GCSE Maths Homework Pack 3: Higher Tier - Bemrose

GCSE Maths Homework Pack 3: Higher Tier

Teacher’s Notes This pack is intended to cover all of the topics required by candidates in the GCSE Higher Tier examination. The pack can be used in a variety of ways: •

As a homework pack – The pack provides 90 homeworks for Years 10 and 11. The homework sheets can be attempted in any order to fit in with the school’s scheme of work. If two homeworks are completed each week this will allow the pack to be completed before the mock GCSE examinations. The pack can then be used again for revision in Year 11 either for homework or in class.

•

As – – –

•

As supplementary material – The pack can be used by students after school or in lessons. Worksheets can be supplied to students who wish to do extra work.

•

As a pupil profiling pack – The pack contains a series of recording sheets which can be used to provide a profile of each student. This can be extremely useful at Key Stages 3 and 4. At Key Stage 3 teachers are expected to be able to identify the students’ weaknesses and strengths. Profile Sheet 1 (page 114) simplifies the process and worksheets provide evidence.

a classroom resource – The pack can be used: To provide class tests at the end of the topic. For class revision in Year 11. As a battery of tests in preparation for the mock examination or GCSE examination. The tests will highlight any weaknesses. – As a worksheet resource bank.

At Key Stage 4 it is even more important to identify students’ weaknesses so that a student can be directed to revise the correct material for the GCSE examination. The worksheets correspond to the GCSE Mathematics Revision Guides*. If a student has difficulties with, say, Worksheet 27, they can be directed to revise page 27 of the Higher Tier Revision Guide.

Profile Sheet 1 – Individual assessment (page 114). This can be used to record the marks of each student on each homework sheet. Marks for each topic can be totalled, eg graphs, total the marks for worksheets 24 to 35 and use the mark/grade converter on the profile sheet to produce a grade, ie 60 or above = A, 49 or above = B, etc. An A or B grade would indicate a strength, a D or E would indicate a weakness. This will produce a complete profile of each pupil. Profile Sheets 2 to 6 – Class assessment (pages 115 to 119) A simpler alternative is to use the profile sheets for class assessment. These can be used in the same way as a normal mark book. A vertical column of poor marks would alert the teacher to a difficult topic for the whole class. A horizontal line of poor marks would alert the teacher to a particular student’s difficulties. Profile Sheet 7 – Class assessment (page 120) A blank class assessment profile sheet has been provided for teachers who wish their students to attempt the worksheets in a different order to the one given in this pack. Simply fill in the topic, worksheet numbers and possible marks for the areas you want to cover. Strengths and weaknesses for a particular student can easily be identified. This makes it easy to advise a student about areas requiring careful revision. * GCSE Mathematics Higher Tier Revision Guide can be obtained from Pearson Publishing, Chesterton Mill, French’s Road, Cambridge, CB4 3NP, telephone 01223 350555, fax 01223 356484, for less than £2 per copy for class sets. Toot Hill School

Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP

1


In the event of a parental enquiry or an OFSTED inspection it is a simple task to transfer marks from the class assessment sheets to Profile Sheet 1.

Using the homework pack in conjunction with the Revision Guides The worksheet pages in this pack correspond with the pages in Pearson Publishing’s GCSE Mathematics Higher Tier Revision Guide. If students have both, it extends the ways in which this pack can be used: • Students can revise from the Revision Guide in preparation for using a worksheet as a test in class. • Worksheets can be used for revision homework. If students have forgotten the topic they can use the Revision Guide to refresh their memory. • If a few students in a foundation examination class wish to attempt the Intermediate examination the Revision Guide can be used to support their learning and the homework worksheets used to provide additional work. If the students have difficulties with questions they can be directed to revise the appropriate pages in the Revision Guides. This is particularly useful as the GCSE examination approaches.

Using the speed marking system 1 2 3

First photocopy the answer pages. Cut out the answers for the page to be marked. (You may find it quicker to fold the answer page for most worksheets.) Place the answers in the marked section of the student worksheet.

1 28

28 ✔ 1 ....................... ■

2 72

61 0 2 ....................... ■

Use 1 and 0

3 18

18 1 3 ....................... ■

or ✔ and ✗

Minimum mark 9 Circle grade A

7

6

3

B

C

D

E

12

Use this box to convert the mark to a grade if you wish (In general A = 80% B = 65% C = 50% D = 35%)

Unlike most answer pages the answer will be next to the student’s answer to allow marking to be carried out more quickly. The system is designed to allow the student to answer on the worksheet itself. However, in the majority of worksheets, it is possible for the student to answer on blank A4 paper. This will allow the worksheet to be re-used.

Toot Hill School


2


Explain the method to pupils as shown below:

Blank A4

Worksheet

Factorise: 1

10a + 8

1 ...................■

_______________________________

■

2

12a - 3c

2 ...................■

_______________________________

■

3

10a - 8c

3 ...................■

_______________________________

■

4

25a - 20c + 15

4 ...................■

_______________________________

■

5

3a4 + 2a3

5 ...................■

_______________________________

■

Minimum mark 9 Circle grade A

7

6

3

B

C

D

E

Pupils should use a ruler to draw answer lines

Draw mark boxes or leave a space

12

The pack can also be used as traditional worksheets with the teacher reading the answers and students marking their own or each other’s work.

Toot Hill School


3


Worksheet 1

1

2

Worksheet 2

3/ (3) 1

1

31.36

-16.422

2

6.22093

1/ 2

4

17/ (17) 1

5

9/ 25

6

Irrational

3 2

4

1069.22

5

Irrational

9

Irrational

10

Irrational 8/ 99

12

377/ 1000

8

15

3.10029

0.537285

0.00195313

1

4.76

2

11.34

3

31.8

4

80.23

1

480 000

2

620

3

0.0047

4

0.0000274

5

8 100 000

6

0.34

7

0.00072

8

0.00132

5

31.39

9

7.3 x 102

6

5.561

10

6.82 x 103

11

3.72 x 105

7

161/5 (16.2)

12

6.42 x 10-1

13

7.8 x 10-4

8

521/4 (52.25)

14

8.23 x 10-2

15

2.7 x 103

9

124/5 (12.8)

16

4.2 x 10-5

2.81473 10a £29 176

b 1 872 000

245/ 999

18a 3.39 x 104

-370.101

7/ 100 2/ 3

Worksheet 5

17a 1.87 x 106

6 14

11.2870

470835 7

5

11

13

4

Worksheet 4

8.96696

37/ 99 6

8

1525.88

170.123

(36/100)

3 7

Worksheet 3

Irrational 1

3

Answers

b £38 913

b 33 887 9

(6/9)

74.8953 11a £38

7

19a 8.94 x 104

0.223324

b 89361.7 16

28

20a 4.40 x 10-1 b 0.440123 8

17

b £6.65

70.0637

10

-866.489

200

12

£611

21a 3.28 x 10-2 b 0.032768

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Worksheet 6

1a

Answers

Worksheet 7

Worksheet 8

8.2 b

£11 560

1a b

c

£6 034

2a b

d

1993

3a b 4a b

2a

b

2.3.73

2

8.5 → 580.125

Fibonacci sequence

8.3 → 538.587 3a b

Triangle numbers

2.45

2

400

3

1.56

42

8.2 → 518.568

67 914

8.25 → 528.515625

4

4.63

5

1.2

6

6.57

7

2.43

8

38

9

-2.27

10

2

11

0.3

12

0.171

13

0.175

14

2.45

64, 343 Cube numbers

£26 997

24.3.7

4

£39 962 5a

c

2015

d

£21 336

2, 3

b

1, 2, 3, 9

c

3, 9, 27, 54

22.33.5.7

5

6a d

£18 238

e

7.6

84

1, 4, 9 b

e

9 → 693

8, 55

15, 21, 28

1

8 → 480

9, 49 Square numbers

Worksheet 10

2.32.7.11

1

£13 600

Worksheet 9

15 120

7 → 441 8 → 640

1, 27

7.5 → 534.375 7.6 → 554.496 3 Accept rounded

7a

1/ 16

(0.0625)

7.55 → 544.373875

answers. a i 28 991 6a

5, 31

ii 13 797 iii 12 191

b

1999

b

1, 5

c

75, 960

d

1, 64, 169

e

1, 64

b

c

8/ 7

(1.142857…)

-1/5 (-0.2)

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Worksheet 11

1

Worksheet 12

Answers

Worksheet 13

A = C2

A = √√

B 5

1

15

0.190023

1a i Converges ii 0.750

4

a = kc (k = 3)

c

7

3E – D + 5 A= 4

2

A=

10C 3

ii 2.667 2a

6

A=

c i Diverges

-C

3

b

1715 4

A = 3.5Y

A=

a-3

d

a-8

e

12a5

f

a6

g

a5

h

4a9

i

a-7

j

a-4

k

a12

0.255390

15.6539

C B

2a

A = CD 5BE

any order.

3a

C A = 3(2D – 7)

p = qk (k = 8)

2a i xn + 1 = x -6 n+5 b

11

c

A = √√7C + 4D

Solutions shown in 10

a7

4

5 9

29641.2

(k = 5)

c 8

x = ky3

3

ii No answer 7

b

0.131979

b i Converges 5

a11

A = √√ D b

3

Worksheet 15

1a 1a

2

Worksheet 14

6

b

7

c

1

d

2

e

0.125

1.46988

0.4

ii -2 -6 i xn + 1 = xn – 5 c

2401

7

4

0.0150845

ii -3 12

A = 4CE – D

13

A = √√ 3CD B

10 b i xn + 1 = xn – 3 4a

14

A=B+C–D F

ii -2 10 i xn + 1 = xn + 3 b

15

A=

2Y 5C – 3D

M=

k R3

3a

a21

(k = 1000)

b

11 a /15

1

c

1 a /12

d

3 a /4

ii 5

c

4

Toot Hill School


96


Worksheet 16

Worksheet 17

Answers

Worksheet 18

Worksheet 19

1 1

2(2a – 5)

1

Answers in any order

(x + 2)(x + 5)

1

6a7c6 2

4a2d2

2 3

4

(x + 4)(x + 7)

9(4a – 3x) 2 9(2a – 3c + y) (x – 3)(x – 7) 3

5

y(5y – 7)

6

4y(3y – 5)

x = 1.87 or x = -0.535

3

5

(4a – 9)(4a + 9)

16a12 4

x = -3.79 or x = 0.791

4(4x + 3y) 2

3

(y + 7)(y – 7)

15a6 1

2

Worksheet 20

x = -4 or x = -8

12y – 24 4

3

(x + 3)(x – 5)

a = -1.21 or a = 3.71

6

12a2 + 6ay3 7

7

2a5(8a3 + 5)

6a5 + 21a4

4 5

8

(a + 5)(a – 4)

x=3 or x = 8 4

2ac(5a2c – 4)

y = 1.55 or y = -0.804

8

-24a4 + 18ac2 9

5a3cy(5c – 2a2y2)

6

(y – 2)(y – 8) 5

9

x=2

6a2 – 8a – 30 or x = -7 10

10

11

12ad(5c – 4a)

20y2 – 42y + 18

5 7

11

5a2(3a – 5c + 2ay)

12

2a3(4a5 – 3a2 + 5)

6 8

12

or x = -5.27

(y + 1)(y + 7)

6a2 + 23a + 20 (a + 3)(a - 4)

16y2 – 56y + 49

x = 2.27

x = -6 or x = 7

6

x = 0.370 or x = 3.38

Toot Hill School


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Worksheet 21

1

Worksheet 22

1

2

2a – 3 5a + 7

4 5

1

2

3

4

x+4 x–3

x–7 x–3

3

4

Worksheet 24

1

H

2

B

3

G

4

D

5

E

6

A

7

F

8

C

19a + 16 6

34y – 23 20

x=2 y = -5

3

Worksheet 23

x=3 y=4

2

Answers

c + 14 12

-6c – 26 21

x = -3 y = -6

4

a = 4.2

5

2a3 5c2

5

88C – 54 14

6

8a6 15c7

6

a–9 6

9 x y

c = 3.4

7

2 5a

7

-4 -3 -2 -1 0

1

2 3

4

-4 -0.5 2 3.5 4 3.5 2 -0.5 -4

7a – 1 (a + 2)(a – 3) 4

x x

x

3

5

a=6 y=5

8

14c2d 3a

8

2

x

3a – 5 (a + 5)(a + 1)

x

1 x

-4

-3

-2

-1

0 -1

x

1

2

3

4

-2 -3 x

-4

x

Toot Hill School


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Worksheet 25

Answers

Worksheet 26

Worksheet 27

-2

-1 -1/2 0

1/ 2

1

2

y

2

0

-1/4

3/ 4

2

6

x

-2

-1 -1/2 0

1/ 2

1

2

0

11/2

21/2

3

4

x

y 1x=1

1

0

2

Worksheet 28

y=2 1a b 2a b 3a b 4a b

Answers are approximate

5a b

-1/2 y = -1/2 x + 1 2 y = 2x – 2 -1 y = -x + 2 1/ 3

y = 1/3 x – 3

1/ 2

y = 1/2 x – 2 1

2x=1 a y = -2

x

-3

-2

-1

0

1

2

3

y

4.5

2

0.5

0

0.5

2

4.5

0.6 or -1.6

Accept anything close. b

1.4

a

2

or -1.4

b

1

c

-0.5

d

-1.5

Toot Hill School


99


Worksheet 29

Worksheet 30

Answers

Worksheet 31

Worksheet 32

y 1

2 1

-4

-3

-2

x

0

-1

1

2

3

4

1

2

3

4

1

2

3

4

1

2

3

4

-1 1a

Assume the

-2

graph is correct if it goes through (0, 15) and

y

2

(400, 95).

2 1

f

1 2

c

-4

-3

-2

x

0

-1 -1

1a b

1/ 4

3

m

-2

3

y

3

2 4

o

1 5

h

-4

-3

-2

x

0

-1 -1

6

e

-2

y

4

2

b

£P = £(0.2N + 15)

c

£615

d

237

2a

1/ 2

b

1/ 2

c

32.5

7

a

8

g

1

-4

-3

-2

0

-1

x

-1 9

n

-2

Toot Hill School


100


Answers

Worksheet 33

Worksheet 34

Worksheet 35 Worksheet 36

y

1

-4

-3

-2

2

1 a = 70°

1

b = 70°

-1

c = 110°

x

0

1

2

3

4

-1 2 d = 70°

-2 y

2

2 1

-4

-3

-2

3 e = 80° f = 20°

x

0

-1

1

2

3

4

g = 80°

-1 -2

Any answer between:

3 1

y 3

1

06.00

2

2

15 km/h

1

3

10 km

4a

09.00 and 09.30

4 h = 105°

415-440 m

5 i = 75° j = 105° k = 75°

x

0 90

180

270

360

-1

b

Steepest part

c

60 km/h

6 l = 98°

-2

m = 82°

-3 4

n = 98° 5a

y

12-13 km/h (approx)

3

b

40 km/h

2

c

40 km/h 7 o = 80°

6

1

p = 30°

x

0 90

180

270

360

7

41/2 hours

Any answer between:

8

Cyclist B overtook

2a

-1 -2

1230

cyclist A

8 2x = 72° 150-165 m 3x = 108° b

Less

-3

Toot Hill School


101


Worksheet 37

Worksheet 38

Answers

Worksheet 39

1

Worksheet 40

Worksheet 41

1

2 Translation -4

2

Reflection in the

( )

SSS

line y = 2x + 1 2 1a

2.4 cm

b

4.5 cm

Not 1a

3

AAS or ASA

b

47°

6.2 cm

3a

Rotation 60° anticlockwise, centre of rotation (5, 2)

c

8 cm b

4

Rotation 300° clockwise, centre

AAS or ASA

of rotation (5, 2)

5

Pythagoras’

Allow ± 2o 1

037o

2

021o

3

002o

4

267o

5

236o

6

346o

7

083o

8

263o

9

166o

10

183o

11

114o

12

153o

RHS (use

2a

12 cm

b

2.4 cm

4

theorem)

Enlargement, scale factor -1/3, centre of enlargement (5, 1)

6

2a

DEC

b

DCB

SAS 5

Enlargement, scale factor 5/2, centre of enlargement

7

AAS

c

CDB or BDC

d

CDE or EDC

(-2, 6)

6 e 3a

centre of rotation (0, 0)

7.65 8

b

ACB or BCA

Rotation 180°,

Not

7.875

Toot Hill School


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Worksheet 42

Worksheet 43

Answers

Worksheet 44

Worksheet 45

Worksheet 46

.

Accept 4.9 instead of 5 for maximum values,

.

eg 1.349. 1

86.2 km/h

1

18.28

2 2

2 h 31 min

36.8 km/h

3 3

542.3 km

1A’ (10, 13) B’ (11, 13) C’ (11, 12)

8 h 25 min

8 h 24 min 37 sec

1.22 g/cm3 5a

B´ (-4, -8)

b

D´ (-1, -2) 6

1.25 kg

2a

28.5 cl

b

27.5 cl

3a

25.5

b

24.5

4a

1.725 m

b

1.715 m

5a

1.2835 t

b

1.2825 t

6a

15.35 cm

b

15.25 cm

7a

13.285 ml

b

13.275 ml

32 min

C´ (-4, -2)

2D’ (4, 11) E’ (5, 11)

5

b

302.4 km b

1A´ (-1, -8)

1.35 kg

13.35

4a 4

1a

8a

74.35 l

b

74.25 l

32 min 23 sec

68.295 g

2E´ (2, -4)

9a

16.005 cm

b

15.995 cm

F’ (5, 10) G’ (4, 10) 3D” (7, 9) E” (9, 9)

F´ (1, -4) 10a 30.05 kg G´ (1, -2) H´ (2, -2)

F” (9, 7)

6a 7

2 h 11 min

b 29.95 kg

64.08 km/h 11a 790 g b

G” (7, 7)

2 h 11 min 16 sec

b 770 g

4H’ (11, 2) I’ J’

(10, 2) (10, 3)

3a

(7, 1) 12a 332.5 ml

b

-1/2

b 327.5 ml

Toot Hill School


103


Worksheet 47

1a

285 ml

Worksheet 48

1a b

b

c

2a

b

Worksheet 50

228

b

Worksheet 51

8.73 cm 43.6 cm2

a

40°

b

50°

a

100°

1a

85°

c

20°

b

120°

b

45°

d

80°

c

50°

1.27 cm2

e

50°

3.44 cm

f

50°

g

110°

h

70°

i

40°

j

160°

k

80°

l

10°

m

30°

n

60°

272

3a

36.0 cm

b

126 cm2

c

60°

d

70°

e

25°

2

140°

f

50°

3a

90°

g

50°

b

90°

8.6061

c

40°

8.5251

d

50°

1.4426 1.1595

c

Worksheet 49

275 ml

2a d

Answers

h

40°

4a

452 cm2

i

50°

b

905 cm3

j

40°

k

70°

0.91895

4

TOB

0.91534

d

37.7 cm3

14.056

5a

13.802

b

5 cm

l

60°

c

47.1 cm2

m

90°

5

15.8 cm

Toot Hill School


104


Worksheet 52

1a b

Worksheet 53

b

Worksheet 54

105 cm3

1a b

120 cm2

31.8 cm 52.5 cm2

1

Length 1a

60 cm

66 cm3

2a b

2

None

3

None

4

Area

5

None

6

Length

4:7

b

16:49

c

64:343

64 m 161 m2 2

27:512

3a

128 cm2

23.2 cm2

7

3

Area

773.5 cm3 or 0.0007735

4

Worksheet 56

24 cm

2

3

Worksheet 55

36 cm2

1 2a

Answers

b

m3

8

Area

9

Volume

10

None

11

Length

12.5 km2

561 000 cm2 or 0.561 m2

5

160 cm

b

12.5 m2

c

5.12 kg

5 cm 4

720.896 cm3

3a

190 m2 12

b

6

4a

1.52 m3

Volume

2.5 cm

Toot Hill School


105


Worksheet 57

1

2

Worksheet 58

Answers

Worksheet 59

Worksheet 60

9.40 m 1 a = 21.5°

1 a = 13.3 cm

2 b = 69.5°

2 b = 8.18 cm

1a

8.36 cm

3 c = 52.5°

3 c = 5.01 cm

4 d = 42.2°

4 d = 6.15 cm

5 e = 24.0° 4

113 sec

8.26 m b

3

Worksheet 61

22.2 cm2

1a

44.1 m

b

5.34°

c

474 m

5 e = 2.14 cm

f = 66.0°

6 g = 22.4°

22 651 m

2a

10.1 m

b

15.7 m

6 f = 8.45 cm

h = 67.6°

5

8.94 cm

7 i = 45°

7 g = 4.58 cm h = 6.31 cm

8 j = 58.6°

2a

7.07 cm

b

8.66 cm

c

35.3°

8 i = 4.37 cm

k = 31.4°

Toot Hill School


106


Worksheet 62

Answers

Worksheet 63

1a

Worksheet 64

Worksheet 65

75.0° 105°

1a

1

x

y

0o

1

1 1

x

y

0o

1

30o

2

60o

2.73

150o -0.866

90o

3

180o

120o 2.73

30o 0.866 60o 90o

0.5

b

0

255° 285

120o -0.5 -1

150o

2

240o -0.5

180o

1

270o

210o

0

210o -0.866

300o

140°

0

53.3 km

10.4 cm

2

11.3 cm

3

53.8°

b

309°

2a

73.4°

240o -0.732

0.5

330o 0.866 360o

2a

Worksheet 66

b

270o

400°

-1

300o -0.732

1 500°

If table is correct

330o

0

360o

1

assume graph is correct.

3a

20°

If table is correct

Accept values between:

assume graph is

a

40°-50°

correct.

b

None

c

None

d

310°-320°

e

400°-410°

f

670°-680°

g

None

h

130°-140°

i

220°-230°

j

None

k

490°-500°

l

580°-590°

b

160° 340°

a

210°

4

46.5°

330°

4a

153°

b

c 387°

6870 m2

Accept 220°-235° Accept 305°-320°

207°

b

b

Accept 5°-25° Accept 155°-175°

5

19.7 cm2

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107


Worksheet 67

Worksheet 68

Answers

Worksheet 69

1a

b 1a

( ) 2 ( -3-4) 3 ( 03 ) 4 ( 13 ) 5 ( -52) 6 ( 40 ) 7 (18 -6 ) 8 (10 -4 ) 9 ( -1-3) 10 3 ( -6) 11 24 (2 ) 12 -1 (2) 13 -9 (2) 14 3 ( -3) 15 27 (-10) 1

~

~x – ~y

c

1/ y 2

d

-1/2 x + 1/2 y

e

-y + 1/2 x

f

-1/2 y + x

25 N

b

127°

~

2a

2a

1a

202°

1/ x 2

b

6 -2

21.5 km/h

Worksheet 70

x=4

104°

b

7.75 m

c

10 min 45 secs

2a

060.6°

y = 11 b

x = -5 y=2

c

b

463 km/h

x = -3 y=2

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108


Worksheet 71

Answers

Worksheet 72

Worksheet 73

Accept any sensible answers. 1 Do not ask personal questions or should have an age range.

1

1

16 30 39 15

2 cm 2 Which box would a person aged 30 tick?

2 Do not accept decimals, eg 16.65 a

17 or 16

b

21 or 20

a person aged 20,

c

9 or 8

40, 60 or 80 tick?

d

14 or 13

3 Which box would

or 20, 40, 60 and

A

2

80 are shown twice.

Total 60

B

4 What does ‘young’, ‘middle aged’ and ‘old’ mean? or

C

3 Bad – children should be asked but they are not on the electoral roll.

different meanings to different people: a child might think

Good

30 is old; a senior citizen might think 30 is young.

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109


Answers

Worksheet 74

Worksheet 76

Worksheet 75

1 1

Questionnaire

0.3 0.5 0.9 0.8 0.2

2

Experiment Assume graph is correct if table is correct.

3

Observation or questionnaire

4

Questionnaire

5

Experiment

1a

Boys x

8

x

7

7

x

6

Experiment Frequency

6

x

5

x

x

4 3 2

Observation

x

1

x

0 8

Girls

x x 5

10 15 Time (seconds)

20

25

Observation or questionnaire or experiment

9

2

6 1

Questionnaire b

The frequency polygon shows that boys

8

generally take longer to thread a needle 10

Questionnaire

than girls.

6 5

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110


Worksheet 77

Answers

Worksheet 78

Worksheet 79

1a 1a

7

Worksheet 80

1a

5.625

b

1.576

30

12

54

30

Worksheet 81

1a

54 400

96 70 100 98 1a

2a

5

b

2

100

40 – under 50

b

2000

c

16%

2a

3200

b

1700

c

675

d

125

Accept any answers in the range: b

c

53-55 3a

10.4

b

5.00

56-58

4a b

b

Check point

b

graph a mark.

graph a mark.

Accept any answers in the range: b 44-48

c

Accept any answers in

Check point

correct give

correct give

31-50

5.87

(170, 54). If

(180,70). If

2a

12

e

167-169

d

174-176

e

156-158

f

16-20

5a

Adam 21.6 3.93

the range: c

172-178

d

181-184

e

165-169

f

12-19

g

7-13

48-50 g

Any valid comparison, eg boys are taller than girls; any comparison should mention both medians and both interquartile ranges.

Barry 22.8 25.8

b

Adam

c

Any valid explanation, eg Adam has a lower sd and therefore is more consistent.

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111


Worksheet 82

a

Check points (180, 18) and (190, 21). If correct award mark. Accept any reasonable line.

b

Worksheet 83

Answers

Worksheet 84

1a

1a

Worksheet 85

1a

0.3

b

0.3

c

0.027

Worksheet 86

0.7

0.4

b

0.32

c

0.24

d

0.04

b

0.3

1a

c

0.4

d

0.7

e

d

f

b

di ii

19 cm (approx) 190 cm (approx)

2a

Mrs Jarvis asked more people.

b

Accept rounded answers.

iii 15.5 cm (approx)

Size 8

iv 178 cm (approx)

Size 10

18 300

v

Size 12

32 000

Size 14

27 500

Size 16

16 800

21.5 cm (approx)

2/5

c

21/40

d

19/40

0.03

0.42

Positive correlation g

b

0.3

2a

c

75

5/24

0.46

h

0.3

i

0.12

2a

1/10

b

3/10

c

3/5

0.00024

c

0.03752

d

0.96224

5400

j

0.88

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112


Worksheet 87

Answers

Worksheet 88

Worksheet 89

1

1a

0.03125 (1/32)

2

3 b

0.972 (35/36)

x ≤ -8 or x ≥ 8

0.999228395

6 ≥ x > -3

5

x < -9

6

x≥8

7

3

x≤6

0.96875 (31/32) 4

2

x>6

1 1 right, 6 up or 1 6

( )

( )

4a

1

800

2

500

3

30

4

40

5

0.06

6

3

7

0.3

8

0.1

9

160 000

10

500 or 450

11

0.007

12

0.3

13

500 000 or

x≥1

2 8 right, 3 up or 83

.

Worksheet 90

-9 3 9 left or 0

( )

0.16 (1/6)

8

y < -2

-1 4 1 left, 3 up or 3

( )

b

0.5 (1/2)

8 5 8 right, 6 down or -6

( )

400 000

14

700

15

6

Answers in any order. c

.

0.3 (1/3 )

9 6

R (5, 2)

7

R (-3, -5)

8

R (-6, 1)

9

R (4, -5)

x≤3 y ≤ -1 y ≥ -x

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113

Teacher Total

NUMBER General topic Worksheet number

1

Mark

Out of

2

3

4

8

17 17

35 28 22 15

10 26 44

5

6

Number Patterns

C = 44 D = 30

21 17 13 9

88

14 13 27

Total

ALGEBRA

Fractions, A = 70 Number and B = 57 Calculator Skills Decimals Percentages Skills 13 11 8 5

Profile Sheet 1 Individual Assessment Higher levels 7-10 Varia- tion

Equations

23 18 14 10

7

8

9

18 11 29

2

36 29 22 15

10 11 12

9 7 6 3

13

Algebraic Skills 85 69 53 37

14 15 16 17 18 19 20 21 22 23

14 15 14 45

A = 154 B = 125 C = 96 D = 67

7

12 12

20 12 12

8 107

8 10 12 10 8

193

Grade (A to E)

General topic Worksheet number

Simi- larity

Angles

Graphs 60 49 38 26

24 25 26 27 28 29 30 31 32 33 34 35

Mark

Out of

10

4

6

10

5

4

5

9

4

4

12

24 19 15 10

36 37

18 12 30

6

3 76

38

Congruence Transformations

5 4 3 1

12 10 8 5

39 40

6

8

8

41 42 43

7

16

Measurement

24 20 15 10

44 45 46 47

14 10 31

7

9

Circles 41 33 26 18

48 49 50 51

24 12 52

Perimeter, Area and Volume

General topic

Total

Worksheet number

52 53 54 55 56

Mark

Out of

8

4

6

57 58 59 60 61 62 63 64 65 66

39

12 9

Vectors

Pythagoras’ Theorem and Trigonometry 31 25 19 13

5

11

9

4

6 14 13

8

5

4

63 51 39 27

Locus 28 23 18 12

67 68 69 70

15 12

79

5

4

71

2 - 1 -

A = 332 B = 269 C = 207 D = 145

36

2

2

415

Grade (A to E) Total

HANDLING DATA General topic Worksheet number

72 73 74

Mark

Out of

4

114

Grade (A to E) Main strengths Main weaknesses

Tables and Graphs

Questionnaires

20 16 12 8

75 76 77

11 10 25

3

10

6

15 12 9 6

Cumulative Frequency 78 79

19

17 14 11 7

Standard Scatter Deviation Diagrams 80 81

11 11 22

14

7

16 13 10 7

82

6 5 4 2

8

83 84 85 86 87

21

Probability

8

10 10

8

7

7

33 27 21 14

Total

A = 109 B = 89 Additional Topics C = 68 D = 47 88 89 90

42

137

9

A= B= C= D=

28 22 17 12

Overall Total: A = 694 B = 564 C = 434 D = 303

11 15

35

11 13 10 14 48

Grade (A to E) SHAPE, SPACE AND MEASURES

38 31 24 16

868


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Name Class

Class

Teacher

Total Fractions, Decimals and Percentages

Calculator Skills

2

3

4

8

10

26

44

5

6

14

13

27

Number

88

Grade A= B= C= D=

70 57 44 30


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Gene ral to pic Number Work sheet Skills numb er 1 Mark out o f 17 17 Name

Profile Sheet 2 Class Assessment Higher levels 7-10: Number

115

Class

Teacher

Total Equations

9

10

11

12

2

14

15

14

Variation

13 45

12

12

Algebraic Skills

14

15

16

17

18

19

20

21

22

23

7

20

12

12

8

10

12

10

8

8

107

Algebra

Grade

193

A = 154 B = 125 C = 96 D = 67


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Gene ral to pic Number Patterns Work sheet numb er 7 8 Mark out o f 18 11 29 Name

Profile Sheet 3 Class Assessment Higher levels 7-10: Algebra

116

Class

Teacher

Total Gene ral to Shape, Space pic Work Angles Similarity Congruence Transformations Measurement Graphs sheet and Measures Grade numb A = 168 er 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Mark B = 137 out o C = 105 f 4 6 10 5 4 5 9 4 4 12 3 18 12 6 8 8 7 14 10 7 9 24 12 10 76 30 6 16 31 52 211 Name D = 73


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Profile Sheet 4 Class Assessment Higher levels 7-10: Shape, Space and Measures – 1

117

Class

Teacher

Gene ral to pic Perimeter, Area Work Circles Pythagoras’ Theorem and Trigonometry Vectors Locus sheet and Volume numb er 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 Mark out o f 11 13 10 14 48 8 4 6 12 9 39 5 11 9 4 6 14 13 8 5 4 79 15 12 5 4 36 2 2 Name

Total

Shape, Space and Measures Grade

204

A = 163 B = 132 C = 102 D = 71


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Profile Sheet 5 Class Assessment Higher levels 7-10: Shape, Space and Measures – 2

118

Class

Teacher

Total Cumulative Frequency

78 79

Standard Scatter Deviation Diagrams

80 81

82

11 11 22 14 7 21 8

Probability

Handling Data

Grade

137

A = 109 B = 89 C = 68 D = 47

83 84 85 86 87 8 10 10 8

7

7 42

Total Additional Additional Grade Topics Topics

88 89 90 9 11 15

35

A= B= C= D=

28 22 17 12


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Gene ral to pic Questionnaires Tables and Graphs Work sheet numb er 72 73 74 75 76 77 Mark out o f 4 11 10 25 3 10 6 19 Name

Profile Sheet 6 Class Assessment Higher levels 7-10: Handling Data

119

Class

Gene ral to pic Work sheet numb er Mark out o f Name

Teacher

Profile Sheet 7 Class Assessment


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120


Contents Teacher’s Notes ................................................................................................................... 1 Number Number Skills ................................................................................................................... 4 Calculator Skills ............................................................................................................... 5 Fractions, Decimals and Percentages .............................................................................. 8 Algebra Number Patterns ............................................................................................................. 10 Equations........................................................................................................................ 12 Variation......................................................................................................................... 16 Algebraic Skills ............................................................................................................... 17 Shape, Space and Measures Graphs ............................................................................................................................ 27 Angles............................................................................................................................. 39 Similarity......................................................................................................................... 41 Congruence..................................................................................................................... 42 Transformations.............................................................................................................. 44 Measurement.................................................................................................................. 47 Circles ............................................................................................................................. 51 Perimeter, Area and Volume .......................................................................................... 55 Pythagoras’ Theorem and Trigonometry......................................................................... 60 Vectors ............................................................................................................................ 70 Locus............................................................................................................................... 74 Handling Data Questionnaires ................................................................................................................ 75 Tables and Graphs.......................................................................................................... 78 Cumulative Frequency..................................................................................................... 81 Standard Deviation ........................................................................................................ 83 Scatter Diagrams ............................................................................................................ 85 Probability....................................................................................................................... 86 Additional Topics............................................................................................................ 91 Answers............................................................................................................................... 94 Profile Sheets..................................................................................................................... 114

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