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13+ revision & practice

Mathemat ics

length

we use metres and the abbreviation

For For For For For

9 Geometry and measures (1)

mass time

grams

seconds

approved

capacity

litres bytes

digital storage B and there are a few others that scientists use. (Can you find any other examples?) So what are the prefixes?

9.1 Measures Reading scales

Mathemat ics for Common Entrance 13+ Revision Guide

Effect

Put this in front

Say this

There are many common scales used for measuring so take care when reading them.

×1

(nothing)

×1000 (×10 3 )

kilo

120

130

140

150

×1000000 (×10 6 )

mega

×1000000000 (×10 9 )

giga

×1000000000000 (×10 12 )

tera

÷10 (÷10 1 or×10 −1 ) ÷100 (÷10 2 or×10 −2 ) ÷1000 (÷10 3 or×10 −3 ) ÷1000000 (÷10 6 or×10 −6 ) ÷1000000000 (÷10 9 or×10 −9 )

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

deci

centi

milli

An essential revision guide that covers all the key content for the new mathematics ISEB 13+ syllabus which was first examined in autumn 2016.

100

150

micro

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 ...’

This one goes up in fifties, so each division is worth 10. The arrow here therefore points to 70

180

170

160

150

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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

■ Revise all topics with extensive, level-differentiated content for Levels 1, 2 and 3

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

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!

■ ‘Test yourself’ questions and ‘Exam-style questions’ at the end of each section allow children to check their revision has been successful

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!

■ Improve technique with revision tips, guidance and glossary

103

104

Mathematics for Common Entrance 13+ Revision Guide – Chapter 9: Geometry and measures (1)

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Mathemat ics for Common Entrance 13+ Exam Practice Questions

5 (a) Simplify,bycollectingliketerms:24 m +3 n −7 n −19 m

(2)

4 Algebra

(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

4.1 Equations and formulae

■ Over 250 differentiated exam-style questions for comprehensive coverage across number, calculations, problem solving, algebra, geometry and measures, and statistics and probability

(2)

(b) Simplify:2 x 2 ×3 x 3

(2)

In this section the questions cover the following topics: ● Terms and expressions ● Simplification; brackets ● Substitution

18 6

Level2 ●

(2)

8 (a) Simplify:8 y −4+2 y +3

(2)

(b) Removethebracketsandsimplify:2( x +3 y )+3( x −2 y )

(3)

● 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:

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9 (a) Removethebracketsandsimplifywherepossible: (i) 7(2 a +5)

(1)

■ Aim high with rigorous preparation for Levels 1, 2 and 3 in Mathematics for Common Entrance 13+ Exam Practice Questions

Level3 ¢

(ii) (5 a −3)−( a −5)

(2)

12 (a) 3 a +8

(3)

4 Algebra

(b) Factorise:

(b) 4(2 a – 3 b )

(2)

(i) 6 a +10

(2)

(iii) 3 2 a

(2)

Level2 ●

(ii) 8 ab −12 bc

(2)

(ii) 24 a 9

(2)

■ Mathematics for Common Entrance 13+ Exam Practice Questions Level 3 specifically prepares children for scholarship and CASE examinations with extension questions

10 Simplify:

+ 3 2

a a

4 a +3 a

(i) 4.1 Equations and formulae 1 (i) 7 a (1)

(1)

(2)

(iii)

(i)

13 (a) 3(1 – 12 y )

(b) 2 x

(2)

15 p 2 −17 p 3 −9 p 2 +4 p 3

(2)

(ii) 4 a ×3 a

(iv) 2 a −3 a − a

(2)

(ii) 2(5+3 h )−4(2 h −5) (iii) 2 a

(2)

14 (i) 9 a 2 – 2 ab

(iii) 11 x

(2)

(3)

(2)

− w w w

2 Simplifythefollowingexpressions:

5 3 4

(iv) – 2 a

(ii) 12 a 2

Level2 ●

(iii) (2

(2)

(ii) 5

(3)

3 a −4 b + b −2 a

(2)

(i)

2 (i) a – 3 b

(iii) 1 2

11 (a) Simplify: (2)

(2)

15 (i) 8

(1)

(iv) 16

(2)

(ii) 3 a 2 ×4 a 3

(2)

(i) 2 y 3 +2 y 3

(1)

(ii) 12 a 5

(2)

(v) – 35

(ii) 1

(1)

(2)

6 12 a

Level2 ●

(2)

(iii)

(ii) 2 y 3 ×2 y 3

(2)

3 (a) (i) a

(b) (i) 2 x + y

(2)

(iii) 6

(2)

12 3

Level2 ● (ii) 2 a +3 b

(2)

(iii)

Simplify

3 (a)

(ii) a +3 b

(2)

(3)

16 (i) 13

(2)

(iii) 9

(2)

+ a b 8 12 4

(b) Multiplyoutthebracketsandsimplify:3(2 p −5 q )−5( p +3 q )

(i) 3 a −4 a +2 a (2)

(3)

(2)

(ii)

4 (a) 5( n – 3)

(b) p +4 q

(2)

(3)

(ii) – 3

(iv) – 24

(2)

Mathemat ics for Common Entrance 13+ Exam Practice Answers

Level3 ¢

(2)

(b) Multiplyoutthebracketandsimplify: (i) 2( x + y )− y (2)

5 (a) 5 m – 4 n

(b) 6(2 a + 3 b )

(2)

17 (i) 6

(2)

(iii) 25

(2)

12 (a) Multiplyoutthebracketsandsimplify:2(3 a +1)−3( a −2)

(3)

(ii) 3( a − b )−2( a −3 b )

(3)

(b) 5(2 u + 3)

6 (a) − 8

(3)

(2)

(ii) 4

(2)

(b) Factorise:8 a −12 b

(2)

4 (a) Factorisecompletely:5 n −15

(2)

7 (a) 3 x 2 + 5 x – 2

(2)

18 (i) 11

(2)

(iii) 9

(2)

(b) Multiplyoutthebracketsandsimplify:2( p +3 q )−( p +2 q )

(3)

(b) 6 x 5

(2)

(ii) – 3

(2)

8 (a) 10 y – 1

(b) 5 x

(2)

(3)

19 (i) 1

(2)

(iii) 6

(2)

■ Clean, clear layout for easy marking

Mathematics for Common Entrance 13+ Exam Practice Questions – Chapter 4: Algebra

846922_MFCE13_Exam_Prac_C04_043-065.indd 44 9 (a) (i) 14 a +35

(b) (i) 2(3 a +5)

(1)

(2)

(ii) 0

(2)

846922_MFCE13_Exam_Prac_C04_043-065.indd 43

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(ii) 4 a +2

(ii) 4 b (2 a – 3 c )

(2)

(iii) – 3

20 (i) 18

(1)

(3)

■ Includes worked examples and diagrams to aid understanding

10 (i) 6 p 2 – 13 p 3

(iii) 1 2

(2)

(ii) 12

(2)

(ii) – 2 h +30

(2)

– 1 4

(2)

(iii) 4

(2)

21 (i)

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11 (a) (i) 4 y 3

(b) p – 30 q

(1)

(3)

(ii) – 1 6

(2)

(ii) 4 y 6

(2)

22 (i) 390

(1)

(iii) 575.9

(1)

(iii) 4 4 y

(2)

(ii) 185.9

(1)

Mathematics for Common Entrance 13+ Exam Practice Answers – Chapter 4: Algebra

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2 8

2 9

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

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