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An essential revision guide that covers all the key content for the
new mathematics ISEB 13+ syllabus which was first examined in
autumn 2016.
■
Revise all topics with extensive, level-differentiated content for
Levels 1, 2 and 3
■
‘Test yourself’ questions and ‘Exam-style questions’ at the end of each
section allow children to check their revision has been successful
■
Improve technique with revision tips, guidance and glossary
Mathemat ics for Common Entrance
13+ Revision Guide
■
Clean, clear layout for easy marking
■
Includes worked examples and diagrams to aid understanding
Mathemat ics for Common Entrance
13+ Exam Practice Answers
■
Over 250 differentiated exam-style questions for comprehensive
coverage across number, calculations, problem solving, algebra,
geometry and measures, and statistics and probability
■
Aim high with rigorous preparation for Levels 1, 2 and 3 in
Mathematics for Common Entrance 13+ Exam Practice Questions
■
Mathematics for Common Entrance 13+ Exam Practice Questions
Level 3
specifically prepares children for scholarship and CASE
examinations with extension questions
Mathemat ics for Common Entrance
13+ Exam Practice Questions
Mathematics for Common Entrance 13+ Revision Guide –
Chapter 9: Geometry and measures (1)
Mathemat ics
103
9
Geometry and measures (1)
9.1
Measures
Reading scales
There are many common scales used for measuring so take care when reading
them.
120
130
140
150
?
In this first example, we can see that the scale is going up in tens, using
intervals of two. This arrow is therefore pointing to
134
0
50
100
150
?
This one goes up in fifties, so each division is worth 10. The arrow here
therefore points to
70
180
170
160
150
?
Attention!
This one is going down not up! The scale is marked in tens and
divided into twos, so the arrow here is pointing to
166
135
140
145
150
?
This scale is simply going up in fives, with each division representing one.
The arrow here is therefore pointing to
142
147
148
149
150
?
Finally a decimal scale: each unit is divided into 5 divisions, so each one
represents 0.2 units (1 ÷ 5). The arrow here is pointing to
148.4
Themetric system
The metric system is based on powers of 10; that means 10, 100, 1000 and so
on, as well as 0.1, 0.01, 0.001 etc. The scale goes outwards both ways.
Using a simple system of prefixes or ‘multipliers’, we can talk about any
position on this scale. The actual unit of measurement is the same each time!
846892_MFCE13_C09_103-120.indd 103
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104
For
length
we use
metres
and the abbreviation
m
For
mass
grams
g
For
time
seconds
s
For
capacity
litres
l
For
digital storage
bytes
B
and there are a few others that scientists use. (Can you find any other
examples?)
So what are the prefixes?
Effect
Put this in front
Say this
×1
(nothing)
(nothing)
×1000 (×10
3
)
k
kilo
×1000000 (×10
6
)
M
mega
×1000000000 (×10
9
)
G
giga
×1000000000000 (×10
12
)
T
tera
÷10 (÷10
1
or×10
−1
)
d
deci
÷100 (÷10
2
or×10
−2
)
c
centi
÷1000 (÷10
3
or×10
−3
)
m
milli
÷1000000 (÷10
6
or×10
−6
)
µ
micro
÷1000000000 (÷10
9
or×10
−9
)
n
nano
Now let us try it out!
250cm is the same as (250 ÷ 100)m = 2.5m
5.75kg is the same as (5.75 × 1000)g = 5750g
Write 4.8cm in mm like this: (4.8 ÷ 100) is the same as (48 ÷ 1000) so it is
48mm. Or just remember that 10mm makes 1cm and go from there.
Revision tip
This is sillybut ithelps!Youhave to say itout loud tomake itwork:
‘One thousandmetres inakilometre,one thousandgrams inakilogram
andone thousandwhales inakillerwhale ...’
Commonunits
It is a very useful skill to be able to make reasonable estimates using units in
common use. The guidance in this section should improve your reliability!
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43
4
Algebra
4.1
Equations and formulae
In this section the questions cover the following topics:
●
Terms and expressions
●
Simplification; brackets
●
Substitution
●
Equations
●
Formulae
●
Modelling
●
Inequalities
●
Trial and improvement (this section is included for interest only)
Many questions cover several topics.
In this section you should answer the questions without using a calculator except
where indicated by
1
Simplifythefollowingexpressions:
(i)
4
a
+3
a
(1)
(ii)
4
a
×3
a
(2)
(iii)
+
3
2
a a
(2)
(iv)
2
a
−3
a
−
a
(2)
2
Simplifythefollowingexpressions:
(i)
3
a
−4
b
+
b
−2
a
(2)
(ii)
3
a
2
×4
a
3
(2)
(iii)
6
12
a
a
2
(2)
3 (a)
Simplify
(i)
3
a
−4
a
+2
a
(2)
(ii)
+
a b
8 12
4
(2)
(b)
Multiplyoutthebracketandsimplify:
(i)
2(
x
+
y
)−
y
(2)
(ii)
3(
a
−
b
)−2(
a
−3
b
)
(3)
4 (a)
Factorisecompletely:5
n
−15
(2)
(b)
Multiplyoutthebracketsandsimplify:2(
p
+3
q
)−(
p
+2
q
)
(3)
Level3
¢
Level2
●
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44
5 (a)
Simplify,bycollectingliketerms:24
m
+3
n
−7
n
−19
m
(2)
(b)
Factorise:12
a
+18
b
(2)
6 (a)
Multiplyoutthebracketsandsimplifythefollowingexpression:
2(5−3
n
)+6(
n
−3)
(3)
(b)
Factorisecompletely:10
u
+15
(2)
7 (a)
Simplify,bycollectingliketerms:2
x
+3
x
2
−2+3
x
(2)
(b)
Simplify:2
x
2
×3
x
3
(2)
(c)
Simplify:
x
x
18
6
2
3
(2)
8 (a)
Simplify:8
y
−4+2
y
+3
(2)
(b)
Removethebracketsandsimplify:2(
x
+3
y
)+3(
x
−2
y
)
(3)
9 (a)
Removethebracketsandsimplifywherepossible:
(i)
7(2
a
+5)
(1)
(ii)
(5
a
−3)−(
a
−5)
(2)
(b)
Factorise:
(i)
6
a
+10
(2)
(ii)
8
ab
−12
bc
(2)
10
Simplify:
(i)
15
p
2
−17
p
3
−9
p
2
+4
p
3
(2)
(ii)
2(5+3
h
)−4(2
h
−5)
(2)
(iii)
−
w w
w
5 3
4
(2)
11 (a)
Simplify:
(i)
2
y
3
+2
y
3
(1)
(ii)
2
y
3
×2
y
3
(2)
(iii)
y
y
12
3
2
6
(2)
(b)
Multiplyoutthebracketsandsimplify:3(2
p
−5
q
)−5(
p
+3
q
)
(3)
(c)
Factorisecompletely:15
a
2
+25
a
(2)
12 (a)
Multiplyoutthebracketsandsimplify:2(3
a
+1)−3(
a
−2)
(3)
(b)
Factorise:8
a
−12
b
(2)
Level2
●
Level2
●
Level2
●
Level2
●
Level3
¢
846922_MFCE13_Exam_Prac_C04_043-065.indd 44
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21
4
Algebra
4.1
Equations and formulae
1 (i)
7
a
(1)
(iii)
2
a
(2)
(ii)
12
a
2
(2
(iv)
–
2
a
(2)
2 (i)
a
–
3
b
(2)
(iii)
1
2
a
(2)
(ii)
12
a
5
(2)
3 (a)
(i)
a
(2)
(b)
(i)
2
x
+
y
(2)
(ii)
2
a
+3
b
(2)
(ii)
a
+3
b
(3)
4 (a)
5(
n
–
3)
(2)
(b)
p
+4
q
(3)
5 (a)
5
m
–
4
n
(2)
(b)
6(2
a
+
3
b
)
(2)
6 (a)
−
8
(3)
(b)
5(2
u
+
3)
(2)
7 (a)
3
x
2
+
5
x
–
2
(2)
(c)
3
x
(2)
(b)
6
x
5
(2)
8 (a)
10
y
–
1
(2)
(b)
5
x
(3)
9 (a) (i)
14
a
+35
(1)
(b)
(i)
2(3
a
+5)
(2)
(ii)
4
a
+2
(2)
(ii)
4
b
(2
a
–
3
c
)
(2)
10 (i)
6
p
2
–
13
p
3
(2)
(iii)
1
2
(2)
(ii)
–
2
h
+30
(2)
11 (a) (i)
4
y
3
(1)
(b)
p
–
30
q
(3)
(ii)
4
y
6
(2)
(c)
5
a
(3
a
+5)
(2)
(iii)
4
4
y
(2)
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22
12 (a)
3
a
+8
(3)
(b)
4(2
a
–
3
b
)
(2)
(c) (i)
a
3
+5
a
2
(2)
(iii)
3
2
a
(2)
(ii)
24
a
9
(2)
13 (a)
3(1
–
12
y
)
(2)
(b)
2
x
(2)
14 (i)
9
a
2
–
2
ab
(2)
(iii)
11
x
(3)
(ii)
5
(3)
15 (i)
8
(1)
(iv)
16
(2)
(ii)
1
(1)
(v)
–
35
(2)
(iii)
6
(2)
16 (i)
13
(2)
(iii)
9
(2)
(ii)
–
3
(2)
(iv)
–
24
(2)
17 (i)
6
(2)
(iii)
25
(2)
(ii)
4
(2)
18 (i)
11
(2)
(iii)
9
(2)
(ii)
–
3
(2)
19 (i)
1
(2)
(iii)
6
(2)
(ii)
0
(2)
20 (i)
18
(1)
(iii)
–
3
(3)
(ii)
12
(2)
21 (i)
–
1
4
(2)
(iii)
4
(2)
(ii)
–
1
6
(2)
22 (i)
390
(1)
(iii)
575.9
(1)
(ii)
185.9
(1)
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Mathematics for Common Entrance 13+ Exam Practice Questions –
Chapter 4: Algebra
Mathematics for Common Entrance 13+ Exam Practice Answers –
Chapter 4: Algebra
Te l :
0 2 0 3 1 2 2 6 4 0 5
I
V i s i t :
g a l o r e p a r k . c o . u k
Te l :
0 2 0 3 1 2 2 6 4 0 5
I
V i s i t :
g a l o r e p a r k . c o . u k
13+ revision & practice
2 9
2 8