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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
GCSE Maths Homework Pack 3: Higher Tier
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 2
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
GCSE Maths Homework Pack 3: Higher Tier
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 3
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
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 94
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 95
Worksheet 6 Worksheet 7 Worksheet 8 Worksheet 9 Worksheet 10
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 96
Worksheet 11 Worksheet 12 Worksheet 13 Worksheet 14 Worksheet 15
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 97
Worksheet 16 Worksheet 17 Worksheet 18 Worksheet 19 Worksheet 20
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 98
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 99
Worksheet 25 Worksheet 26 Worksheet 27 Worksheet 28
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 100
Worksheet 29 Worksheet 30 Worksheet 31 Worksheet 32
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 101
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 102
Worksheet 37 Worksheet 38 Worksheet 39 Worksheet 40 Worksheet 41
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 103
Worksheet 42 Worksheet 43 Worksheet 44 Worksheet 45 Worksheet 46
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)
.
.
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 104
Worksheet 47 Worksheet 48 Worksheet 49 Worksheet 50 Worksheet 51
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 105
Worksheet 52 Worksheet 53 Worksheet 54 Worksheet 55 Worksheet 56
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 106
Worksheet 57 Worksheet 58 Worksheet 59 Worksheet 60 Worksheet 61
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 107
Worksheet 62 Worksheet 63 Worksheet 64 Worksheet 65 Worksheet 66
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 108
Worksheet 67 Worksheet 68 Worksheet 69 Worksheet 70
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 109
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 110
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 111
Worksheet 77 Worksheet 78 Worksheet 79 Worksheet 80
1a 40 – under 50
Accept any answers in
the range:
b 53-55
c 56-58
2a 31-50
Accept any answers in
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.
Accept any answers in
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 112
Worksheet 82 Worksheet 83 Worksheet 84 Worksheet 85
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
GCSE Maths Homework Pack 3: Higher Tier Answers
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 113
Worksheet 87 Worksheet 88 Worksheet 89 Worksheet 90
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
Pearson Publishing, Chesterton M
ill, French’s Road, C
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
Pearson Publishing, Chesterton M
ill, French’s Road, C
ambridge C
B4 3N
P116
Class Teacher Profile Sheet 3 Class Assessment
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
General topicWorksheet numberMark out ofName
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
P117
Class Teacher Profile Sheet 4 Class Assessment
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
General topicWorksheet numberMark out ofName
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
P118
Class Teacher Profile Sheet 5 Class Assessment
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
General topicWorksheet numberMark out ofName
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
P119
Class Teacher Profile Sheet 6 Class Assessment
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
General topicWorksheet numberMark out ofName
Toot Hill School
GCSE Maths Homework Pack 3: Higher Tier
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP 120
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
GCSE Maths Homework Pack 3: Higher Tier
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