KS3 Maths Level by Level Pack C: Level 6longhill.org.uk/resources/Maths/Year 7/KS3/Level 6.pdf · 5...

Introduction

The Key Stage 3 Mathematics series covers the new National Curriculum for Mathematics(SCAA: The National Curriculum Orders, DFE, January 1995, 0 11 270894 3). Detailed curriculumreferences are provided. Each pack is designed to be flexible and can be used in a variety ofways:

• A complete course for Level 6 – The worksheets can be used to provide complete coverageof: Number and Algebra; Shape, Space and Measures; and Handling Data. The problem-solving tasks provide experience for the pupils in Using and Applying Mathematics.

• Individual lessons – The teacher can explain the tasks and provide the worked examples,either on the board, as overhead transparencies or as photocopied sheets for the students.Students should then attempt the exercises.

• Teacher’s lesson notes – The notes and examples are useful for new teachers and can formthe basis of lesson plans.

• Absent students – The notes, examples and exercises can be used by students during long-term absence or to help students catch up after absence.

• Teacher’s absence – If a teacher is absent, a double-sided worksheet (notes and examples onone side, exercises on the other) can be provided for students. This will allow the students tocontinue with learning the curriculum.

• Examination revision – The notes and examples can be issued to students shortly before theexamination for revision purposes.

The pack includes:

• Notes and worked examples

• Exercises

• Coursework tasks for AT1 – Using and Applying Mathematics

• Examination papers containing National Curriculum-type questions

• Using and Applying Mathematics problem-solving tasks

• Pupil’s record form

• Answers.

Using the notes and examples

Pupils should fold the worksheet so that the answers cannot be seen. They can then read thenotes, try the questions, and then check their answers.

Exam papers

Each paper is set on three or four sides of A4 paper. This will allow the exam paper to be placedon one sheet of A3, in order to remove the onerous task of writing and stapling exam papers. Ifboth papers are set, the contents of Number and Algebra, Shape, Space and Measures, andHandling Data will have been covered at Level 6.

Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP Tel 01223 350555 Fax 01223 356484 1

KS3 Mathematics C: Level 6 Introduction

Stockwell Park High School

Each question is related to a specific part of the National Curriculum as indicated on the charton pages 58 and 59.

It is also possible to use each exam paper as homework sheets in preparation for the end of KeyStage 3 examinations.

Pupil’s record form

This form, provided on page 60, allows the success of pupils to be recorded using the results onthe exercises and exam questions. Either a tick/cross system or a mark system may be used.

End of term activities

‘The Quadrilateral Game’ on page 30 will help pupils to become familiar with the names ofquadrilaterals. Experience will show them that the probability of numbers thrown with two diceare not equal.

Using and Applying Mathematics

Three problem-solving activities are provided on pages 54 to 57. ‘Diamonds’ is a very interestingproject for producing patterns for wall displays.

Stafford BurndredOctober 1995


KS3 Mathematics C: Level 6 Introduction


Test 1

1 Caroline wants to find the value of x in the equation x2 + x = 17.4.

First she tries 5

52 + 5 = 30. The answer is too high.

Then she tries 2

22 + 2 = 6. The answer is too low.

Continue using trial and improvement methods to find the value of x correct to onedecimal place.

2 These four containers each hold a litre when full. Orange squash is poured in to the levels shown.

a Which container has the most orange squash?

b Explain how you worked this out.

c Which container has the least orange squash?

d Explain how you worked this out.

3 Two shops are selling identical television sets. InBlack’s TV Store, all items are for sale at 75% of theirnormal price. In White’s Discount Warehouseeverything is for sale at 4/5 of its normal price.

a What is the cost of the television in each shop?

b Which shop should you buy from and how much will you save?

80% full

Andrea’s container

7/10 full

Brenda’s container

2/3 full

Karen’s container

Deborah’s container

has 0.65 litres


KS3 Mathematics C: Level 6 Test 1


Television set

normally £400

4 Karen has attempted the following five questions. Two of her answers are wrong.Which answers are wrong and what are the correct answers? Can you explain Karen’s mistakes.

Question 1 Write 5/8 as a decimal

Karen’s answer 5 ÷ 8 = 0.625

Question 2 Write 5/16 as a percentage

Karen’s answer 16 ÷ 5 x100 = 320%

Question 3 Write 20.8% as a decimal

Karen’s answer 0.208

Question 4 Write 0.3 as a percentage

Karen’s answer 30%

Question 5 Write 0.7% as a decimal

Karen’s answer 70%

5 These are the recipes for toad in the hole, one of the recipes is wrong. The other two are correct, identify the wrong recipe and correct it.

6 This is a scale diagram of a classroom. The length of the classroom is 6 m.

a Express the scale as a ratio in its simplest terms.

b What is the width of the classroom?

7 John’s pattern 3, 7, 11, 15, 19, 23

Mandy’s pattern 5, 8, 11, 15, 17, 20, 23

a What is the rule to produce John’s pattern?

b What is the fifteenth term of John’s pattern?

c Mandy has made an error in her pattern. Find the error and correct it. How did you find the error?

Recipe for 6 people

300 g

24 g

3

420 ml

360 g

Recipe for 8 people

420 g

35 g

4

550 ml

500 g

Recipe for 10 people

500 g

40 g

5

700 ml

600 g

Plain flour

Salt

Eggs

Milk

Sausage meat




6 cm

2 cm

8 James and Zoe have exactly the same number of sweets.

Each bag contains the same number of sweets.

a Form an equation.

b Solve it to find the number of sweets in each bag.

9 A man buys B bananas at Y pence. The total cost is 48 pence.

a Form an equation to show this.

b Use your equation to find the value of B when Y = 6p.

c Use your equation to find the value of Y when B = 12.

10 Complete the table and then draw the graph of f(x) = x2 -6.

11 This is the net to make a die.

a Opposite faces of die add up to 7, complete the numbers on the net.

b Look at the edge marked x indicate, using the letter Y, the other edge this will touch when the die is folded.

123

x

35

6

x -3 -2 -1 0 1 2 3

y

James has two bags plus thirteen loose sweets

Zoe has five bags plus one loose sweet




Test 2

1 a Name this quadrilateral. b Fill in the missing angles.

2 This is a regular hexagon. Find the size of each angle shown. Explain how you found each angle. You must not use a protractor.

3 Find the size of angles a, b and c. You must not use a protractor.

a b

c

130° 40°

b

a

c

x

y

30°70°




4 This is a diagram of a garden with an ornamental pond. The remainder of the garden is a lawn.

a What is the perimeter of the pond?

b What is the area of the pond?

c What is the perimeter of the garden?

d What is the area of the lawn?

5

a Enlarge T by a scale factor of 4, centre of enlargement is the point (16, 4)

b T’’ is produced from T by an enlargement.

i What is the centre of enlargement?ii What is the scale factor of the enlargement?

Pond 6 m

6 m

6 m

2 m

3 m

3 m

20 m

10 m




20

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

4 6 8 10 12 14 16 18 20 22 24 26 28 30

T

T''

6 These are the heights (in centimetres) of twenty people in a room: 153 132 140 162 135 171 169 145 173 152163 169 177 137 147 143 150 152 165 155

Complete and show this information in:

a A frequency table b A frequency diagram

7 Sixty people were asked to name their favourite television programme. Completethe table and pie chart to show the information. Label each sector of the pie chart.

Programme

Coronation Street

Eastenders

Brookside

Emmerdale

Frequency

19

17

10

14

Angle at the centre of the pie chart

140130

1

2

3

4

5

150

Height (cm) 130 - under 140 140 - under 150

Tally Frequency




8 a What does this scatter graph tell you about the relationship between the number of people on a beach and the temperature?

b What sort of correlation is shown?

9 a Paul decides to buy one ice-cream and one sandwich. List all of the possible combinations of ice-cream and sandwich Paul can buy.

b This bag contains some red, yellow and blue counters.

The probability of picking a red counter is 20%, the probability of picking a yellow counter is 50%.

i What is the probability of picking a blue counter?

ii Explain how you worked this out.

Ice-cream flavours

Raspberry

Vanilla

Sandwiches

Ham

Chicken

Salad




Tem

per

atur

e

Number of people on a beach

xx x

xx xx x

x x xx x

National Curriculum references


KS3 Mathematics C: Level 6 National Curriculum references


Pupils order and approximate decimals when solvingnumerical problems and equations such as x2 = 20,using trial-and-improvement methods.

Pupils are aware of which number to consider as 100per cent, or a whole, in problems involvingcomparisons, and use this to evaluate one number asa fraction or percentage of another.

They understand and use the equivalences betweenfractions, decimals and percentages, and calculateusing ratios in appropriate situations.

When exploring number patterns, pupils find anddescribe in words the rule for the next term or nthterm of a sequence where the rule is linear.

They formulate and solve linear equations with wholenumber coefficients.

They represent mappings expressed algebraically,interpreting general features and using graphicalrepresentation in four quadrants where appropriate.

Trial and improvement 1 1

Calculating fractions and percentages 1 1 2Calculating fractions and percentages 2 1 3

Equivalences between decimals andpercentages 1 4Equivalences between decimals, fractionsand percentages 1 4Ratio 1 1 5Ratio 2 1 6

Explore number patterns 1 7

Solving linear equations 1 8Formulating linear equations 1 9

Graphical representation 1 10

Exam

pap

er

Que

stio

n

Number and Algebra Level 6 Topic title


KS3 Mathematics C: Level 6 National Curriculum references


Pupils recognise and use common 2-D representationsof 3-D objects.

They know and use the properties of quadrilaterals inclassifying different types of quadrilateral.

They solve problems using angle and symmetryproperties of polygons and properties of intersectingand parallel lines, and explain these properties.

They devise instructions for a computer to generateand transform shapes and paths.

They understand and use appropriate formulae forfinding circumferences and areas of circles, areas ofplane rectilinear figures and volumes of cuboids whensolving problems.

They enlarge shapes by a positive whole-number scalefactor.

Pupils collect and record continuous data, choosingappropriate equal class intervals over a sensible rangeto create frequency tables. They construct andinterpret frequency diagrams.

They construct pie charts.

Pupils draw conclusions from scatter diagrams, andhave a basic understanding of correlation.

When dealing with a combination of two experiments,pupils identify all the outcomes, using diagrammatic,tabular or other forms of communication. In solvingproblems, they use their knowledge that the totalprobability of all the mutually exclusive outcomes ofan experiment is 1.

2-D representation of 3-D shapes 1 11

Properties of quadrilaterals 2 1

Regular polygons 2 2Intersecting and parallel lines 2 3

Not included. Suggestion:Use a computer package eg DART – –

Circumferences and area of a circle, areasand volumes 2 4

Enlargement 2 5

Collect and record continuous data infrequency tables and frequency diagrams 2 6

Constructing pie charts 2 7

Scatter diagrams 2 8

Probability 2 9

Exam

pap

er

Que

stio

n

Shape Space and Measures Level 6 Topic title

Handling Data Level 6

Pupil’s record form

Name: _____________________________ Form:___________________

Teacher: ____________________________ Test marks: ______________

Exercises Exam Exam questionscompleted paper answered

Number and AlgebraTrial and improvement 1 1

Calculating fractions and percentages 1 1 2

Calculating fractions and percentages 2 1 3

Equivalences between decimals and percentages 1 4

Equivalences between decimals,fractions and percentages 1 4

Ratio 1 1 5

Ratio 2 1 6

Explore number patterns 1 7

Solving linear equations 1 8

Formulating linear equations 1 9

Graphical representation 1 10

Shape, Space and Measures2-D representation of 3-D shapes 1 11

Properties of quadrilaterals 2 1

Regular polygons 2 2

Intersecting and parallel lines 2 3

Circumference and area of a circle,areas and volumes 2 4

Enlargement 2 5

Handling DataCollect and record continuous data

in frequent tables and frequencydiagrams 2 6

Constructing pie charts 2 7

Scatter diagrams 2 8

Probability 2 9


KS3 Mathematics B: Level 6 Pupil’s record form


Answers

Trial and improvement (page 4)1 2.24 2 4.47 3 4.12

4 6.71 5 3.27 6 2.5

7 3.6

8 a 4 b 6 c 2

d 7 e 10 f 15

g 18 h 7 i 20

j 10

Calculating fractions and percentages (page 6)1 15% 2 12.5% 3 40%

4 56%

5 a 63/4 b 111/4 c 41/2

d 101/8 e £6 f £135

g £157.50 h £180 i £236.25

6 a £4 b £8 c £3

d £5 e £4.20 f £5.20

g 8.40 h 10.60 i 14.20

7 a 50% b 25% c 45%

d 60% e 90% f 85%

g 34% h 36% i 41%

j 65%

8 7%

Calculating fractions and percentages (page 8)1 a £24 b £320 c £304

d £4 e £2.40 f £12.80

g £3.60 h £2.88 i £5.76

j £4.28 k £6.12 l £16.04

2 a i £840 ii £1595 iii £1110

iv £3437.50

b i £40 000 ii £80 000 iii £32 000

iv £110 000 v £29 000 vi £98 000

3 a £460 b £483 c AA Electrics, £23 less

Equivalences between decimals and percentages (page 10)1 a 0.38 b 0.23 c 0.06

d 0.26 e 0.8 f 0.05

g 0.45 h 0.03 i 0.6

j 0.07 k 0.0232 l 0.25

m 0.485 n 0.4 o 0.005


KS3 Mathematics C: Level 6


p 0.5 q 0.036 r 0.75

s 0.2732 t 0.368

2 a 27% b 72% c 47%

d 54% e 63% f 60%

g 3% h 90% i 27.2%

j 45.3% k 10% l 1%

m 2% n 24% o 40%

p 372% q 201% r 410%

s 0.72% t 10.4%

3 a 50% b 25% c 75%

d 33.3% e 0.667 f 0.125

g 0.1 h 0.01

Equivalences between decimals, fractions and percentages (page 12)1 a 39/50 b 93/100 c 47/100

d 3/5 e 4/5 f 1/20

g 7/100 h 49/50 i 63/100

2 a 0.25 b 0.6 c 0.875

d 0.625 e 0.3 f 0.7

g 0.58 h 0.87 i 0.2875

3 a 0.5625, 56.25% b 17/50, 34% c 51/200, 0.255

d 28/125, 22.4% e 0.875, 87.5% f 1/25, 4%

4 a 75% b 50% c 37.5%

d 80% e 10% f 20%

g 93.75% h 62.5% i 85%

5 a 1/4 b 47/100 c 7/25

d 37/100 e 39/100 f 427/1000

g 3/5 h 3/10 i 2/25

Ratio 1 (page 14)1 a 60 g, 240 ml, 1 egg b 180 g, 720 ml, 3 eggs c 300 g, 1200 ml, 5 eggs

2 a 220 g, 25 g, 1 onion, 300 g, 175 g b 660 g, 75 g, 3 onions, 900 g, 525 g

c 1100 g, 125 g, 5 onions, 1500 g, 875 g

3 a 1:4 b 1:2 c 5:3

d 5:2 e 6:4:3 f 3:5:7

4 a 8 b 12 c 3

d 4.5 e 7.6

5 a 5 cm b 8.2 cm c 13.5 cm


KS3 Mathematics C: Level 6 Answers


Ratio 2 (page 16)1 a 2:3 b 5:6 c 3:2

d 5:1

2 a 1:50 b 1:1000 c 1:2000

d 1:200 e 1:1600 f 1:750

3 £1125, £1500, £1875

4 £3500, £4200

5 a 440 b 80, 160, 200

6 a 50 cm b 30 m c 2.5 cm

d 0.5 cm e 12 m

Explore number patterns (page 18)1 a 2N b 30 c 254

2 a 6N b 90 c 762

3 a 3N b 45 c 381

4 a 4N-2 b 58 c 506

5 a 5N-2 b 73 c 633

6 a 2N+3 b 33 c 257

7 a 3N+1 b 46 c 382

8 a 4N-7 b 53 c 501

9 a 3N-8 b 37 c 373

10 a 5N+22 b 97 c 657

11 a 5N+1 b 76 c 636

12 a 8N-5 b 115 c 1011

13 5, 8, 11, 14, 17 14 11, 15, 19, 23, 27 15 3, 5, 7, 9, 11

16 5, 11, 17, 23, 29 17 -1, 2, 5, 8, 11 18 -8, -6, -4, -2, 0

Solving linear equations (page 20)1 3 2 13 3 2

4 -5 5 -11 6 -14

7 4 8 7 9 6

10 2 11 0.5 12 0.2

13 -1 14 -6 15 -3

16 4 17 5 18 -4

19 -6 20 -0.5 21 4

22 5 23 2 24 4

25 2 26 4 27 6

28 -3 29 -3 30 5

31 15 32 32 33 14

34 12 35 2 36 8

37 16 38 9 39 8

40 4




Formulating linear equations (page 22)1 7 2 36 3 9

4 9 5 26 6 250

7 16 8 36 9 8

10 £40

Graphical representation (page 24)2 a 5, 0, -3, -4, -3, 0, 5 b -7, -2, 1, 2, 1, -2, -7 c -1.5, -4, -5.5, -6, -5.5, -4, -1.5

3 a 9, 7, 5, 3, 1, -1, -3 b 22, 7, -2, -5, -2, 7, 22 c 7.5, 5, 3.5, 3, 3.5, 5, 7.5

d 6, 3, 2, 3, 6, 11, 18

2-D representation of 3-D shapes (page 26)1 cylinder 2 c and d

Properties of quadrilaterals (page 29)1 a rectangle b rhombus c trapezium

d parallelogram e square

2 a rhombus b parallelogram c kite

d rectangle e trapezium f square

3 a 118° b a = 50°, b = 130°, c = 130°

c d = e = 140°

Regular polygons, intersecting and parallel lines (page 33)1 a 72°, 108° b 60°, 120° c 40°, 140°

d 36°, 144° e 30°, 150°

2 a 8 b 15 c 20

3 a 36 b 30 c 18

4 a x = 60°, y = 120° b b = e = g = 50°, a = c = d = f = 130°

c x = z = 45°, y = 135° d a = 110°

e a = 80°, b = 40°, c = 60° f x = 50°

Circumference and area of a circle, areas and volumes (page 35)1 a 31.4 cm, 78.5 cm2 b 75.4 m, 452 m2 c 44.0 m, 154 m2

d 20.1 cm, 32.2 cm2 e 37.7.cm, 113 cm2 f 62.8 m, 314 m2

g 28.3 cm, 63.6 cm2 h 15.1 m, 18.1 m2

2 264 m2

3 a 235 m b 2372 m2

4 a 54 m b 138 m2

5 228 m2




Enlargement (page 38)1 top left hand coordinate is (13, 12)

2 top left hand coordinate is (5, 13)

3 top left hand coordinate is (8, 30)

4 (5, 10) SF2

5 (6, 17) SF3

Collect and record continuous data (page 40)1

Constructing pie charts (page 42)1 112°, 32°, 100°, 116°

2 36°, 72°, 96°, 84°, 72°

3 210°, 90°, 40°, 20°

4 150°, 80°, 60°, 70°

Scatter diagrams (page 44)1 a positive correlation

2 a no correlation

3 a negative correlation

4 b positive correlation

Probability (page 46)3 UU, UD, DU, DD

4 CB, CP, LB, LP, OB, OP

5 b 36 c i 5/36 ii 6/36 = 1/6

6 a 3/11 b 8/11

7 0.98




130 – under 140 4

140 – under 150 5

150 – under 160 7

160 – under 170 4

Test 1 (page 47)1 table (2 marks)

3.7 (2 marks)

2 a Andrea (2 marks)

b explanation (1 mark)

c Deborah (2 marks)

d explanation (1 mark)

3 a Black’s £300 (2 marks)

White’s £320 (2 marks)

b Black’s £20 (2 marks)

4 Question 2 5 ÷ 16 x 100 = 31.25% (2 marks)

correct explanation (1 mark)

Question 5 0.7% = 0.007 (2 marks)

decimal point moved the wrong way (1 mark)

5 8 people wrong. Should be 400 g, 32 g, 4, 560 ml, 480 g (3 marks)

6 a 1:100 (1 mark)

b 2 m (1 mark)

7 a 4N-1 (2 marks)

b 59 (2 marks)

c 5, 8, 11, 14, 17, 20, 23 (2 marks)

add 3 each time (1 mark)

8 a 2B+13 = 5B+1 (2 marks)

b 4 (2 marks)

9 a BY = 48 (2 marks)

b B = 8 (1 mark)

c Y = 4 (1 mark)

10 3, -2, -5, -6, -5, -2, 3 (2 marks)

correct graph (2 marks)

11

a (2 marks)

b (2 marks)

Total 50 marks




5 4

6

y

Test 2 (page 50)1 a trapezium (1 mark)

b x = y = 130° (2 marks)

2 a 120° + explanation (2 marks)

b 30° + explanation (2 marks)

c 90° + explanation (2 marks)

3 a 50° (1 mark)

b 40° (1 mark)

c 90° (1 mark)

4 a 30.8 m (2 marks)

b 64.3 m2 (3 marks)

c 60 m (2 marks)

d 98.7 m2 (3 marks)

5 a top left corner (4, 24) (3 marks)

b i (10, 4) (2 marks)

ii SF3 (2 marks)

6 a frequency 3, 4, 5, 5, 3 (3 marks)

b correct diagram (3 marks)

7 114°, 102°, 60°, 84° (4 marks)

pie chart (3 marks)

8 a higher the temperature, the more people on the beach (2 marks)

b positive (1 mark)

9 a RH, RC, RS, VH, VC, VS (2 marks)

b i 30% (2 marks)

ii must add up to 100% (1 mark)

Total 50 marks

Blocks (page 54)A Triangle numbers, Formula H(H+1)

2Height of 10 = 55Height of 20 = 210Height of 100 = 5050

B Formula H(H+1)

Height of 16 = 272Height of 30 = 930Height of 200 = 40200

C Square numbers Formula H2

Height of 10 = 100Height of 15 = 225Height of 100 = 10000




Diamonds (page 55)

Stage Square Stage Square Stage Squares Stage Squares2 4 3 4 5 4 9 4

4 12 6 12 10 127 12 11 128 36 12 36

13 1214 3615 3616 108

Diamond squares at stages: 2, 4, 8, 16 32, etc.

Note: Stage 5 = Stage 9Stage 6 = Stage 10Stage 7 = Stage 11Stage 8 = Stage 12Stage 5 x 3 = Stage 13Stage 6 x 3 = Stage 14Stage 7 x 3 = Stage 15Stage 8 x 3 = Stage 16

The Symmetry Puzzle (page 57)




Contents

Introduction ............................................................................................ 1

Number and AlgebraTrial and improvement ................................................................................. 3

Calculating fractions and percentages ........................................................ 5

Equivalences between decimals and percentages...................................... 9

Equivalences between decimals, fractions and percentages ...................... 11

Ratio 1 ........................................................................................................ 13

Ratio 2 ........................................................................................................ 15

Explore number patterns ............................................................................. 17

Solving linear equations............................................................................... 19

Formulating linear equations ....................................................................... 21

Graphical representation.............................................................................. 23

Shape, Space and Measures2-D representations of 3-D shapes .............................................................. 25

Properties of quadrilaterals .......................................................................... 27

Regular polygons ......................................................................................... 31

Intersecting and parallel lines ...................................................................... 32

Circumference and area of a circle, area and volumes................................ 34

Enlargement................................................................................................. 36

Handling DataCollect and record continuous data in frequency tables and

frequency diagrams ................................................................................ 39

Constructing pie charts ................................................................................ 41

Scatter diagrams .......................................................................................... 43

Probability .................................................................................................... 45

Tests.................................................................................................................. 47

Activity and investigationBlocks ........................................................................................................... 54

Diamonds ..................................................................................................... 55

The Symmetry Puzzle ................................................................................... 57

National Curriculum references ............................................................ 58

Pupil’s record form ................................................................................ 60

Answers ........................................................................................................... 61

Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP Tel 01223 350555 Fax 01223 356484

KS3 Mathematics C: Level 6


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