KS2 Mental Arithmetic 3 Schofield & Sims

-

Name

Schofield & Sims Mental Arithmetic

The Language of Maths Boost your number vocabulary by learning the meanings of the maths terms listed below - all of them are used in this book.

area - the amount of surface space inside the perimeter of a shape. We often measure area in square centimetres (cm') or square metres (m').

average - to find the average or mean of 3, 7 and II+-, you have to find the total of the numbers (3 + 7 + II+- = 21+-). You then divide the total (21+-) by the number of items in your list (3). 21+- divided by 3 = 8. The average is therefore 8. Use the same method to find averages of other lists of numbers. capacity - the amount that something will hold. We may talk about the capacity of a glass or the capacity of a football stadium. circle - a round two-dimensional (2-D) shape. A complete turn in a circle is 360 degrees (360 °).

distance - the word we use to tell us how far it is from one place to another. One way of finding out a distance is to measure it using a ruler or measuring tape. To calculate a longer distance (for example, one that you would travel on a bike or in a car) you can use this formula: distance= time x speed. perimeter - the distance all the way round the edge of something.

perpendicular - a line is perpendicular to another line if it meets it at right angles.

quadrilateral - a two-dimensional (2-D) shape with four straight sides and with internal (inside) angles that add up to 360 degrees (360 ° ). Some quadrilaterals have special names (for example, 'square' or 'parallelogram'). rhombus - a two-dimensional (2-D) shape. It has four sides that are equal in length. Its opposite sides are parallel. squared - a number that is squared is to be multiplied by itself (for example, '7 squared' is 7 x 7). We sometimes write squared with a very small number 2 placed after the number and raised up high. For example, '7 squared' is written as '7'' triangle - a two-dimensional (2-D) shape with three straight sides and three angles that always add up to 180 degrees ( 180 °). There are many different types of triangle (equilateral, isosceles, scalene, right-angled): try to find out about each type. 21+-hour clock - the clock that we use for timetables. The 21+--hour clock uses four digits. The first two are for hours and the second two are for minutes. For example, 1 .30 p.m. is shown as 13:30 on the 21+--hour clock.

Contents

Section I

Tests I to 12, covering revision of Book 2 plus the following topics:

Number: Thousands, hundreds, IOs, units. Place value. Reading and writing numbers to 10 OOO. Decomposition of numbers. Use of signs =, +, -, x, +, and associated vocabulary. Number facts to 18; IOs and units; hundreds and IOs. Multiplication and division tables 2 to 10. Multiplication with addition. Division with remainders. Four rules, miscellaneous examples.

Fractions: Practical applications. Easy fractional parts of given quantities. Equivalent fractions; addition and subtraction.

Money: Coins to £I . Coin manipulation; equivalents, conversions. Writing amounts as pence, as fs. Shopping calculations, change. Four rules, miscellaneous examples. Measures: Length: mm, cm; cm, m; m, km; mm, m. Mass: g, kg. Capacity: m� l. Fractional parts, conversions.

Time: Telling the time. a.m., p.m. Clocks: fast and slow. Miscellaneous examples using min, h, days, weeks, months, years. Finding periods of time. Time, distance, speed, km/h. Shapes and angles: Squares, rectangles. Circles - diameter. Triangles - identification by angles (right-angled, acute, obtuse). The compass, direction. Right angles, turning.

Section 2

Progress Test

16

Tests I to 12, covering topics from Section I plus the following:

18

Progress Test I Results Chart

17

Number: Multiplication by 10; by 100. Series. Square numbers

Fractions: Equivalent fractions including conversion of tenths to hundredths. Reduction to lowest terms. Decimals; tenths, hundredths. Equivalents. Multiplication by 10, b y 100, division by 10, by 100. Miscellaneous examples.

Money: Decimal fractions of £I . Unequal sharing. Discounts. Costings. Best buys.

Measures: Length. Mass. Capacity. Introduction of decimal parts. Approximation to nearest m, 5' m, km; kg, 5' kg;� 5' l. Reading dials. Interpretation of lines drawn to different scales.

Shapes and angles: Perimeter. Parallel lines. Perpendiculars. Rhombus. Circles: circumference; angle at the centre. Number of degrees: in a triangle, in a quadrilateral.

Time: Equivalence; s, min; s in 1 min; in � min; in min. Conversion: 12-hour clock times; 21.+--hour clock times. Miscellaneous problems.

t

Section 3

Progress Test 2

30

Tests I to 12, covering topics from Sections I and 2 plus the following:

32

Progress Test 2 Results Chart

Number: Averages. Approximation to nearest whole, 10, 100, 1000.

31

Measures: Mass/capacity relationship of water: I kg, 1 l; I g, I ml

Shapes and angles: Radius. Hexagon. Triangles: identification by sides (isosceles, equilateral, scalene). Degrees in a straight angle. Parallelogram.

Time: Timetable; 21.+--hour clock. Days in a year, a leap-year. The calendar. Check-up Tests

Area: By counting squares; l x b. Comparison of surface area. Number

l+I+

Measures and Shapes

1+7

Money and Time

1+6

Section 1 ThH TU

2 3 4

5 6 7

8 9

10 11 12

Ell 1 2 3 4 5 6 7 8 9

10 11 12

Write in words the number shown on the abacus picture.

Test 1

ANSWER

ANSWER 1

(3 x 9) + 6

5+

= 13

mm

9 cm 4 mm=

237p = £ 80 x 10

£

mm

£6 =

FIFTIES

1 h 50 min = 300 - 175

24 + 28 == x + 12 Find the value of x.

3

How much greater is 4 x 7 than 4 + 77

evening

5 FIFTIES

min

min

Add four hundred to one thousand and ten. Answer in figures.

2

p

£

28p + 80p= £

�SWER

Multiply £0-40 by 8.

Write 87 to the nearest 10.

£

7

(54 + 9) + (6 x 6)

27p =

FIVES plus 6 TWOS

How many tenths in 1 ;? Subtract 36p from £1.

How many TWOS have the same value as 4 TENS?

Find the cost of one if 10 cost £1.

p £

0 7 9 1

Arrange these figures to make the largest possible number.

9

Find the diameter of each of the circles.

Divide 200 by 10.

Write as £s the sum of 26p, 28p and 50p.

By how much is the value of 15 TWOS less than the value of 9 FIVES? If 100 grams of grapes cost 30p how much will 350 grams cost?

8

p

This clock is 14 min slow. Write the correct time using a.m. or p.m.

6

Increase 29 by 33.

Find the change from a FIFTY after spending 28p.

Which of these numbers will not divide into 36 without a remainder?

4

(18 + 3) - (16 + 4)

3 TENS - 23p

2 4 6 8 9

10

£

11

FIVES

p

mm

If 2 kg costs 86p, how much will � kg cost?

£

Posts on a motorway are 100 m apart. Find in km the distance between 11 of the posts.

km

12

w

TWOS

x

v

Name the two rectangles each of which has three quarters shaded.

p

4

El 1

2 3 4

5

6 7

8 9

10 11 12

II 1

2 3 4 5 6 7 8 9

10 11 12

illl Th H T U

180 + 30

ANSWER

98 mm =

cm

mm

204 cm =

m

cm

(8 x 8) + 7

240 - 70

cm

mm

m

cm

£1·00

2

3

5

h

min

p = 53p

min

·h

p

6

Write in figures three thousand one hundred and fourteen.

Divide 1 metre by 5. Answer in cm.

7

����g

Find the change from a FIFTY after spending 16p.

Find the cost of one if 10 cost£2.

cm

8

p

9

p

How many eighths in 5 whole ones? ____8�

84p = 7 TENS +

TWOS

Find the sum of£0·24 and£0·69.

What must be added to 75p to make£1·50?

How many min from 7.47 a.m. to 8.15 a.m.?

One costs£0·49. Find the cost of 3. Find the difference between 7 x 9 and 9 x 6.

£

10

TWOS

11

p £

What number other than 1 , 3 and 27 will divide into 27 without leaving a remainder?

w

x

y

z

One quarter of a class of 32 children wear spectacles. How many children do not wear them?

Which 3 coins are given in change from£2 after spending£1·35?

� 0�,j [;t �

Write the total mass of the 4 tins in kg and g.

ANSWER

By how many g is 820 g less than 1 kg?

Take two thousand and twenty from 2222.

Which of the triangles is a right-angled triangle and has two equal sides?

TWENTIES

� of 25 + ; of 7

22 + 8 + 34

1

4

TWENTIES

75 min =

ANSWER

Write in words the number shown on the abacus picture. � -- - _ _ _ - _ _ _ - - _ _ _ _ _ _ _ -

600 + 10

£4 =

Test 2

Section 1

min

12

If Jack walks at 6 kilometres per hour, how far will he walk from 8.30 a.m. to 11.00 a.m.?

km

Find the difference between (7 x 10) and (7 x 100).

Mother bought a box containing 500 straws. If she uses 20 straws each week, for how many weeks will the straws last?

Write the sum of£0·36, £1 ·24 and£1·40.

£

class 1 class 2 class 3 class 4 24 25 26 25 How many children altogether in the 4 classes? If meat is sold at£2 per � kg, how many grams can be bought for �)£1 (b) 50p?

5

g

kg

g �) -----=

g (b) ----�

Test 3

Section 1 1 2 3

4 5 6 7 8

9 10 11 12

II 1 2 3

4

5 6 7 8

9 10 11 12

ANSWER

910 + 90

1

18p + 7p = 1 TWENTY +

15 x 10

p

p

3

43 + 47

400 - 120

FIVES

2 TWENTIES 6 T ENS 9 FIVES 4 TWOS

g

1 h 45 min =

FIVES

TENS + 7p

TENS

(� of 42) + (� of 30)

Find the total of 29 and 81.

cm

Write 124 mm to the nearest cm.

cm

Multiply 6 by 7 and add 8.

TWOS

; kg costs£1 ·50. What is the cost of 100 g?

How many FIVES are equal to£2·75?

How many times greater is £4·20 than 42p?

How many days altogether in the 6th and 7th months of the year?

How much change from 4 TWENTIES after buying 8 buttons at 9p each?

Katie made this list of the coins she had saved. How much had £ she altogether ? ----

1 TWENTY and a FIVE were given as change from£2. How much had been spent?

•

How much greater is the distance round the rectangle than the distance round mm the square?

20 mm

8

£

Write the missing signs + , - , x or -;. in place of • and• . 9 e 4 = 25 • 5

7

p

Decrease 20 cm by 20 mm.

£0·68 = 1 FIFTY +

6

ANSWER

What is the change from a FIFTY after spending 19p and 18p?

What sum of money is six times greater than£0· 197

5

min

min

If 1 kg costs£1, find the cost of (a) 100 g

(a)

(b)

(b) 300 g.

9

£

10

TWOS

11

p FIVES

Add three-quarters of 24 to one-seventh of 56.

5 biscuits of equal value cost 40p. What do 3 of the biscuits cost?

Tom

400 m

I

School ) I(

I

6

p

p

600 m

Tom and Sophie travel from home to school and back once a day. How many km more does Sophie travel in 5 days than Tom?

p

p

Samina was born in January but Hassan was born 5 months earlier. In what month was Hassan born?

12

days

g

(4 x 0) + (1 x 9) + (10 x 1)

4

1 kg - 250 g

£2·67 =

z How many more grams must be placed on pan Z to make the scales balance?

p

(10 x O) + (4 x 8)

£3 =

Write this date in figures.only. T he twenty-first day of August nineteen eighty-three

2

A FIFTY - 18p

ANSWER

Sophie

km

Test4

Section 1

El 1 2 3 4 5 6 7 8 9 10 11 12

II 1 2 3 4 5 6 7 8

9 10 11 12

485 =

tens + 5 units

2; kg =

g

2000 + 900 + 70 + 6

9000 + 10

37 + 4 =

rem.

4

TV-./OS

TWOS

1 litre - 350 mi

mt'

(9 x 9) + 8

5

ANSWER

� of a number is 8. What is the number? Multiply £2·08 by 6.

Add 6 to the product of 7 and 7.

7

£

p

8

Find the remainder when 71 is divided by 8.

28p plus 46p plus

9

p = £1

p

Add the odd numbers between 24 and 28. Increase 12, cm by 25 mm.

How many metres in 25 cm x 8?

m

8 badges cost 64p. What did one cost?

11

p

How many years from 1875 to 1985? If one costs £0·05, find the cost of 100.

10

cm

1

A man walked steadily from 11 a.m. to 2.30 p.m. at 5 kilometres per hour. How far did he walk?

Find the change from £3 after spending £1·38 and £0·22.

If 6 lemons cost 90p what is the cost of (a) 1 lemon (b) 4 lemons?

6

Subtract £1·27 from £2.

Write the time 12 hours after 8 p.m Use a.m. or p.m.

km

(a) Which of the shapes has two pairs of parallel lines, four sides of equal length and four right angles? ..:...(a)-'- ___ _ (b) (b) Name this shape. -----

p

3103 + 97

ANSWER

3

p

rem.

p - 8p = 5p

£2 =

2

mm

mm

£1·00 - 82p

1

TENS

g

25 cm =

B

ANSWER

12

By how many is i of 20 greater than,;3 of 20? -

7

..:...(a..c...) ____,__P

-'-(b)_ __�P

Write the total capacity 570 � 570 of the 3 cans � mt mt in £ and mt'. £ mf -----

In a class of 14 boys and 16 girls 3 children were absent. What fraction of the children were (a) absent (b) present? (a)

+

(b)

A boy faces North. He turns left until he faces East. Through how many right angles does he turn?

How many packets of sweets each having a mass of 250 g can be made from a 4;-kg pack?

The distance round a triangle having equal sides is 54 cm. Write the length in mm of each side.

mm

A packet of biscuits has a mass of 188 g. Write the mass of 10 packets (a) to the nearest 100 g _(a_) --�g (b) to the nearest kg.

£

£

_(b-'--) ___k�g

Test 5

Section 1

ANSWER

ANSWER 1

A FIFTY - 13p

2

500=

3

2 - 32

4

186 cm=

5 6 7

8 9 10

11 12

tens

tens

2200 + 800 167 mm=

m

cm

cm

mm

11.16 a.m. to noon=

210 x 10

15-6=

77p + 25p

1

p

min

m

cm

cm

mm

2

min

+3

3

How far will a cyclist travel in hour if he cycles at 18 kilometres per hour?

4

How many months in a year have 31 days?

5 £

(5 x 9) + 16

(72 + 9) + (0 + 3)

2 3 4

5 6 7 8 9 10

11 12

Find the sum of £1·80 and £0·18.

Subtract 40 mm from 15 cm.

Write in figures three thousand and fifty-nine.

Multiply 9 by 90.

Add £0·19 to £2·36.

Find the difference between £5 and £3·44.

Write in figures the number which is half of nine thousand.

Find the cost of one if 10 cost £25.

What fraction of the circle is (a) shaded (b) unshaded? ---(a) (b)

By how much is 25p divided by 5 less than 25p multiplied by 8?

£

Sundeep saved 55p each week for 8 weeks. How much short of £5 has he saved?

£

10

11

£

1

Sophie had 45p left after spending £1 ·08 and £0·27. How much had she at first? The children were placed in two mixed classes ...._____.______. of equal numbers. How many children were there in each class?

p

12

8

p

£

SILVERSIDE SCHOOL

NUMBER ON ROLL

cm

What is the product of 5 and 75?

km

8

£

Find in cm, f6 of a half metre.

What must be added to 13p and 16p to equal 40p?

A man travelled 400 km in 3 days. On the first day he travelled 130 km and on the second day 228 km. How far did he travel on the third day?

Tape costs 12p per 1 metre. Find the cost of 125 cm.

9

£

km

7

cm

Write in figures the time which is 4� hours after midday. Use a.m. or p.m.

TWENTIES

i

6

£

Olivia exchanged these coins for TWENTIES. How many did she geP

3 TENS 14 FIVES 8 TWOS 4 pennies

-------

ANSWER 1

Find the cost of 1� kg at.�p per kg. ----� p

BOYS 33 GIRLS 29

Write the missing signs +, - , x or + in place of • and"-. 9.5 ... 6= 8

•

Test 6

Section 1

II

ANSWER 1

2 3 4

5 6

8000 +

+ 40 + 8 = 8548

5 weeks =

days

days

420 + 10

£1·00 - 28p

p

1 e - 450 me

m£

1030 + 70

7

£1·50 =

8

6 +

9

63 cm + 38 cm =

10

1

(7 x 6)

TWENTIES + 2 FIVES

=9+4

+

(4 x O)

11

(� of 54) + (� of 12)

12

4 ( x 5) + (4 + 5)

m

2

Divide the sum of 4p, 6p, 8p and 1Op into 4 equal amounts. How much is each amount?

3

What number must be subtracted from 58 to leave 29?

2 3 4 5

6 7

5

18 + 9- x = 10 Find the value of x.

6

Find the change from£1 after buying 6 pencils at 14p each.

p

7

How much greater is £0·72 + 8 than 42p + 6?

p

8 9 10 11

12

cm

How many thirds in 3 whole ones? Divide£4·20 by 7.

9

cm

Subtract 60 cm from 11 m.

Write in figures the time which is 2! hours after 11 a.m. Use a.m. or p.m.

18p + 18p + 18p + 18p

8

p

1

£0·70 = 3 TENS + 3 FIVES +

£

What is the mass in kg and g of (a) kg g (a) the 6 tins of tomatoes ------� (b) kg g ---�--�

Which of the triangles is (a) a right-angled triangle (b) an acute-angled triangle (c) an obtuse-angled triangle?

p FIFTIES

£ Find the cost of 10 if one costs 25p. -----

How many biscuits each costing 4p can be bought for£2?

Find the total cost of 6 tins of �� tomatoes and 3 tins .......,_� of tuna.

10

p

p

£

� �l

(b) the 3 tins of tuna?

£

How many FIFTIES would be exchanged for£9·50? Multiply£1·99 by 3.

, How much will 36 cards cost?

cm

Find the difference in cm between 5 m and 465 cm.

Find the sum of£0·48 and£1·54.

p

4

ANSWER 1

From five thousand subtract nine hundred. Write the answer in figures.

TWENTIES

m

cm

ANSWER

11

£

12

9

(a)

(b) (c)

Take 4 of 100 from 10 of 100. 1

7

How many minutes longer is it from 9.10 a.m. to noon than from 1.30 p.m. to 4.00 p. m.?

min

Section 1 1 2 3

4 5 6 7

8 9 10 11 12

1

3,:1 metres =

cm

2000 +

8 9 10 11 12

p

3

Find the cost of 500 g if 200 g cost 40p.

4

How many times larger than 25 is (a) two hundred and fifty

min

(b) two thousand five hundred?

17 - 8 - 4 25 TWOS =

5

TENS

TENS

(49 + 7) + (36 + 6)

Find the product of 6 and 14.

Find the total of the odd numbers between 6 and 12.

7

A car travels at 75 km/h. How far will it travel in 4 hours?

4046 + 54

3

6

2

(9 x 7) + (8 x 5)

How much greater is £5 than £3·31?

5

h

ANSWER

£

How many fifths are equal to eight tenths?

Write as £s the value of 39 FIVES.

10

cm

How many times smaller is 80 than 8000?

£

A concert started at 7.15 p.m. The programme lasted for 1� hours. There was also a 10-minute interval. At what time did the concert end?

Find the change from £2 after buying 3i kg at 40p per kg.

cm

Write 96 mm to the nearest cm.

(b) -----

(b) mm.

(a )

(b)

p.m. cm

mm p

Five less than three thousand one hundred. Write the answer in figures. 1 30

35

39

42

How much greater is the sum of the odd numbers in the box than the sum of the even numbers?

p

Find the difference in length between 1 � m and 135 cm.

(a) -'-'-----

7

8

g

4 pencils cost 60p. Find the cost of 1 pencil.

£

Write 4 m 45 cm as (a) cm

p

Subtract 200 g from i kg.

km

6

9

Multiply 12p by 7.

100 cost £4·00. What is the cost of one?

Ahmed has £1 ·56 and Ka.tie has £1 ·44. If they share their money equally, how much £ does each have?

mf

A FIFTY - 21p

70 x 100

1

£

+ 6 = 2036

From noon to 4.15 p.m. h min

ANSWER

cm

mf

2

4

ANSWER

£1·50 + 65p = £

1 £ 600 mf=

Test 7

11

p

12

10

Emily has 80p pocket money. She saves � and spends the remainder. How much does she (a) save

•

(b) spend?

(a )

p

(b)

p

9 trays each containing 6 cakes were bought for a party. If 9 cakes were left over, how many had been eaten? Write all the numbers between 40 and 60 which can be divided by 7 without a remainder.

Section 1

Test a

II

ANSWER

1 2 3 4 5 6 7 8

1

2x 2x 2

p + £1·28 = £1·50

290 + 120

21 metres =

p

cm

3000 ..,.. 100

cm

10p + 10p + 5p - 14p 110 mm =

28 FIVES =

11 12

(b) the length of the rectangle.

g 4

days

days

a of 27) - (� of 8)

5

2 3 4 5 6

1

8 9

10 11 12

Find the change from 2 TWENTIES after spending 23p.

p

kg

Write 4750 g to the nearest kg. Find the product of 8 and 65.

7

How many months in 5 years?

What must be added to£2 · 5 2 to make£5? A 64-cm strip is cut into eight equal pieces. Write the length in mm of one piece.

£ mm

Multiply 16 by 7.

Decrease 5 4 m by 50 cm. Answer in m.

Find the difference between (136 + 66) and (10 x 20).

How many TWOS have the same value as 20 FIVES?

£

11

12 TWOS

11

cm

This clock is 12 minutes fast. What is the correct time? Use a.m. or p.m.

Mr Brown is 34 years 5 months old and his wife is 33 years 8 months old. How many months older is Mr Brown than Mrs Brown?

months

A B c What fraction of � � � 1kg is each mass? 9 A

m

p

Find the value of n. 13 + 19 = n + 25

� � �

1

If 1 costs 9p, find the cost of 100.

10

km

The distance round the rectangle is 20 cm. If the length is 6 cm, what is the width?

morning

9

cm

(b )

4 sweets cost 9p. Find the cost of 20 sweets.

8

How many badges costing 6p each can be bought for£3·00?

cm

(a)

A boy cycles at a speed of 9 km per hour. At this rate, how far will he travel in 3� hours?

6

ANSWER

1

What is the number nearest to 60 which will divide by 9 without a remainder?

Find in cm (a) the width of the rectangle

TWENTIES

(7 x 6) + (8 x 0)

48 hours =

cm

3

cm

9

10

What must be added to 25 cm ' ... and 39 cm to make 1 metre?

p

cm

TWEN TIES

2

ANSWER

kg

B

kg

kg

c

Write these fractions in order of size, the smallest first. �' fa, { Write the missing signs + , - , x or ..,.. in place of • and .A . (5 e 5) A 5 = 20

•

Section 1

Test 9

ANSWER

1

£2·40 + 70p = £

£

6p x 100 = £

£

cm

2

3 4

5

6 7 8 g

10

11 12

II 1 2 3 4

5 6 7

8 g 10

11 12

cm

17 mm + 18 mm= (6 x 8) - (4 x 7)

£3·00 - £2·18 =

59 ..;.- 6 =

rem.

p

4500 m = 6 ll =

24 months =

years

11.25 a.m. to 12.15 p.m. =

cm

A

cm

p

3

p

4

years

Add twenty-five to one thousand and eighty.

Find the cost of one if 10 cost £5- 40. How many sixths in �?

How many me must be added to 270 me ta make ; litre?

Find the total of 4� m and 2; m.

Write 5300 g to the nearest kg.

Divide the sum of 19 and 16 by 5.

How many FIFTIES can be exchanged for 75 TWOS?

c'

B

'o

mm

Tom has 29 ca rds a nd James has twice as many. How many have they altogether? How many bottles each holding 300 me can be filled from a can holding 1 e ?

i

Write, in cm, the distance all round this regular hexagon.

cm

� 25 mm

Subtract 8 from 103.

By how many cm is 2 m greater than the sum of 80 cm and 90 cm?

t��1�l�111!111�l�111l111�l�111l111�l�111I111�!�111!111�1�}

5

ANSWER

Find six tenths of 80 cm.

p

By how many mm is the line AB longer than the line CD?

min m1n -----

Write the name of the coin which has the same value as £0·10.

Subtract (50p x 10) fmr.o (5p x 100).

2

km

km

quarters

1

rem.

A FIFTY - 12p

ANSWER

cm

6

How much greater is � of 12 than � of 12?

7

A car travels 40 km in 30 minutes. If the car travels at the same speed, how far will it travel in 3 hours?

km

8

The diagram shows how the children shared £5. How much did each child have?

cm

Hassan £

9

p

10

me m

11

kg

Olivia £

Which 3 coins are given in change from £1 after spending 83p?

P __P_ __P_ __

If January 27th 1s a Wednesday, what date is the following Wednesday?

The scale shows the mass of a bag of nuts.

How much will it cost if the price is 30p for 100 g? 12

FIFTIES

12

Ali £

By how many is 15 times 100 less than 3 times 1OOO?

f

Section 1

Test 1 0

II

ANSWER 1 2 3 4

[

5 6 7 8 9 10

11 12

1 2 3 4 5 6 7 8 g 10

11 12

£1 ·00 - 14p

cm

15 mm x 10 = £1 ·50 + £2·60

5450 m =

27p x 4 = £ 56 FIVES =

5 days =

km

m

km

� of £3·00 =

p

p

TWENTIES

£ £

hours

(56 + 7) - (9 + 9) "1 f - 389 mf = 1

1m =

p

1WENTIES

hours

1

From the sum of 24 and 29. �ke 13. -----

2

Arrange the figures 4, 0, 2, 5, to make the largest possible even number.

3

The distance round a square is 72 cm. What is the length of one side?

4

Write the next two numbers in this series. 8, 4, 2, 1,

5

A -------------- B

cm

m

mm

How far is it from C to B?

ANSWER

Half of a sum of money is 49p. What is the whole amount?

7

What is the smallest number into which both 4 and 6 will divide exactly?

8

A school was opened in 1958. How many years will the school have been open by the year 20207

9

If 1 litre costs 70p, find the cost of (a) 100 mf (b) 400 mf. (a)

p

How many 10-cm lengths are there in 5 m? Multiply the sum of 5 and 4 by 8.

p

How many p in ! of 40p?

7 x y = 98 Find the value of y.

Write the time j h before 12.05 p.m.Use a.m. or p.m.

10

420 minus 80 equals 300 plus

Find the difference between � and

cm p

13

9 TWOS 3 FIVES 7 TENS

p --� (b) p

Katie had these coins. How much more is needed to make her money up to £1 ·20?

p

•

11

Write the missing sign + , - , x or + in place of • and A . (12 e 3) A 6 = 10

12

Which two coins are gi ven in change from £2 after spending 83p and 66p? __P __ P

t - - ---

How much short of 3 m i s 265 cm?

Add 3 TENS, 7 FIVES and 6 TWOS.

£

m

A boy stands at point x and faces point y. In which direction is he facing?

6

Increase 57 by 35.

What is the cost of 8 if one costs £0·19?

920 m

mm

(9 x 6) + (10 x 5)

cm

680 m

mf

me

ANSWER

Section 1

Test 1 1 ANSWER

ANSWER 1 2

3 4 5

6 7 8

9 10 11

II 1

2 3 4

5

1 m 50 cm + 10 j: kg + 375 g

7300 7 100

=

=

g

£3·00 - £1·13

£

£2·47 + £1 ·63

£

450 km - 360 km mm

(7 x 8) - (5 x 6) 25 mm x 8

=

Write the next two numbers in this series. 49, 42, 35, Find the total of£2·36 and £0·99.

fa of a sum of money is£45. Find the whole amount.

Write in cm the length remaining when 10 cm is reduced by 55 mm.

8

11 12

km

3

mm

What is the difference between 42 and 420?

Write 250 mm as m.

Add 2 times 9 to 5 times 9.

If 5 sweets cost 30p, what will 15 cost?

I n the number 9440, how many times greater is the 4 marked x than the 4 marked y?

What fraction of 1 hour is (a) 20 minutes

min

5

PAC K OF 4 for 90p

7

Which number when multiplied by itself equals 64?

8

v·

g

9

p 12

14

m

Lucy has three times as much as Daniel who has 45p. How much have they altogether?

cm m

£

This is a plan of a playground. How many times round it must the children run in order to run 1 km? If j: kg costs 40p, find the cost of (a) p (a) 100 g (b) 600 g. ----'In the number 6365, what must be added to the 6 marked y to make it equal in value to the 6 marked x? x

xy

h

(b)

m

11

g

Write the length of a line 100 times longer than the line YZ (a) (a) in cm

10

p

h

,�.�.�t. ,...�1�."'"J�··il11·�I�,,.1,..�r.,1..,�t.·111,�1· z �}

(b) in m.

cm

(b)

How many hours will it take a car travelling at 70 km/h to travel 280 km? By how many m is the sum of 870 m and 650 m more than 1 j: km?

£

h

How much will 20 cans cost? £

6

£

(a)

8 kg 500 g is divided into 10 equal quantities. What does one of the quantities weigh?

4

cm h

In a class library there are. 138 fiction books and 144 non-fiction books. How many books are there altogether?

(b) 40 minutes?

Write the name of the coin which has the same value as£0·02

Six cost£2 ·16. What is the cost of one?

10

2

ANSWER

How many g are there in Yo kg?

9

£

cm

10.24 a.m. to 12.10 p.m. h min

1

g

f of£16

6

7

cm

cm

y

p (b)__,___

.;__;_

Section 1

II 1 2 3 4

s 6 7 8

9 10 11 12

II 1

2

3 4 5 6 7 8 9

10 11

12

100 x 21

cm

14 cm + 1 5 cm + 16 cm

3x 3x 3

TEN5 + 6p m

8 a.m. to 6 p.m. =

1 ; kg - 600 g =

(5 x 7) + (10 x 8) £ £ - 200 me =

g

s

g

6

7

ANSWER

Write 1560 mm as m and mm.

How many 30-cm lengths can be cut from a 3-metre length?

me

(36 + 9) + (100 + 10)

Find the sum of 73 and 48.

2

m h

me

Divide the sum of 7, 11 , 6 a� 4 by 7.

4

TENS

h

1

3

£

28p + 25p + 45p = £ -fu of 1 km =

B

ANSWER

5505 - 500

£10·46 =

Test 1 2

8

Find half of the sum of 12p and 18p. ----� p

9

What is the product of 4, 5 and 6?

How many eighths are there in 7 whole ones?

Find the cost of 24 articles at 6p each.

What is the remainder when 61 is divided by 9?

Find the cost of 3� metres at 16p per m.

300 pencils cost£18. Find the cost of (a) 100 pencils (b) 10 pencils. (a)£

(b)

What must be added to 7 + 9 to equal 7 x 9?

t

Through how many right angles does a boy turn when turning from East to West?

CHESS SET

I LIST PRICE £3·60

Daniel goes to bed at 7.45 p.m. and gets up at 7.45 a.m. How many hours is he in bed?

1 50 cm

1 30 cm

£

h

Amy

£

T he diagram shows two children's heights. How much taller is Fatima than Amy cm (a) in cm (a)

(b) in mm? (b)

mm

1 20 cm

What number is 101 less than 1OOO? Add the numbers between 20 and 35 which can be divided exactly by 8.

£

1 40 cm

How many years are there from 1984 to the year 2020? 100 cost£10·00. Find the cost of one.

Find the cost of 2 e 250 me if 1 e costs£2.

William bought the chess set at a quarter less than the list price. How much did he pay?

mm

m

ANSWER

10

How many 200-mf bottles can be filled from a can holding 4 n

11

What is half of 3;?

12

p

There are 2055 people in a village. Write the number of people (a) to the nearest 10 (a) ----(b) to the nearest 100

(c) to the nearest 1OOO.

(b) ---(c) -----

Next work Progress Test 1 on page 1 6. Enter the result and the date on the chart.

p

15

PROGRESS TEST 1 Write the numbers 1 to 20 down the side of a sheet of paper. Write alongside these numbers the answers only to the following questions. Work as quickly as you can. Time allowed - 10 minutes. 1 2 3

4

5 6

7 8

170 + 280

a of 45) - (j of 63) (8 x 8) + (6 x 6)

(450

+

10) - (3500

+

100)

Write in figures nine thousand and sixteen.

0

The diameter of this circle is 1 cm 6 mm. What is the radius of the circle in mm?

Add the numbers between 40 and 50 which can be divided by 7 without a remainder. 3 4

2 5"

5 li

3 g

5 TO

25 TOTI

Which of the fractions has the same value as a half?

9

� � (fijJ

How much more than 1; kg is the total mass of the three boxes?

10 11 12

13

14 15

Which 3 coins are given in change from £2 after spending 60p and 78p? Find the cost of one pencil if 10 pencils cost £1·10.

+

How many minutes are there from 11.17 a.m. to 12.15 p.m.?

A boy stands facing West and turns left through 3 right angles. In which direction is he then facing?

Find the cost of 300 mf if ; f costs 35p.

If a car travels at a speed of 80 km/h, how far will it travel from 9.30 a.m. to noon?

16

The diagram represents the 64 cars which passed a school in one hour. How many of the cars were blue?

17 18 19

20

What fraction in its lowest terms is 900 g of 1 kg?

Write to the nearest £ the sum of £3· 80 and £2·69. Find the cost of 100 buttons if one button costs 8p.

[,oc,1

�

50 TWE N T I ES

Write as £s the total of the contents of the packets.

This page from Mental Arithmetic 3 may be photocopied after purchase for use in the purchaser's teaching establishment only.

16

© Schofield & Sims Ltd

PROGRESS TEST

1

RESULTS CHART

You wi l l work Prog ress Test 1 at four d ifferent ti mes. When you fi rst work the test (a) col o u r the fi rst col u m n to show the n u m ber of exa m ples co rrect o ut of 2 0 (b) enter t h e date. Each time you work the test, enter the resu lt a nd the date i n the ma rked col u m ns.

20

1 st

2 nd 3 rd

4th

19 18 17 16 v

Cl>

0

v

Ill

Cl>

-

E

Cl>

0

Cl>

E

15 14 13 12 11 10 9 8 7 6 5 4 3 2

0 ..,___..,___..,_..,...,....,.

This page from Mental Arithmetic 3 may be photocopied after purchase for use in the purchaser's teaching establ ishment only.

17

© Schofield & Sims Ltd

Test 1

Section 2 1 2 3 4

5 6 7

8 9

10 11 12

El 1 2 3 4

5 6

7 8 9

10 11 12

II

ANSWER

7 + 33 + 9

1

8 1 4 ..;- 2

(19 + 5) - (7 + 8) Li m = 1

1 minute =

mm

9 + 9 + 9 +9 �= 3

3

From 1 0.1 4 a.m. to noon h mm

4

h

1 FIFTY - yp = 1 7p. Find the value of y in pence. 61 ..;- 8 =

TB

£

34p x 6 = £

8 2 = 50 +

min

7

ANSWER

There is 69p change from£2. How much has been spent?

Write 1 700 g to the nearest kg.

£

Take 6 plus 5 from the total of 8 and 1 7. (a)

Find the sum of the odd numbers between 56 and 60.

Which 2 coins must be added to a FIVE and 3 TWOS to make 23p? Find the cost of 2� kg at 28p per kg.

8

kg p

Divide£2·94 by 6.

9

s (b)

Find � of 84.

George had £1 . He spent 28p on nuts and 42p on bus fares. How much had he left?

p

The perimeter of this square is 60 mm. Find the length of one side.

j 1 TWENTY

2 TEN S

8 FIVES

Torn exchanged these coins for FIFTIES. How many FIFTIES did he get7

10

p __P p

11

12

p

18

mm £

1 0 TWOS I FIFTIES

The first day of Joshua's holiday was June 29th and he returned to school on August 3rd. For how many days was he on holiday? Sophie 1

Shahid 1

2

Sam 6

Sophie The diagram shows how the children Shahid shared£4·20. How much did each receive? Sam

s

h

How many 600-mf bottles can be filled from 6 f ?

3

What must be added to 5 plus 80 to equal 5 multiplied by 80? ---If 2 f cost 48p, find the cost of i t

A plane flew 2400 km at a speed of 800 km/h. How long did the J ourney take?

(a) - -(b) �----

Ahmed has 28p and his sister has 4 times as much. How much have they altogether?

rem.

Write in figures nine thousand seven hundred and nine.

Write as a decimal fraction (a) the shaded part

5

p

rem.

How many seconds in (a) � min (b) 1 i min?

2

s

tenths

I ·I� I

(b) the unshaded part.

mm

seconds

ANSWER

The sum of 3 numbers is 94. Two of the numbers are 36 and 3 5 . What is the third number?

How many weeks will it take Chen to save£5·00 if he saves 2 5p each week? 6__ _ 72�1 64____ 1 3_ � _5 4____

Which two of these numbers can be divided by both 4 and 9 without a remainder?

£

£

£

Section 2

Test 2 ANSWER

ANSWER 1

1

25 + 5 + 1 6 + 4

2

2009 - 1 0

3

85p x 4 = £

4

900 mf + 870

5

3 =

6

30 - (7 x 4)

7

2670 m +

8

£2 · 58 + 3

9

( 1 5 - 6) + (33 - 4)

18

2

£

me

me

me =

m

3

4

1 80 + y = 9. Find the value of y.

11

Find (a)

12

22 + 32 =

(b)

7

s of 72 .

(a)

Clock X is 1 8 m i n fast

(a)

(b)

Clock Y is 25 min slow.

(b)

Find the cost of 61 metres of ribbon at 1 8p per metre .

£

A tin of fruit has a mass of 4509 . Find to the nearest kg, the mass of 6 tins.

Which line is para l lel to the l ine AB?

ANSWER

6

1

Write as a deci mal fraction 5 3 (a) w (b) Tii·

2

How many h and m i n i n 9 5 m i n?

3

Which 3 coi ns together eq ual 57p? ____e ____e ____e

4

Su btract 50 from 8000 .

5

Write 43 5 cm to the nea rest 1 m .

6

If 1 0 marbles cost 3 2 p, what will be the cost of 40 ma rbles?

7

What is the total of seven, twenty­ n i ne and fou rteen?

.:._: (a)_ _ (b)

1 kg costs £ 1 · 2 8. What is the cost of 250 g?

h

kg

5

(b)

(a)

II

8

lt11·I

p

10

� of 72

li·MI

km

Write, i n 24-hour clock time, the correct time fo r each d ig ita l clock if

whole ones

m = 3 km

A ca r travels at 1 00 km/h . How fa r will it travel i n 1 5.mi n?

min

7

m £

p

9

9 FIVES plus 6 TWOS

p

10

How many g m ust be added to 970 g to make 1 1 kg?

g

11

M u ltiply the sum of 1 6 and 9 by 8 .

12

Su btract 8 from the product of 9 and 7 .

(a)

obtuse

(b)

acute?

(a) ----(b) -----

9

Find the difference between (8 + 8 + 8 + 8) and 8 ti mes 6 .

12

p

Which o f the ang les w, x, y, z are

What must be added to one-sixth of 48 to equal ; of 637

11

19

Jessica bought the following : ca rrots 45p, potatoes 6 5 p. H ow much change d i d she get from £ 2 7

8

10

-----

What is a half-share of the sum of 6 FIVES and 8 TWOS? TOMATO PUREE 21 p per tin

* 6 tins for £1 · 1 4

How much i s saved per tin by buying 6 tins at a time?

50 m i l k straws a re used on each of 5 days in a week. H ow many weeks will 2000 straws last?

p

p

Section 2

Test 3

ANSWER 1

2 3 4

s

6 7 8 9 10 11 12

II 1 2 3 4 5 6 7 8

9 10 11 12

ill

T U tenths

(5 x 6) + 4

80 tenths 3 =

ANSWER 1

Write the number shown on the abacus picture as a decimal.

Write the length of the line YZ (a) (a) in cm and mm mm cm -------

units

=

sixths

(b)

2

46 + 64

125 x 4 4 min =

3

s

s

(9 + 9) - (4 + 8)

(32 + 4) + (O + 8)

£8·54 + 7

1 1 2 km - 560 m

£5·00 - £

=

£

m

= £3·46

£

m

6

How many h and min from noon to quarter to four in the afternoon?

cm (b)

cm

h

min

Write 6 m 875 mm to the nearest m.

7

l of a sum of money is 21p. Find

9

Multiply 6 by 6 and divide the answer by 9.

Add the even numbers between 35 and 39.

A

L

How much will be paid for an article which cost £3 before the sale? £

E

ALL GOODS REDU CED BY 15p IN THE £

Find the sum of money which is 30p less than the sum of 7 TENS and

I l

1 3

1 5

5 8

p

6 4

The perimeter of a square is 10 cm. Find the length of one side (a) cm mm (a) in cm and mm ------cm (b) -------

A shopkeeper wrote 130 kg on an order form instead of 13 kg. By how many kg was the order too much? kg Write in figures the times shown on the clock faces.Use a.m. or p.m. (a )

morning

10

p 11

How many FIVES are equal in value to £7?

Make each of the following 10 times smaller (a) 8 (b) 131.

S

p

Find one half of four thousand five hundred. Write the answer in figures.

Subtract the sum of 23p and 28p from £1.

How many days altogether in April, May and June?

(b) in cm.

m

8

Find the total of (16 + 9) and (5 x 5).

p

Which two of the fractions when added together equal one whole one?

p .Find the cost of 4i kg at 16p per kg. ----�

the sum of money.

cm (b) -------

7 TWOS .

ANSWER

Write as a decimal fraction of a cm (a) 5 mm (b) 8 mm. (a)

Find the difference between 1 3 4 of £0·76 and 4 of £0·76.

4

5

in cm.

12

(a) (b) ---

20

evening

(b)

In a class of 28 children, there were 4 more girls than boys. How many boys were there in the class?

Cups cost 44p each and saucers half as much. Find the total cost of £ 6 cups and 6 saucers. -----

Emily and Lucy are twins. For their birthday they were given 3 FIFTIES and 9 TWEN TIES which they shared equally. £ How much did each have?

Section 2

El 1

7.6 cm + 4 mm =

3

p

5 6 7

8 9

10 11

12

D 1

2 3

p = 27p

( 1 7 - 8) + ( 1 1 - 7)

10 of 1 I' = 1

me

3

quarters

(8 x 3) - (0 x 5)

17p x 7 = £

Find (a) � of £45

(b)

(b) � of £45.

44 ..,. 9 =

rem.

·,

5 6 7 8

9 10

11 12

£

4

£

5

rem.

15 FIVES + 3 TENS

£ 6

ANSWER Write as a decimal (a) 36 tenths (b) 104 tenths. (a)

(b)

7

-'-'----

By how many is 44 greater than 1 97 ----Write as a vulgar fraction in its km lowest terms (a) 100 m of 1 km (a)

____

8

Find the cost of 20 packs of sweets £ if 5 packs cost 77p. ----From half-past eight to twenty to ten in the morning = h min h min

9

From the product of 1 0 and 1 0 subtract 1 3. Find five-sixths of £54.

How many me must be added to 4i e to make 5 e ?

Make each of the following 10 times larger. (a) 0.7 (b) 2.3 Multiply 6 1 p by 9.

Which 3 coins make up 54p?

.:....;___

(b)

km

ANSWER

p

Sophie walked at a steady speed from 1 0 a.m. to 1 2.30 p. m. She covered a distance of 1 0 km What was her walking speed in km/h?

@

(b) p --�

The circumference of the wheel is 1.5 m. How many m will the wheel travel (a) in (a) 1 0 turns

km/h

(b)

It takes Mrs Brown 75 minutes to get to work. At what time must she leave home to arrive at work at 8.30 a.m.? F

M

N

W

X

m

m

Z

In which of these letters are there two pairs of parallel lines? (a) How many SOO-me bottles can be filled from 5 e ? (b) How many SO-me bottles can be filled from 5 e 7

When a number is divided by 8 the answer is 6 remainder 6. What is the number?

(a) -----

(b) -----

Find the missing numbers in this series. 1.6, 1 .4, 1 .2, Name (a) the acute-angled triangle ----(a) (b) the right-angled triangle

10

£

11

me

12

� �

£ -----

(b) -----

(c) the obtuse-angled triangle. -'-'----(c)

Josh had £ 1 80 and Leah had half as much as Josh. How much had they altogether? Find the cost of 90 g of wool at 40p for 20 g. � of £ 1 2

11

� of £ 1 2

What is the value of (a) the largest of these amounts

11

£ £

i of £12 (a) £ -----

(b) (b) the smallest of these amounts? ----£ Turn back to page 16 and work for the second time Progress Test 1 . Enter the result and the date on the chart.

_ __ P __ P _P

Write the missing signs + , - , x or ..,. in place of • and A . 1 4 e 7 = 35 A 5

Find the whole amount of money when (a) � is 30p (b) � is 40p. (a)

(b) 1 00 turns?

£

(a)

(b) 700 m of 1 km

4

2

me

1 0 OOO + 900 + 8

3 43 =

1

cm

cm

Write as a decimal 1 00 + 1 0 + 1 + �-----

4

II

ANSWER

2

50p -

Test 4

•

21

Test 5

Section 2

El 1 2 3 4 5

6 7 8 9 10 11 12

2.9 =

49 + 63

tenths

tenths

1 x 2 = "°T6· Find x.

(8 x 5) + (3 x 7)

10 m - 5.5 m =

84 - 57

3£ km + 300 m =

2

m km

From 10.20 a.m. to 12.25 p.m. h

m1n

3 TWENTIES + 3 FIFTIES (30 ..;- 5) + (18 ..;- 6)

2

By how many cm is 2.4 cm less than 6 cm?

5 6

7 8 9

10 11 12

m

h

min

4

p

6

ANSWER km 7

cm

What must be added to £3 ·66 to make £4·50?

Increase£2 ·46 by£1·26.

Find the cost of 20 cm at £2·00 per m.

Subtract 1 of£24 from £ of£28.

8

Write as a vulgar fraction in its lowest terms 900 me of 1f.

9

£

10

£

p

11

f

Which 3 coins are given in change from£3 after spending£2·84? _____e _____e _____e Change 10 to hundredths. 8

After using oil from a can holding 3 e 300 me only 2£ e remained. How many me had been used?

me

Find the total cost of 4 magazines at £2 ·2 5 £ each and 3 comics at £ 1 · 50 each. ----£ 0·70 0·25 0·18

Find the change from£2 after paying these amounts.

p

5 5 cm Find the total length of the two lines in mm.

xy

37. 7 How many times greater is the 7 marked x than the 7 marked y?

C

rhombus which are perpendicular to each other.

6 7 cm

p

By how many is 25 minus 6 less than 25 plus 6?

km

Jg; B Name two lines in the D

5

What fraction of 42 is 7?

g

A plane flies at a speed of 900 km/h. How far does it travel in km (a) (a) 20 min (b) 10 min? -'------

3

£

10 articles cost£1 · 50. Find the cost of one article.

Write 9 km 700 m to the nearest km.

4

km

Find the difference in g between the masses shown by pointers X and Y.

(b)

m m

ANSWER

1

6090 ..;- 3

1

3

II

ANSWER

12

Too

22

mm

Mr Robb arrived home at 9 . 50 p.rr- . after travelling for 2* hours. At what time did he start his journey? 10 tins of beans have a mass of 3 kg. Find the mass in g of 1 tin. The bus fare to town is£1·80, and children travel half price. Find the total bus fare for 2 adults and 2 children.

A square has a perimeter of 1 m 60 cm. Find the length of one side in cm.

Lucy spent two-thirds of her savings when she bought a radio for £50. How much had she saved at first?

g

£ cm £

Test 6

Section 2 1

2 3 4 5 6

7 8 9 10 11

12

1 2 3 4

5 6 7 8 9 10 11

12

1 9 .4 cm =

mm

mm

(18 + 7) - (6 + 6) (4 x 1000) x 1)

(9

+

(8 x 100)

2

p

Write 4 r 500 me to the nearest f.

9.3 cm

28

+

+

25

g=

p

(a)

i kg

TI (b)

5 6

5 articles cost £1·10. 1 article costs p.

1 8 cm divided by 10 =

T8 cm

= 74

Multiply 4.3 by 10.

4

g

6.8 cm +

3

r

p

Write ; as a decimal. 1 b a 3 = 12 = T8 120 g +

1

+

£4·00 - £3·24

£ 1 · 32 -;- 6 =

El

ANSWER

p 7

cm

Write in 24-hour clock time (b) (a) (a) 8.00 a.m. (b) 8.00 p.m. ----10

8

+ 2999

From £4 take the total of £1 ·40 and £1·65.

9

p

3 batteries cost £2·25. Find the cost of one battery.

What is the cost of 3 kg 100 g if 1 kg costs £1?

What is the difference in mf between 2 e 700 mf and 2580 mf ? fa of a sum of money is £2·70. Find the sum of money.

___

.___

h

y x 10 = 320 What is the value of y?

Amy's father gave her 28p to make her money up to £ 3 · 1 5. How much had Amy at first?

£

1 m of ribbon costs £3·20. Find the cost of 1} m.

£

t N

In which direction must (a) Ahmed walk to � reach Hassan (a) ----(b) Hassan walk to H assan reach Ahmed? ----(b)

A 2p coin is 1 .8 mm thick. Find the height in mm of a pile of (a) mm (a) 10 TvVOS ----1 15

18

20

24

mm (b) -----

30

Which of these numbers can be divided by 2, 3 and 5 without a remainder?

Megan received 3 TENS, a FIVE and a TWO in change from £1. How much had she spent?

p

cm

B

T he line AB is drawn to scale and represents a distance of 2.5 metres. m What length is represented by 1 cm? ----10

£

11

mf £

By how many is 8 2 greater than 7 2 ? -----

Share £6 equally among 8 children. How much does each child receive?

If a man vyalks at a steady speed of 6 km/h, how long _, will it take him to walk to Derby?

A

p

How many 50-cm lengths can be cut from 18 m?

DE RBY 21 km

(b) 100 TvVOS.

ANSWER cm.

ANSWER

12

p

23

Find the difference between 4 5 s of £30 and ii of £30.

T he mass of three parcels is shown on the dial. If they are of equal mass , write the mass in g of one parcel.

A computer game can be bought for £27 cash or by 20 weekly payments each of £1·50. By how much is the total of the weekly payments greater than the cash price?

£

£

g

Section 2

El 1

2 3 4 5 6 7 8

9

10 11 12

II 1

2 3 4

Write as a decimal the number shown on the abacus picture

illl

50 - (6 x 7)

£

Find � of 28 kg.

6 7 8

9

10

11

12

3

p

p = 2 TWENTIES

p

g

£

£1·49 + £1·49 + £1·49 rem.

0.6 + 1.8 + 0.5

0.1 m =

2

kg

1 article costs 19p. 5 articles cost p. 1i kg - 700 g =

• .

£1·09 + 68p = £

4

g

ANSWER

Write as a decimal fracti6rr-the part of the whole square which is (a) shaded (a) (b) unshaded.

5

cm

How many hundredths are equal in value to (a) 0.4 (a)

How many cm are there in 1.8 m?

Change these 24-hour clock times to 12-hour clock times. Use a. m. or p.m. (a) (a) 06.00

(b)

2

C-o=,H 4

a.m.

7

(b)

8

Subtract 0.03 from a whole one. Write the answer as a decimal fraction.

Find the cost of 12 sweets if 2 sweets cost 5p. Find the difference between 30 multiplied by 10 and 30 divided by 10.

By how many g is 5 times 250 g less than 2 kg?

340.4 How many times larger is the 4 marked x than the 4 marked y ? x y

p.m.

hundredths km

Clock A shows the time. Daniel left home and clock B shows the time he returned.

How many h and min was he away? ----h min

cm

kg Write 6 kg 650 g to the nearest i kg.-----=-

By how many mm is 10.0 cm greater than 7.9 cm?

hundredths

A motor cyclist travelled for 1i hours at a speed of 60 km/h. What distance did he travel?

ANSWER

Multiply 6 by 47.

p

If 4; m of string is divided into 25-cm lengths, how many lengths will there be?

6

Write fa + ,}a as a decimal fraction. -----

(b)

How much less than £6 is the sum of £1·85 and £3 ·45?

(b) 0.9?

rem.

cm

(b)19.00

5

1

(19 + 8) - (6 + 7)

68 + 7 =

Ill

ANSWER

T U t h

33p +

Test 7

9

10

mm

11 g

12

How much greater is ; than ! ?

24

How many packets each with a mass of 100 g will together have a 1 mass of 3L kg? By hof many twelfths is � greater than 3 ?

Find the change from a £10 note after buying 6 toys costing £1·25 each. ----£

Yasmin's father pays ; of the cost of a bicycle. Yasmin pays the remainder. The cost of the bicycle is £70. Yasmin How much does each pay? 200 g of meat costs 80p. Find the cost of 1i kg.

D

Father

£

£

£ -----

The circumference of this circle is approximately 11 cm and the diameter is 3.5 cm. How much longer is the perimeter of the square than the circumference cm of the circle?

Section 2

El

£1·60 + 4

2

0.47 =

3

(0 x 9) + 8

6

250 + 350 + 400

8

Find * of 27.

7

20 = 1

12

1 2

3

4 5

6 7

8

10 11

12

2

£6·09 +

s

= £8·00

10 OOO - 100

5

ANSWER

6

7 8

p

Write 3 £ 800 me to the nearest f £. How many cm in (a) 3.6 m (a)

cm

9

cm

10

e

(b) 2.25 m? cm (b) Find the cost of 750 me if "J £ £ costs £0·74. Divide the product of 14 and 9 by 6. Arrange these figures Q to make the largest .... . ______._ possible odd number. ----How many hundredths are there in (aH (a)_ __1�0=0 _

I

4

(b)

i

(c) � ?

9 1

(a) £

(b) £

The sum of the three angles of a triangle is 180 ° Find the size in degrees of the angle o marked x. £ m

Mr Jones arrived at the station at 3.45 p.m. His train left at 16.20. How long had he to wait?

The dial shows the mass of a parcel in kg and g. How many g less than 3� kg is the mass of the parcel?

(a)

(b) 2.20 p.m. (b) Write as a decimal the number which is 100 times smaller than 6.

Multiply the sum of 7 and 5 by 10. From £2 take the total of 58p, 42p and 36p. Decrease 10 cm by 28 mm. Give the answer in cm.

(b) 1 p?

ANSWER

4

s

£

(81 + 9) - (24 + 3)

Write the total of 20, fo and ,6o as a decimal. Write in 24-hour clock times (a) 3.57 a.m.

What decimal fraction of £1.•_is (a) 1Op

3

hundredths

241 m1n =

9

11

hundredths

(42 - 5) + (21 - 4)

5

10

1

£

hundredths

4

B

ANSWER

10.0 + 0.2 + 0.05

1

Test a

11

I

12

(b)_ __1�0�0 _

After spending one quarter of his money Ali had 54p left. How much had he at first?

Find the total cost of 2 packets of crisps costing 35p each and 6 biscuits costing 1 Op each.

25

g p

£ -----

T here are 163 boys in a school and there are 37 more girls than boys. How many children are there in the school altogether? Put a decimal point in each of the numbers so that the value of the 8 is 8 units. (a) 4386 (a) (b) 2891

(b)

Katie has 1 7p and Emily has 25p. How much must Emily give Katie so that they each have the same amount?

p

� of a class of 24 children are girls. (a) What fraction of the class are boys? (a) ----(b) (b) How many boys are there? -'---'-----

Turn back to page 1 6 and work for the third time Progress Test 1 . Enter the result and the date on the chart.

(c�)___1�0=0 _

min

-Section 2

El 1

2

3

Write as a decimal fraction (b) 6 hund redths . (58

+

1 43 m1n

5) - (4

s

=

6

0. 4 x 1 00

8

3050 g

9

10 11

12

+

6

Find

8000

+

7 )53

'fu of 80. =

+

(b)

9)

£ 1 · 00 - 28 TWOS

g

=

s

7 2 - 62

rem .

g

kg

p

2 3

4 5 6 7

8

10 11 12

(a) £

(c) 1 FI FTY?

(c) £

(7 x 6) + (6 x 3)

£

28p x 7

Write 4 £ 1 50 mf to t h e nearest 21 I'1tre.

2

C h l oe is 1 . 3 5 m ta l l a n d Ja mes is 8 cm smal ler. cm What is J a mes's height i n cm?

3

H ow many bottles each holding � £ can be fil led from a cask holdi ng 6; e ? All the angles at the centre of the circle a re equa l . How many degrees are there 0 i n the marked angle?-----

5

How many cm less than � m is 0. 62 m?

6

A s u permarket sold one h u n d red 1 2 p p l u ms a n d twenty 9p p l u ms . What was the £ total va l u e of the p l u ms7 -----

7

The prod uct of two n u m bers is 56. One of the n u m bers is 7 . What is the other n u m ber? I ncrease 23 by 1 8 and m u lti p ly the a nswer by 1 0 .

8

H ow m uch less than £ 1 is the sum of 1 8p and 39p?

p

9

Divide the total of 1 9 and 1 7 by 4 .

Write as a decimal fraction of a metre

(a)

(a) 20 cm

How many g Y heavier is box Y � than box X? 2.s kg

(b)

(b) 3 5 cm . 0. 1 2

1 .02

m

10

0. 2 1

11

Write as a decimal the n u m ber which is 1 0 times smaller than 8. 8.

Write as decimals the next two n u m bers in this series. 1 OOO, 1 00, 1 0, 1 ,

By how rr1a1y months is (aJ Be1 aide· than (a) Lea h -----

(b) Sanjay younger (b) than Lea h -----

Two a n g les of a triangle each measure 45 ° . Find the size i n deg rees of the third angle .

(b) the total cost of the T-shirts. 12

p

(a) p ----�

(b) £ -'---'------

1 cm on a plan represents 1 m . What does 1 m m on the plan represent (a) in cm

(b) i n mm?

26

0

Amy's T-shirt cost £ 1 2 · 70 a n d George's cost £ 1 1 85 . Find (a) the d ifference in price

Write each of these fractions i n its lowest terms. (a) f2 (b) � � �

Find the cost of 3 1 kg if 1 kg costs 1 6p.

Date of bi rth

Sanjay 28/2/99 Ben 30/9/97 Lea h 30/8/98

m

cm

Mother uses 50 g of cocoa each day. How many days wi l l it take her to use � kg?

Fi nd the d ifference between 1 4 plus 9 and 1 4 minus 9 .

1 1 . 20

(b) £

p

Add the largest of these decimals to the smallest.

9

What decimal fraction of £ 1 is

(a) 1 TWO

4

ANSWER 1

ANSWER

(b) 1 TWENTY

= 8286

+

kg

1

(a)

(a) 1 7 hundredths

80

7

II

ANSWER

4 5

Test 9

cm (a) -----

mm (b) -'-'-----

Test 1 0

Section 2 1

500 g x 10

3

1000p

2

4 5

6 7

8

9

10 11 12

1

2

3 4

5

6 7

8

10

11 12

ANSWER

kg

kg

=

(36 - 7) - (32 - 8)

£

£

=

+ 62p

6 rem. 2

=

9 Jx

£

£3·00

1

(b) in mm.

£

2

Find x.

Write 243 hundredths as a decimal. ----(10 x 5) - (4 x 7) w of 1 mm 1

=

s

s

� of 64 km 10 articles cost 19p. 100 articles cost £

612

+

y

=

9989 + 12

6. Find y.

Write 41p as (a) a vulgar fraction of £1

(b) a decimal fraction of £1. Make each of these numbers 10 times smaller. (a) 29

(b) 1. 7 Write in 24-hour clock time quarter to five in the afternoon. How much more than a FIFTY is the sum of 8p, 18p and 28p?

3

km

£

4

ANSWER (a)

(b)

(a)

£

5

£

6

(b)

7

p

8

of a number is 9. What is the number? Write these fractions in their lowest terms. (a) fefo (b) � � Qi__ What is the change from £5 after spending £1·36 and £2·40? £ ----If 10 models cost £5· 20, what will be the cost of (a) 1 (a) p

I

x

(b) 7?

1 _L 5 - 100

5 - 1 00 Find the value of x and y.

1 f costs 60p. Find the cost of 51 f. If wool costs 80p for 50 g, what is the cost of � kg?

(b)

(a)

cm

(b)

The four angles of any quadrilateral together equal 360 ° . , Find in degrees the size of the angles marked x.

50

mm

-,

-;-d ..,.x---,.-

Ar o-

0

Nadeen saved a FIFTY each week for a whole year. £__ H ow much did she save altogether? ___ M1 LONDON 75 km

5.5

0.2

If a tanker travels at a steady speed of 50 km/h how long will it take to reach London?

0.55

h

0.02

Which of these decimals is equal to (a) -Mo (b) 4? (a) -'-'--- (b) N ame the three coins given in change from £4 after spending £3·77.

__ P __ P __ P

Subtract 9 from the total of 53 and 47. -----

1

Find the total of 3.8 m·a-'ld 0.5 m (a) in cm

ANSWER

9

What remains from a 10-metre length of cloth after using 3.3 m and 2.8 m?

*

£

morning

x

11

y

£

12

£

27

Each side of this shape is 0.7 cm long. Find the perimeter of the shape in cm.

After spending 49p and £ 1 ·36 Amy has 1 5p left. How much had she at first?

10

m

cm

£

What time will be shown on the clock after 47 min? Use a.m. or p.m. ____ _

Find the difference between 1 1 10 of 7000 and Tii5 of 7000.

A school outing will cost Ryan £10·80. He has mad e 8 weekly payments of £1 20. How much has he yet to pay 1

£

Section 2 1

2

3

(35 + 7) x (30 + 6)

3 £ 300 m£ -

6

45p + 29p +

8

0.75 m x 100

10

2 kg 750 g + 900 g =

7

9

11

12

£

m + 140 cm

4 5

i£ =

135 min =

h

£

min

m£

e

h

p = £1

(40 + 8) x 7

(b) hm =

m

Find � of 30 e.

1

m

(8 + 56) - (15 + 9)

�) } km =

II

ANSWER

£2·26 + £1·87

5.4 m =

Test 1 1

m£

2

min p

3

m kg

kg

g

m

(a)

(b)

4

g

5

m

m

e 6

Find the product of 7 and 18.

2

Find the number which is 100 times (a) smaller than (a) 240 ------

3

Write as cm (a) 3. 25 m

4

How many grams more than 1 kg is the sum of 280 g and 270 g?

6

Decrease 43 by 16 and multiply the answer by 10.

5

7

8 9

10 11

12

(b) 37.

(b) 4.06 m.

7

(b) -----

cm (a) -----

8

cm (b) -----g

What must be added to 39 to make 57?

9 10

From the sum of £1·17 and £1 ·33 subtract 60p. £ ----Find the remainder when 113 is divided by 6.

Write as a decimal fraction of a kg (a) 500 g

kg (a) -----=

1 pencil costs 9p. Find the cost of 200 pencils.

£ -----

(b) 100 g.

What is the perimeter of a rectangle 7 metres long and 61 metres wide?

11

kg (b) ----�

How many newspapers each costing 40p can be bought for £8·00?

Find in degrees the measurement of each of the angles a and b.

a

b

0 0

How many TWOS have the same value as (a) 12 FIVES

(a) ------

(b) 5 boxes.

(b) g ----�

(b) 3 FIFT IES? (b) ----Write all the numbers between 48 and 68 which can be divided by 7 without a remainder. 10 boxes have a mass of 11 kg. g Find the mass in g of (a) 1 box (a) ----= B rotley

Carley

45 km

ANSWER

1

ANSWER

12

m

A cyclist started from Brotley at 11.30 a.m. and arrived at Carley at 2.30 p.m. If he travelled at the same rate, what was his speed in km/h? km/h · Katie's mother gave her £ 1 45 to add to her savings and her father gave her £2·70. She then had £5. How much had she at first? p Radios are reduced by 10p in the £ off the list price. What is the LIST PRICE £18 ------� new price? ----£ There are 1 86 pages 1n a book. Tom read 64 pages and then 56 pages. How many more pages ras he to read? 1 , 0.0 1.04 1. 96 1.11 0.99 I Multiply the largest of these numbers by the smallest. In a class of 32 children ! of them are 10 years old, are 9 and the rest are 8 years old. (a) What fraction of the children are 8? (a) -----

i

(b) How many children are 8? (b) ----The circumference of a wheel is 1.85 m. Find in m the distance the wheel will travel in (a) 10 turns (a) m (b) 100 turns. 3 kg of meat cost £ 1 8·00 . Find the cost of (a) 500 g (b) 750 g.

(b)

£ (a) -----£ (b) -----

Turn back to page 16 and work for the fourth time Progress Test 1 . Enter the result and the date on the chart.

28

m

Section 2

Test 1 2

Ill

ANSWER

m

m

1

290 cm =

2

(82 -4) + (18 - 9)

3 4 5 6 7 8

9

10

1

(17 x 3) + 6 T 28

=

2

whole ones

1 article costs £0· 07. 100 articles cost £ 346 + 78

10 of 9 km = 1

5 )£10·10

£

m

£

£2 ·00 - 25 FIVES

10 2

-

3

m p

92

11

Write £8·84 (a) to the nearest 1Op -'-'----(a) £

12

£10·00 ..,.. 8

(b) to the nearest £.

4

Write as £ and m£ (a) 3457 m£

£

(b) 4070 m£.

2 3 4 5 6 7

8 9 10

11 12

£

(b)

Find the difference between (15 + 15 + 15) and (4 x 15).

£

6

p

Find in cm the perimeter of a triangle having equal sides each measuring 48 mm. How many h and min from 11.40 to 18.1O?

Write as a decimal fraction (a) 1

l o.3

0.15

0.09

(b)

1 .1

t

0.99 1

h

(a)

9

10

cm

min

(b)

11 12

Add the smallest of these decimals to the largest.

If 10 cost £2 ·70, what is the cost of 17

Find the cost of 300 g if � kg costs 30p.

(b) ----(b) g ----� £

How many bottles each holding 150 m£ can be filled from a can holding 1� e ?

This is a sketch map of a park. What is the perimeter of the park in km?

m£

Divide the total of 29 and 27 by 8.

(a) -----

A 1p coin has a mass of 3.56 grams. g (a) Find the mass of (a) 100 coins ----�

m£

8

How much greater is 7 multiplied by 9 than 7 plus 9?

By putting in a decimal point make (a) the 5 in 2056 equal to 5 tenths (b) the 7 in 1870 equal to 7 hundredths.

7

52 plus 70 minus 32

Subtract 6 times 14p from £1.

884 1 765 Which of these numbers will divide by 2, 5 and 10 without a remainder? -----

� of a sum of money is £1·10. What is the whole amount?

(b) £ -----

(a)

How many ;mall SRuares are there in i6 of this diagram? -----

(b) 50 coins.

ANSWER 1

•

ANSWER

km

1 £3 ·73 £3 ·54 £3·37 £3·36 Which two of these amounts when added together equal £7?

@

£3 · 63 1 £

Sophie and Olivia shared 60p so that Olivia had 1 Op more than Soph ie. How much did Sophie have? Write as a decimal fracfon the part_ of the circle which 1s �) shaded (b) unshaded.

£ p

�) -----

(b) -----

The length of a steel rod is 1.75 m. Write the length of a rod 4 times as long. m �---PET FOOD

LARGE TINS (340 g) 67p EACH SMALL TINS (1 70 g) 1 0 for £3 · 50

How much is saved when buying p 10 large tins rather than 2 0 small tins? ----� Next work Progress Test 2 on page 30. Enter the result and the date on the chart.

p p

29

PROGRESS TEST

2

Write the numbers 1 to 20 down the side of a sheet of paper. Write alongside these numbers the answers only to the following questions. Work as quickly as you can. Time allowed - 10 minutes. 1

Write the sum of £0·44, £0·56 and £1·55 to the nearest TEN.

The circle is divided into three equal parts. How many degrees are there in the angle marked at the centre?

2

3

4 5 6 7

A car travelled for 15 minutes at a speed of 48 km/h. What distance did it travel?

The circumference of a wheel is 1.25 m. How many m will it travel in 10 turns?

Make 306 one hundred times smaller.

Write as a decimal the total of 20, Subtract � of 27 from � of 45.

ih and ,fu.

8

9

10

Clock A is 10 minutes fast. How many minutes slow is clock B? By how many m is 648 m less than � km?

Write the decimal fraction which is half-way between 0.4 and 0.38.

8ggg •4

I This reading is taken from a dial in a car. It shows the number of km travelled. What will be the reading after travelling a further 700 m?

11

I

12

If one article costs £0·44 what will be the cost of 100?

13

Find the cost of 4� kg at 40p per kg.

15

Which 3 coins were given in change from £3 after spending £1·28 and £1·56?

14

16

By how many sixths is � less than � ?

3� litres + 900 mf' + 600 mf' =

17

Which of these 24-hour clock times is nearest to twenty to seven in the evening? 18

19

20

How many g more than � kg is the sum of 334 g and 286 g?

50 cm of tape cost 28p. Find the cost of 1.25 m.

Find in cm the perimeter of the shaded shape.

This page from Mental Arithmetic 3 may be photocopied after purchase for use in the purchaser's teaching establishment only.

30

© Schofield & Sims Ltd

PROGRESS TEST 2

RESULTS CHART

You wil l work Prog ress Test 2 at four different times. When you fi rst work the test (a) colour the first col u m n to show the n u m ber of examples correct out of 20 (b) enter the date. Each time you work the test, enter the result and the date in the marked col u m ns.

r

20

1 st 2nd 3 rd 4th

19 18 17 16 v

CV

0

v

Ill

CV

15

14 13

E

12

......

11

0 CV

E

10 9 8 7 6

5

4 3 2

_..,.._....,_-!

0 .........

This page from Mental Arithmetic 3 may be photocopied after purchase for use in the purchaser's teach ing estab lishment only.

31

© Schofield & Sims Ltd

Section 3

Test 1 II

ANSWER 1

2 3 4 5

6 7

8 9 10 11 12

Th H T U

How many less than six thousand is the number shown on the abacus picture? -----

4 km 720 m =

m

35p x 10 = £

� f - 340 m£ =

£

mf

50p + 50p + 50p + 35p = £

23 + 9 + 18

2 h 25 min = £5·70 =

£

1 of 8 f

3

mf

4

5

f

6

ANSWER Write in figures: four thousand two hundred and four.

2

Subtract £0·49 from £1 ·00.

p

What is the cost of 8 pencils at 2 for 17p?

p

3 4 5 6 7

Find the average of 6, 8 and 10.

50 cm is cut off a 3.5-m roll of ribbon. How many metres are left? Change to 24-hour clock times (a) 11.55 a m.

(b) 1.40 p.m. 8 9 10

11 12

Subtract j of 30p from � of 30p.

How many mf in 0.5 e ? 12

24

33

18

7

8

10

(a ) (b)

p

What fraction of this strip is (a) shaded

(b)

(a )

Write these times in figures using a.m. or p.m. (a) 2� hours after 10.00 a.m. (a) ----(b) ----'---'--

,s .7�rn Find, to the � Bistow ··--....._ nearest km, the Bant Crock total distance from Bant to Crock. km James saved £1 ·25 each week for 8 weeks. How much did he save?

£

How many g less than 4 kg is the total mass of 10 parcels each having a mass of 345 g7 ma rbles Large

Small

each

each

4p

g

Find the total cost of 6 large marbles and 6 small marbles.

A car travelled at an average speed of 90 km/h for 1� hours. What distance did it travel?

11

me (a) the largest area

Which of these numbers can be divided by 2, 3, 6 and 9 without a remainder? What fraction, in its lowest terms, is 400 m of 1 km?

(b) the smallest area. 12

Find the difference between 0.3 and 0.03

32

0

1111 1 1 1

6p

p

p

Tom had 40 marbles. f--le lost 1 6 and then won 24 . How many marbles had he then ?

9

m

Divide £1 ·28 by 8.

�

Angle ABC is a right angle. How many degrees are there in the angle marked y ?

(b) 7 hours after 7.00 pm

mm

1

A

(b) unshaded?

g

mm

How much change from £1·00 after buying 8 labels at 9p each?'

s Bc

m

TENS

g = 650 g

32.4 cm =

2

min

min

TENS

1hg -

1

ANSWER

v

w

8080

(a ) (b)

How many times larger is the 8 marked V than the 8 marked W?

km

Section 3 1

8 + 7000 +

3

46 x 6

2

4

rm-

= 7808

85p +

7

7 cm - 1 .5 cm =

8

9

10 11

12

1

2

3 4

g

5 kg 60 g =

£9·00 -;- 100 =

� of 35 kg

200 min =

m

h

4 kg + 130 g + 1

£

p = £1·15

2.75 m =

p

g = 1 kg

Divide the sum of 53 and 65 by 2.

The change from £2·00 was 43p. How much had been spent?

Find the product of 8 and 8.

10 gift cards cost £1·20. Find the cost of 1 card.

From 360 ° subtract the sum of two right angles.

10 11

12

kg

5

km/h

kg

Grapes cost £3·60 per kg. What is the cost of 2 kg 500 g? e

nd

£

JH1 N

1 1 11 II wh 1ch are equal in L.J.....&....1,...a....L.J...J,....L.....L.J1.....1...1.-L.J...1....L-L...L..LI area. Name the two shapes. ----

6

ANSWER £

8

p

9

0

How many km and m are equal to m km 1560 m? ------

10

Write 9� to the nearest whole number.

Change to 12-hour clock times.Use (a) a.m. or p.m. (a) 15.45 ------

(b) --'---'-----

How many whole ones are equal to 36 quarters?

11

How many tens have the same value as 5010?

12

The sum of two numbers is 17. The difference between them is 1. What are the two numbers?

33

1

Josh had 1 50 stamps. He put 1 5 stamps on each of 8 pages in his album. How many stamps had he left?

This clock is 15 minutes fast. Write the correct time in figures using a.m. or p.m.

7

I 0.2 0.4 0.6 0.8

(b) 00.15

£

A car travelled 240 km in 3 hours. What was the average speed in km/h?

:t.�r����� ;:r

g

6

9

4

min

h

min

p

cm

m

cm

Find the change from £5 pfter spending £1·33 and £2·57"."

Find the average mass of the three boxes.

mm

mm

ANSWER

3

g

Write the next two numbers of this series.

8

2

p

5

7

1

Find the value of x.

5

6

I.I

ANSWER

£6·00 - £1·95 = £

7

Test 2

morning

A pack of 4 tins of ham can be bought for £5·12. Find the cost of 1 tin.

£

At a football match there were 12 498 spectators. Write the number of spectators (a) ("!) to the nearest hundred ----(b) to the nearest thousand.

(b) ---'-----

These angles are equal. (a) How many right angles are equal to the sum of the five angles? ----(a) (b) How many degrees are there in each of the 0 five angles? ----(b)

Share 80p between Ali and Katie so that Ali has 20p more than Katie. Ali p ---� Katie p

There were 2.5 e of milk for 4 children. 100 me were spilt and the remainder was divided equally. What was one share?

me

Test 3

Section 3 ANSWER

1

9999 + 9

2

25 + 26 = 1 1 +

3

368 cm =

4

£1 · 1 7 x 7

5 1

1

m

7

6 ) £4 · 02

8

5.7 f =

9

4 weeks =

10

3 . 2 1 x 1 00

p

2 3

mf

x 7 = 37 - 9 1 . 7 cm + 4 . 5 cm =

mm

mm

Take two hundred from

Write 600 m as a decimal fraction of 1 km .

km

8

9

Write as a decimal fraction the d ifference between 0. 1 and a half.

How many days altogether i n April a n d May?

10

Write the next two n u m bers in this series. 8. 0, 8 . 5, 9 . 0, 9 . 5 ,

9

B y how many c m i s -rtJ m longer 1 than 1 00 m?

10

200 mf cost 1 5p. Find the cost of 1 f. ----� p

11

g

Write the missing signs + , - , x or -c- in place of • and A . 6•3 = 96 9

How many m ust be added to the n u mber shown on the a bacus picture to make four thousand7 -----

How long will it take a truck travelling at a n average speed of 60 km/h to travel a distance of 3 60 km?

cm

•

11

12

Katie wrote a ri answer of £0 · 60 i n stead of £0 · 06 . By how many pence was her answer wro n g 7

p

--6 cm__� F i n d (a) t h e a rea )I � (b) the peri meter of the recta ngle . In each case g ive the u n it (a_ ) ____ of measurement. _ (b)

In a school d i n i n g room there were 25 tables each set with 6 places . 1 1 of the places were not used . How many stayed for dinner?

0

The diagra m shows the time a boy spends at home and at school . What fraction of his time does he spend (a) at home (b) at school?

(a) (b) ---

I n Ja mes rrioriey box there were 30 TWE f\J�I ES a n d twice as many TE NS . How much was that a ltogether? Write the mass shown by the pointer (a) in kg a nd g (a) (b) in kg as a dec1ma .

£

kg

(b)

In a school of 57 chi ldren, there is a small class of 9 children a nd two classes of eq ual n u m bers . How many children a re there in each of the larger classes?

How many mf more does a can conta ining 2 . 5 f hold than the total contents of two cans each holding 850 mf ? SWEETS

I

g kg

mf

1 2p each or 1 0 for £ 1 · 1 0

H ow much is saved on each sweet by buying 1 0 at a ti me?

34

h

How many rig ht ang les a re equal to the sum of the three ang es of a triang le?

£

22 222.

Find the difference i n g between 1 . 7 kg and 2 . 5 kg .

Th H T U

7

£ 1 · 84 x 1 0 . Write the a nswer to the nea rest £.

Divide 9 1 2 by 4.

12

6

ANSWER

5

8

5

days

How many times larger is £2 · 50 than 25p?

7

4

mf

4

6

3

£

II 1

2

1

2 + li

12

£

p x 1 0 = £ 1 · 40

6

11

m

ANSWER

p

• 1

2 3 4

5

..

6 7 8

9

10 11 12

Test 4

Section 3

II

ANSWER

1 0 OOO - 1 00

4.93 m

To of £ 1

=

7

=

6.06

=

p

1

= 1

2

p

3

1 00

0.7 kg + 0.4 kg 2

cm

cm

3.93 + 0.07

1

mf

270 mf + 300 mf

=

1

kg

kg

g

g

2 3 4

5

6 7

8 9

10 11 12

-

-

=

1 0p

From 1 1 _.25 a.m. to 1 2.45 p.m. min. 1 kg 700 g x 5

=

How many FIVES must be added to 5 FIFTIES to make £2·80?

kg

5

6

(a) ---------'---

Which two of these fractions are of equal value? 2 1 4 4 3 3 4 s 6 4

1 } f of a 2-f can are used. How many mf are left?

The average of 3 numbers is 9. What is the total of the three numbers?

cm

7

8

9

J osh has completed 4.4 km of a 5-km journey. m How many metres has he still to travel - ?----

10

Multiply 1 .8 by 5.

11

How many times shorter is 1 5 cm than 1 .5 m? A square has sides each 9 cm long. What is the area of the square? Give the unit of measurement.

111111�1�1 {

:

James had £4·00 spending money. He spent 80p each day. For how many days did his money last?

z

How many grams must be added to the scale pan to make 4 kg?

cm cm

g

J osh's holiday is from the 1 8th January until the 1 3th February inclusive of both dates. How many days is that?

Find the average •••••• ••• number of dots in 1-• .;:....;;•_•;;....:;•--.....1 a row.

•••••••

mf

How many years from 1 985 to the year 2000?

2 biscuits cost 1 5p. Find the cost of half a dozen.

l�r

,�1�1�1�,111I·1�1�1111111�1�1I11·11�1�·11li1

(b) -'--'-----

Write 268 mm to the nearest cm.

--

To pay for two pens costing 75p and 85p Mandeep gave the shopkeeper two £1 coins and a TEN. What coin did he receive in changei-----'--p

2 ------------------....i The ruler is marked in mm. y Write, in cm, the length of each line Y and Z.

min

kg

Write as a decimal (a) 3,1n (b) 4�.

---

� of this rectangle is shaded. What fraction is unshaded?

y

3 - 6

ANSWER

1

Afte1· losing 25 marbles, .L!_!cy had 9 blue and 8 red ones left. How many had she at first7

4

91

£1 ·30 .;..

ANSWER

12 p

M rs J ones travelled on a motorway from 1 1 .00 a.m. to 1 2. 1 5 p.m. Her average speed was 100 km/h. What distance did she travel? How many degrees are there in the angle marked y ?

How much change from £5 after buying 8 tins of fruit at 55p each?

How far is it round a rectangular playground which is 75 m long and 60 m wide?

Turn back to page 30 and work for the second time Progress Test 2. Enter the result and the date on the chart.

35

km

p

m

Section 3

El 1

2 3 4 5 6 7 8

ANSWER

2.9 =

£4·07 =

p

3 h 50 min = 7x

(1000 x 10) + (100 x 5) + (10 x 7)

11

3i f =

II 1

2 3 4

5 6

7 8

0.6 kg -

f

10 11 12

2

cm

cm

mf

£

11p x 100 = £

What decimal fraction must be added to the number shown on the abacus picture to equal 50?

T U t

What fraction of 28 kg is (a) 7 kg (b) 4 kg?

I

3

I

4

Write a quarter of a metre (a) in cm

.

1 816193

By how many months . 1s 18 February 1994 later than the given date?

months

(a)

cm

8

5

mf

6

ANSWER

Find the missing number in this series. 1, 10, 100, , 10 OOO

7

Find the product of 10 and 45.

How many times greater than 0.1 is 1O?

X

5 6

5 7

The radius of this y circle is 0.9 cm. Find the length of mm the line XY in mm. -----

5 8

Find the difference in pence between 15 TENS and 40 FIVES. A journey of 7 km cost 91p. How much was the charge per km?

Write to the nearest ! kg (a) 1 kg 620 g

p

By how many pence is � of £3 greater than � of £3?

mm.

Write as a decimal fraction of a kg the sum of :t kg and 450 g.

(b) in mm.

PRICE C H A RT

mass cost

10

(b) kg -----=-

x 11

p

mm

12

kg

36

(a) (b) ---

The perimeter of this regular hexagon is 7.2 cm. Find the length of one side (a) in cm (a) (b)

km/h

cm

mm

1 00g 1 50g 200g 250g 300g 1 8p

x

36p

Find the value in pence of x and y.

kg (a) -----"'

Find the area of a rectangle 7 cm long and 3 cm wide. Give the unit of measurement.

58 cm divided by 10 =

9

p

5 To

A cyclist travelled 72 km in 3 hours. What was his average speed in km/h?

8

p

5 9

Which of these fractions is (a) the largest (b) the smallest?

What distance in km and m is twice m km as long as 4.8 km? ----Divide 52p exactly by 4.

m

(b) as a decimal fraction of a metre. (b)

g

g = 340 g

(b) 2 kg 390 g.

9

min

£

76p + 5 FIVES = £

Find ! of 3}

12

£

= 43 - 8

5.08 m =

1

p

min

24p x 5 = £

ANSWER

tenths

tenths

9

10

Test 5

y

54p

How many degrees are there in the angle 0 marked x ? -----

Amounts spent

Tom 1 Op Katie 20p Salma 40p Daniel 30p

Find the average amount spent by the children.

p

Daniel takes four 5-mf spoonfuls of medicine each day. For how many days will 0.2 f last him?----'days

Test 6

Section 3 ANSWER +

1 2 3 4

5 6 7 8 9

10 11

12

II 1 2

�=

6 + 9000 + 400 = 9456 hundredths

£4·05 - 50p = £

£ -----

24 + 24 + 24 + 24 + 24 + 24 + 24 -----

1 f 600 mf + 8 = £3·60 + 10 =

p

mf

9.6 cm - 15 mm =

10 2 - 5 2

8 km - 1700 m = hg - 260 g = ; of £63

g

4 5

6 7

8 9 10 11 12

--- -

How much change from a FI_FTY after buying 4 badges at 9p each?

2

Write as a decimal fraction the difference between fu and ,fu.

me

mm

TWENTIES

TWENTIES

4

km

5

km £

g

How many times greater is £8 than 8p?

Reduce 125 by 99.

How many hundreds are there in 10 OOO? Multiply 55p by 10.

How many hours in 3 days?

Write in £s the total of 7 FIVES, 4 TENS and 9 TWOS. 500 g cost 28p. Find the cost of 1i' kg.

Multiply 9.5 cm by 100. Write the answer in m.

Write the sum of 4{u and 3fu as a decimal.

cm

(a)

7

Munch Bars are 63p for a packet of 6. Find the cost of 2 bars.

9

£

9 7

6

In a test the average score of the four children was 8. What was Sam's score?

The length of Hassa n's pace is 50 cm. How many paces does he take when walking 1 km? Name this triangle (a) by its angles

£

(b)

by its sides.

p m

11

Which two of the boxes together have a mass of 1.5 kg?

What is the number?

---

Mandeep Emily Sam Jessica

10

! of a number is 9.

A 4-m length of ribbon is cut into 5 equal pieces. Find the length in cm of one piece.

An aircraft left Gatwick at 11.00 and by 13.00 it had travelled 1 850 km. What was its average speed in km/h?----km/h Write the number nearest to 99 which can be divided exactly by 8.

8

mm

(b)

15th of November was on a Wednesday. On which d ay of the week was the 29th of November?

6

ANSWER

Find the diameter of a circle the radius of which is (a) 5.5 cm

p

How many mf remain from 2 e after filling the 3 bottles?

p

mm

£3·10 = 3 FIFTIES +

1

3

me

(b) 46 mm.

3

ANSWER

cm

12

37

19 rem. 5

6 JX

Find the value of x.

p

Test 7

Section 3 ANSWER 1

2 3

4 5

6 7 8

9 10 11

12

El 1

2 3

tenths

1.6 = (a) T6 +

(b)

11

23 + 25

0.78 m

57 ..,.. 3

=

1

=

_ (a_) _____te_n_ th _s

hundredths hundredths -------(b) x 6

cm

£1·00 - (23p + 38p) =

7 FIVES

=

£

mm

=

TWOS + 1p

kg

1 kg 600 g + 3 kg 800 g =

Find the radius in cm of a circle which has a diameter of (a) 68 mm (a)

5 6 7 8 9 10

11 12

Reduce each fraction to its lowest terms. (a) � (b) 1i

4

p

5

6

£

Write as a decimal the total of 3 tens, 7 tenths and 8 hundredths.

cm cm

(b)

(a)

m

a

(b)

9

Find the missing numbers in this ,54, 45 series. 90, 81,

10

� = 36 ..,.. Y. Find the value of Y.

Find the difference between £0· 50 and one quarter of £1.

11

Divide £8·40 by 10 and add 16p to the answer.

£

3.6 kg x 6.Write the answer to the nearest kg.

Find one quarter of 10 metres (a) in m

(b) in cm.

(b)

14

I Find the ri' east..re....,e t in degrees of tre angle marked Y -----0

What is the area of a corridor 21 m wide and 20 m long? Give the unit of measurement. T I M E-TAB L E

B O R D E N NOTLEY x 17. 30 18 03 18 30 y 19 . 03 z 19.30 20. 03 A R RIVE

25 cm of tape cost 1 4p. Find the cost per m.

Which bus X, Y or Z (a) arrives N otley at 7.03 p.m. ---(a)

(b) leaves Borden at 7.30 p.m.? ---(b) p

Katie bought 4 pencils each costing 18p. N ari'e the three coins she gave in exact payment. __P __P __P

How many 250-me bottles can oe filled from 2; f ?

M O N. TU ES. W E D. T H U R S . F R I . 7 11 10 6 6

min

A lorry travelled at an average speed of 60 km/h for a distance of 75 km. How long did the journey take? h min -----

12

kg (a)

Y

35

The chart shows t'le number of minutes Daniel took to walk to school each day. Find his average time.

p

What fraction of 10 is 1*?

42

A litre of water has a mass of 1 kg. (a) ----= g Find the mass in g of. (a) 0.5 e -'--'(b) * f. (b) g ----�

LEAVE

ANSWER

Increase £4·55 by 90p.

(b) 3.6 cm.

4

mm

kg

Write 864 cm to the nearest m.

w 50

TWOS

10 articles cost £2 · 50. One will cost p.

Which number other tha1; 1 wi1 d1v1de exactly into each of these 'l L.mbers7 28

3

£

5.6 cm - 38 mm

2

p

(6 x 6) - (3 x 9)

£3·50 x 8

•

Writ� the part of the square...which is shaded (a) as a decimal fraction (a) (b) as a vulgar fraction i'1 its lowest terms. ----(b)

.

cm

=

1

ANSWER

The diagram shows the lengths of the roads from Mandeep's to Hassan's house. (a) km Find the total distance in (a) km -----

m

cm

(b) m.

38

m (b) -----

Test 8

Section 3 1

2

3

4 5

6 7

8 9

10 11

12

II 1

2 3 4

5 6 7

8

9

10

11

12

ANSWER

39 + 67

0.1 + 10 + 0.06

2 h - 28 min

9 cm + 10 3

s+

2

m1n

=

500 - (40 x 9)

mm

mm

=

1

3

3 To

(9 x 6) + (3 x 8) mf x 10

1.4 kg - 850 g

£

7

6 metres

+

� 1 6 mm II How many 7p sweets can be bought for£2·1O?

4=

cm

p

5 6

cm

(b)

(b) 11�.

Write 39p as a decimal fraction of£1.

How many times can 0.2 be taken from 1?

8

£

How many days in (a) a year

(a) ---'-----

What sum of money is equal to 5 times 88p?

£ -----

(b) a leap year?

9 10

(b) -----

Which of these fractions is equal to � ? 16

20

15

Io

16

'M

11

12

T8

Find the difference in g between 1 2 kg and 0.3 kg. Multiply 8.33 m by 100.

By how many cm is 2.46 m greater than 1. 95 m?

g

m

12

cm

Find the average of 8, 13, 10 and 9. ----By how many is the sum of 15 and 1O less than the product of 15 and 1O? -----

Write the amount of liquid in this jug as (a) a decimal fraction £ (a) of 1 f ----(b) a fraction of 1 f in £ its lowest terms. ----(b)

I 4,0,8, 7 I

.

The cost of 2i kg of rice is£5·50. Find the cost of 500 g. 154 **

67

£

Find the missing number.

A bus travelled a distance of 150 km at 60 km/h. How long did the journey take?

h

Name this triangle by (a) its angles ---'-----(a) ( b) its sides. (b)

�

------

T he readings show the number of km travelled by a car before and 1 o 000.0 - after a journey. km Find in km the length of the journey. -----

I

I

9996.8 -

I

w

x

length 7 cm 4 cm breadth 1 1 cm 3 cm

y

z

5 cm 8 cm 2 cm 1 ! cm

The chart shows the length and breadth of 4 rectangles. Which two of the rectangles have the same area?

Turn back to page 30 and work for the third time Progress Test 2. Enter the result and the date on the chart.

Re-arrange these figures to make the largest possible even number. -----

39

mm

Which 3 coins are given in change from£5 after spending£4·76? _e _e _ e

ANSWER

Write to the nearest whole number (a) (a) 8.5

.c._;_ ___ _

T he perimeter of this triangle is 75 mm. Find the length of the side AB.

g

p

g

Find (a) the diameter (b) the radius of the largest circle which (a) mm can be drawn in this _ (b_) ___m_m _ square.

mf

g

=

£1 - (8p x 6) = s of£56

How many g less than 5 kg is the total of 2.7 kg and 1. 5 kg?'"

4

4f

=

ANSWER

Section 3

El

1

m = (a)

2

21 thirds =

5 6 7 8 9

10 11 12

(b)

50p

cm

(a)

cm

2

4

II

ANSWER

1

3

Test 9

mm

(b)

mm

whole ones

p

p = 21p p

£8 + 10 =

cm

=6

3

- 99.25 = 0.75

TWENTIES + 3 FIVES

£1·95 =

TWENTIES

£0· 78 + £0·46

2. 7 km - 1900 m = 0.4 m - 0.04 m =

4

£

m

m

5

cm

cm

ANSWER 1

How many pence have the same value as (a) £0·1

2 3

4 5 6 7 8 9

10

Find in m£ io of 15 £.

12

m£

Two angles of a triangle measure 90 ° and 55 ° . Find the measurement of the third angle.

8

0

Divide the sum of the digits from 1 to 6 inclusive by 3.

Write the time 35 min before 18.10 in 24-hour clock time.

9

Subtract 1 8 from 6. 3

Find the difference in g between i kg and fa kg.

10

How many articles costing 6p each can be bought for 84p?

i £ costs 8p. Find the cost of 21 £.

Change each of these fractions to hundredths. (a) -do ( b)

11

7

p

(b)

(b) £0·9?

6

p

(a)

to

(a)

Write the missing numbers in this , 64 series. 2, 4, 8, � of a sum of money is £35. Find the whole amount.

Too

(b)

7 .kg

0.4 kg

1

1.1 kg

Find the difference in g between the largest and the smallest of these masses.

CS) evening

£

(8p x 8) + (4p x 9)

300 g

I g

2

p

Find 0.1 of 10 cm.

408 +

1

ANSWER

p

11

Too

12

This clock is 7 min slow. How many minutes is it from the correct time to midnight?

x-t-Hr

Which of the lines are perpendicular to the line XY?

M N 5 metres of cloth cost £3·00. Find the cost of (a) 1 m

K L

min

(b) 20 cm.

(a)

(b)

Through how many right angles does the hour-hand of a clock turn in 24 hours? AB is a part of the circumference of a circle 2.8 cm in Dr::_D diameter. Find in A centre mm the length of the line OD.

p p

mm

T he average age of the children ,s 9 years. How old is years Emily7 A tape 20 m long is cut into 100 equal pieces. Find the length 1n cm cm of one piece. At a sale, shorts were reduced by 12p in the £1. How much was paid for the shorts £ which cost £10 before the sale? In a class library there were 158 non­ fiction books and 132 fiction books. How many short of 350 books was the total? Wasim James Emily Sunil

10 years 9 years years 10 years

Write the letter of the shape which is (a) (a) a rhombus ----(b) (b) a parallelogram. ----·

£

40

Test 1 0

Section 3

El

ANSWER

ANSWER

1

£15·00 + 100

p

1

2

1.8 kg - 900 g

g

2

3

4

5 6 7 8 9

10 11 12

1 2 3

4 5 6 7 8 9

10 11 12

47 x 7 1 1 2- s

10 of 1 hour =

min

3

1 80 mi x 100 =

f

6.30 p.m. to midnight =

5 FIVES +

TENS = £3·65

0.35 x 6

0.3 + 0.07 + 3.5

3.05 m - 0.5 m =

£4 -

p

=

£3·11

4

h

h

5

cm

6

p

ANSWER 7

(a) -----

Biscuits cost 9p for 2. Find the cost of 18. Name this triangle (a) by its angles (b) by its sides.

p

(a)

(b)

Find (a) the area of a rectangle 6 m long and 3i m wide (a) -'--'----(b) the perimeter of the rectangle.

8

The average of 8 numbers is 7. Find the sum of the eight numbers. How many cm in 'io of 6.2 m?

cm

Find the total distance in km of 3 350 m, 900 m and 4 km.

km

Divide 2 by 5. Write the answer as a decimal fraction.

Find the cost of 2 i, if 200 mi cost 8p.

m (b) (b) in m. ----Write the1 next fraction in this 1 3 1 series. 8, 4, 8, 2, Use this part MARCH of a calendar 7 1 4 2 1 28 Mon to find (b) the day of the week upon which (b) 1st April falls. -'-'-----

How many times can ,;. be taken from a whole one?

Reduce £6 by £1·73.

T Find the length of a line 10 times the cm (a) length of the line ST (a) in cm �----

s

(a) the date of the 3rd Monday in March

Multiply 2.5 by 6.

What fraction of £3 is 30p?

55 mm

Tues 1 8 1 5 22 29

TENS

cm

Complete this series. 950, 975, , 1050

3

How many 75-mi bottles .Ccln be filled from 7i n

9

10

(b) -----

In each case give the unit of measurement. s ��� �fs �il� � the mass of box X. Find in kg and g the total mass kg of the two boxes. g -�---= Chloe and Jack shared £5 so that Jack had sop less than C hloe. £ How much did Jack have? cm

1

2

3

4

5

11111I11111.11d111:lrrrdu,:LIIrll'flllfIII11::I

M N The line MN is drawn to a scale of 1 cm to 1 m. Write in m and cm the length represented by the line MN.

£ p

11

The circumference of a wheel is 50 cm. How many times will it turn in j: km? -----

12

Write the fraction in its lowest terms which lies midway between � and �. -----

m cm Of the money Amy receives each week she spends � and saves the remainder which is 20p. How much money altogether does she receive each week? p A pack of 20 pins costs 40p. Find the cost of (a) 1 pin (a) p ----� (b) 10 packs of pins.

41

(b) £ ----

-

• 1

2 3 4 5 6 7 8 9

10 11 12

Test 1 1

Section 3 9000 +

3.01 x 1 00

4.05

7

+

ANSWER

7 + 70 = 9777

1

9

(0. 1 of £ 1 ) + (0.01 of £1 ) =

p

p

TWENTIES = £9 5

£

36p + 45p + 1 9p = £ 1 . 1 km - 640 m =

50 min + 28 min +

£19

3

TWENTIES

13 + 6

� of 72

7

5

m

4

m

min

min = 2 h

5

£

ANSWER 1 2 3

4

6

Find how many (a) cm (b) mm there are in 0.7 m.

; kg c0sts 20p. Find the cost of (a) 1 00 g. By how much is 99p less than 24 FIVES?

Multiply £5·09 by 7 and write the answer to the nearest £.

Write as a decimal fraction (a) �

8

Find the difference between (4.0 + 6.0) and (0.4 + 0.6).

10 11 12

(b) �-

o9

0.01

cm

(a) (b)

mm

(a)

p

p

(b)

(a)

8

9

p

1 00 pieces of cheese each having a mass of 55 g are packed in a box. The box has a mass of 500 g. Find the total mass of the full box.

William scored 5 1 with 3 darts. He scored 1 9 and 1 6 with the first two darts. What was his third score1_____ Mon.

Tues. Wed . Thurs.

10

(a)

12

p

42

kg

The mass of some bananas is shown on the dial. Find their cost at 30p per kg. __ £__

11

How many pennies are 24 TWOS more than 9 FIVES?

1

Write the next two fractions in this 1 1 . 2 , 1 , 2, 4, series.

(b)

Add 6 2 and 4 2 .

o.75

Find the difference between a half of 1 8 and one sixth of 30.

Fri.

£

o.o9

Which two of these fractions when added together equal .:.... (a.:....)____ (a) a whole one (b) one tenth? (b) -'-'-----

£

(b)

0.25

thousands

Change 1 050p to £s.

Name (a) the sixth month (b) the ninth month of the year.

I

7

How many thousands equal fifty hundreds?

7

9

6

Subtract 0.01 from 0. 1 .

(b) 800 g.

5

Bottle X holds twice as much as bottle Y. Write the amount bottle X holds in t' and mF.----e me

2

(7 x 7) = 1 00 -

1

Add 8.3 to 5. 1 9 and write the answer to the nearest whole numoe"t.

ANSWER

28 T

=

36 x

1 50 1 50 1 00 1 00 1 00

km km km km km

Mr Gupta travelled these distances in 5 days What was his average daily jour11ey7

km

The two circles have the same centre. The 1 rner c,rcle has a diameter of 1 5 mm. The outer circle has a diameter of 25 mm. Find the width of the shaded part. mm ----In this right-angled triangle, what is the size in degrees of the angle marked 0 A?

Find the value of x.

Test 1 2

Section 3

El 1

£1·45 + 86p = £

2

a+

3

4 5

1

6 7

8

9

10

11

12

El 1

1

£

34.94

1

40.5 ..;.. 10 2

)

£1·93

Find the value of x.

£x

117 min =

0.4 kg -

= £0·72 h

h

min

g = 130 g

£

cm

4

350 mf x 8 =

15 km - 10.5 km =

m

8

9 10

11 12

6

ANSWER

Write as a decimal 403 hundredths.

Write 1O f 250 me to (a) the nearest e

7

8

9

p (a)

10

(b)

(b) the nearest i f.

Reduce each of these fractions to its lowest terms. (a) -;{ (a) (b) (b) ,6Jh ---

What must be added to 3 TEN S and 6 FIVES to make 90p? 1.0 m

120 cml

Subtract the shortest measurement from the longest.

11 p

12

cm

Find the average of 5, 6, 7, 8 and 9. ----8 strips each measure 65 cm. Find their total length in m. m 600 mf cost 42p. Find the cost of 1 e.

Find the size in degrees of

£ LX

..,___

43

0

A Dinky caravan is 3350 mm in length and a Comfort caravan is 3.5 m long. By how many mm is the Comfort longer than the Dinky? mm The total length of the sides of an isosceles triangle is 840 mm. The shortest side measures 240 mm. Find the length of each of the other two sides.

A motorist travelled to Blackpool in 2i h at an average speed of 64 km/h. What Jistance did he travel? 60p is made up of an equal number of FIVES and TEN S. H ow many FIVES are there?

The diameter of a 1Op coin is 24.5 mm. Ten coins are placed side by side in a straight line. Find the length of the line in cm.

The circumference of this circle is 22 cm and the radius is 3.5 cm. Find the perimeter of the semicircle.

Turn back to page 30 and work for the fourth time Progress Test 2. Enter the result and the date on the chart.

____ p

0 0

LZ

Divide the sum of £3·50 and 75p by 5.

�m

Write the unit of measurement in each case. H ow many pens each costing 60p can be bought for £4·80?

L X, L Y, L Z.

How many TWENTIES are equal in value to £0·8?

I 0.24 m

(b)

Find the total value of the coins.

m

Find the difference between 4 (, + ,) and 7.

7

(a)

5

4

6

Find (a) the area of the shaded triangle (b) the perimeter of the rectangle.

g

What fraction of 1 hour is 1 2 minutes? -----

5

1 0 cm

min

45 ..;.. 9 = 40 +

999 x 3

Find the difference between the 4 marked x and the 4 marked y.

3

cm x 10 = 1.40 m

£3 - £

ANSWER

H ow many packets eacb !;_Ontaining 250 g can be made from 10 kg? x y

= 12

7

2

3

II

ANSWER

mm km FIVES

cm

cm

CH ECK- U P TEST

N u m ber

A

Write in figures.

B

+ 9 = 3569 3000 + 500 + 6000 + + 80 + 1 = 6881 3 + 40 + 9000 = (1000 x 4) + (100 x 9) + (10 x 3) =

c

nine hundred and sixty four hundred and eight eight thousand and seventy ---

456 903 1875 5102 9040

= = = = =

tens + 6 units tens + 3 units tens + 5 units hundreds + 2 units hundreds + 4 tens

D

Write the value of the figure underlined.

E

How many times smaller is

G

tens tens tens hundreds hundreds

one point one nine twenty point Aought two 7.0 + 0.5 + 0.01 10.0 + 0. 4 6.0 + 0.02 20.0 + 0.08

Write as a decimal. 1 tenth 1 hundredth 101 tenths 105 hundredths

9 Tii 18 Too

95 1 00 20 Too

467 8479 32.5

3751 2008 160.2

32.14 10.95 0.56

5 than 50 7 than 700 270 than 2700

96 than 960 23 than 2300 54 than 5400

0.6 than 6.0 0.1 than 10.0 0.08 than 8.0

0.3 than 30 0.07 than 0. 7 0.25 than 25?

390 than 39 4500 than 45 3100 than 31

400 than 40 9000 than 90 6140 than 614

8.0 than 0.8 16.0 than 1.6 9.0 than 0.09

50 than 0.5 0.4 than 0.04 17 tha'l 0.17?

How many times larger is

F

four thousand and six ten point one three point nought five ---

7 6 9 4 8 9 7 5 4 9 8 6 3 8

+8 + 5 + 9 + 7 +3 + 7 + 5 + 9 +8 + 4 + 9 +6 +8 +6

Find the value of x.

x-9=3 8 + x = 15 x-7=4 x + 2 = 11

17 8 59 5 46 7 38 4 69 8 77 9 43 6

14 x 9 + x-

+ + + + + + + + + + + + + +

7 25 6 76 8 89 7 59 5 34 6 68 9 87

865.8 40.06 20.02

11 13 15 11 14 12 17 14 12 14 13 11 13 16

x= 5 5= 8 x = 15 8= 8

-

6 8 9 8 7 3 8 9 7 8 6 7 4 7

x + 7 = 13 12 - X = 4 9 + x = 18 x - 5= 7

44

26 22 43 61 85 93 32 54 72 41 82 95 67 56

-

8 + x = 14 x- 7= 9 x + 9 = 17

9 6 S 4 7 9 8 6 5 3 9 6 9 8

___

_

_____________________..................................................!!!!!!!!!!

__

CH ECK- U P TEST A

B

c

5 x x = 40 x + 6 = 5 x x 7 = 42 27 + x = 9 9 x x = 63 1

L 1

1

0 1

9

1

1

6 1

9

F

18 of 2 1 of 36 of 45

1

of

4 1

5 1

g

1

To

Find the whole number when 3

E

9) + 8 8) + 7 7) + 6 3) + 2 9) + 5 7) + 6 9) + 6 7) + 4 6) + 3 8) + 5 5) + 3 8) + 7 9) + 5 7) + 4 6) + 5 8) + 6 7) + 4 9) + 8 6) + 4 6) + 4

Find the va lue of x.

3

D

(6 x (4 x (5 x (6 x (1 x (2 x (3 x (7 x (5 x (6 x (0 x (8 x (4 x (8 x (9 x (2 x (4 x (8 x (7 x (3 x

7x7 8x 6 3x 7 5 x 9 7x 8 6x 6 4x 5 9 x 2 O x 3 9x 9 8x 5 6x 7 3x 8 9x 4 4 x6 7x 9 4x 3 9 x 8 7x 4 3x 5

N u m ber

8 IS 7 is 4 is

11 1 00 1 45 15 1 20 1 04

x x x x x x

1

'5 1

8

1

To

28 of 40 of 32 of 1 00

2

2 5

----ro

3 4 -

12

6

---,--g-

5

6 7

g

3

To

is

+ + + + + +

9

5

10

7 20

35

5

6 7

8

4

9

1 .3 0.96 0.02 1 0. 8 0.05 1.13

10 10 10 1 00 1 00 1 00

Find the m issin g nu merator or denomi nator.

5

3

4

6 is 9 is 1 2

1

20

3

60

5 5

25 1

45 ---

.

30 + 8 16 + 9 io + 3 54 + 8 80 + 9 63 + 8 20 + 7 53 + 9 21 + 8 3+ 5 40 + 7 19 + 5 69 + 9 48 + 7 16 + 6 45 + 8 57 + 6 31 + 8 61 + 7 62 + 9

rem . rem . rem . rem . rem . rem . rem . rem . rem . rem . rem . rem . rem . rem . rem . rem . rem. rem. rem . rem .

36 + x = 9 4 X X = 24 16 + x = 4

x + 8 = 9 5 x x = 45 x + 9 = 9 x x 4 = 32 21 + x = 3

of

1 30 800 4620 1 900 6500 1 0 OOO

10 10 10 1 00 1 00 1 00

36 + 9 49 + 7 30 + 5 72 + 8 24 + 6 0+4 27 + 9 42 + 6 64 + 8 40 + 5 18 + 9 56 + 7 28 + 4 32 + 8 81 + 9 36 + 6 35 + 5 54 + 9 48 + 6 63 + 7

4

x x 8 = 64 x + 4 = 7

20 of 54 of 48 of 70

of

2

5

4

7 7

9

9

To

30 is 2 1 is 36

4

is

x x x x x x

5 2

7

7

To

10 10 10 1 00 1 00 1 00

4.0 66.0 0.3 7.0 1 9.0 403.0 1

T5

"""'foo

T5

1 00

T5

1 00

3

7

45 of 35 of 63 of 80

of

16 is 1 2 IS 49. IS

+ + + + + +

10 10 10 1 00 1 00 1 00

50 1 00

75 1 00

20 1 00

1 3

CH ECK- U P TEST A

Write in each box the coins which make up the given amount. Use the least possible number of coins.

I I I

3 2p 80p 26p

B

Find the change from each amount.

Amount 50p 50p 50p 50p 50p 50p 50p 50p

c

D

E

F

Money and Time

10 FIVES 6 FIVES 14 FIVES 100 FIVES 12 FIVES 50 TENS 45 TENS 65 TENS

24p 39p 25p 63p 82p

+ + + + +

36p 41p 75p 28p 63p

CHANGE

Spent 24p 35p 12p 37p 28p 19p 23p 16p

+ + + + +

50p 22p 9p 12p 15p

Find the cost of

1WOS 1WOS TENS TENS 1WE NTIES 1WENTIES FIFTIES FIFTIES

5 kg at 25p per kg 3; kg at 30p per kg 4L1 kg at 20p per L1 kg 2 kg at 50p per 200 g 6; kg at 60p per kg

p p p p p p p p

£ £ £ £ £

II II II

II II II

54p 67p 71p

Amount 90p 60p 30p 45p £1 £1 £2 £2

£7·50 £10·00 £3·80 £10·00 £5·00 £7·50 £5·00 £2·20

£1·35 £2·70 £4·60 £2·29 £3·20

Spent 81p 52p 23p 41p 24p 37p £1·69 £1·06

-

60p 85p 99p £0·74 £2·93

CHANGE

FIFTIES FIFTIES 1WENTIES 1WENTIES TENS TENS FIVES FIVES

£ £ £ £ £

1 8p 59p

Amount

£2·55 £1·72 £2·78 £4·30 £3·80 £4·25 £2·90 . £1·64

£ £ £ £ £

1 ; f at 28p per f 3 e at 55p per f 2; e at 22p per e L f at 60p per 100 me 1 750 me at 26p per L e

£ £ £ £ £

p p p p p p p p

£3 £4 £4 £5 £5 £5 £5 £5

Write the times shown on these clocks (a) in 12-hour clock times using a.m. or p.m. (b) in 24-hour clock times.

morning

(a)

(a)

(a)

(b)

(b)

(b) morning

afternoon

46

I· � I I

65p

£2·24 £4·75 £1 ·62 £1-50 £3·87

Spent £2·13 £1·25 £2·48 £3·09 £2·46 £1·67 £2·11 £0·88

£ £ £ £ £ £ £ £

CHANGE

1WENTIES, 3 FIVES 1WENTIES, 6 1WOS 1WENTIES, 9 1WOS TENS, 1 FIFTY FIFTIES, 3 TENS FIFTIES, 5 FIVES FIFTIES, 4 TENS FIFTIES, 7 1WOS

+ + +

£3·09 £2·80 £1 ·38 £0·77 £0·45

£ £ £ £ £

5 m at £1-18 per m £ 75 cm at £1 per m £ 1 4L rn at 50p per m £ 1 1 14 m at 20p per L m £ 2 m at 30p per 20 cm. £

8 evening

(a) (b)

J __

CH ECK- U P TEST A

B

mm mm cm cm cm

1 cm 0.1 cm = 1m 0.1 m 0.8 m

184 mm 307 mm

c

3000 g 5280 g 8090 g

kg kg

4400 g 7250 g

D

E

F

240 g 370 g 406 g 215 g 198 g

0.01 m = 0.25 m = 0.75 m = 1m 0.5 m =

mm mm

cm cm m m m

465 cm 1000 cm 340 cm

g g

+ +

+

g

g g

+

+

kg g g

cm cm cm mm mm

5000 me 2884 me 6160 mf 7300 mf 900 mf

kg kg

Hg l kg l kg l kg l kg

1

e+

a

e+

�e + 1f+

lf +

f f

mf mi' mf mf mi'

592 me 634 mi' 827 mi' 310 mf 425 mf

101 953 £4·83

£

cm m km kg kg f

7 cm 2 mm 8 m 51 cm 12a km 4 kg 300 g 6 kg 200 g 5 f 400 me

mm mm m m m

3258 m 5106 m

cm cm

£

109 mm 730 cm 18 km 900 m 9 kg 550 g 12 kg 380 g 9 £ 600 mf

4m 1m 4m 1 . 1m 4m

e mf mf

cm cm cm mm mm

...

m m

km km

8200 m 6500 m 7 750 m

m m m

800 cm 330 cm 785 cm

km km km g g g

j kg .\kg Hg �f

e e

me mf

le

820 g - 0.7 kg 925 mi' - 0.8 £ 0.6 kg + 60 g 0.25 f + 120 mf = 0.75 kg + 240 g =

14.4 1326 £32·50 cm m km kg kg

e

£

39 .6 cm 15. 3 m 78.5 km 99. 25 kg 5 kg 600 g 3.7 f

g mf g mi' g

11.5 2950 £129· 28 £ cm m km kg kg f

j

a �[; �

Write the letter of the shape which is a right-angled triangle G

0. 25 m 0. 75 m 1 km 0.5 km 0.75 km =

390 mm 412 mm

cm cm cm

Work across the page. Write to the nearest whole number 19� 308 nearest hundred £17 · 09 nearest £1 nearest cm nearest m nearest km nearest kg nearest 1 kg nearest e

Measu res and Sha p es

.

an obtuse-angled triangle

a rhombus

a rectangle

a parallelogram

How many degrees are there in each of the angles marked x, y and z 7

� Angle x

0

Angle y

� Angle z

0

47

an isosceles triangle

Angle x Angle y

0 0

the long-established educational publisher specialising in maths, English and scieriC'e

Mental Arithmetic 3 This book is one of a series providing carefully graded questions that develop pupils' essential maths skills and prepare thefl'l for all aspects of the Key Stage 2 maths tests, including mental maths. Schofield & Sims Mental Arithmetic is designed primarily for pupils in Key Stage 2 who are working at levels 3 to 6. However, the Introductory Book may also be suitable for use at Key Stage 1 , and books 5 and 6 provide a bridge to Key Stage 3. Every Schofield & Sims Mental Arithmetic book is divided into three sections, each comprising 1 2 one-page tests presented in a standard format that pupils will quickly become familiar with. Every test in Mental Arithmetic 3 contains: • Part A: 12 questions where use of anguage is kept to a minimum - based on the signs =, +, -, x and .;. • Part B: 1 2 questions using number vocabulary - particularly the language associated with the four signs • Part C: 1 2 questions presented in word form as one- or two-stage problems. A useful Language of Maths glossary on the nside front cover helps to develop pupils' number vocabulary. Two 1 0-minute Progress Tests are provided, with accompanying Results Charts, and final Check-up Tests on number. money, time. 11easures and shapes help pupil and teacher to identify any gaps in understanding.

Also available: the remaining pupil books as listed below. Separate books of answers - for quick and easy marking may also be obtained from Schofield & Sims. Mental Arithmetic Introductory Book Mental Arithmetic 1 Mental Arithmetic 2

ISBN 978 072 1 7 0798 3 ISBN 978 072 1 7 0799 0 ISBN 978 072 1 7 0800 3

Mental Arithmetic 4 Mental Arithmetic 5 Mental Arithmetic 6

ISBN 978 072 1 7 0802 7 ISBN 978 0721 7 0803 4 ISBN 978 072 1 7 0804 1

Other Key Stage 2 maths materials available from Schofield & Sims include: Understanding Maths - eight learning workbooks for Key Stage 2 Key Stage 2 Maths Revision Guide - comprehensive coverage of every topic likely to be covered in the Key Stage 2 tests Key Stage 2 Maths Practice Papers - with each page cross-referenced to the Revision Guide.

This edition copyright © Schofield and Sims Ltd .. 2007 Eighteenth impression 2014 First edition compiled by J. W. Adams and R. P. Beaumont, and edited by T. R. Goddard: copyright © Schofield & Sims Ltd . . 1 976 British Library Cataloguing in Publication Data: A catalogue record for this book is available from the Br;tish Library. All rights reserved . Except where otherwise indicated. no part of this publication may be reproduced, stored in a •etrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying. recording or otherwise, without either the prior permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Limited, Saffron House, 6-1 0 Kirby Street, London EC1 N BTS. Front cover design by Curve Creative. Bradford; redesign of selected pages at reprint by Ledgard Jepson. Sheffield. and Wyndehani Gait Ltd., Grimsby Printed in the UK by Wyndeham Gait Ltd. , Grimsby, Lincolnshire

ISBN 978-072 1 7-080 1 -0

Schofield&Sims

9

7807 2 1 7080 1 0

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