addition and subtraction of whole … sheets units 1-8/7a hwk...7a national curriculum mathematics...

7A NATIONAL CURRICULUM MATHEMATICS HOMEWORK SHEETS 1

© S Chandler, E Smith

ADDITION AND SUBTRACTION OF WHOLE NUMBERS

HOMEWORK 1.1AdditionRemember toshow all yourworking.

1 Find the sum of three thousand and forty five, four hundred and six andten thousand and nine.

2 Add the value of the figure 8 in the number 287 to the value of thefigure 5 in the number 3577.

3 The sequence of numbers 8, 15, 22, 29, ... is formed by starting with 8and adding 7 each time.Write down the next six numbers in the sequence.

4 Find the missing digit; it is marked with �: 35 + 49 = �4

5 Explain why the answer to 305 + 98 cannot be 393.

6 Complete this cross-number puzzle: Across Down 1 1479 + 1058 1 18 + 73 15 + 27 2 528 + 2124 147 + 153 4 179 + 1775 15 + 15 +15 6 The value of the7 6020 + 120 figure 2 in the

number 1025.


HOMEWORK 1.2SubtractionRemember toshow all yourworking.

1 Find the missing number; it is marked �: 108 + � = 570

2 Explain why the answer to 708 – 21 cannot be 787.

3 Subtract two thousand and sixty five from ten thousand five hundred.

4 Write down the value of the figure 5 in the number 256 340.

5 Find 185 – 204 + 38.

6 Explain an easy way to find in your head.197 58−−−−

7 Find the difference between the sum of 45 and 78 and the sum of 105and 64.

8 The sequence of numbers 100, 88, 76, 64, ... is formed by starting with100 and subtracting 12 each time. Write down the next three numbers in the sequence.

9 Write down an instruction for obtaining this sequence of numbers:66, 59, 52, 45, ...




HOMEWORK 1.3ApproximationRemember toshow all yourworking.

1 Write each number to the nearest ten and use your approximations toestimate the value of

a 478 + 62 b 57 – 39 c 251 – 49 – 131 – 17

2 Write each number to the nearest hundred and use your approximationsto estimate the value of

a 5976 – 2479 b 26 370 + 539

3 Explain, without working it out, why the value of 432 + 226 must begreater than 600.

4 There are many ways to make a quick estimate of the value of 121 – 94.Here are three possibilities:

a Round each number to the nearest hundred. Write down the estimate that this gives.

b Round each number to the nearest ten. Write down the estimate that this gives.

c Round the first number to the nearest ten and the second number to the nearest hundred. Write down the estimate that this gives.

Write down one advantage and one disadvantage of each method.



MULTIPLICATION AND DIVISION WITH WHOLE NUMBERS

HOMEWORK 2.1MultiplicationRemember toshow all yourworking, withoutusing acalculator unlesstold to do so.

1 Find a 143 60 b 209 400× ×2 Find the missing digit, marked with � in the following calculations.

Explain why you do not need to do the complete multiplication to find theanswers:

a 36 27 = 97 � b 53 58 = 307 � × ×3 Use a calculator to find a 73 47 b 429 51 c 509 263 d 3271 77.× × × ×4 Multiply two hundred and seven by twenty-seven.

5 A flight to the USA took 9 hours. How many minutes is this?

6 Jane buys five loaves of bread costing 64 p each and pays with a £5 note.How much change does she get?

7 Joe throws three darts. The first scores treble 19, the second double 13 andthe third treble 7. What is Joe’s score?

8 The sequence 4, 12, 36, ... is formed by starting with 4 and multiplying thelast number by 3. Write down the next two numbers in the sequence.

9 My grandmother was born in November 1904 and died in August 1983. How old was she when she died?

MULTIPLICATION AND DIVISION WITH WHOLE NUMBERS

HOMEWORK 2.2DivisionRemember toshow all yourworking.

1 The sequence 8192, 4916, 2408, ... is formed by starting with 8192 anddividing the last number by 2. Write down the next four numbers in thesequence.

2 How many times can 7 be taken away from 60?

3 Find, without using a calculator, giving the remainder when there is one: a 480 30 b 1610 70 c 485 8 d 831 6 ÷ ÷ ÷ ÷

4 Explain, without calculating, why 2493 will not divide exactly by 5.

5 Use a calculator to find, giving the remainder a 3458 24 b 6921 37 c 8274 57÷ ÷ ÷

6 Find the missing digit, denoted by � in the following calculations,a 322 2 � = 14 b 1323 2 � = 63 c 94 � 35 = 27, r 3÷ ÷ ÷

7 An exercise has 35 questions. For homework a class is asked to do everythird question starting with Number 1. How many questions are set?

8 Find, without using a calculator, a 12 4 6 3 9 b 8 2 5 15 5÷ − × ÷ ÷ × − ÷



COLLECTING AND DISPLAYING DATA

HOMEWORK 3.1Frequency Tablesand Observation Sheets

1 This is a list of the scores obtained when an ordinary six-sided dice was thrown twenty times.

2 4 3 6 2 5 2 1 3 5 6 4 5 6 6 4 2 1 3 5

Make a frequency table for these scores.

2 Mr Penn expects that every pupil in his maths class has a pencil, a pen, aruler, a calculator and a work book with them. Design an observation sheet that Mr Penn can use to check which of theseitems each pupil has with them.

3 Jay does a traffic survey. He counts the number of people in each car thatpasses him. He uses this data collection sheet.

a One of these columns is not needed. Which one is it and why?

b Why are more columns needed?

c Make your own observation sheet.



COLLECTING AND DISPLAYING DATA

HOMEWORK 3.2Bar Charts andPictograms

1 This bar chart shows the information from a maths test.

a What was the lowest mark scored and how many pupils got this mark?

b How many pupils took the test?

c All those pupils who scored less than 5 had to retake the test. How many pupils had to retake the test?

2 Draw a bar chart to illustrate this information:

3

a How many young people bought breakfast on Monday?

b How many more young people bought breakfast on Thursday than did on Wednesday?

c On Friday, 3rd of May, 15 young people bought breakfast at school. Copy the pictogram and add this information to it.



NUMBER AND PATTERNS

HOMEWORK 4.1Prime Numbersand IndicesRemember toshow all yourworking.

1 a Which of the numbers 10, 11, 12, 13, 14, 15, 16, 17 are prime numbers?

b Write down all the prime numbers between 70 and 80.

2 a Write 25 as the sum of two prime numbers.

b Write 27 as the sum of three odd prime numbers.

3 Write the following products in index form.a 5 5 5 b 2 2 2 2 2 2.× × × × × × ×

4 Find the value of a 33 b 52 c 73

5 Express 64 as the power of a prime number.

6 Which is the larger and by how much 53 or 35 ?

7 Find the value of 23 52.×

8 Write the following products in index form.a 3 3 3 11 11 b 2 5 5 2 5 5.× × × × × × × × ×

NUMBER AND PATTERNS

HOMEWORK 4.2Factors andMultiplesRemember toshow all yourworking.

1 Without doing the division, explain if a 9274 divisible by 3 b 17088 divisible by 6?

2 Express in prime factors a 1056 b 1080.

3 Find the largest whole number that will divide exactly intoa 16, 24 b 28, 42, 63 c 36, 48, 72

4 Find the smallest number that the given numbers will divide into exactly.a 5, 6 b 3, 4, 8 c 5, 6, 7

5 Find the largest number that will divide exactly into 24, 40, 72 and 104.

6 Find the smallest number that 9, 12 and 15 will divide into exactly.

7 Is 6230 exactly divisible by 20? Give a reason for your answer.

8 A room measures 550 cm by 400 cm.Find the side of the largest square carpet tile that can be used to carpetthe floor without any cutting.



NUMBER AND PATTERNS

HOMEWORK 4.3PatternsRemember toshow all yourworking.

1 Write down the next three terms for the pattern a 6, 11, 16, 21, ... b 2, 6, 18, 54, ...

2 Write down the next three terms for the patterna 40, 36, 32, 28,... b 35, 34, 32, 29, 25,...

3 a Write down the sixth square number. b Write down the sixth triangular number.

4 Write down the next three numbers for the pattern 8, 12, 17, 23, 30, ...

5 A sequence is formed by starting with 7 and then adding the oddnumbers 5, 7, 9, 11,... one at a time to give the subsequent terms. The first three numbers are 7, 12, 19.Write down the next three numbers in this sequence.

6 Write down the next three terms for the pattern a 3, 9, 27, 81, ... b 5, 3, 8, 11, 19,...

7 Give the next two shapes for the following patterns.a

b



PARTS OF A WHOLE

HOMEWORK 5.1Fractions andDecimals Remember toshow all yourworking.

1 Write down the fraction that is shaded in each of the following diagrams.a b c

2 Explain why it is not true that half of this diagram is shaded.

3 Copy the fractions and fill in the missing numbers to make equivalentfractions.

a b c 1 35 ==== 3

4 20==== 38 64====

4 Write as an equivalent fraction with a denominator of 36.79

5 Simplify the following fractions.a b c d 6

123

155075

936

6 Write down the value of the figure 5 in each of these numbers.a 2.5 b 51.2 c 0.125 d 20.05

7 Write these fractions as decimals. a b c 24100

910

7100

PARTS OF A WHOLE

HOMEWORK 5.2Percentages,Fractions andDecimalsRemember toshow all yourworking.

1 There are one hundred small squares in this diagram.a What percentage of this diagram is shaded?b What fraction of the diagram is

shaded?c How many more squares need to be shaded so that 40% of the diagram is shaded?d How many small squares in total need to be shaded so that 0.34 of the diagram is shaded?

2 Express each percentage as a fraction in its lowest terms.a 30% b 45% c 75% d 60%

3 Express each percentage as a decimal. a 84% b 56% c 12% d 6%

4 Express each fraction as a decimal. a b c d 34

1750

121 1

20

5 Express each of the following as a percentage.a 0.8 b c 0.08 d 12

2545

6 Write each decimal as a fraction. a 0.4 b 3.7 c 0.125



PARTS OF A WHOLE

HOMEWORK 5.3Fractions andPercentages of aQuantityRemember toshow all yourworking.

1 Find a of 40 miles b of £15 c of 64 eggs.58

23

34

2 Find a 60% of £200 b 25% of 16 kg c 5% of 3000 people.

3 One shop offered a discount of 10% on a book priced at £12.Another shop offered a discount of on the same book at the same price.1

8

a What sum of money was the discount in the first shop?b How much money was taken off the price in the second shop?

4 To get to work, Ann Jones takes a bus and then a train.In 2000, the bus fare was £1 and the train fare was £2.50.By 2003, the bus fare had increased by 5% and the train fare had gone upby one fifth. How much more did Ann Jones pay to get to work in 2003 compared to2000?

5 Ras gets £10 a week for a paper round. He gets a pay increase of 20%.Sara earns £20 a week as a part-time checkout operator. She gets a payincrease of 5%.Who gets the larger pay rise as a sum of money?Explain your answer.

PARTS OF A WHOLE

HOMEWORK 5.4Comparing theSizes of Fractionsand DecimalsRemember toshow all yourworking.

1 Which is the bigger fraction? Explain your answer.a or b or c or 5

779

34

1924

23

58

2 Write these numbers in order of size, with the largest first. a 0.28, 5.01, 5.1, 0.82 b 20.5, 101, 10.9, 50.2

3 Copy the numbers and place either < or > between them. Explain your reasons. a b 1.02 1.2 c 0.74

523

35

4 The money raised from a school raffle was used to buy equipment.20% of the money was spent on books for the library.One quarter of the money was spent buying new footballs.a Explain why you do not need to know the sum of money raised from

the raffle to find out whether more of the money was spent on books oron footballs.

b Was more of the money spent on books than on footballs? Explain your answer.

c Later in the year, the school raised money from a bring-and-buy sale and 30% of this money was spent on library books.

To find out whether more money was spent on books from the first sum of money raised or from the second, explain why you do need to know the sum of money raised on each occasion.



ADDITION AND SUBTRACTION OF FRACTIONS AND DECIMALS

HOMEWORK 6.1Addition andSubtraction ofFractionsRemember toshow all yourworking. Do notuse a calculator.

1 Add the given fractions, simplifying your answer where possible a + b + c + + 5

838

310

110

213

413

713

2 Find a + b + c + 15

14

37

12

29

310

3 Find a + b + c + + 512

16

12

38

12

14

18

4 Without adding the fractions together, decide whether + is more13

14

than or less than . Give a reason for your answer.12

5 Find, simplifying where possible, a – b – c – 58

38

1112

16

715

15

6 Find a – + b + – c – + 35

310

12

16

23

712

78

1940

35

7 At a football match of the spectators are men, are women and the712

14

remainder are children. What fraction of the spectators are children?

8 Des can paint the end wall of a cottage in 2 hours and Tom can paint it in 3 hours. What fraction of the wall can each paint in 1 hour? What fraction remains to be painted if they both paint for 1 hour?


HOMEWORK 6.2Mixed NumbersRemember toshow all yourworking.

1 Change these mixed numbers to improper fractions: a b c d 2

32 357 5

75 786

2 Find each of the following divisions giving each answer as a mixed

number: a 62 7 b 93 5 c 37 4 d 30 8 ÷ ÷ ÷ ÷

3 Find a b 3 14 83 1++++ 52

3 67 3++++

4 Find 31 14 8 24 3 2+ ++ ++ ++ +

5 Is bigger or smaller than ? Justify your answer.127 3 1

4 52 4++++

6 Find a b c d 3 34 83 1−−−− 4 2

5 36 2−−−− 5 37 45 3−−−− 7 5

12 82 1−−−−

7 How much less than 2 is the difference between and ?344 2

33

8 How much more than 3 is the difference between and ?577 5

92




HOMEWORK 6.3Addition andSubtraction ofDecimalsRemember toshow all yourworking.

Do not use a calculator for any of these questions.

1 Finda 5.3 + 4.7 c 9.77 + 1.8 e 0.43 + 0.049

b 6.23 + 2.49 d 9.77 + 0.045 f 0.0004 + 5.4

2 Find the sum of a 3.74 and 16.215 b 0.246 and 1.008

3 A rectangle measures 4.2 cm by 2.98 cm. Find its perimeter.

4 Find a 3.42 1.78 c 5 2.924 e 8.7 6.224− − −

b 2.094 1.7 d 9.8 0.046 f 10.08 6.99− − −

5 Subtract 3.24 from the sum of 1.93 and 4.77

6 Last week George had lunch out on Monday, Wednesday and Friday. His lunch on Monday cost £7.44 and on Friday it cost £6.89. Altogether on the three lunches he spent £23.87. How much did his lunch cost him on Wednesday?

7 Sally bought three books in a shop and paid with two £20 notes. The costs of the books were £8.99, £7.49 and £15.95. How much change did she get?



MORE ON DECIMALS

HOMEWORK 7.1Multiplication andDivision of aDecimal by aWhole Number.ChangingFractions toDecimalsRemember toshow all yourworking.

1 Find, without using a calculatora 3.25 × 100 b 0.05 × 10 c 1.0025 × 1000

2 Find, without using a calculatora 13.2 ÷ 100 b 0.5 ÷ 10 c 566.7 ÷ 1000

3 Find, without using a calculatora 3.8 × 4 b 12.02 × 5 c 4.6 × 200

4 Find, without using a calculatora 7.6 ÷ 4 b 0.5 ÷ 2 c 1.5 ÷ 500

5 First find an estimate, then use a calculator to finda 3.21 × 17 b 0.35 × 21 c 1.28 × 114

6 First find an estimate, then use a calculator to finda 57.5 ÷ 46 b 88.2 ÷ 18 c 615.4 ÷ 34

7 Janine buys 200 recordable CDs for £35.a How much does one of these CDs cost?b Blake buys 40 of these CDs from Janine. How much should they cost him?

8 Without using a calculator, express these fractions as decimals. Remember to check your answers.a b c 7

203

16782

MORE ON DECIMALS HOMEWORK 7.2Multiplication bya Decimal.Decimal Places.Remember toshow all yourworking.

1 Find, without using a calculatora 3.25 × 0.3 b 0.15 × 0.1 c 1.25 × 0.5

2 Find, without using a calculatora 7.5 × 0.2 b 1.77 × 0.01 c 0.008 × 9

3 A mini-cab firm charges £1.08 per kilometre. How much should a journeyof 6.3 kilometres cost?

4 First estimate, then use a calculator to find, correct to 2 decimal placesa 12.5 × 1.877 b 23.889 × 0.144 c 0.000557 × 287

5 Use a calculator to express the fractions , , and as decimals37

917

512

1733

correct to 2 decimal places. Hence write them in order of size with thesmallest first.

6 Decide, without using a calculator, which of these is the smallest andwhich is the largest. Explain how you reached your decision.

, 1.29, , 12.5 ÷ 14.712191 13

271



MORE ON DECIMALS

HOMEWORK 7.3Division by aDecimalRemember toshow all yourworking.

1 Find, without using a calculator, the exact value ofa 1.25 ÷ 0.05 b 8.32 ÷ 0.4 c 0.096 ÷ 0.0012Check your answers by reverse working.

2 First estimate then, without using a calculator, find correct to 2 decimalplacesa 1.25 ÷ 0.3 b 4.77 ÷ 0.07 c 12.8 ÷ 15.6

3 The width of one floor board is 14.4 cm. How many of these floorboardsare needed to cover a floor that is 360 cm wide? Check your answer.

4 A stack of 5 reams of paper is 230 mm high. (A ream of paper is 500 sheets.)a Find, correct to 2 decimal places, the thickness of 1 sheet of paper.b Find exactly the thickness of 1 ream of paper. c A pamphlet with 40 pages is made from this paper. How thick is the pamphlet? (Think carefully about this one.)

MORE ON DECIMALS

HOMEWORK 7.4Mixed QuestionsinvolvingDecimals,Fractions and PercentagesRemember toshow all yourworking.

1 Choose a sensible approximation for each number and use yourapproximations to estimate the value ofa 478 ÷ 1.21 b 17.5% of £391 c 0.099 × 27.3

2 Which is the larger sum of money and by how much? of £27.36 or 6% of £1753

8

3 Find, without using a calculator: 0.256 × 10 – 1.87

4 Find, without using a calculatora b 2 1

5 4+ 723 81 −−−−

5 Place these numbers in order of size with the smallest first.1.36, , 140%, 4

91 5121

6 In this triangle, the shortest side is 12 cm long,the next shortest side is times the length1

32of the shortest side,the longest side is 25% longer than themiddle length side.How long is the longest side?



METRIC UNITS

HOMEWORK 8.1Length and Mass.Changing fromLarge Units toSmall UnitsRemember toshow all yourworking.

1 a Which metric unit would you use to measure the width of a road?b Using a straight edge, but not a ruler, draw two lines, one that you think is about 5 cm long and another that you think is about 12 cm long.

Measure both lines. How accurate were you? Repeat this question at the end of this exercise to see if you can be more accurate.

2 Express a 3 metres in centimetres c 4.8 km in metres b 5.2 cm in millimetres d 2.3 km in millimetres.

3 Express a 7.5 tonnes in kilograms c 3.2 grams in milligrams b 8.4 kilograms in grams d 0.06 kilograms in grams.

4 Which is the shorter, and by how much, a walking stick 82 cm long or one 814 mm long? Give your answer in millimetres.

5 Which is heavier, and by how much, a load of sand weighing tonne or34

25 bags of cement, each weighing 25 kg? Give your answer in kilograms.

6 Arrange these lengths in order of size with the shortest first: 256 cm, 174 mm, 24 cm, 0.83 m, 2436 mm.

7 Arrange these masses in order of size with the heaviest first: 82 g, 0.83 kg, 824 g, 8100 mg.

METRIC UNITS

HOMEWORK 8.2Addition andSubtraction ofMetric QuantitiesRemember toshow all yourworking.

1 Find, giving your answer in metres:a 3 m + 74 cm c 220 m + 1.5 kmb 47 cm + 225 mm d 64 cm + 150 mm + 2 m

2 Find, giving your answer in millimetres: a 54 cm + 70 mm c 2 m + 53 cmb 6 mm + 6 cm d 48 mm + 1 m + 53 cm

3 Find, giving your answer in grams:a 2 kg + 80 g c 8.2 kg + 0.6 kgb 350 g + 3 kg d 0.04 kg + 134 kg

4 Find, expressing your answer in the unit in brackets:a 5 m 125 cm (cm) c 3 t 756 kg (kg)− −b 2.3 kg 64 g (g) d 0.6 m 28.2 cm (mm)− −

5 A tin of salmon weighs 213 g.a What is the weight, in kilograms, of 6 of these tins?b Use your answer to find the weight, in kilograms, of 24 of these tins.

6 Is it possible to draw a triangle with sides of length 24 mm, 3.4 cm and 6 cm? Give a reason for your answer.



IMPERIAL UNITS

HOMEWORK 9.1Imperial Unitsand theirApproximateEquivalence withMetric UnitsRemember toshow all yourworking.

1 Jill had an operation and lost 9 lb in weight. Before the operation sheweighed 8 stone 5 lb. What did she weigh after the weight loss? Give your answer in stones and pounds.

2 How many ounces is lb?122

3 Harry uses an old cake recipe that asks for cake to be cooked in an 8 inchround tin. The tins he has are 15 cm, 20 cm and 24 cm round tins. Which one should he use? Give a reason for your answer.

4

The diagram represents an island with villages A, B, C, D, E, F and Gtogether with the road distances between them, marked in kilometres.a Gary’s car instruments record distances in miles. He drives from

village A to village F via E and G. How far is this in miles?b When Gary gets to village F he finds that he is running low on petrol.

He estimates that he has enough to travel about 5 miles. Should he risk driving back to G before filling up? Give a reason for your answer.

5 Which is heavier a 500 grams or 1 lb b 4 oz or 100 grams? Explain your answers.

6 Which is longer a 1 mile or 1 km b 10 cm or 4 inches? Explain your answers.

7 A group of Year 7 pupils were asked how tall they were.These are some of the answers:

1.5 metres, 4 ft 8 in, 78 cm, 250 cm, 45 inches

Two of these heights are probably wrong.Which are they and why?



INTRODUCING GEOMETRY

HOMEWORK 10.1AnglesRemember toshow all yourworking.

1 How many degrees does a hand of a clock turn through when it moves a from 6 to 9 b from 10 to 5 c from 2 to 8?

2 If you stand facing west and turn clockwise through one quarter of a turn,in which direction are you facing?

3 What type is each of these angles? Estimate the size of each angle.a b c d

4 If you stand facing south and turn anticlockwise through revolutions,121

in which direction are you facing?

5 Draw, without using a protractor, an angle that is about each of the givenvalues. Now use a protractor to see how accurate each estimate is.a 60o b 45o c 20o d 150o e 200o f 300o

6 Use a protractor to draw accurately, the angles listed in question 5.

INTRODUCING GEOMETRY

HOMEWORK 10.2Finding AnglesRemember toshow all yourworking.

Find the size of each angle marked with a letter. Give reasons for youranswers. 1 4 7

2 5 8

3 6 9

10 Each of the angles marked p is 35o . Angles p and q are supplementary angles. Find the size of the angles q and r.



SYMMETRY

HOMEWORK 11.1Line Symmetryand RotationalSymmetryRemember toshow all yourworking.

1 Copy the diagram and complete it so that the dotted lines are lines ofsymmetry.a b

2 Write down the letter(s) of the shape(s) that have a line symmetry or rotational symmetry but not both,b line symmetry and rotational symmetry.

3 State whether or not the two figures are congruent. If you are not sure,trace one figure and see if the figure will fit exactly over the other figure.a c

b d

4 Each of these solids has a plane of symmetry.Draw the section that is made by slicing through a plane of symmetry. Mark any lengths and angles that you know.a b



TRIANGLES AND QUADRILATERALS

HOMEWORK 12.1TrianglesRemember toshow all yourworking.

1 Make a freehand drawing of a triangle ABC in which AB = 8 cm,A = 30o and B = 60o. ∠ ∠

Now use a protractor and ruler to see how accurate you have been.

Find the size of each angle marked with a letter.

2

3

4

5

6

7




HOMEWORK 12.2ConstructionsRemember toshow all yourworking.

1 Construct triangle ABC using the measurements given on the diagram..

2 Construct triangle PQR using the measurements given on the diagram..

3 Construct triangle ABC in which AB = 4.5 cm, BC = 6 cm and angle B = 60o.

4 Construct triangle DEF in which DE = 3.8 cm, DF = 6.5 cm and angle D = 90o.

5 Construct triangle XYZ in which XZ = 72 mm, angle X = 60o and angle Z = 45o.

6 Can you draw two different triangles using the measurements :AB = 7 cm, BC = 5 cm and angle BAC = 40o. Use constructions to justify your answer.




HOMEWORK 12.3Quadrilateralsand SpecialTrianglesRemember toshow all yourworking.

Find the angles marked with letters. Give reasons for your answers.

1 5

2 6

3 7

4 8



PROBABILITY

HOMEWORK 13.1Chance,Outcomes andProbabilityRemember toshow all yourworking.

1 Decide whether each of the following events is impossible, possible, orcertain to happen.a There will be no people in the next car that passes you.b One letter chosen from the word APPLE is P.c Tickets numbered 001 to 507 are sold for a raffle and the winning

ticket is number 561. d A number chosen from the following list is a multiple of 3:

9, 18, 30, 45.

2 Write down all the possible outcomes of the following actions.a Choosing a letter from the letters of the word DEBIT.b Throwing an ordinary six-sided dice.c Taking a piece of fruit from a bowl containing an apple, an orange, a banana and a pear.

3 One number is chosen at random from the numbers 1, 2, 3, 4, 5. What is the probability that it is a multiple of 3?

4 One card is chosen at random from an ordinary pack of 52 playing cards.What is the probability that it is the ace of spades?

5 One number is chosen at random from the first twenty whole numbers.What is the probability that it is a common factor of 42, 48 and 72?

PROBABILITY

HOMEWORK 13.2ProbabilityRemember toshow all yourworking.

1 How many ways are there of choosing a multiple of 2 from the integers 1 to 10 inclusive? List them.

2 One card is chosen at random from an ordinary pack of 52 playing cards.How many ways are there of choosing an ace? List them.

3 One card is chosen at random from an ordinary pack of 52 playing cards.What is the probability that it is a a ten b a black card c a two, a three or a four?

4 One number is chosen at random from the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 a What is the probability that it is a multiple of 3?

b What is the probability that it is a prime number?c What is the probability that it is a factor of 12?

5 You will need two dice for this question.Roll both dice together 50 times and record whether you get a “double” ornot. (A double is when both dice show the same number on top.)Use a table like this one to keep track ofyour experiment.

Use your results to estimate the probability of getting a double when youroll two dice.



AREA

HOMEWORK 14.1CompoundFiguresRemember toshow all yourworking.

1 Find the area of a a square of side 3 cm b a rectangle measuring 4 cm by 7 cm.

2 Find the area of each shape.a b

3 The area of a rectangle is 48 m2 . It is 8 m long. Find its breadth.

4 The perimeter of a lawn is 37 m. The lawn is 12 m long. Find its area.

5 For this shape find a the perimeter b the area.

6 This shape is formed by removing a rectangle measuring 5 cm by 4 cm from a rectangle measuring 20 cm by 12 cm. Sketch the diagram and mark on it the length of each side. Find a its perimeter b its area.

AREA

HOMEWORK 14.2Changing UnitsRemember toshow all yourworking.

1 Express a 5 m2 in cm2 b 0.7 m2 in cm2 c 4.5 cm2 in mm2.

2 Express a 8600 cm2 in m2 b 1640 mm2 in cm2 c 200 000 m2 in km2.

3 Express a 0.2 cm2 in mm2 b 8000 cm2 in m2 c 0.045 km2 in m2.

4 a Find the area, in square centimetres, of a rectangle measuring 8 cm by 40 mm.b Find the area, in square metres, of a rectangle measuring 45 cm by 6 m.

5 A rectangular rug has an area of 14 m2. It is 350 cm wide. How long is it?

6 How many carpet squares of edge 50 cm are needed to cover a rectangularroom measuring 5 m by 4.5 m?

7 A strip of wood is 2 m long and 25 mm wide. Find the area of one of its largest faces. Give your answer in square centimetres.



PARALLEL LINES

HOMEWORK 15.1CorrespondingAngles Remember toshow all yourworking.

1 Write down the angle that corresponds to the shaded angle.

2 Draw an isosceles triangle ABC in which AB is 9 cm long and in whichangle A is 45o. Draw a line BD that is parallel to AC and is 6 cm long.

3 Write down the size of the angle marked h in each of the followingdiagrams.a c

b d

PARALLEL LINES

HOMEWORK 15.2Alternate AnglesRemember toshow all yourworking.

1 Write down the angle that isalternate to the shaded angle.

2 Find the size of each marked angle.a d

b e

c f



PARALLEL LINES

HOMEWORK 15.3Mixed QuestionsRemember toshow all yourworking.

Find the size of each marked angle. Give reasons for your answers.

1 5

2 6

3 7

4 8



COORDINATES

HOMEWORK 16.1Plotting pointsand usingPositiveCoordinatesRemember toshow all yourworking.

The sketch shows the lay-out of a caravan site. It is drawn on a grid.

1 What are the coordinates of the main gate A?

2 The emergency gate is at E. What are the coordinates of this gate?

3 What is the x-coordinate of the manager’s bungalow which is at F? 4 Which letter on the map has coordinates (5, 3) ?

5 Which letter is south-east of C?

6 B, D, E and F are joined to give a quadrilateral. What special name do wegive to this type of quadrilateral?

7 A recycling point, P, is the same distance from gate, A, as it is from thepath leading directly from E to F. Write down the coordinates of P.

8 The manager installs a fire hydrant exactly halfway between the bungalowand the main gate.What are the coordinates of the fire hydrant?



COORDINATES

HOMEWORK 16.2Special QuadrilateralsRemember toshow all yourworking.

1 A(2, 3), B(2, 8), C(9, 8) and D (9, 3) are the vertices of a rectangleABCDE. Draw the rectangle ABCD on your own set of axes.a Which sides of the rectangle are of equal length?b Write down the pairs of sides that are parallel.c What is the size of each angle of a rectangle?

2 P(3, 2), Q(4, 6) , R(11, 8) and S(10, 4) are the vertices of a quadrilateralPQRS. Draw the quadrilateral PQRS on your own set of axes. a What type of quadrilateral is PQRS?b Write down which sides, if any, are parallel.c Write down which sides, if any, are the same length.d Write down which angles, if any, are equal.

3 Plot the points A(1, 3), B(3, 7), C(7, 5) and D(5, 1) on your own set ofaxes and write down which type of quadrilateral it is.

4 Plot the points W(4, 6), X(8, 6), Y(8, 1) and Z(3, 1) on your own set ofaxes and write down which type of quadrilateral it is.

5 Plot the points P(3, 2), Q(1, 4), R(3, 7) and S(5, 4) on your own set ofaxes and write down which type of quadrilateral it is.

COORDINATES

HOMEWORK 16.3 SpecialQuadrilateralsRemember toshow all yourworking.

1 Write down a the x-coordinate of Ab the y-coordinate of Bc the x-coordinate of Cd the y-coordinate of Ee the coordinates of Df the coordinates of F.

2 Write down the coordinates of a point G such that ABGD is a square.

3 Write down the coordinates of a point H such that ABCH is a rectangle.

4 Write down the coordinates of a point J such that ABDJ is a parallelogram.

5 Write down the coordinates of the midpoint of a BC b AD.



FORMULAS

HOMEWORK 17.1Making and UsingSimple FormulasRemember toshow all yourworking.

1 The perimeter of a square is found by multiplying the length of a side by 4.Write down a formula connecting the perimeter and the length of a side.

2 Write each formula in a shorter form.a H = 5 × L b y = x × 8 c A = v ÷ 10 d b = c × 5 ÷ 4

3 Insert multiplication and/or division symbols where appropriate into eachformula

a A = bw b c d m = 5 + 2p3RC ==== 3

4xy ====

4 A number y is always 5 more than a number x.a Write down a formula connecting x and y.b Find y when x is i 2 ii 9

5 Copy the table and complete it using the formula y = x – 4.

6 Copy the table and complete it using the formula P = 10 – T.

FORMULAS

HOMEWORK 17.2Using FormulasRemember toshow all yourworking.

1 The number of matchsticks needed, N, to make this pattern with n triangles is given by the formula

N = 2n + 1.

a How many sticks are needed to make a pattern with 12 triangles?b The pattern is made with 15 sticks. How many triangles are there?c What is N when n is 21?d Find the value of n when N is 51.

2 Use the formula C = 3p – 4 to find a C when p = 12b C when p = 3c p when C = 2.

3 Use the formula y = 3x + 2z to find y when a x = 2 and z = 4 b x = 7 and z = 2

4 Use the formula to find V whenAV w====

a A = 18 and w = 3 b A = 2 and w = 0.5

5 Given that S = ut - 20, find S when a u = 6 and t = 4 b u = 5 and t = 8



FORMULAS

HOMEWORK 17.3Directed NumbersRemember toshow all yourworking. 1 Find, using the number line if it helps you

a 6 – 8 b – 5 + 7 c – 1 – 3 d – 2 – 6

2 Finda 5 – 3 – 1 b 4 + 2 – 8 c – 3 + 8 – 5 d – 6 – 2 + 9

3 Finda 4 + (– 3) b – 6 – (+5) c 8 – (+11) d – 5 + (– 5)

4 Finda 4 + (3 – 6) b 7 – (– 8 + 9) c 2 – (7 – 1) d – 4 + (3 – 5)

5 Finda 4 × (– 6) b (– 8) ÷ 2 c (– 4) × 7 d 9 ÷ (– 3)

6 The formula can be used to convert a temperature of9 325cf = += += += +

c degrees Celsius to f degrees Fahrenheit. Use the formula to give these temperatures in degrees Fahrenheit.

a 15oC b – 5oC c – 20oC d – 8oC

7 Use the formula y = 3x - 5 to find y whena x = 3 b x = 1 c x = – 1 d x = – 3



STRAIGHT LINE GRAPHS

HOMEWORK 18.1Line GraphsRemember toshow all yourworking.

1

The graph shows the takings for a butcher’s shop for one week.

a On which day of the week was the shop closed?

b On which day of the week do you think the shop closes for a half-day?

c What were the takings on i Tuesday ii Saturday?

d Which day, when the shop was open, were the takings i greatest ii least?

e What were the total takings for the week?

2

This conversion graph converts between miles and kilometres.

a Use the conversion graph to find the rough equivalent in kilometres of i 20 miles ii 40 miles iii 35 miles.

b Use the conversion graph to find the rough equivalent in miles of i 30 km ii 40 km iii 55 km.



18.1 continued 3

This graph converts between pounds sterling (£) and euros (€).Use the graph to answer the following questions.

a Convert i £80 to euros ii €50 to pounds sterling.

b Ken went to Brussels on the train for the day. He changed £40 into euros. How many euros did he get?

c Use your answer to part b to find the value of £1 in euros.

d When Sally returned from holiday she changed €35 into pounds. How many pounds did she get?

e Use you answer to part d to find the value of one euro in i pounds ii pence.

f Explain how you could use this graph to convert i £750 into euros ii €400 into pounds.

.



STRAIGHT LINE GRAPHS

HOMEWORK 18.2Coordinates andStraight LinesRemember toshow all yourworking.

1 The points A, B, C, D and Eall lie on the same straight line.

a Copy and complete this table for the coordinates of the points A, B, C, D and E.

b F is a point on the line. Its x-coordinate is 5; what is its y-coordinate?c G, H, I and J are other points on the line. Copy and fill in the missing coordinates: G(3, ), H( , 8), I( 3, ), J( , 2).∗ ∗ − ∗ ∗ −d How is the y-coordinate of each point related to the x-coordinate?

2 The points A, B, C, D and E all lie on the same straight line.

a Copy and complete this table for the coordinates of these points.

b F is a point on the line. Its x-coordinate is 5; what is its y-coordinate? c G, H, I and J are other points on the line. Copy and fill in the missing coordinates: G(6, ), H( , 1), I( 3, ), J( , 13).∗ ∗ − − ∗ ∗ −d How is the y-coordinate of each point related to the x-coordinate?



SUMMARISING AND COMPARING DATA

HOMEWORK 19.1Mean and RangeRemember toshow all yourworking.

1 Six people put the following amounts into a charity collection tin:

20 p, 50 p, 10 p, 50 p, 70 p, 40 p.

What was the mean amount?

2 These are the marks obtained by ten pupils in a test:

7, 8, 5, 7, 8, 9, 10, 7, 9, 6

What is the mean mark and what is the range of these marks?

3 Twenty people contributed to a leaving present. The mean amountcontributed was £1.50. What was the total amount contributed?

4

a How many cars passed Oakfield bus stop during this survey?

b What was the mean number of passengers in a car? Give your answer correct to 1 decimal place.

5

In this second survey,

a How many cars were counted in this survey?

b What was the mean number of passengers in a car? Give your answer correct to 1 decimal place.

c Compare the results of this survey with the survey carried out earlier in the day in question 4.




HOMEWORK 19.2Mode andMedianRemember toshow all yourworking.

1 Find the median and the mode of each set of figures.

a £10, £5, £4, £8, £10, £12, £5, £7, £12

b 12 km, 18 km, 45 km, 20 km, 18 km

c 50%, 30%, 45%, 60%, 30%, 70%, 34%, 65%, 70%, 65%

2 Here is that traffic survey again.

a Find the modal number of passengers in a car.

b Is it true that more cars had no passengers in them than cars that had one or more passengers in them? Give a reason for your answer.

c Find the median number of passengers in a car.

d Is it true that more than half the cars in this survey had 3 or more passengers in them? Give a reason for your answer.

3 The table shows the heights of 80 adult men measured to the nearest 10 centimetres.

a Find the mean, median and modal height.

b What is the range of the heights?

Which of the following statements are true? Give reasons for your answers.

c The heights of more than half the men were 1.8 metres or more.

d The height of one man in this group was more than the mean height of the group. This means that more than 40 of the group were shorter

than this man.



SOLIDS

HOMEWORK 20.1Cubes andCuboidsRemember toshow all yourworking.

1

This cuboid is 3 cm long, 2.5 cm wide and 2 cm high.

a How many faces does it have?

b Sketch these faces showing their measurements.

c On 1 cm grid paper, draw a net that will make this cuboid.

2

This net will make a cube with edge 4 cm.

a Write down the length of i NF ii EI

b What edge meets i JI ii BC iii AN?

c What corners meet at M?

3

i iiHere are two arrangements of 6 rectangles. All measurements are in centimetres. Copy them on 1 cm squared paper.

a Which of these arrangements is a net for a cuboid?

b What are the dimensions of this cuboid?

c What is the area of one of the largest faces?

d Draw, on 1 cm squared paper, another net for this cuboid.



SOLIDS

HOMEWORK 20.2VolumeRemember toshow all yourworking.

1 Find the volume of a cuboid measuring 8 cm by 7 cm by 20 cm.

2 Find the volume, in cubic centimetres, of a cuboid measuring 1 m by 50 cm by 15 cm.

3 a Find, in cubic centimetres, the volume of a cuboid measuring 8 cm by 6 cm by 5 cm.

b Find, in cubic metres, the volume of a cuboid measuring 4 m by 60 cm by 30 cm.

4 Draw a cuboid measuring 6 cm by 4 cm by 4 cm. How many cubes of side 2 cm would be needed to fill the same space?

5 A box is a cuboid measuring 8 cm by 6 cm by 3 cm.a How many cubes of side 1cm are needed to fill this box?b What is the largest number of cubes of side 2 cm that will fit inside this box? Explain why all the space cannot be filled.

6 A rectangular brick measures 20 cm by 10 cm by 5 cm. How many similarbricks can be fitted inside a cubical box with a side of 1 metre?

SOLIDS

HOMEWORK 20.3CapacityRemember toshow all yourworking.

1 a Express 1.2 cm3 in cubic millimetres.

b Express 50 cm3 in i cubic millimetres ii cubic metres.

2 Express a 1.3 litres in cubic centimetres

b 5400 cm3 in litres.

3 How many litres are needed to fill a rectangular oil tank measuring 40 cm by20 cm by 15 cm?

4 a Give roughly, the number of pints equivalent to 40 litres.

b Roughly, how many gallons is 60 litres?

c Give the approximate number of litres equivalent to 5 gallons.

5 A recipe needs 200 ml of cream. Will a quarter of a pint carton be enough?Give a reason for your answer.



EQUATIONS

HOMEWORK 21.1Equations withOne OperationRemember toshow all yourworking and toexplain what youare doing whenyou solve anequation.

1 Solve each equation.a x + 2 = 7 b p + 4 = 12 c 4 + x = 15 d 7 + a = 18

2 Barry thinks of a number that he calls x. When he adds 5 to the number hegets 15.a Use the information to form an equation.b Solve the equation.

3 Solve each equation.a x + 2 = 1 b y + 7 = 5 c 4 + x = 1 d 9 + b = 6

4 Solve each equation.a x – 2 = 4 b t – 7 = 8 c x – 9 = 1 d y – 1 = 6

5 Solve each equation.a 2x = 4 b 5t = 8 c 4 = 8x d 0.4 = 2d

6 The temperature at midnight was t o C. By 6 am it had fallen by 2oC to – 1oC.Use this information to form an equation and then solve it to find thetemperature at midnight.

EQUATIONS

HOMEWORK 21.2Equations withTwo OperationsRemember toshow all yourworking. Explain the stepsin your solutionand include acheck on youranswer.

1 Solve each equation.a 2x + 4 = 10 b 5y – 8 = 7 c 2 + 3c = 11 d 9 = 5 + 2k

2 Solve each equation.a 7p – 9 = 5 b 15 + 8x = 7 c 10 = 3y – 2 d 4x – 1 = 1

3 Greg thinks of a number. When he doubles it and then subtracts five, theresult is 35.Use the information to form an equation, then solve the equation.

4 The perimeter of a rectangle is 42 cm and the width is 9 cm. Use the diagram to help make an equation.Solve the equation.What is the length of the rectangle?

5 A wood floor board is 200 cm long. A length of 40 cm is cut from it.The remaining length of floor board is cut into two equal length pieces eachk cm long.Use this information to form an equation.Solve the equation.What is the length of one of the two equal length pieces?



EQUATIONS

HOMEWORK 21.3Simplifying andSolving EquationsRemember toshow all yourworking.Explain the stepsin your solutionand include acheck on youranswer.

1 Simplify each expression.a 2x + x + 5x b 4x – 2x + x c – 4x + 7x – x d 7 + a – 4a

2 Simplify each expression.

a 2x + x + 5 – 8 d 3x - y + 2x + 2yb 9p – 7 + 4p + 3 e 5a – 2b – 8a – 5bc – 4x + 8 – 2x – 1 f 3a + 2b - 5c + 2a – 6b

3 Solve each equation.a 3x + 2 = x + 6 b 5y + 7 = 4y – 2 c 9x – 6 = 4x – 21

4 Solve each equation.a 3x – 8 = 12 – 2x b 4 – 3x = 12 + x c 12 – 2t = 6 + t

5 Solve each equation.a x + 5x + 1 = 7 b 3y + 2 – 2y = 9 c p + 5 – 6 + 2p = 8

6 Solve each equation.a 9 – x = 4 – 2x b 6 – 3x = 7 – x c 12 – 5y = 2 + 7y

7 Solve each equation.a 2 – x = 8 b 4 – 3t = 1 c 14 – 7s = 0




HOMEWORK 22.1Grouping DataRemember toshow all yourworking.

1 The following marks were scored by a group of Year 7 pupils in an exam.

42 50 58 79 73 52 67 77 70 92

78 71 52 60 35 62 54 46 48 58

58 32 82 68 72 82 47 62 28 67

42 62 37 27 85 38 59 8 41 47

52 68 81 39

a How many pupils were there in the group?

b Copy and complete this frequency table

Draw a bar chart to illustrate the information in this frequency table.

d Why is it impossible from the bar chart to tell how many pupils scored more than half marks? Can you find out how many pupils scored more than half marks? Explain your answer.

2

This bar chart illustrates a survey into the number of times each of thepupils in a class had been abroad.

a How many pupils have never been abroad?

b How many pupils are there in the class?

c How many pupils had been abroad?

d How many pupils had been abroad at least twice.




HOMEWORK 22.2Pie ChartsRemember toshow all yourworking.

1

Sixty girls were each asked to choose one of the colours red, yellow, greenor blue.This pie chart illustrates their choices.

a Which colour is the favourite choice for this group?

b What fraction of the total number choose i yellow ii blue?

c How many girls i chose green ii did not chose red?

2 Emily did a survey of the number of people in each car that passed herhome one afternoon. Her results are recorded in the table.

a How many cars passed Emily’s home while she was watching?

b Draw a pie chart to represent this data.

c Joe said that there were at least two people in more than half the cars. Is this statement true or false? Justify your answer.



ANSWERS1.1 1 13460 2 580 3 36, 43, 50, 57, 64, 71 4 8 5 e.g. 305 + 98 > 400 6 Across: 2537, 42, 300, 45, 6140Down: 25, 740, 356, 20

1.21 462 2 e.g. 708 - 21 < 708 3 8435 4 50 000 5 19 6 e.g. 200 - 60 - 3 + 2 7 46 8 52, 40, 28 9 Start with 66 then subtract 7 eachtime

1.31a 540 b 20 c 50 2a 3500 b 26900 3 e.g. 432 + 266 > 400 + 200 4a 0; quick but rough b 30; good estimate but not so quick c 20; reasonable estimate and fairly quick

2.11a 8580 b 83 600 2a 2 b 4, e.g. the unit in the answer comes from multiplying the units in the product 3a 3431 b 21 879 c 133 867 d 251 8674 5589 5 540 6 £1.80 7 104 8 108, 324 9 78

2.21 1024, 512, 256, 128 2 8 3a 16 b 23 c 60 r 5 d 138 r 3 4 doesn’t end in 0 or 5 5a 144 r 2 b 187 r 2 c 145 r 9 6a 3 b 1 c 8 7 12 8a 1 b 17

3.1 1 Score 1 2 3 4 5 6

Frequency 2 4 3 3 4 4

2 pencil pen ruler calc book

Annetc

3a first - a car needs at least one person it it - the driverb Some cars carry 4 or more passengers.c as given but starting with 1 and ending with 4, 5 or more.

3.21a 1, 2 b 56 c 112

3a 18 b 6 c 3faces and three-quarters

4.11a 11, 13, 17 b 71, 73, 792a 23 + 2 b 3 + 11 + 13 3a 53 b 26

4a 27 b 25 c 343 5 26 6 35, 1187 200 8a 33 × 112 b 22 × 54

4.21a no, sum of digits not divisible by 3 b yes, divisible by 3 and by 2 as it is even and the sum of its digits is divisible by 3.2a 11 ×3 × 25 b 23 × 33 × 53a 8 b 7 c 12 4a 30 b 24 c 210 5 8 6 180 7 no; 623 not even 8 50 cm

4.31a 26, 31, 36 b 162, 486, 14582a 24, 20, 16 b 20, 14, 73a 36 b 21 4 38, 47, 57 5 28, 39, 52 6a 243, 729, 2187 b 30, 49, 79

5.11a b c 1

438

2 16 3=

2 e.g. shaded area < unshaded area3a 15 b 15 c 24 4 28

36

5a b c d12

15

23

14

6a b 50 c d510

51000

5100

7a 0.24 b 0.9 c 0.07

5.2 1a 25% b c 15 d 341

4

2a b c d 310

920

34

35

3a 0.84 b 0.56 c 0.12 d 0.064a 0.75 b 0.34 c 1.5 d 0.055a 80% b 48% c 8% d 80%6a b c2

57

103 18

5.31a 25 miles b £10 c 48 eggs2a £120 b 4 kg c 150 people3a £1.20 b £1.50 4 55 p5 Ras: 20% of £10 = £2, 5% of £20 = £1

5.41a b7 45 49

9 63 63; < 19 18 1924 24 24; <

c 16 1523 24 24; >

2a 5.1, 5.01, 0.82, 0.28 b 101, 50.2, 20.5, 10.93a b 1.02<1.20 1012

15 15>

c 35 0.6 0.7= <

4a =25% > 20% b no; 20% <14

14

c 20% of one amount could be more or less than 30% of a different amount

6.11a 1 b c 1 2a b c 2

5920

1314

4790

3a b c 712

78

78

4 more; 1 1 1 1 13 4 3 4 2, so> + >

5a b c 6a b c 114

34

415

45

14

7 8 Des , Tom , 16

12

13

16

6.21a b c d8

3385

407

558

2a b c d678 3

518 149 3

43

3a b 4 5 <, 784 1

211 1810 3 1

4 5 1+ <

6a b c d 382 2

154 27281 23

24

7 81112

10632

6.31a 10 b 8.72 c11.57 d 9.815 e 0.479 f 5.40042a 19.955 b 1.254 3 14.36 cm4a 1.64 b 0.394 c 2.076 d 9.754 e 2.476 f 3.095 3.46 6 £9.54 7 £5.57

7.11a 325 b 0.5 c 1002.5 2a 0.132 b 0.05 c 0.56673a 15.2 b 60.1 c 920 4a 1.9 b 0.25 c 0.0035a 60; 54.57 b 8; 7.35 c 100; 145.926a 12; 1.25 b 4.5; 4.9 c 20; 18.17a 17.5 p b £7 8a 0.35 b 0.1875 c 2.875

7.21a 0.975 b 0.015 c 0.6252a 1.5 b 0.0177 c 0.072 3 £6.80 (or £6.81)4a 20; 23.46 b 2.4; 3.44 c 0.18; 0.165 5 3 17

12 7 339

17

(0.42), (0.43), (0.52),(0.53)

6 12.5 ÷ 14.7 < 1 so is the smallest, only so is the largest12

191 1.5>

7.31a 25 b 20.8 c 802a 3; 4.17 b 70; 68.14 c 0.8; 0.823 25 4a 0.09 mm b 0.092 mm c 1.84 mm

7.41a e.g 480 ÷ 1.2 = 400 b e.g 15% of £400 = £60 c 0.1 × 30 = 32 6% of £175 by 24 p 3 0.694a b 13

201924

5 1.36, 140% (1.4), (1.41), 5121

(1.44)491

6 35 cm

8.11a metre 2a 300 cm b 52 mm c 4800 m d 2 300 000 mm 3a 7500 kg b 8400 g c 3200 mg d 60 g4 walking stick 82 cm long by 6 mm5 sand by 125 kg6 174 mm, 24 cm, 0.83 m, 2436 mm, 256 cm7 8100mg, 82 g 824 g, 0.83 kg

8.21a 3.74 m b 0.695 m c 1720 m d 2.79 m2a 610 mm b 66 mm c 2530 mm, d 1578 mm3a 2080 g b 3350 g c 8800 g d134040g4a 375 cm b 2236 g c 2244 kg d 318 mm5a 1.278 kg b 5.112 kg6 no, 24 mm + 3.4 cm < 6 cm

9.11 7 stone 10 lb 2 40 oz 3 20 cm (8 × 2.5 = 20) 4a 20 miles b no; 11 km ~ 7 miles5a 500 g (500g ~ 1.1 lb) b 4 oz (100 g ~ 3.5 oz)6a 1 mile (~ 1.5 km) bsame using 1 in ~ 2.5 cm, 10 cm using 1 in ~ 2.54 cm7 78 cm (very short for a 12 year-old, 250 cm (extremely tall adult)

10.11a 90o b 210o c 180o 2 north3a obtuse, 120o b obtuse 150o c reflex, 320o d acute 80o

4 north

10.21 130o vert opp 2 128o supp 3 90o supp4 g = 125o supp, h = 180o st line5 60o angles at a pt6 110o angles at a pt7 100o angles at a pt 8 75o supp9 69o angles at a pt 10 q = 145o, r = 55o

11.11a b

2a A b B 3a yes b yes c no d no4a or or b

12.12 81o 3 98o 4 25o 5 35o 6 h = 55o, i = 125o 7 j = 45o, k = 35o

12.26 yes:

12.31 70o 2 70o 3 110o

4 g = 60o, h = 80o, i = 1000 5 80o

6 75o 7 m = n = 70o, p = 110o

8 q = 75o, r = 30o, s = 30o, t = 120o

13.11a impossible b possible c impossible d certain2a D, E, B, I, T b score 1, 2, 3, 4, 5, 6 c apple, orange, banana, pear3 4 5 (including 1)1

51

5215



13.21 5; 2, 4, 6, 8, 10 2 4: 3a b c1

1312

313

4a b c (including 1)13

49

59

14.11a 9 cm2 b 28 cm2 2a 86 cm2 b 108 cm2 3 6 m 4 78 m2

5a 32.4 m b 43.96 m2 6a 74 cm b 220 cm2

14.21a 5000 cm2 b 7000 cm2 c 450 mm2

2a 0.86 m2 b 16.4 cm2 c 0.2 km2

3a 20 mm2 b 0.8 m2 c 45 0 00 m2

4a 32 cm2 b 2.7 m2 5 4 m 6 907 500 cm2

15.11 d 3a 140o b 37o c 30o d 45o

15.21 d 2a a = 25o, b = 65o b c = 52o, d = 128o

c e = f = 65o d g = 70o, h = 40o

e i = j = k = 125o f n = 64o, m = 72o

15.31 a = b = 115o 2 c = 78o 3 d = 110o

4 e= 135o 5 f = 35o 6 g 50o 7 h = 70o 8 i = 30o, j = 40o, k = 140o

16.1 1 (2, 3) 2 (10,7) 3 10 4 B 5 B 6 trapezium 7 (6, 3) 8 (6, 2)

16.2 1a AB & CD, AD & BC b AB & CD, AD & BC c 90o

2a parallelogram b PQ & RS, QR & PS c PQ & RS, QR & PS d ,P R Q S∠ = ∠ ∠ =3 square 4 trapezium 5 kite

16.3 1a 2 b 5 c 5 d – 5 e (2, 2) f (–5, 3) 2 (5, 2) 3 (2, – 3) 4 (– 1, 2) 5a (5, 1) b (2, 3.5)

17.1 1 perimeter = 4 × length of side2a H = 5l b y = 8x c A = d b =10

v 54c

3a A = b × w b C = R ÷ 3 c y = 3 × x ÷ 4 d m = 5 + 2 × p4a y = x + 5 bi 7 ii 145 x: 16, 10, 6, 4, 16 P: 2, 4, 4.5, 5.7, 9.5

17.21a 25 b 7 c 43 d 252a 32 b 5 c 2 3a 14 b 254a 6 b 4 5a 4 b 20

17.31a – 2 b 2 c – 4 d – 82a 1 b – 2 c 0 d 1 3a 1 b – 11 c – 3 d 04a 1 b 6 c – 4 d – 65a – 24 b – 4 c – 28 d –36a 59 0F b 23 0F c – 4 0 F d 17.6 0F7a 4 b – 2 c – 8 d – 14

18.11a Sunday b Monday ci £2500 ii £3500 di Friday ii Monday e £18 5002ai 32 km ii 64 km iii 56 km bi 19 miles ii 25 miles iii 34 miles3ai €120 ii £32.50 b €60 c €1.50 d £22.50 ei £0.64 ii 64 p fi e.g. convert £75 to euros then multiply by 10. ii e.g. convert €100 into £, then multiply by 4

18.21a x: 2, 0, –2, –4, –6; y: 5, 3, 1, –1, – 3 b 8 c 6, 5, 0, – 5 d y = x + 32a x: – 1, 0, 1, 2, 4; y: 7, 5, 3, 1, – 3 b – 5 c –7, 3, 11, 9 d y = 5 – 2x

19.11 40 p 2 7.6, 5 3 £30 4a 49 b 1.85a 17 b 1.6 c the average number of passengers in a car is lower and the range is smaller in the second survey compared with the first.

19.21a £8, £10 & £12 b 18 km, 18 km c 55%; 30%, 65%,70%2a 0 b no; 14 had none, 35 had 1 or more c 1 d no, median is 1 so less than half had 3 or more passengers3a 1.785 m, 1.8 m, 1.8 m & 1.9 m b 0.6 m c true, the median is 1.8 m d e.g. not necessarily true, the mean height is less than median so is in the lower half of the heights (or any sensible answer that allows for rounding of heights)

20.11a 6 b 2 ×

2ai 16 c m ii 8 c m bi ML ii BD iii EF c G, I3a ii b 8cm × 4cm × 2cm c 3 2 c m2

20.21 1120m3 2 75 0 00 cm3 3a 240 c m3 b 0.72 m 3 4 125a 144 b 12, can’t fit 2 along the 3 c m sides6 1000

20.31a 1200 mm3 bi 50 0 00m m3 ii 0 . 0 0 0 0 5 m3

2a 1300c m3 b 5.4 litres 3 12 4a 70 pints b 13 gallons c 22.5 litres5 no; a quarter of a pint ~ 140 ml

21.11a 5 b8 c 11 d 11 2a x + 5 = 15 b 103a –1 b –2 c –3 d –34a 6 b 15 c 10 d 75a 2 b 1.6 c 0.5 d 0.2 6 – 1 = t – 2, 1 oC

21.21a 3 b 3 c 3 d 2 2a 2 b –1 c 4 d 0.53 35 = 2x – 5, 20 4 x + 9 = 21, 1 2 c m5 2k + 40 = 200, 80 c m

21.31a 8x b 3x c 2x d 7 – 3a2a 3x – 3 b 13p – 4 c 7 – 6x d 5x + y e – 3a – 7b f 5a – 4b – 5c3a 2 b –9 c –3 4a 4 b –2 c 25a 1 b 7 c 3 6a –5 b –0.5 c 5

6

7a –6 b 1 c 2

22.11a 44 b frequencies: 5, 15, 16, 8 c

d the bar chart shows how many got marks in the range 36 -55 not how many got more than 50; yes by counting from the list of individual marks2a 12 b 34 c 22 d 12

22.21a red bi ii ci 15 ii 401

416

2a 90 b

c true; there were at least 2 people in 48 cars and 48 is more than half of 90.

addition and subtraction of whole … sheets units 1-8/7a hwk...7a national curriculum mathematics...

Documents