Mathematics Homework

Transcription

1 Two-Tier GCSE Mathematics Homework Pack : Foundation Tier Stafford Burndred

2 Two-Tier GCSE Mathematics Homework Pack : Foundation Tier Stafford Burndred ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz-&!?,'.()[]/\*@;: ISBN Pearson Publishing 997 Published by Pearson Publishing 997 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

3 Place value What is the next whole number after fifty thousand? Write your answer in figures.... What is the number before one thousand? Write your answer in figures Write seventeen thousand and thirty in figures Write six thousand and four in figures Write 3 00 in words Write 5030 in words Here is a list of numbers: a Which is the largest number? 7a... b Which is the smallest number? b... c Write the numbers in ascending order. c d Write the numbers in descending order. d... 8 What is the value of the 4 in these numbers? a 46 8a... b 34 b... c 48 c... 3 Pearson Publishing Tel:

4 C = / x = Multiplication facts What is the missing number in these sums? 7 x 6 =... x 8 = x = = = = Work out the following: 7 4 x x x Mr Smith bought 00 pencils at 4p each. What was the total cost? Mrs Green bought 0 trees for 70. What was the cost of each tree? Pearson Publishing Tel:

5 3 Negative numbers The picture shows the heights, in metres, of several objects. 50 Coastguard station Car 50 0 Sea level Submarine -50 Treasure chest -00 Give the difference in height between the following: a coastguard station and submarine a... b submarine and treasure chest b... c car and treasure chest c... d coastguard station and treasure chest d... e car and submarine e... f coastguard station and car f... Place these numbers in order, smallest first: a -5, 3, -7,, 6 a... b 4, -, -6, -8, 3 b... c 5, 0, -, -6, 7 c... 3 Work out the answers to these questions: a a... b b... c 3 5 c... Pearson Publishing Tel:

6 4 Negative numbers Place these numbers in order, smallest first: a -6, 4, -9, -, 5 a... b 0, -, -7, 6, b... c -, -7, -5,, -3, 4 c... d -, -8,,, 0, -4 d... Place these numbers in order, largest first: a -8, -7, 3, 0, -4, a... b -, -5, 6, 0, -3, b... c -4, -,, 0, 6, - c... d 8, 3, -5, -, -3, d... 3 Work out the answers to these questions without using a calculator: a 6 0 3a... b -3 b... c c... d d... 4 Work out the answers to these questions. You must use a calculator. Show the calculator keys: a a... b -5 - b... c 6-4 c... d d... e -8 x -3 e... f 6 x -4 f... g -7 x 3 g... h -50 / 0 h... i -30 /-6 i... j 8 / -80 j... 5 The temperature at 5.00 is 3 C. The temperature at 8.00 is -7 C. By how much has the temperature fallen? The temperature at is - C. The temperature rises by 4 C. What is the new temperature? 6... Pearson Publishing Tel:

7 C = / x = 5 Solving problems without a calculator x 8 x John had 87 stamps. He bought 468 more. How many stamps did he have altogether? A classroom had 36 chairs. They were placed in rows of 4. How many rows were there? 0... Sally had 8. She spent 86. How much did she have left?... There were 7 buses in a bus station. Each bus had 7 passengers. How many passengers were there?... Pearson Publishing Tel:

8 6 Calculation checks Write the following correct to the nearest whole number: Write the following correct to the nearest ten: Write the following correct to the nearest hundred: Estimate the total amount of money: Pearson Publishing Tel:

9 C = / x = 7 Mental arithmetic shortcuts 60 x x x x x Pearson Publishing Tel:

10 C = / x = 8 Mental arithmetic shortcuts 40 x x x x x x Pearson Publishing Tel:

11 C = / x = 9 Mental arithmetic shortcuts x x x x x x x x Pearson Publishing Tel:

12 C = / x = 0 Mental arithmetic shortcuts x x x x x x x x x x x x x Pearson Publishing Tel:

13 C = / x = Decimals You must show all of your working x x John had 5. He spent.0. How much change did he receive? Sara bought 4 packs of coffee at.36 each. What was the total cost? Pearson Publishing Tel:

14 C = / x = Decimals You must show all of your working x x A woman had a 0 note. She bought a loaf at 0.76 and a book at How much change did she receive? 0 John bought six Christmas cards at.7 each. What was the total cost? Pearson Publishing Tel:

15 C = / x = 3 Long multiplication and division You must show all of your working. 358 x x x x In each question, give the whole number answer and the remainder. 5 3 ) ) Pearson Publishing Tel:

16 C = / x = 4 Long multiplication and division You must show all of your working. 357 x x x x In each question, give the whole number answer and the remainder Pearson Publishing Tel:

17 C = / x = 5 Checking You must show all of your working. Check the following sums. Show how you checked. If the answer is correct, write correct in the answer column. If the answer is wrong, write the answer you get in the answer column What are the missing numbers in these sums? Jayne bought 89 pens at p each. Estimate the total cost. 7 Estimate the cost of 387 packs of coffee at. each. 8 Estimate the cost of 6 calculators at 7.95 each Pearson Publishing Tel:

18 C = / x = 6 Checking You must show all of your working. Check the following sums. Show how you checked. If the answer is correct, write correct in the answer column. If the answer is wrong, write the answer you get in the answer column John bought 478 cans of Coke at 3p each. Estimate the total cost Fill in the missing rows of numbers Estimate the cost of 685 boxes of nails at.95 each Estimate the cost of 8 m of carpet at 6.95 per m Pearson Publishing Tel:

19 C = / x = 7 Checking 3 Round the following numbers to one significant figure Estimate the answers to these questions (show your working) x x x x Pearson Publishing Tel:

20 8 Using a calculator: Brackets and memory Give your answer correct to six significant figures where appropriate. Show your calculator keys for questions and ( ) ( )... 3 ( ) ( ) x x ( ) 7... (7.8 x 3.69) x x 4.89 The make and type of my calculator is... Pearson Publishing Tel:

21 9 Using a calculator: Powers, roots, memory Use your calculator to find the answers. Show your calculator keys. Give your answer correct to six significant figures where appropriate / / y = 4x 3 + 3x - x Calculate the value of y when x = Use an efficient calculator method. 0 y = 7x 3 4x + 3x 0... Calculate the value of y when x = Use an efficient calculator method. The make and type of my calculator is... Pearson Publishing Tel:

22 0 Standard form Write the following as ordinary numbers. 6.3 x x x x x x x x Write the following numbers in standard form Give the answers to the following: a in standard form (correct to three significant figures); b as an ordinary number (correct to six significant figures where appropriate). Show your calculator keys for question x 0 3 x.6 x 0 7a... 7b x x 0 5 8a... 8b x 0-3 x 4.7 x 0 7 9a... 9b x 0 4 x 3.6 x 0 5 0a....8 x x 0 3 0b....7 x 0 - x 4.3 x 0 6 a....8 x 0 - x 3.6 x 0 4 b... (6.8 x 0 ) 3 a... b... The make and type of my calculator is... Pearson Publishing Tel:

23 Fractions and percentages a Shade / 3 of this shape: a b What fraction is left unshaded? b... a Shade 3 / 5 of this shape: a b What fraction is left unshaded? b... 3 John has squares of chocolate. He eats / 4. a How many squares does he eat? 3a... b How many squares does he have left? b... 4 a Shade 5% of this shape: 4a b What percentage is left unshaded? b... 5 Shade 50% of this shape: 5 Pearson Publishing Tel:

24 Fractions and percentages Find 3% of Find 4% of Increase 40 by 8% Increase 3 by 7% Decrease 69 by 5% Decrease 40 by 0% Find 4 / 5 of Find / 7 of Increase 35 by 3 / Decrease 40 by 5 / A woman earns pa. She receives a 5% increase each year. a How much does she receive after one year? a... b How much does she receive after three years? b... (Give your answer to the nearest pound.) A washing machine costs 30 plus 7.5% VAT. What is the total cost?... 3 A car was bought for 000. It depreciates by 5% each year. How much is it worth after: a one year? 3a... b three years? b... Pearson Publishing Tel:

25 3 Fractions For questions and, show your working or the calculator keys you used. 3 / 5 x / / + / / 3 / / 5 / Find / 3 of Find 3 / 8 of Find 3 / 5 of Write 8 / 99 as a fraction in its lowest terms Write 4 / 7 as a fraction in its lowest terms Write 36 / 448 as a fraction in its lowest terms people out of 80 owned a computer. Write this as a fraction in its lowest terms.... A tennis club had 360 members. 60 were female. a What fraction of the members were female? Give your answer in its lowest terms. a... b What fraction of the members were male? Give your answer in its lowest terms. b... 3 There were 480 people in a cinema. / 4 were men, / 5 were women, / 8 were boys. The rest were girls. a How many men were in the cinema? 3a... b How many women were in the cinema? b... c How many boys were in the cinema? c... d What fraction were girls? d... Pearson Publishing Tel:

26 4 Fractions For questions and, show your working or the calculator keys used. 3 4 / 5 x / / / / 7 / / 5 5 / Find / 3 of Find 3 / 5 of Find 3 / 8 of Find 7 / 8 of Write 7 / 36 as a fraction in its lowest terms Write 7 / 08 as a fraction in its lowest terms Write 64 / 36 as a fraction in its lowest terms... Write 5 / 380 as a fraction in its lowest terms people out of 40 wore glasses Write this as a fraction in its lowest terms. 4 A golf club had 480 members. 50 were female. a What fraction of the members were female? 4a... Give the answer in its lowest terms. b What fraction of the members were male? 4b... Give the answer in its lowest terms. 5 There were 360 people in a hall. / 5 were men, / 6 were boys, / 3 were women. The rest were girls. a How many men were in the hall? 5a... b How many women were in the hall? 5b... c What fraction were girls? 5c... Pearson Publishing Tel:

27 5 Changing between decimals and percentages Convert the following percentages to decimals. 3%... 4% % % % % % % 8... Convert the following decimals to percentages Pearson Publishing Tel:

28 6 Changing between decimals and percentages Convert the following percentages to decimals. 8%... 34% % % % % % % 8... Convert the following decimals to percentages Pearson Publishing Tel:

29 7 Changing between decimals, percentages and fractions Convert the following percentages to fractions. Give the answer in its lowest terms. 6%... 4% % % 4... Convert the following decimals to fractions. Give the answer in its lowest terms Convert the following fractions to decimals. 9 5 / / / / Convert the following fractions to percentages. 3 / / / / Pearson Publishing Tel:

30 8 Changing between decimals, percentages and fractions Convert the following percentages to fractions in their lowest terms. 4%... 34% % % 4... Convert the following decimals to fractions in their lowest terms Convert the following fractions to decimals. 9 / / / / Convert the following fractions to percentages. 3 3 / / / / Pearson Publishing Tel:

31 9 Ratio Simplify these ratios. 5: : : : Write 4: in the ratio :n Write 8:5 in the ratio :n Write 4:0 in the ratio n: Write 3:8 in the ratio n: The scale of a map is : a b c d The distance between Ayton and Beton is cm on the map. What is the actual distance? Give your answer in kilometres. 9a... The distance between Beton and Cedon is 3 cm on the map. What is the actual distance? Give your answer in kilometres. b... The distance between Cedon and Deton is 7 km. What is the distance on the map? Give your answer in centimetres. c... The distance between Deton and Exton is 4 km. What is the distance on the map? Give your answer in centimetres. d... 0 This is a recipe for soup for four people: 800 ml water g salt 40 g beef tomatoes How much of each ingredient should be used for six people? 0a Water... b Salt... c Beef... d Tomatoes... 6 Pearson Publishing Tel:

32 30 Ratio Simplify these ratios. 0: : : : Write 8:3 in the ratio :n Write 5: in the ratio :n Write 9:4 in the ratio n: Write 3:0 in the ratio n: The scale of a map is : a The distance between Hayle and Langham is 4 cm on the map. What is the actual distance? 9a...km b The distance between Langham and Melbury is 5 cm on the map. What is the actual distance? 9b...km c The distance between Melbury and Whitchurch is 36 kilometres. What is the distance on the map? 9c...cm d The distance between Whitchurch and Sarum is 80 kilometres. What is the distance on the map? 9d...cm 0 This is a recipe for vegetable soup for six people: 900 ml water 8 g salt 3 carrots onions How much of each ingredient should you use for 5 people? 0a Water... b Salt... c Carrots... d Onions... Pearson Publishing Tel:

33 3 Ratio 3 The ratio of men to women on a train was 5:8. There were 00 men. a How many women were on the train? a... b What was the total number of men and women on the train? b... A drink is made by mixing pineapple juice, orange juice and lime juice in the ratio :7:3. Sally makes 600 ml of the fruit drink. a How much pineapple juice is used? a... b How much orange juice is used? b... c How much lime juice is used? c... Karen has 600 ml of lime juice and an unlimited supply of pineapple juice and orange juice. d What is the maximum amount of the drink Karen can make? d... e How much pineapple juice would she use? e... f How much orange juice would she use? f is left in a will to be shared between Alan, Ben and Carol in the ratio 5:7:4. a How much does Alan receive? 3a... b How much does Ben receive? b... c How much does Carol receive? c... Pearson Publishing Tel:

34 3 Ratio 4 The ratio of boys to girls on a school trip was 5:7. There were 56 girls. a How many boys were on the school trip? a... b How many pupils were on the school trip? b... A fruit drink is made by mixing lemon juice, orange juice and lime juice in the ratio 5::3. James makes 400 ml of the fruit drink. a How much lemon juice is used? a... b How much orange juice is used? b... c How much lime juice is used? c... Kelly has 40 ml of lime juice and an unlimited supply of lemon juice and orange juice. d What is the maximum amount of fruit drink Kelly can make? d... e How much lemon juice would she use? e... f How much orange juice would she use? f... 3 Andrea, Barbara and Carolyn share 4400 in the ratio 4:5:. a How much does Andrea receive? 3a... b How much does Barbara receive? b... c How much does Carolyn receive? c... Pearson Publishing Tel:

35 33 Percentages Show your working or your calculator keys. Write 4 out of 0 as a percentage. Write 57 out of 90 as a percentage Jayne had 400. She spent a What percentage did she spend? b What percentage did she have left? 3a... 4 Mr Brown earned 30 per week. Calculate his percentage increase if he received a rise of: a 6.40 b... b 4 4a... c 0.4 b... 5 There were 300 people in a room. 45 wore glasses. What percentage wore glasses? c... 6 In a sale, a video recorder was reduced from 360 to 88. Calculate the percentage reduction Pearson Publishing Tel:

36 34 Percentages Show your working or your calculator keys. Write 48 out of 60 as a percentage.... Write 68 out of 70 as a percentage John had 50. He spent a What percentage did he spend? 3a... b What percentage did he have left? b... 4 A man earned 360 per week. Calculate his percentage increase if he receives a rise of: a 8 4a... b.5 b... c 4.3 c... 5 There were 400 men on a train. 8 had beards. What percentage had beards? The price of a coat was reduced from 40 to 6. Calculate the percentage reduction Pearson Publishing Tel:

37 35 Calculating percentage parts Find 0% of Find 3% of Find 5% of Increase 36 by % Increase 7 by 8% Decrease 38 by 6% Decrease 70 by 80% Mrs Randall earns 35 per week. She receives a 3% pay rise. Calculate: a the pay rise 8a... b her new weekly wage b... 9 In a sale, everything is reduced by 0%. A DVD player normally costs 40. Calculate the sale price Pearson Publishing Tel:

38 36 Patterns you must recognise a b Write the next two numbers in each pattern. What is the name of the pattern?, 3, 6, 0, 5, a... b..., 4, 9, 6, 5, 36 a... b... 3, 8, 7, 64, 5, 6 3a... b... 4,,, 3, 5, 8, 3, 4a... 5 Here is a list of numbers: b......, 3, 5, 6, 8, 5, 30, 64, 5 a Which numbers are prime? 5a... b Which numbers are multiples of 5? b... c Which numbers are factors of 6? c... d Which numbers are square numbers? d... e Which numbers are cube numbers? e... 6 Here is a list of numbers:, 3, 5, 8, 8, 7, 36, 49, 75, 79 a Which numbers are prime? 6a... b Which numbers are multiples of 4? b... c Which numbers are factors of 5? c... d Which numbers are square numbers? d... e Which numbers are cube numbers? e... Pearson Publishing Tel:

39 37 Patterns you must recognise Here is a list of numbers:, 4, 9, 6, 5, 36, 49, 64, 8, 00 Find: a The next two numbers in the pattern. b The name of the pattern. a... b... Here is a list of numbers:,, 3, 4, 7, 9,, 4, 64 a Which numbers are prime? a... b Which numbers are factors of? b... c Which numbers are multiples of 3? c... d Which numbers are square numbers? d... 3 Here is a list of numbers:,, 4, 7, 5, 7, 8, 9, 343 a Which numbers are prime? 3a... b Which numbers are factors of 4? b... c Which numbers are multiples of 7? c... d Which numbers are square numbers? d... 0 Pearson Publishing Tel:

40 38 Number patterns: The nth term Here is a pattern made out of matchsticks: a Draw the next pattern. a... b What is the rule to find the nth term? (Give your answer using algebra.) b... c Use your rule to find the number of matchsticks in: i the 0th term ci... ii the 54th term cii... d Which term has 8 matchsticks? d... Here is a pattern: 7,, 5, 9. a What is the next number in this pattern? a... b What is the rule to find the nth term? (Give your answer using algebra.) b... c Use your rule to find: i the 5th term ci... ii the 8th term cii... 3 Here is a pattern:, 8, 4, 0. a What is the next number in the pattern? 3a... b What is the rule to find the nth term? (Give your answer using algebra.) b... c Use your rule to find: i the 0th term ci... ii the 54th term cii... Pearson Publishing Tel:

41 39 Product of primes, highest common factor Write 646 as a product of primes.... Write 00 as a product of primes Find: a the HCF of 646 and 00. 3a... b the LCM of 646 and 00. b... 4 Write 3675 as a product of primes Write 88 as a product of primes Find: a the HCF of 3675 and 88. 6a... b the LCM of 3675 and 88. b... 7 What is the reciprocal of: a 4? 7a... b / 5? b... c -8? c... Pearson Publishing Tel:

42 40 Using formulae This is an instruction: Choose a number multiply by 4 take away 3 What is the result if you choose: What number was chosen if the result was: The cost of hiring a bus is calculated as follows: Fixed daily rate + per kilometre = total cost 7 Calculate the total cost if the fixed daily rate is 7 and the bus travels 0 kilometres Calculate the total cost if the fixed daily rate is 7 and the bus travels 5 kilometres Calculate the number of kilometres travelled if the total cost is 6 and the fixed daily rate is Pearson Publishing Tel:

43 4 Writing in algebra John is x cm tall. Andy is 4 cm taller. How tall is Andy?... Sharon has y books. Andrea has 6 more than Sarah. a How many books does Andrea have? a... b What is the total number of books? b... 3 Amy has x. Barry has twice as much money. Carolyn has 4 more than Barry. a How much money does Barry have? 3a... b How much money does Carolyn have? b... c What is the total amount of money? c... 4 Julie buys 7 kg of potatoes at x per kilogram. a What is the total cost in s? 4a... b What is the total cost in pence? b... 5 Here is a room. It is A m long, B m wide. A m a What is the area? B m 5a...m b What is the perimeter? b...m c The room is H m high. What is the volume? c...m 3 6 Pens cost x pence each. a What is the cost of y pens? 6a...p b How many pens can be bought with z pence? b... Pearson Publishing Tel:

44 4 Writing in algebra John has x, Louise has 3 more. How much does Louise have?... Michelle weighs k kilograms. Paula is 8 kilograms heavier. a How much does Paula weigh? a... b What is their total weight? b... 3 Sally can type W words per minute. David can type twice as fast as Sally. Vicky can type seven words per minute faster than David. a How many words per minute can David type? 3a... b How many words per minute can Vicky type? b... c How many words can Sally type in six minutes? c... d How many words can Vicky type in six minutes? d... 4 A room is L metres long and W metres wide. a What is the area? 4a... b What is the perimeter? b... 5 Martin buys B books at 0 each. What is the total cost? Mandy can run one kilometre in M minutes. James takes N minutes less. How long does James take? Bananas cost x pence per kilogram. a What is the cost of B kilograms of bananas? 7a... b How many kilograms can be bought with Y pence? b... 8 What is the cost of V videos at P each? 8... Pearson Publishing Tel:

45 43 Using algebra Given a = 0, b =, c =, d = 3, e = 4, work out the following. Show your working. d + e... de... 3 d e ad + bc c + 3de b + 3a d(b + c) cd(a + b + c) (d + e)c e(3d + c) 0... y = 3(A + B) Find y when A = 4 and B = A = B C a Find A when B = 8 and C =. a... b Find A when B = -6 and C = -3. b... c Find B when A = -8 and C = 5. c... 3 A = B + C D + E Find A when B =, C = 8, D = 3, E = Pearson Publishing Tel:

46 44 Using algebra Given a = 0, b =, c =, d = 3, e = 4, work out the following (show your working): cd... cde... 3 c + d + e abc ad + ce c(d + e) d(c e) cd(a + c) (c + d)e d + 3ce 0... A = (B C) Find A when B = 3 and C = C = A B a Find C when A = 0 and B = 4. a... b Find A when C = 7 and B =. b... c Find B when C = -3 and A = -7. c... 3 A = BC D - E Find A when B = 0, C = 6, D = 8 and E = Pearson Publishing Tel:

47 45 Rules: Equations Solve these equations: x + 4 = 0 x 3 = y = 4 4 8a = a = 7 6-8y = c = 8 8 a = x = a 5 = a 7 = 3a + 5 6a 5 = 8 - a x + = 6 4 3x = Pearson Publishing Tel:

48 46 Rules: Equations Solve these equations: a + 3 = 8... a - 5 = a = a = a = c 5 = d 3 = x + 3 = a - 6 = 3a y + 0 = 6y a + 3a - 5 = 7a a - 4a + 5 = 8 - a... 3 a 3 + = a 5 = Pearson Publishing Tel:

49 47 Writing equations I think of a number. I double it, then add 6. The answer is 0. Use N for the number. a Write an equation to show this. a... b Solve the equation. Show your working. b... Mr Hammond buys D desks at 8 each. He spends 44 in total. a Write an equation to show this. a... b Solve the equation. Show your working. b... 3 A gas bill is calculated by the formula: gas bill = 5 standing charge + 8 pence per unit used Let B be the gas bill and U the number of units used. a Complete the formula B = 3a... ( + ) b Use the formula to calculate the cost if U = 57 b... c Calculate the number of units used if B = 83.3 c... 7 Pearson Publishing Tel:

50 48 Writing equations I think of a number. I multiply by 3, then take away 4. The answer is 7. Use N for the number. a Write an equation to show this. a... b Solve the equation. Show your working. b... Mrs Roberts buys c chairs at 5 each. She spends 05 in total. a Write an equation to show this. a... b Solve the equation. Show your working. b... 3 The cost of hiring a car is 30 plus 5 pence per mile. Let c be the cost and m be the number of miles. a Complete this formula: 3a c = ( + ) b Use the formula to calculate the cost if m = 86. b... c Calculate the number of miles covered if c = c... Pearson Publishing Tel:

51 49 Trial and improvement You must show all of your working. x 3 = 00 Find the value of x correct to one decimal place using trial and improvement methods.... x + 5x = 90 Find the value of x correct to one decimal place using trial and improvement methods.... Pearson Publishing Tel:

52 50 Trial and improvement You must show all your working. x - 3x = 6 Find the value of x correct to one decimal place using trial and improvement methods.... x 3 + 3x = 30 Find the value of x correct to one decimal place using trial and improvement methods.... Pearson Publishing Tel:

53 5 Harder equations Give the answer to three significant figures where appropriate. a = c - 5 = x = x = a + 3(4a - 5) = (c - 3) = 6(c - ) a - 4(a - 5) = 3(a + ) a + 6 = 0.7a x + = y + = y = y - 4 = 8... Pearson Publishing Tel:

54 5 Rewriting formulae In each question, make Y the subject. Y = x... Y = x... 3 A = Y + B C = 3Y + A A = 4C - Y A = 3C - 4Y A = 3Y A = 3Y C A = 8-3Y C = 4 + 3Y 0... Y C = A... A Y = B... 3 Y A = C C = A Y A = 3C Y A = Y(C + D) 6... Pearson Publishing Tel:

55 53 Using algebraic formulae In each question, find the value of y correct to six significant figures where appropriate. a = 5.6 b = 5 7 c = -.3 d = 5.37 e = -7 9 y = 3a - 4b d... y = 4a(bd + 3) de... 3 y = a ( bd) c + a 3... ( ) 4 y = 5ce a + c 4... ( d + e ) 5 y = a + b + c y = 5a + 3b - c d - 3e 7 y = a + b y = a + c b Pearson Publishing Tel:

56 54 Expansion of brackets Simplify: 5a 3 x 3a a 3 c x 3a 5 c a 4 x 4cd (a 3 ) a 8 c 4 4a c 5... Expand: 6 7(3a - 4) y 3 (4y + 6y) a(4a - 3c ) a 3 (3a 4 + 5a ) (4a + ) (3a - 5) 0... (5a - 3) (a + 6)... (6a - 4) (5a - )... 3 (3a - ) 3... Pearson Publishing Tel:

57 55 Factorisation Factorise: 0a a - 3c a - 8c a - 0c a 4 + a a 5 + 5a a 5 + 4a a b + 4ab a 3 c - 5a 4 c acd - 30a d 0... a 4 + 8a + 4ad... 6a 6 + 4c 6 + d 3... Pearson Publishing Tel:

58 56 Coordinates Give the coordinates of the points shown. 8 7 A x B x 6 A=... 5 C x B=... 4 C=... 3 D x E x D=... E= Mark these points on the graph: V = (, 5) W = (5, 4) X = (, 3) Y = (4, ) Z = (3, ) V W X Y Z 0 Pearson Publishing Tel:

59 57 Drawing lines Which letters represent the following lines? x = 0 y... 5 y = 0 3 y = x y = -x A 3 5 y = y = -3 7 x = x = -3 B x C D -3-4 E -5 F G H Complete this table of values and draw the graph of y = x 3. x y Table... Graph... 0 Pearson Publishing Tel:

60 58 Drawing lines Which letters represent the following lines? y = - y... x = y = x = y = x y = -x y = x y = -x + 3 A x B C H D -5 G E F 9 Complete this table of values and draw the graph of y = / x 4. x y Table... y x Graph... 0 Pearson Publishing Tel:

61 59 Speed, time and distance graphs This graph shows the journeys made by a cyclist and a runner. Stoke 50 Cyclist 40 Distance (kilometres) Runner Manchester a What time did the runner and cyclist meet? a... b How far were they from Stoke? b... How many times did the runner stop?... 3 What time did the cyclist start his journey? a Between which times did the runner travel fastest? 4a... b How did you decide? b... 5 How long did the cyclist stop during his journey? Where did the cyclist finish his journey? How far is it from Stoke to Manchester? What was the speed of the runner at: a 0.00? 8a... b.00? b... 9 What was the speed of the cyclist at: a 0.30? 9a... b 4.30? b... Time Pearson Publishing Tel:

62 60 Inequalities Solve these inequalities: 8x x - 7 >... 3 x < < 3x - < x x > Pearson Publishing Tel:

63 6 Using a protractor Measure each angle. a... a b... b c... d... c e... f... e d f Pearson Publishing Tel:

64 6 Using a protractor Measure each angle. a a... b... b c c... d d... e... f... e f 6 Pearson Publishing Tel:

65 63 Angles Give the special names of these angles: a b a... b... c... c d d... e... f... f g... e h... g h Pearson Publishing Tel:

66 64 Angles Give the special names of these angles: Pearson Publishing Tel:

67 65 Intersecting and parallel lines Find the missing angles in these diagrams: 70 o 30 o a=... b=... a b c c= d=... d e 70 o e=... 4 g 4 f=... g=... h=... f 35 o h 5 i=... 6 j=... 5 i 6 k=... 8 o j k 7 o 7 l= o l 8 o m=... n=... m n o 8 o=... 5 Pearson Publishing Tel:

68 66 Intersecting and parallel lines Find the missing angles in these diagrams: 80 c 0 a=... b=... c=... a b d=... 4 e=... d 70 e 5 g 5 f=... g=... f 75 8 Look at question h 80 i k 6 h=... 7 i=... j=... k=... l=... m=... n=... o=... a What is the special name used to describe angles k and o? 8a... b What is the special name used to describe angles k and m? b... j 65 l o m n Pearson Publishing Tel:

69 67 Regular polygons Calculate: a the exterior angle b c the interior angle the sum of the interior angles of the following regular polygons (you must show all of your working). A regular nine-sided polygon. a... b... c... A regular twelve-sided polygon. a... b... c... 3 Each exterior angle of a regular n-sided polygon is o. How many sides does the polygon have? Each interior angle of a regular n-sided polygon is 70 o. How many sides does the polygon have? Pearson Publishing Tel:

70 68 Regular polygons Calculate: a the exterior angle Calculate: b the interior angle Calculate: c the sum of the interior angles of the following regular polygons (you must show all of your working). A regular pentagon. a... b... c... A regular ten-sided polygon. a... b... c... 3 Each exterior angle of a regular n-sided polygon is How many sides does the polygon have? 4 Each interior angle of a regular n-sided polygon is Pearson Publishing Tel:

71 69 Bearings N x Y B x Key L is a lighthouse x R x S C is a coastguard station R is a radio mast B is a buoy L x Y is a yacht S is a ship What are the bearings of: B from Y?... B from R?... 3 Y from C? Y from S? Y from R? R from L? R from Y? S from B? S from Y? L from S? 0... L from B?... C from S?... x C Pearson Publishing Tel:

72 70 Common -D shapes ABCD is a square. Complete the diagram. A B C The shape EFGH is turned and moved to form the shape E F G H. E F are shown. Complete the diagram and mark the points G H. G E' F' F E H 3 HIJK is a rectangle. Complete the diagram. I J H 4 The shape LMNO is turned over and moved to form the shape L M N O. L M are shown. Complete the diagram and mark the points N O. L M O N M' L' Pearson Publishing Tel:

73 7 Properties of quadrilaterals This is a rhombus. Write two facts about the sides This is a parallelogram. Complete the diagram. 3 This is a description of a quadrilateral: The quadrilateral has four equal angles. Name the quadrilateral Give the order of rotational symmetry for the following quadrilaterals. Tick the appropriate box. a No rotational symmetry Order Order 3 Order 4 4a b b c c Pearson Publishing Tel:

74 7 Properties of quadrilaterals This is a parallelogram. Write two facts about the sides This is a rhombus. Complete the diagram. 3 This is a description of a quadrilateral: The quadrilateral has one pair of parallel lines. Name the quadrilateral Give the order of rotational symmetry for the following quadrilaterals. Tick the appropriate box. No rotational order order order symmetry 3 4 a kite 4a b trapezium b c square c d rectangle d e rhombus e f parallelogram f Pearson Publishing Tel:

75 73 Properties of quadrilaterals and triangles Draw the axes of symmetry on these shapes. If there is no axis of symmetry, write none in the shape. rhombus parallelogram 3 trapezium 4 rectangle 5 This triangle has three equal sides. a Name the triangle. 5a... b What is the value of x? b... x o 6 This triangle has two equal sides. a Name the triangle. 6a... b What is the value of y? b... c What is the value of z? c o z y Pearson Publishing Tel:

76 74 Properties of quadrilaterals and triangles Draw the axes of symmetry of these shapes: Rectangle Square 3 Kite 3 Name these triangles: Pearson Publishing Tel:

77 75 Congruent shapes Here are some rectangles. A D B C F E H I G K L J Rectangle A is congruent to... Rectangle D is congruent to... 3 Rectangle F is congruent to Rectangle K is congruent to Rectangle J is congruent to Rectangle G is congruent to 6... Pearson Publishing Tel:

78 76 Rotational symmetry If a shape does not have rotational symmetry, write none. If a shape does have rotational symmetry, write the order, eg order Pearson Publishing Tel:

79 77 Rotational symmetry If a shape does not have rotational symmetry, write none. If a shape does have rotational symmetry, write the order, eg order Pearson Publishing Tel:

80 78 Symmetry of -D shapes a b Draw the axes of symmetry on these shapes. Name the shapes. a b... a b a b a b... 8 Pearson Publishing Tel:

81 79 Symmetry of -D shapes a Draw the axes of symmetry of these shapes. b Name the shapes. a b... a b... Pearson Publishing Tel:

82 80 Symmetry of -D shapes 3 The dotted lines are axes of symmetry. Complete the shapes. 3 4 Pearson Publishing Tel:

83 8 Reflection The dotted lines are mirror lines. Reflect the following shapes in the mirror lines. You may use tracing paper Pearson Publishing Tel:

84 8 Enlargement Draw the enlargements and give the coordinates of the enlargements H K S I J D G R E F 5 4 A 3 B T C New coordinates Enlarge triangle T by a scale factor of 3. A... The centre of enlargement is the point (,). B... Label the new triangle A B C. C... Enlarge rectangle R by a scale factor of. D... The centre of enlargement is the point (,4). E... Label the new rectangle D E F G. F... G... 3 Enlarge square S by a scale factor of. 3 H... The centre of enlargement is the point (,). I... Label the new square H I J K. J... K... Pearson Publishing Tel:

85 83 Enlargement Draw the enlargements and give the coordinates of the enlargements B E C T F G 4 R 3 A D Enlarge rectangle R by a scale factor of 3. A =... The centre of enlargement is the point (, ). B =... Label the new rectangle A B C D. C =... D =... Enlarge triangle T by a scale factor of. E =... The centre of enlargement is the point (3, 0). F =... Label the new triangle E F G. G =... 3 Enlarge triangle T by a scale factor of 3. 3E =... The centre of enlargement is the point (6, 3) F =... Label the new triangle E F G. G =... 0 Pearson Publishing Tel:

86 84 Enlargement F 4 E 3 0 C B A 3 D B is an enlargement of A. a What are the coordinates of the centre of enlargement? a... b What is the scale factor of the enlargement? b... C is an enlargement of A. a What are the coordinates of the centre of enlargement? a... b What is the scale factor of the enlargement? b... 3 D is an enlargement of A. a What are the coordinates of the centre of enlargement? 3a... b What is the scale factor of the enlargement? b... 4 E is an enlargement of F. a What are the coordinates of the centre of enlargement? 4a... b What is the scale factor of the enlargement? b... Pearson Publishing Tel:

87 85 Enlargement D F 0 E B C 4 3 A You must show any lines you draw to find the answers. B is an enlargement of A. a What are the coordinates of the centre of enlargement? a... b What is the scale factor of the enlargement? b... A is an enlargement of C. a What are the coordinates of the centre of enlargement? a... b What is the scale factor of the enlargement? b... 3 D is an enlargement of E. a What are the coordinates of the centre of enlargement? 3a... b What is the scale factor of the enlargement? b... 4 F is an enlargement of E. a What are the coordinates of the centre of enlargement? 4a... b What is the scale factor of the enlargement? b... Pearson Publishing Tel:

88 86 Enlargement by a fractional scale factor A B 0 T 9 8 C D E R 4 3 G F Enlarge the triangle T by a scale factor of /. Centre of enlargement is the point (, 0). A =... B =... C =... Enlarge the rectangle R by a scale factor of / 3. Centre of enlargement is the point (6, 7). D =... E =... F =... G =... 7 Pearson Publishing Tel:

89 P Two-Tier GCSE Maths Homework Pack : Foundation Tier 87 Translations y 5 4 D A 3 P R Q C - B -3 x -4 Describe the translation that moves: -5 A to B A to D C to A C to B B to C Translate the triangle PQR using the following instructions. Draw the shape and give the new coordinates of PQR. 6 Two units right, one unit up. 6P... Q... R... 7 Three units right, five units down. 7P... Q... R... 8 Four units left, one unit up. 8P... Q... R... 9 Seven units left, four units down. 9P... Q... R... Pearson Publishing Tel:

90 88 Metric units of measure This is a car speedometer. It shows the speed in kilometres per hour. What speed is shown? Which of these units would you use to measure the capacity of water in a bath: litres, millilitres, centilitres?... 3 Which of these units would you use to measure the weight of a full suitcase: grams, kilometres, litres, kilograms, metres, tonnes? This giraffe is standing next to Mr Green. Guess the height of: a Mr Green 4a...metres b the giraffe. b...metres 5 Pearson Publishing Tel:

91 89 Rough metric equivalents of imperial units Here are some measurements given in imperial units. Convert the imperial units to metric units. A ruler is 6 inches long. What is this in centimetres?... A cat is 3 feet long. What is this in centimetres?... 3 A cake weighs 4 pounds. What is this in kilograms? The distance from Poole to Winchester is 40 miles. How many kilometres is this? A dog weighs stone. What is this in kilograms? [4 pounds = stone] A girl is 4 feet 0 inches tall. What is this in centimetres? [ inches = foot] A petrol car holds 4 gallons. How many litres is this? A tank holds 0 gallons. How many litres is this? 8... Pearson Publishing Tel:

92 90 Rough metric equivalents of imperial units Here are some measurements given in imperial units. Convert the imperial units to metric units. A book is 6 inches wide and 8 inches long. a The metric width is a... b The metric length is b... A boy is 5 feet tall. How many centimetres is this?... 3 My father travels 0 miles to work. How many kilometres is this? A recipe requires 4 ounces of sugar. How many grams is this? An encyclopaedia weighs 6 pounds. How many kilograms is this? The petrol tank in a car holds gallons. How many litres is this? A man is 5 feet 8 inches tall. What is this in centimetres? 7... Pearson Publishing Tel:

93 9 Converting one metric unit to another Convert 84 millimetres into centimetres... Convert 36 centimetres into metres... 3 Convert 3.4 kilometres into metres Convert. kilograms into grams Convert 370 grams into kilograms Convert 0.38 tonnes into kilograms Convert.8 centilitres into millilitres Convert 8 millilitres into litres Convert 0.73 litres into millilitres Convert 3.7 kilometres into metres 0... Convert 38 centimetres into metres... Convert 0.8 centimetres into millimetres... 3 Convert 0.7 metres into centimetres Convert 0.3 tonnes into kilograms Convert 8 grams into kilograms Convert 37 kilograms into tonnes Convert 0.08 kilograms into grams Convert 0.3 litres into millilitres Convert 0.3 litres into centilitres Convert.8 centilitres into millilitres 0... Pearson Publishing Tel:

94 9 Converting one metric unit to another Convert 38 millimetres into centimetres... Convert 47 centimetres into metres... 3 Convert 7. kilometres into metres Convert 7.4 kilograms into grams Convert 873 grams into kilograms Convert 0.78 tonnes into kilograms Convert 3.8 centilitres into millilitres Convert 478 millilitres into litres Convert 0.8 litres into millilitres Convert 0.08 kilometres into metres 0... Convert centimetres into metres... Convert 0.8 centimetres into millimetres... 3 Convert 3.4 metres into centimetres Convert 0.07 tonnes into kilograms Convert grams into kilograms Convert 3684 kilograms into tonnes Convert 0.3 kilograms into grams Convert 3.8 litres into millilitres Convert 0.78 litres into centilitres Convert 5.3 centilitres into millilitres 0... Convert 74 millilitres into centilitres... Convert 0.03 kilometres into centimetres... 3 Convert tonnes into grams Convert kilometres into centimetres Convert 3.6 metres into millimetres 5... Pearson Publishing Tel:

95 93 Making sensible estimates Estimate the following using metric units: The height of a classroom door... The weight of a newborn baby... 3 The length of your calculator The weight of your ruler The capacity of a teacup The capacity of a teaspoon Which metric unit would you use to measure the following: 7 The length of your bedroom The weight of a ship The capacity of a glass The weight of a pair of spectacles 0... The capacity of a bath... The distance from London to Manchester... 3 The length of a postcard The height of a giraffe? Miss Jones is standing by a house. Estimate the height of the house Pearson Publishing Tel:

96 94 Making sensible estimates Estimate the following (use metric units): Your weight... Your height... 3 The length of your pencil The weight of your pencil The capacity of a can of cola The capacity of a large bottle of lemonade 6... Which metric units would you use to measure the following: 7 The distance from London to New York? The weight of a fully loaded lorry? The capacity of a wine glass? The weight of a dog? 0... The capacity of a swimming pool?... The weight of a packet of chewing gum?... 3 The length of a pencil? The height of a tree? The length of a fly? Mr Roberts is standing by an elephant. Estimate the height of the elephant Pearson Publishing Tel:

97 95 Time A train journey started at 6.3 and finished at a How long did the journey take in hours and minutes? a...hours...mins b How long did the journey take in minutes? b...mins A commercial break had three adverts. Advert lasted for minute 8 seconds, advert lasted for 48 seconds, advert 3 lasted for minute 7 seconds. What was the total length of the commercial break?...mins...secs 3 A bus journey took 3 hours 7 minutes. The journey finished at 6.3. What time did the journey start? A train left Glasgow at.5 on Monday and arrived in London at 05.7 on Tuesday. How long did the journey take? 4...hours...mins 5 A car journey started at and lasted for 7 minutes. What time did the journey finish? 5... Pearson Publishing Tel:

98 96 Time A train left Edinburgh at It arrived in London at How long did the journey take?... A plane left London at.47 on Monday and arrived in New York 6 hours 5 minutes later. What was the time in London when the plane landed in New York?... 3 A car travelled from Liverpool to Ipswich. The journey took 4 hours 47 minutes. The car arrived in Ipswich at What time did the car leave Liverpool? A train travels 46 kilometres at an average speed of 97 kilometres per hour. Calculate the time taken: a to the nearest minute 4a... b to the nearest second. b... 5 A car travels 89 kilometres at an average speed of 67 kilometres per hour. Calculate the time taken: a to the nearest minute 5a... b to the nearest second. b... 6 How many seconds are there in one day? 6... Pearson Publishing Tel:

99 97 Compound measures A train travels 568 kilometres in 7 hours 8 minutes. Calculate the average speed, correct to three significant figures.... A plane travels 86 kilometres in hours 37 minutes. Calculate the average speed, correct to three significant figures A car travels at an average speed of 78 kilometres per hour for 3 hours 4 minutes. Calculate the distance travelled A car travels at a speed of 56 kilometres per hour for 48 minutes. Calculate the distance travelled A liquid has a volume of 68.3 cm 3 and a mass of 78.5 g. Calculate the density A car travels at a speed of.3 metres per second. Calculate this speed in kilometres per hour The density of a block of wood, volume 38.4 cm 3 was 0.7 g/cm 3. Calculate the mass Pearson Publishing Tel: