3 l A B C D E 0 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

7 6 Using a calculator (brackets and memory) Give your answers correct to six significant figures where appropriate. Show your calculator keys for questions and 5..6 (5.83.9) ( )... 3 ( ) (3.87 x 6.34) (8.75.7) x x ( ) (.7 x 3.85) x x.987 The make and type of my calculator is: A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

8 7 Using a calculator (using the memory) Find the value of y by using the memory. Give your answers correct to six significant figures. x =.364 in all of the questions. y = x 3 + x + x... y = x 5 x 4 + x y = 6x 8 3x 5 + x y = 8x 9 7x 5 + 6x y = 3x 4 x 3 7x + 8x y = x 3 4x + 6x y = 7x 3 3x y = x 8 3x 6 + 4x y = 7x 6 3x 5 4x y = 3x 5 x 4 3x y = 6x 8 4x 5 3x 4... y = 4x 7 3x 5 x A B C D E Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

9 8 Solving problems An empty tank is filled with water at the rate of 00 cc per second. The dimensions of the tank are m by 3 m by 4 m. What fraction of the tank is filled after two hours? Give your answer in its lowest terms.... A small packet of soap powder costs 33p and contains 750 g. A large packet of soap powder costs.68 and contains 5 kg. Mrs Wright needs to buy 5 kilograms for her laundry business. How much money will she save by buying the large packets instead of the small packets of soap powder?... 3 The selling price of a car comprises the cost of material, the cost of production and the profit. The ratio of cost of production to the cost of material is 5:7. A car was sold for % of the selling price was profit. What was the cost of the material used in the car? Jason had a cough. He bought a 0. litre bottle of cough medicine for.40. The label on the bottle stated Take a 5 ml spoonful of medicine three times each day. Jason took the medicine for seven days. What was the value of the medicine left in the bottle? A B C D E 4 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

10 9 Fractions and percentages Find 5 6 of 4... Find 3 8 of Increase 8 by Increase 6 by Decrease 75 by Decrease 60 by Find 4% of Find 3% of Increase 80 by 0% Increase 50 by 36% 0... Decrease 300 by 8%... Decrease 80 by 7%... 3 A meal costs 8 plus 7.5% VAT. What is the total cost? pupils attended a school in 998. In 999 numbers increased by 8. How many pupils attended in 999? A class had 5 pupils. 6% of the pupils owned a computer. How many pupils owned a computer? A bus journey normally takes 35 minutes. Road works increased the time by 5. How long did the journey take? A B C D E 6 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

11 0 Number patterns Here is a pattern made out of matchsticks:? a Draw the missing matchsticks in the pattern. a... b c What is the rule to find the nth term? (Give your answer using algebra.) b... Use your rule to find the number of matchsticks in: i the 8th term. ci... ii the 64th term. cii... Here is a pattern: 7, 0, 3, 6, 9 a What is the next number in the pattern? a... b c What is the rule to find the nth term? (Give your answer using algebra.) b... Use your rule to find: i the 0th term. ci... ii the 40th term. cii... 3 Here is a pattern: 0,, 6, 4, a What is the next number in the pattern? 3a... b c What is the rule to find the nth term? (Give your answer using algebra.) 3b... Use your rule to find: i the 38th term. 3ci... ii the 70th term. 3cii A B C D E Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

12 Number patterns For questions to 3: a Give the next number in each pattern. b Give the special names of these patterns., 4, 9, 6, 5, 36 a... b..., 3, 6, 0, 5, a... b... 3, 8, 7, 64, 5, 6 3a... 3b... 4 Give the next number in each pattern: a,,, 3, 5, 8, 3, 4a... b 4b..., 3, 3 4, 4 5, 5 6 For questions 5 to 7: a Give the next number in each pattern. b What is the rule to find the nth term? c What is the 0th term? d What is the 40th term? 5 3,, 7, 64, 75, 08 5a... 5b... 5c... 5d... 6, 6,, 0, 30, 4 6a... 6b... 6c... 6d ,, 4, 40, 60, 84 7a... 7b... 7c... 7d A B C D E 0 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

13 Simultaneous equations x + 3y = 3x + 4y = 9 x=... y=... x + 5y = 4 5x 7y = 8 x=... y= a 5c = 7 a + 4c = 6 3 x=... y=... 4 a 3c = 3 3a 5c = 4 x=... y= a 5c = 8 3a c = 5 x=... y=... 6 x + 3y = 3 3x 5y = 9 6 x=... y= x y = 3 x + 3y = 5 7 x=... y= x = 3 y 5y = 3x + 8 x=... y= A B C D E 6 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

14 3 Solving simultaneous equations by drawing graphs y y = 0 x y = x 3y = x x y = x 0 3 5y + x + 3 = Solve the following simultaneous equations by using the graph above: 3y = x + 6 and y = x x=... y=... y = x 0 and y = x x=... y= y + x + 3 = 0 and y = 0 x 3 x=... y=... 4 y = x and y = 0 x 4 x=... y= A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

15 4 Inequalities Solve these inequalities: 5x > x x x 3 < a 4 > y x < y < a < a > a a > a < a x < a 3 > A B C D E 6 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

16 5 Inequalities Describe the shaded regions: y y x 0 3 x 3 y 4 y x 0 3 x 5 y 6 y x 0 x x... 3 y A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

17 6 Enlargement by a fractional scale factor y A B D E C F 4 3 H G x Enlarge the trapezium ABCD by a scale factor of 3. A =... Centre of enlargement is the point (, 6). B =... Label the new trapezium A B C D. C =... D =... Enlarge the quadrilateral EFGH by a scale factor of. E =... Centre of enlargement is the point (6, 5). F =... Label the new quadrilateral E F G H. G =... H = A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

18 7 Accuracy of measurement The following questions give a measurement. In each question give: a The maximum possible value and b The minimum possible value. A book, mass.7 kg a...kg b...kg A room, length 8.3 m a...m b...m 3 A bus, mass 7.6 t 3a...t 3b...t 4 A tea cup, capacity 73 ml 4a...ml 4b...ml 5 A barrel, capacity 48.3 l 5a...l 5b...l 6 A building, height m 6a...m 6b...m 7 John took.83 seconds to run a race 7a...sec 7b...sec 8 An advert lasted 3.64 seconds 8a...sec 8b...sec 9 A packet of tea, mass 7.8 g 9a...g 9b...g 0 A car, length 4.0 m 0a...m 0b...m A boy s height was 60 centimetres, accurate to the nearest centimetre. A can of cola had a capacity of 35 cl correct to the nearest 5 cl. a...cm b...cm a...cl b...cl A B C D E 4 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

19 8 Compound units A car travels 67 kilometres in 8 hours and 7 minutes. Calculate the average speed correct to three significant figures....km/h A train travels for hour 3 minutes at an average speed of 73 km/h. Calculate the distance travelled correct to three significant figures....km 3 A man ran 7 kilometres at an average speed of 4.7 km/h. How long did the journey take? Give the answer to the nearest second h m s 4 A cyclist travels 47 kilometres in hours 6 minutes. Calculate the distance travelled correct to three significant figures. 4...km/h 5 A plane travels for 47 minutes at an average speed of 36 km/h. Calculate the distance travelled correct to three significant figures. 5...km 6 A train travelled 33 kilometres at an average speed of 9 km/h. Calculate the time taken correct to the nearest second h m s 7 A block of wood, volume 38 cm 3, has a mass of 84 g. Calculate the density. Give your answer correct to three significant figures. 7...g/m 3 8 A horse runs at a speed of. m/s. What is this speed in kilometres per hour? 8...km/h A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

20 9 Calculating length, area and volume Find: a The area, b The perimeter of: A square side 8 cm a... b... A rectangle length 0 cm, width 7 cm a... b... 3 cm 3a... 3b... 0 cm 6 cm 4 Find the area of the parallelogram cm 7 cm cm 5 The perimeter of this rectangle is 36 cm. What is the area of the rectangle? 5... x + 8 cm x cm 6 The area of this trapezium is 76 cm. Find x x cm 8 cm cm 7 What is the volume of this cuboid? cm 0.8 m 0 cm A B C D E 0 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

21 0 Calculating length, area and volume cm 8 cm 5 cm a What is the volume? a... b What is the total surface area? b... Find the volume of these prisms: 6 cm 3 7 cm... 4 cm cm 8 cm cm 8 cm cm 3 cm cm 6 cm cm cm 6 cm 3 cm cm 4 cm 4 cm 0 cm 6 The volume of this cube 7 The volume of this 6... is 343 cm 3. FInd the cuboid is 336 cm 3. total surface area. What is the value of x? 7... x cm cm 4 cm A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

22 Calculating length, area and volume 3 You must write down the units in your answer, eg 8 cm 3, 4 m. This is a diagram of a swimming pool with a concrete path m wide all the way around. m 5 m a Find the area of the path. a... b Path The path is made of concrete 8 cm deep. Find the volume of concrete. b... A B ABCD is a square piece of card, side 5 cm. Two semi-circles, diameter 5 cm are cut out. D C a What is the shaded area? a... b What is the perimeter of the shaded shape? b... 3 This is a diagram of a running track. Both ends are semi-circles. 0 m 80 m Calculate the length of the running track Calculate the area of this shape: cm 3 cm 0 cm 4 cm 8 cm A B C D E 6 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

23 Pythagoras theorem Find the length of the sides indicated. Give your answers correct to three significant figures. 4. m...cm 6 cm x 7.5 cm 3 m x...m 3 7 cm cm 8. m x 4...m x cm 6.3 m cm 5.8 cm x 40 cm 0.8 m 6...cm 8.9 cm x 7 x 8 7. m 7...cm 38 cm 70 cm x 5.3 m 8...m A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

24 3 Pythagoras theorem Give answers correct to three significant figures where appropriate. ABCD is a rectangle. ABCD is a rectangle. Calculate the length Calculate the length from of the diagonal AC. B to the mid-point of AC. A B A B...cm 8 cm 0 cm...cm D cm C D 8 cm C 3 This is a square, side 4 ABCD is a rectangle. Calculate 8 cm. Calculate the length the length of the line joining of the diagonal AC. the mid-point of AD to the mid-point of CD. A B A 6 cm B 3...cm 8 cm D C 6 cm 4...cm D C 5 A ship sails 80 km west, then 00 km south. How far is the ship from its starting point? 5...km 6 A plane flies 00 km north. It then flies west. The plane is 50 km from its starting point. How far west did the plane fly? 6...km 7 The sides AB and BC are in the ratio :. AC is 0 m. Calculate the length AB. A 7...m C B 8 A square has a diagonal length of 0 cm. 8...cm Calculate the area of the square A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

25 4 Locus A B X 3 4 D C Y There are two footpaths across this field. (Scale cm represents 0 m.) The first footpath is always an equal distance from B and C. Draw a dotted line to show the footpath. The second footpath is always an equal distance from A and C. Draw a solid line to show the footpath. 3 A goat is tethered in the field at point C. The rope is 0 m long. Shade the area where the goat can graze. 4 There is a drainage ditch from X to Y. It is always 0 m from the edge of the field. Draw this ditch on the plan. (Part of the ditch has been drawn for you.) 4 3 A B C D E 4 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

26 5 Designing questionnaires Look at these questions. Criticise each question. Are you good at maths? Criticism How old are you? Tick one box only. Under Over 40 Criticism Which is your favourite sport? Tick one box. Netball Rounders Hockey Criticism Do you watch TV often? Yes No Criticism A B C D E 4 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

27 6 Hypothesis How could you test these hypotheses? Choose from experiment, observation or questionnaire. Boys can thread a needle quicker than girls.... The most popular food in the canteen is chips Most boys like football Boys can throw the javelin further than girls Girls spend more money on clothes than books Most boys own a bicycle Most pupils wear a tie in school Most teachers can speak French The most popular colour of car is blue If a slice of toast with butter on one side is knocked off the table, it will land butter side down most often A B C D E 0 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

28 7 Comparing data This table shows the time taken, in seconds, for 0 boys and 0 girls to run 800 m. Seconds 0 under under under under under 70 Boys Girls a Present this data in a frequency polygon. Boys Use a dotted line for boys and a solid line for girls. Girls Frequency Boys Girls Time in seconds b Compare the distributions and comment on your findings Comparison... 3 A B C D E 3 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

29 8 Grouped data This table shows the distance, in metres, 00 golfers hit their drives: Distance in metres Frequency 60 under under under under under 0 46 a What is the modal class? a... b Estimate the median. b... c Estimate the mean. c... This table shows the prices of bicycles in a cycle shop: Price 60 under under under 0 0 under under under 80 Frequency a What is the modal class? a... b Estimate the median. b... c Estimate the mean. c A B C D E 6 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

30 9 Scatter diagrams (line of best fit) Ten pupils took some tests. They received marks out of ten. a b Complete these scatter diagrams. Describe the relationship shown by each scatter diagram. c Draw a line of best fit where appropriate. 0 a b c... Music 0 a b c... Music 3 0 3a b c... English Maths PE PE Subject Maths Music PE Pupil English Anna Ben Carol 9 David Eve Fred Gillian Henry Isla John A B C D E 9 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel

31 30 Estimation of probability by experiment Sarah recorded the colours of 00 cars. The table shows the results: Colour White Red Blue Green Frequency Use the results to estimate the probability of the colour of the next car being: (Write your answer as a decimal.) a White a... b Red b... c Blue c... d Green d cases of wine were damaged in an accident. 00 cases were examined and the following number of bottles were broken in each case. Bottles broken Frequency a b If an unchecked case is opened at random, what is the probability that it will contain: (Write your answer as a decimal) i Two broken bottles? ai... ii Four broken bottles? aii... Estimate the number of cases with exactly: i Four broken bottles. bi... ii Five broken bottles. bii A B C D E 8 Pearson Publishing, Chesterton Mill, French s Road, Cambridge CB4 3NP Tel