gcse maths homework pack 3: higher tier - · pdf filegcse maths homework pack 3: higher tier...

Toot Hill School

GCSE Maths Homework Pack 3: Higher Tier

Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 1

This pack is intended to cover all of the topics required by candidates in the GCSE Higher Tierexamination. 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 homeworksheets can be attempted in any order to fit in with the school’s scheme of work. If two homeworksare completed each week this will allow the pack to be completed before the mock GCSEexaminations. The pack can then be used again for revision in Year 11 either for homework or inclass.

• As 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.

• 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 toprovide a profile of each student. This can be extremely useful at Key Stages 3 and 4. At Key Stage 3teachers are expected to be able to identify the students’ weaknesses and strengths. Profile Sheet 1(page 114) simplifies the process and worksheets provide evidence.

At Key Stage 4 it is even more important to identify students’ weaknesses so that a student can bedirected to revise the correct material for the GCSE examination.

The worksheets correspond to the GCSE Mathematics Revision Guides*. If a student has difficultieswith, 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/gradeconverter 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.

Teacher’s Notes

Toot Hill School



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 MathematicsHigher 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 theRevision Guides. This is particularly useful as the GCSE examination approaches.

Using the speed marking system

1 First photocopy the answer pages.2 Cut out the answers for the page to be marked. (You may find it quicker to fold the answer page for

most worksheets.)3 Place the answers in the marked section of the student worksheet.

Use 1 and 0

or ✔ and ✗

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 becarried out more quickly.

The system is designed to allow the student to answer on the worksheet itself. However, in the majorityof worksheets, it is possible for the student to answer on blank A4 paper. This will allow the worksheetto be re-used.

1....................... ■■

2....................... ■■

3....................... ■■

Minimum markCircle grade

9 7 6 3

A B C D E 12

1 28

2 72

3 18

28

61

18

✔

0

1

Toot Hill School



Explain the method to pupils as shown below:

Pupils shoulduse a rulerto drawanswer lines

Draw markboxes or leavea space

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

Factorise:

1 10a + 8 1 ...................■■

2 12a - 3c 2 ...................■■

3 10a - 8c 3 ...................■■

4 25a - 20c + 15 4 ...................■■

5 3a4 + 2a3 5 ...................■■

Worksheet Blank A4

Minimum markCircle grade

9 7 6 3

A B C D E 12

_______________________________ ■■

_______________________________ ■■

_______________________________ ■■

_______________________________ ■■

_______________________________ ■■

GCSE Maths Homework Pack 3: Higher Tier Answers


Worksheet 1 Worksheet 2 Worksheet 3 Worksheet 4 Worksheet 5

Toot Hill School

1 3/1 (3)

2 Irrational

3 1/2

4 17/1 (17)

5 9/25 (36/100)

6 Irrational

7 37/99

8 Irrational

9 Irrational

10 Irrational

11 8/99

12 377/1000

13245/999

14 7/100

152/3 (6/9)

16 28

17 200

1 -16.422

2 170.123

3 1069.22

4 470835

5 2.81473

6 -370.101

7 0.223324

8 70.0637

1 31.36

2 6.22093

3 1525.88

4 8.96696

5 11.2870

6 3.10029

7 0.537285

8 0.00195313

9 74.8953

10 -866.489

1 480 000

2 620

3 0.0047

4 0.0000274

5 8 100 000

6 0.34

7 0.00072

8 0.00132

9 7.3 x 102

10 6.82 x 103

11 3.72 x 105

12 6.42 x 10-1

13 7.8 x 10-4

14 8.23 x 10-2

15 2.7 x 103

16 4.2 x 10-5

17a 1.87 x 106

b 1 872 000

18a 3.39 x 104

b 33 887

19a 8.94 x 104

b 89361.7

20a 4.40 x 10-1

b 0.440123

21a 3.28 x 10-2

b 0.032768

1 4.76

2 11.34

3 31.8

4 80.23

5 31.39

6 5.561

7 161/5 (16.2)

8 521/4 (52.25)

9 124/5 (12.8)

10a £29 176

b £38 913

11a £38

b £6.65

12 £611




Toot Hill School

1a £13 600

b £11 560

c £6 034

d 1993

2a £26 997

b £39 962

c 2015

d £21 336

e £18 238

3 Accept rounded

answers.

a i 28 991

ii 13 797

iii 12 191

b 1999

1a 9, 49

b Square numbers

2a 8, 55

b Fibonacci sequence

3a 15, 21, 28

b Triangle numbers

4a 64, 343

b Cube numbers

5a 2, 3

b 1, 2, 3, 9

c 3, 9, 27, 54

d 1, 4, 9

e 1, 27

6a 5, 31

b 1, 5

c 75, 960

d 1, 64, 169

e 1, 64

1 2.45

2 400

3 1.56

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

1 2.32.7.11

2 2.3.73

3a 42

b 67 914

4 24.3.7

5 22.33.5.7

6a 84

b 15 120

7a 1/16 (0.0625)

b 8/7 (1.142857…)

c -1/5 (-0.2)

8.2

8 → 480

9 → 693

8.5 → 580.125

8.3 → 538.587

8.2 → 518.568

8.25 → 528.515625

7.6

7 → 441

8 → 640

7.5 → 534.375

7.6 → 554.496

7.55 → 544.373875




Toot Hill School

1 A = C2

2 A = √ D

3 A = √ B5

4 A =3E – D + 5

4

5 A = 10C3

6 A = -C3

7 A = 3.5Y

8 A = √ 7C + 4D

9 A = CB

10 A = CD5BE

11 A =C

3(2D – 7)

12 A = 4CE – D

13 A = √ B

3CD

14 A = B + C – DF

15 A = 2Y5C – 3D

√

√

√

√

1a i Converges

ii 0.750

b i Converges

ii 2.667

c i Diverges

ii No answer

Solutions shown in

any order.

2a i xn + 1 = -6xn + 5

ii -2

i xn + 1 = -6 – 5xn

ii -3

b i xn + 1 = 10

– 3xn

ii -2

i xn + 1 = 10

+ 3xn

ii 5

1a a = kc(k = 3)

b 15

c 7

2a x = ky3

(k = 5)

b 1715

c 4

3a p = kq

(k = 8)

b 0.4

c 4

4a M = kR3

(k = 1000)

b 1

c 4

1a a11

b a7

c a-3

d a-8

e 12a5

f a6

g a5

h 4a9

i a-7

j a-4

k a12

2a 2401

b 7

c 1

d 2

e 0.125

3a a21

b a11/15

c a1/12

d a3/4

1 0.190023

2 0.131979

3 29641.2

4 0.255390

5 15.6539

6 1.46988

7 0.0150845




Toot Hill School

1 15a6

2 6a7c6

3 4a2d2

4 16a12

5 12y – 24

6 12a2 + 6ay3

7 6a5 + 21a4

8 -24a4 + 18ac2

9 6a2 – 8a – 30

10 20y2 – 42y + 18

11 6a2 + 23a + 20

12 16y2 – 56y + 49

1 2(2a – 5)

2 4(4x + 3y)

3 9(4a – 3x)

4 9(2a – 3c + y)

5 y(5y – 7)

6 4y(3y – 5)

7 2a5(8a3 + 5)

8 2ac(5a2c – 4)

9 5a3cy(5c – 2a2y2)

10 12ad(5c – 4a)

11 5a2(3a – 5c + 2ay)

12 2a3(4a5 – 3a2 + 5)

1 (x + 2)(x + 5)

2 (x + 4)(x + 7)

3 (x – 3)(x – 7)

4 (x + 3)(x – 5)

5 (a + 5)(a – 4)

6 (y – 2)(y – 8)

7 (y + 1)(y + 7)

8 (a + 3)(a - 4)

1 (y + 7)(y – 7)

2 (4a – 9)(4a + 9)

3 x = -4

or x = -8

4 x = 3

or x = 8

5 x = 2

or x = -7

6 x = -6

or x = 7

Answers in any order

1 x = -3.79

or x = 0.791

2 x = 1.87

or x = -0.535

3 a = -1.21

or a = 3.71

4 y = 1.55

or y = -0.804

5 x = 2.27

or x = -5.27

6 x = 0.370

or x = 3.38

Toot Hill School



Worksheet 21 Worksheet 22 Worksheet 23 Worksheet 24

1 x = 3

y = 4

2 x = 2

y = -5

3 x = -3

y = -6

4 a = 4.2

c = 3.4

5 a = 6

y = 5

12a – 35a + 7

245

3x + 4x – 3

4x – 7x – 3

52a3

5c2

6 8a6

15c7

7 25a

814c2d

3a

119a + 16

6

234y – 23

20

3c + 14

12

4-6c – 26

21

588C – 54

14

6a – 9

6

77a – 1

(a + 2)(a – 3)

83a – 5

(a + 5)(a + 1)

1 H

2 B

3 G

4 D

5 E

6 A

7 F

8 C

9

-4 -3 -2 -1 1 2 3 40

4

3

2

1

-1

-2

-3

-4x

x

x

x

x

x

x

xx

x -4 -3 -2 -1 0 1 2 3 4

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

Toot Hill School




1 x = 1

y = 2

2 x = 1

y = -2

1

Accept anything close.

a 2

b 1

c -0.5

d -1.5

x

y

-3

4.5

-2

2

-1

0.5

0

0

1

0.5

2

2

3

4.5

Answers are approximate

a 0.6

or -1.6

b 1.4

or -1.4

x -2 -1 -1/2 0 1/2 1 2

y 2 0 -1/4 0 3/4 2 6

x -2 -1 -1/2 0 1/2 1 2

y 0 1 11/2 2 21/2 3 4

1a -1/2

b y = -1/2 x + 1

2a 2

b y = 2x – 2

3a -1

b y = -x + 2

4a 1/3

b y = 1/3 x – 3

5a 1/2

b y = 1/2 x – 2

Toot Hill School




1a Assume the

graph is correct if

it goes through

(0, 15) and

(400, 95).

b £P = £(0.2N + 15)

c £615

d 237

1a 1/4

b 3

2a 1/2

b 1/2

c 32.5

1 f

2 c

3 m

4 o

5 h

6 e

7 a

8 g

9 n

y

x

2

1

-1

-2

01 2 3 4-4 -3 -2 -1

y

x

2

1

-1

-2

01 2 3 4-4 -3 -2 -1

y

x

2

1

-1

-2

01 2 3 4-4 -3 -2 -1

y

x

2

1

-1

-2

01 2 3 4-4 -3 -2 -1

1

2

3

4

Toot Hill School



Worksheet 34 Worksheet 35 Worksheet 36Worksheet 33

y

x

2

1

-1

-2

01 2 3 4-4 -3 -2 -1

y

x

2

1

-1

-2

01 2 3 4-4 -3 -2 -1

y

x

3

2

0

-1

-2

-3

1

90 180 270 360

y

x

3

2

0

-1

-2

-3

1

90 180 270 360

1 06.00

2 15 km/h

3 10 km

4a 09.00 and 09.30

b Steepest part

c 60 km/h

5a 12-13 km/h (approx)

b 40 km/h

c 40 km/h

6 1230

7 41/2 hours

8 Cyclist B overtook

cyclist A

1 a = 70°

b = 70°

c = 110°

2 d = 70°

3 e = 80°

f = 20°

g = 80°

4 h = 105°

5 i = 75°

j = 105°

k = 75°

6 l = 98°

m = 82°

n = 98°

7 o = 80°

p = 30°

8 2x = 72°

3x = 108°

Any answer between:

1 415-440 m

Any answer between:

2a 150-165 m

b Less

1

2

3

4




Toot Hill School

1a 2.4 cm

b 4.5 cm

2a 12 cm

b 2.4 cm

3a 7.65

b 7.875

1 SSS

2 Not

3 AAS or ASA

4 AAS or ASA

5 RHS (use

Pythagoras’

theorem)

6 SAS

7 AAS

8 Not

1a 47°

b 6.2 cm

c 8 cm

2a DEC

b DCB

c CDB or BDC

d CDE or EDC

e ACB or BCA

1 Translation 2

-4

2 Reflection in the

line y = 2x + 1

3a Rotation 60° anti-

clockwise, centre of

rotation (5, 2)

b Rotation 300°

clockwise, centre

of rotation (5, 2)

4 Enlargement, scale

factor -1/3, centre

of enlargement

(5, 1)

5 Enlargement, scale

factor 5/2, centre

of enlargement

(-2, 6)

6 Rotation 180°,

centre of rotation

(0, 0)

( )

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




Toot Hill School

1A´ (-1, -8)

B´ (-4, -8)

C´ (-4, -2)

D´ (-1, -2)

2E´ (2, -4)

F´ (1, -4)

G´ (1, -2)

H´ (2, -2)

3a (7, 1)

b -1/2

1 86.2 km/h

2 36.8 km/h

3 542.3 km

4 302.4 km

5 1.22 g/cm3

6 68.295 g

7 64.08 km/h

1 18.28

2 2 h 31 min

3 13.35

4a 8 h 25 min

b 8 h 24 min 37 sec

5a 32 min

b 32 min 23 sec

6a 2 h 11 min

b 2 h 11 min 16 sec

Accept 4.9 instead of

5 for maximum values,

eg 1.349.

1a 1.35 kg

b 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

8a 74.35 l

b 74.25 l

9a 16.005 cm

b 15.995 cm

10a 30.05 kg

b 29.95 kg

11a 790 g

b 770 g

12a 332.5 ml

b 327.5 ml

1A’ (10, 13)

B’ (11, 13)

C’ (11, 12)

2D’ (4, 11)

E’ (5, 11)

F’ (5, 10)

G’ (4, 10)

3D” (7, 9)

E” (9, 9)

F” (9, 7)

G” (7, 7)

4H’ (11, 2)

I’ (10, 2)

J’ (10, 3)

.

.




Toot Hill School

1a 285 ml

b 275 ml

c 272

d 228

2a 8.6061

8.5251

b 1.4426

1.1595

c 0.91895

0.91534

d 14.056

13.802

a 100°

b 120°

c 60°

d 70°

e 25°

f 50°

g 50°

h 40°

i 50°

j 40°

k 70°

l 60°

m 90°

1a 85°

b 45°

c 50°

2 140°

3a 90°

b 90°

c 40°

d 50°

4 TOB

5 15.8 cm

a 40°

b 50°

c 20°

d 80°

e 50°

f 50°

g 110°

h 70°

i 40°

j 160°

k 80°

l 10°

m 30°

n 60°

1a 8.73 cm

b 43.6 cm2

2a 1.27 cm2

b 3.44 cm

3a 36.0 cm

b 126 cm2

4a 452 cm2

b 905 cm3

5a 37.7 cm3

b 5 cm

c 47.1 cm2




Toot Hill School

1a 36 cm2

b 24 cm

2a 120 cm2

b 60 cm

3 23.2 cm2

4 561 000 cm2 or

0.561 m2

5 5 cm

6 2.5 cm

1 105 cm3

2 66 cm3

3 773.5 cm3 or

0.0007735 m3

4 720.896 cm3

1a 31.8 cm

b 52.5 cm2

2a 64 m

b 161 m2

3a 190 m2

b 1.52 m3

1 Length

2 None

3 None

4 Area

5 None

6 Length

7 Area

8 Area

9 Volume

10 None

11 Length

12 Volume

1a 4:7

b 16:49

c 64:343

2 27:512

3a 128 cm2

b 12.5 km2

4a 160 cm

b 12.5 m2

c 5.12 kg




Toot Hill School

1 9.40 m

2 8.26 m

3 8.36 cm

4 22.2 cm2

5 8.94 cm

1 a = 21.5°

2 b = 69.5°

3 c = 52.5°

4 d = 42.2°

5 e = 24.0°

f = 66.0°

6 g = 22.4°

h = 67.6°

7 i = 45°

8 j = 58.6°

k = 31.4°

1 a = 13.3 cm

2 b = 8.18 cm

3 c = 5.01 cm

4 d = 6.15 cm

5 e = 2.14 cm

6 f = 8.45 cm

7 g = 4.58 cm

h = 6.31 cm

8 i = 4.37 cm

1a 44.1 m

b 5.34°

c 474 m

2a 7.07 cm

b 8.66 cm

c 35.3°

1a 113 sec

b 22 651 m

2a 10.1 m

b 15.7 m




Toot Hill School

x

0o

30o

60o

90o

120o

150o

180o

210o

240o

270o

300o

330o

360o

y

1

0.866

0.5

0

-0.5

-0.866

-1

-0.866

-0.5

0

0.5

0.866

1

1a 75.0°

105°

b 255°

285

2a 140°

b 400°

500°

3a 20°

b 160°

340°

4a 153°

207°

b 387°

1

If table is correct

assume graph is

correct.

a 210°

330°

b Accept 220°-235°

Accept 305°-320°

c Accept 5°-25°

Accept 155°-175°

x

0o

30o

60o

90o

120o

150o

180o

210o

240o

270o

300o

330o

360o

y

1

2

2.73

3

2.73

2

1

0

-0.732

-1

-0.732

0

1

1 10.4 cm

2 11.3 cm

3 53.8°

4 46.5°

5 19.7 cm2

1

If table is correct

assume graph is

correct.

Accept values between:

a 40°-50°

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°

1a 53.3 km

b 309°

2a 73.4°

b 6870 m2

Toot Hill School




1 6-2

2 -3-4

3 03

4 13

5 -52

6 40

7 18-6

8 10-4

9 -1-3

10 3-6

11 242

12 -12

13 -92

14 3-3

15 27-10

( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )

1a 1/2 x

b x – y

c 1/2 y

d -1/2 x + 1/2 y

e -y + 1/2 x

f -1/2 y + x

2a x = 4

y = 11

b x = -5

y = 2

c x = -3

y = 2

~

~ ~

~

1a 21.5 km/h

b 202°

2a 104°

b 7.75 m

c 10 min 45 secs

1a 25 N

b 127°

2a 060.6°

b 463 km/h

Toot Hill School



Worksheet 71 Worksheet 72

2 cm

A

B

C

Accept any sensible

answers.

1 Do not ask personal

questions or should

have an age range.

2 Which box would

a person aged 30

tick?

3 Which box would

a person aged 20,

40, 60 or 80 tick?

or 20, 40, 60 and

80 are shown twice.

4 What does ‘young’,

‘middle aged’ and

‘old’ mean? or

different meanings

to different people:

a child might think

30 is old; a senior

citizen might think

30 is young.

Worksheet 73

1 16

30

39

15

2 Do not accept

decimals, eg 16.65

a 17 or 16

b 21 or 20

c 9 or 8

d 14 or 13

Total 60

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

Good

1

2

Toot Hill School

Worksheet 76



Worksheet 74 Worksheet 75

1 Questionnaire

2 Experiment

3 Observation or

questionnaire

4 Questionnaire

5 Experiment

6 Experiment

7 Observation

8 Observation or

questionnaire or

experiment

9 Questionnaire

10 Questionnaire

1a

b The frequency polygon shows that boys

generally take longer to thread a needle

than girls.

Freq

uen

cy

Time (seconds)

8

7

6

5

4

3

2

1

05 10 15 20 25

Boys Girls

x

x

x

x

x

x

x

x

x

x

1 0.3

0.5

0.9

0.8

0.2

Assume graph is

correct if table is

correct.

2 6

1

8

6

5

Toot Hill School




1a 40 – under 50

Accept any answers in

the range:

b 53-55

c 56-58

2a 31-50


the range:

b 44-48

c 48-50

1a 12

30

70

98

100

b Check point

(180,70). If

correct give

graph a mark.


the range:

c 172-178

d 181-184

e 165-169

f 12-19

g 7-13

1a 7

30

54

96

100

b Check point

(170, 54). If

correct give

graph a mark.

e 167-169

d 174-176

e 156-158

f 16-20

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

1a 5.625

b 1.576

2a 5

b 2

3a 10.4

b 5.00

4a 12

b 5.87

5a Adam 21.6

3.93

Barry 22.8

25.8

b Adam

c Any valid explanation, eg Adam has a lowersd and therefore ismore consistent.

Worksheet 81

1a 54 400

b 2000

c 16%

2a 3200

b 1700

c 675

d 125

Toot Hill School

Worksheet 86




1a 0.4

b 0.32

c 0.24

d 0.04

2a Mrs Jarvis asked more people.

b Accept rounded answers.

Size 8 5400

Size 10 18 300

Size 12 32 000

Size 14 27 500

Size 16 16 800

1a 0.7

b 0.3

c 0.4

d 0.7

e 0.3

f 0.42

g 0.46

h 0.3

i 0.12

j 0.88

1a 0.3

b 0.3

c 0.027

d 75

2a 0.03

b 0.00024

c 0.03752

d 0.96224

1a 5/24

b 2/5

c 21/40

d 19/40

2a 1/10

b 3/10

c 3/5

a Check points(180, 18) and (190, 21). If correct award mark.

b Accept any reasonable line.

c Positive correlation

di 19 cm (approx)

ii 190 cm (approx)

iii 15.5 cm (approx)

iv 178 cm (approx)

v 21.5 cm (approx)

Toot Hill School




1a 0.03125 (1/32)

b 0.96875 (31/32)

2 0.972 (35/36)

3 0.999228395

4a 0.16 (1/6)

b 0.5 (1/2)

c 0.3 (1/3)

1 1 right, 6 up or 16

2 8 right, 3 up or 83

3 9 left or -90

4 1 left, 3 up or -13

5 8 right, 6 down or 8-6

6 R (5, 2)

7 R (-3, -5)

8 R (-6, 1)

9 R (4, -5)

( )

( )

( )

( )

( )

1 x > 6

2 x ≤ 6

3 x ≤ -8 or x ≥ 8

4 6 ≥ x > -3

5 x < -9

6 x ≥ 8

7 x ≥ 1

8 y < -2

Answers in any order.

9 x ≤ 3

y ≤ -1

y ≥ -x

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

400 000

14 700

15 6

.

.

Toot H

ill School

GC

SE

Math

s Hom

ework

Pack

3: H

igher T

ier

Pearson Publishing, Chesterton M

ill, French’s Road, C

ambridge C

B4 3N

P114

Name

Class

Teacher Profile Sheet 1 Individual Assessment

Higher levels 7-10

Main strengths

Main weaknesses

General topic

Worksheet number

Mark

Out of

Grade (A to E)

Simi- larity

38

6

5 4 3 1

24 20 15 10

6

Number Skills

1

17

13 11 8 5

17

Varia- tion

13

12

9 7 6 3

12

Locus

71

2

2 - 1 -

2

82

8

6 5 4 2

16 13 10 7

8

10788

Algebraic Skills

16

12

17

12

14

7

15

20

18

8

19

10

20

12

21

10

22

8

23

8

Probability

31

Transformations

41

7

42

14

43

10

35 28 22 15

44

Calculator Skills

2

8

3

10

4

26

Additional Topics

88

9

89

11

90

15

20 16 12 8

25

Questionnaires

72

4

73

11

74

10

15 12 9 6

19

Tables and Graphs

75

3

76

10

77

6

Total

A = 70 B = 57 C = 44 D = 30

193

Total

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

General topic

Worksheet number

Mark

Out of

Grade (A to E)

415

23 18 14 10

29

Number Patterns

7

18

8

11

24 19 15 10

30

Angles

36

18

37

12

12 10 8 5

16

Congruence

39

8

40

8

21 17 13 9

27

Fractions, Decimals and Percentages

5

14

6

13

Total

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

35

Total

A = 28 B = 22 C = 17 D = 12

137

Total

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

General topic

Worksheet number

Mark

Out of

Grade (A to E)

42

83

10

84

10

85

8

86

7

87

7

33 27 21 14

Perimeter, Area and Volume

39

52

8

53

4

54

6

55

12

56

9

31 25 19 13

28 23 18 12

85 69 53 37

79

Pythagoras’ Theorem and Trigonometry

59

9

60

4

57

5

58

11

61

6

62

14

63

13

64

8

65

5

66

4

63 51 39 27

76

Graphs

26

6

27

10

24

10

25

4

28

5

29

4

30

5

31

9

32

4

33

4

34

12

35

3

60 49 38 26

36

Vectors

67

15

68

12

69

5

70

4

36 29 22 15

45

Equations

9

2

10

14

11

15

12

14

41 33 26 18

52

Measurement

44

7

45

9

46

24

47

12

38 31 24 16

48

Circles

48

11

49

13

50

10

51

14

General topic

Worksheet number

Mark

Out of

Grade (A to E)

Scatter Diagrams

21

Standard Deviation

80

14

81

7

17 14 11 7

22

Cumulative Frequency

78

11

79

11 868

Overall Total:

A = 694 B = 564 C = 434 D = 303

NUMBER

SHAPE, SPACE AND MEASURES

HANDLING DATA

ALGEBRA

Toot H

ill School

GC

SE

Math

s Hom

ework

Pack

3: H

igher T

ier



ambridge C

B4 3N

P115

Class Teacher Profile Sheet 2 Class Assessment

Higher levels 7-10: Number

Number Skills Calculator Skills

1

17

2

8

3

10

5

14

6

13

4

26 44 2717 88

Total

Number GradeFractions, Decimals and Percentages

A = 70 B = 57 C = 44 D = 30

General topicWorksheet numberMark out ofName

Toot H

ill School

GC

SE

Math

s Hom

ework

Pack

3: H

igher T

ier



ambridge C

B4 3N

P116


Higher levels 7-10: Algebra

Number Patterns Equations Variation Algebraic Skills

7

18

8

11

9

2

10

14

11

15

12

14

14

7

15

20

16

12

17

12

18

8

19

10

20

12

21

10

22

8

23

8

13

1229 45 12 107 193

Total

Algebra Grade

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


Toot H

ill School

GC

SE

Math

s Hom

ework

Pack

3: H

igher T

ier



ambridge C

B4 3N

P117


Higher levels 7-10: Shape, Space

and Measures – 1

Graphs Angles Congruence Transformations MeasurementSimilarity

24

10

25

4

26

6

27

10

28

5

29

4

30

5

31

9

32

4

33

4

34

12

35

3 76

44

7

45

9

46

24

47

12 52

41

7

42

14

43

10 31

36

18

37

12 30

39

8

40

8 16

38

6 6 211

TotalShape, Space and Measures Grade

A = 168 B = 137 C = 105 D = 73


Toot H

ill School

GC

SE

Math

s Hom

ework

Pack

3: H

igher T

ier



ambridge C

B4 3N

P118


Higher levels 7-10: Shape, Space

and Measures – 2

Circles Pythagoras’ Theorem and Trigonometry Vectors LocusPerimeter, Area and Volume

48

11

49

13

50

10

51

14 48

53

4

52

8

54

6

55

12

56

9

58

11

57

5

59

9

60

4

61

639

63

13

62

14

64

8

65

5

66

4 79

67

15

68

12

69

5

70

4 36

71

2 2 204

TotalShape, Space and Measures Grade

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


Toot H

ill School

GC

SE

Math

s Hom

ework

Pack

3: H

igher T

ier



ambridge C

B4 3N

P119


Higher levels 7-10: Handling Data

Questionnaires Cumulative Frequency

Standard Deviation

Scatter Diagrams Probability Additional

TopicsTables and Graphs

72

4

73

11

74

10 25

76

10

75

3

77

6

84

10

83

10

85

8

81

7

80

1419

78

11

79

11 22 21

87

7

86

7

88

9

90

15

89

1142

82

8 8 35

TotalTotalAdditional

Topics Grade

A = 28 B = 22 C = 17 D = 12137

Handling Data Grade

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


Toot Hill School



Cla

ssTe

ach

erPr

ofile

She

et 7

C

lass

Ass

essm

ent

Gen

eral

top

icW

orks

heet

num

ber

Mar

k ou

t of

Na

me

Toot Hill School


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

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

Contents

gcse maths homework pack 3: higher tier - · pdf filegcse maths homework pack 3: higher tier...

Documents