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.
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Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
1
GCSE Maths Homework Pack 3: Higher Tier
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
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
2
GCSE Maths Homework Pack 3: Higher Tier
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.
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Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
3
GCSE Maths Homework Pack 3: Higher Tier
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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GCSE Maths Homework Pack 3: Higher Tier
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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Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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GCSE Maths Homework Pack 3: Higher Tier
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
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Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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GCSE Maths Homework Pack 3: Higher Tier
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
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Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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GCSE Maths Homework Pack 3: Higher Tier
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
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GCSE Maths Homework Pack 3: Higher Tier
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
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GCSE Maths Homework Pack 3: Higher Tier
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
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GCSE Maths Homework Pack 3: Higher Tier
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
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GCSE Maths Homework Pack 3: Higher Tier
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
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GCSE Maths Homework Pack 3: Higher Tier
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
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GCSE Maths Homework Pack 3: Higher Tier
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
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GCSE Maths Homework Pack 3: Higher Tier
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
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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GCSE Maths Homework Pack 3: Higher Tier
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
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GCSE Maths Homework Pack 3: Higher Tier
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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GCSE Maths Homework Pack 3: Higher Tier
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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GCSE Maths Homework Pack 3: Higher Tier
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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GCSE Maths Homework Pack 3: Higher Tier
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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GCSE Maths Homework Pack 3: Higher Tier
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.
Toot Hill School
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111
GCSE Maths Homework Pack 3: Higher Tier
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
Toot Hill School
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GCSE Maths Homework Pack 3: Higher Tier
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
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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
GCSE Maths Homework Pack 3: Higher Tier
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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
GCSE Maths Homework Pack 3: Higher Tier
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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
GCSE Maths Homework Pack 3: Higher Tier
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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
GCSE Maths Homework Pack 3: Higher Tier
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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
GCSE Maths Homework Pack 3: Higher Tier
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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
GCSE Maths Homework Pack 3: Higher Tier
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
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
GCSE Maths Homework Pack 3: Higher Tier
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP
120
GCSE Maths Homework Pack 3: Higher Tier
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
Toot Hill School
Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP