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National curriculum tests
Key Stage 2
Mathematics
PRACTICE TEST E
Paper 1: arithmetic
First name
Middle name
Last name
Total marks
It is illegal to make or distribute
unauthorised printed or digital
copies of copyrighted material.!
TheSchoolRun’s practice tests are similar in format and style to atypical KS2 SATs paper. They do not include any ofcial questions
and they are not endorsed by any ofcial examining body. © TheSchoolRun
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It is illegal to make or distribute
unauthorised printed or digital
copies of copyrighted material.!
Give your child the test paper along with a pen or sharp pencil.
They may use a rubber, but they can cross out instead of rubbing out if preferred.
Your child is not allowed a calculator or any other kind of mathematical equipment.
Give your child 30 minutes to do the test.
Encourage them to leave out any questions they are not sure of.
Remind them to check their work at the end if they have time.
Do not help your child with any of the questions.
Explain to your child that most questions on this Paper are worth one mark,but some questions are worth two marks. Even if the answer of a two-mark questionis incorrect, one mark may be awarded for using a (correct) formal method.
There is a maximum of 40 marks on Paper 1.
KS2 SATs
Maths arithmetic
TheSchoolRun practice papers
Paper 1: instructions
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89,998 + 3 =
154 x 3 =
1 mark
1 mark
1 mark
3
2
1
3.7 + 1.2 =
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9 x 6 =
4,512 + 375 =
64 ÷ 8 =
1 mark
1 mark
1 mark
6
5
4
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422 - 6 =
4.5 + 0.06 =
3 x 5 x 4 =
1 mark
1 mark
1 mark
9
8
7
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420 ÷6 =
4.9 x 1000 =
1 mark
1 mark
1 mark
12
11
10 + =2 4
9 9
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1 mark
1 mark
1 mark
15
14
13
500,000 - 7000 =
10 =
0.5 x 100 =
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1 mark
1 mark
1 mark
18
17
16 5,400 ÷ 6 =
60% of 500 =
6.37 x 3 =
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1 mark
1 mark
1 mark
21
20
19 + =3 2
6 6
6,273 + 3,628 =
5,600 ÷ 7 =
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1 mark
1 mark
24
22 7 - 3.09 =
13.7 - 4.9 =
54x
98
23
1 / 2 marks
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1 mark
26
1 495 525
x =1 17 3
1 mark
27 99% of 5kg =
1 / 2 marks
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1 mark
1 mark
30
28 839,628 - 45,289 =
6x
932
329
4 x 2 =15
1 / 2 marks
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1 mark
1 mark
1 mark
33
31
32
90 - 9 x 7 =
÷ 2 =110
1 - =1 14 8
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1 mark
35
4 138 2 0 34
1 mark
36 ÷ 3 =19
+ =5 46 5
1 / 2 marks
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END OF TEST
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1 mark
1
ANSWERS
1 mark
2
1 mark
3
1 mark
4
1 mark 5
1 mark
6
1 mark
7
81 mark
89,998 + 3 =
154 x 3 =
3.7 + 1.2 =
90,001
462
4.9
9 x 6 =
4,512 + 375 =
64 ÷ 8 =
54
4,887
8
422 - 6 =
4.5 + 0.06 =
416
4.56
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1 mark
9
1 mark
10
1 mark
11
1 mark
12
1 mark
1 mark
1 mark
16
13
14
15
1 mark
3 x 5 x 4 = 60
420 ÷ 6 =
4.9 x 1000 =
+ =2 49 9
70
4900
69
500,000 - 7000 =
10 =
0.5 x 100 =
493,000
100
50
5,400 ÷ 6 = 900
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1 mark
17
1 mark
18
1 mark
19
1 mark
20
1 mark
1 mark
1 / 2 marks
24
21
22
23
1 mark
Give 2 marks if your child has given thecorrect answer. Give one mark for thelong multiplication method (showingall the working right the way throughto the answer) but with one error.
60% of 500 =
6.37 x 3 =
300
19.11
+ =3 2
6 6
6,273 + 3,628 =
5,600 ÷ 7 =
6
800
7 - 3.09 = 3.91
13.7 - 4.9 =
2,832
8.8
54x
98
5
9,901
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25
1 mark
26
1 mark
27
1 mark
28
1 mark
1 / 2 marks
32
29
30
31
1 mark
Give 2 marks if your child has given thecorrect answer. Give one mark for thelong multiplication method (showingall the working right the way throughto the answer) but with one error.
Give 2 marks if your child has giventhe correct answer. Give one mark forthe long division method (showing allthe working right the way through tothe answer) but with one error. 1 / 2 marks
1 mark
x =1 17 3
99% of 5kg =
121
63
4.95kg or
4950g
839,628 - 45,289 =
4 x 2 =15
794,339
8,487
8 45
90 - 9 x 7 = 27
÷ 2 =110
120
1 495 5
6x 9323
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33
34
1 mark
35
1 mark
36
Give 2 marks if your child has giventhe correct answer. Give one mark forthe long division method (showing allthe working right the way through tothe answer) but with one error. 1 / 2 marks
END OF TEST
1 - =1 14 8
118
+ =5 4
6 5
65
÷ 3 =19
130
127
4 138 2 0
19
1 mark
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National curriculum tests
Key Stage 2
Mathematics
PRACTICE TEST E
Paper 2: reasoning
First name
Middle name
Last name
Total marks
It is illegal to make or distribute
unauthorised printed or digital
copies of copyrighted material.!
TheSchoolRun’s practice tests are similar in format and style to atypical KS2 SATs paper. They do not include any ofcial questions
and they are not endorsed by any ofcial examining body. © TheSchoolRun
-
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It is illegal to make or distribute
unauthorised printed or digital
copies of copyrighted material.!
Give your child the test paper along with a blue / black pen or dark pencil, a rubber (optional), aruler (showing cm and mm), a protractor (angle measurer) and a mirror.
They may use a rubber, but they can cross out instead of rubbing out if preferred.
Your child is not allowed a calculator or tracing paper.
Give your child 40 minutes to do the test.
Encourage them to leave out any questions they are not sure of.
Remind them to check their work at the end if they have time.
Do not help your child with any of the questions.
Explain to your child that most questions on this Paper are worth one mark,but some questions are worth two marks. Even if the answer of a two-mark questionis incorrect, one mark may be awarded for doing some of the working out correctly,so it is important to show your working clearly in the space provided.
There are a total of 35 marks on this paper.
KS2 SATs
Maths reasoning
TheSchoolRun practice papers
Paper 2: instructions
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340
135
365
1 mark
2 marks
Show your
method
is 25 less than
is 25 less than
1
2
Write the missing number. One has been done for you:
In a class of 20 children, 15 children receive £4 pocketmoney a week.
Five children receive £5 pocket money a week.
How much money do the class receive in total over 4 weeks?
£
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1 mark
1 mark
3
4
Claire thinks of a number. She subtracts 20 from it and endsup with - 6.
Express this fraction in its simplest form:
What was her original number?
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5
6
7
What is 100 hours in days and hours?
My train leaves at 13:17 and arrives two minutesbefore 2pm.
How long has the journey taken?
a) Write down a multiple of 32 (other than 32 itself)
b) Write down a common factor for 32 and 320 (otherthan 1 and 32)
1 mark
1 mark
1 mark
1 mark
days hours
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8 A furniture shop is selling dining tables for £220.
Dining chairs usually cost £50 each.
1st offer: If you buy 4 chairs to gowith the table, they cost a total of£180.
2nd offer: If you buy 6 chairs to gowith the table, they cost a total of£240.
b) How much money do you save on the chairs withthe second offer?
c) Mr Campbell chooses the first offer. How much doeshe spend on a table and 4 chairs?
a) How much money do you save on the chairs withthe first offer?
1 mark
1 mark
1 mark
£
£
£
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9 a) Here is a regular pentagon:
b) What size are each of its angles?
Use a ruler to work out its perimeter:
1 mark
1 mark
cm
°
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10
12
11
Write the missing number in this number sentence:
What number is halfway between 1.9 and 2.6?
Here is a number written in Roman numerals:
LXXXWrite the number in figures:
1 mark
1 mark
1 mark
19x = 3,800
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13 Draw a quadrilateral that has both an acute angle andan obtuse angle.
1 mark
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14 Round 5,294,758
To the nearest 100,000
To the nearest 10,000
To the nearest 1000
2 marks
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15 Here are three angles on a straight line.
Calculate the size of the angle marked x .Do not use a protractor.
Not to
scale
2 marks
Show your
method
x is °
23° x
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16 Kayleigh is making a cheese and onion omelette.She buys the following things:
Six eggs £1.80An onion 24p250g of cheese £2.10
For the omelette she uses 2 eggs, half the onion and50g of cheese.
How much does the omelette cost to make?
2 marks
Show your
method
£
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17 Jane went to the front of her house every two hours andcounted the number of vehicles passing in one minute.
Time
8.30am
10.30am
12.30pm
2.30pm
4.30pm
6.30pm
Number of vehicles
15
5
8
4
7
21
What is the mean average number of vehicles thatpassed her house in one minute?
2 marks
Show your
method
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18 This pie chart shows how children in the whole of Year 6travel into school:
There are 52 children in the whole of Year 6.
a) How many children come to school by car?
b) 5 children come to school by taxi. How many children cycle?
c) 17 children come to school by bus. How many children walk?
1 mark
1 mark
1 mark
Car
Cycle
TaxiWalk
Bus
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19
20
Two litres of sparking water costs £1.68.
What does 750ml of sparkling water cost?
I have read of my book.
I have 175 pages left to read.
How many pages are in my book altogether?
2 marks
2 marks
Show your
method
Show your
method
£
£
3
10
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21
22
A rectangle has an area of 45cm².
One of its sides is 9cm long.
What is its perimeter?
A cube has edges of 7cm.
What is the volume of the cube?
1 mark
1 mark
cm
cm 3
END OF TEST
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ANSWERS
340
135
365
1 mark
2 marks
is 25 less than
is 25 less than
1
2
Write the missing number. One has been done for you:
In a class of 20 children, 15 children receive £4 pocketmoney a week.
Five children receive £5 pocket money a week.
Award 2 marks for correct answer of £340.
Award 1 mark for an incorrect answer, if evidence ofappropriate method is shown, for example:15 x 4 = 605 x 5 = 2585 x 4 = wrong answer
How much money do the class receive in total over 4 weeks?
160
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1 mark
1 mark
3
4
Claire thinks of a number. She subtracts 20 from it and endsup with - 6.
Express this fraction in its simplest form:
What was her original number?
14
14
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5
6
7
What is 100 hours in days and hours?
My train leaves at 13:17 and arrives two minutesbefore 2pm.
How long has the journey taken?
a) Write down a multiple of 32 (other than 32 itself)
Any multiple of 32 given: 64, 96, 128, 160, 192, etc.
2, 4, 8 or 16
b) Write down a common factor for 32 and 320 (otherthan 1 and 32)
1 mark
1 mark
1 mark
1 mark
days hours4 4
41 minutes
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8 A furniture shop is selling dining tables for £220.
Dining chairs usually cost £50 each.
1st offer: If you buy 4 chairs to gowith the table, they cost a total of£180.
2nd offer: If you buy 6 chairs to gowith the table, they cost a total of£240.
b) How much money do you save on the chairs withthe secnd offer?
c) Mr Campbell chooses the first offer. How much doeshe spend on a table and 4 chairs?
a) How much money do you save on the chairs withthe first offer?
1 mark
1 mark
1 mark
£
£
£
20
60
400
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9 a) Here is a regular pentagon:
b) What size are each of its angles?
Use a ruler to work out its perimeter:
1 mark
1 mark
cm
°108
15(When printed out atA4 paper size.)
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10
12
11
Write the missing number in this number sentence:
What number is halfway between 1.9 and 2.6?
Here is a number written in Roman numerals:
LXXXWrite the number in figures:
1 mark
1 mark
1 mark
19x = 3,800200
2.25
80
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13 Draw a quadrilateral that has both an acute angle andan obtuse angle.
Any quadrilateral with at least one acute angle (smallerthan 90°) and at least one obtuse angle (measuringbetween 90° and 180°), for example:
1 mark
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14 Round 5,294,758
To the nearest 100,000
Award 2 marks for all three correct.Award 1 mark for two correct.
To the nearest 10,000
To the nearest 1000
2 marks
5,300,000
5,290,000
5,295,000
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15 Here are three angles on a straight line.
Award 2 marks for correct answer of 67°
Award 1 mark for an incorrect answer, if evidence ofappropriate method is shown, for example:23 + 90 = 113°180 - 113 = wrong answer
Calculate the size of the angle marked x .Do not use a protractor.
Not to
scale
2 marks
23° x
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16 Kayleigh is making a cheese and onion omelette. Shebuys the following things:
Six eggs £1.80An onion 24p250g of cheese £2.10
For the omelette, she uses 2 eggs, half the onion and50g of cheese.
How much does the omelette cost to make?
Award 2 marks for correct answer of £1.14
Award 1 mark for an incorrect answer, if evidence ofappropriate method is shown, for example:
£1.80 ÷ 6 = 30p, 30 x 2 = 60p24 ÷ 2 = 12p2.10 ÷ 5 = wrong answer
60 + 12 + wrong answer = wrong answer2 marks
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17 Jane went to the front of her house every two hours andcounted the number of vehicles passing in one minute.
Time
8.30am
10.30am
12.30pm
2.30pm
4.30pm
6.30pm
Number of vehicles
15
5
8
4
7
21
What is the mean average number of vehicles thatpassed her house in one minute?
Award 2 marks for correct answer of 10Award 1 mark for an incorrect answer, if evidence ofappropriate method is shown, for example:
All six amounts added up and divided by 6, but witha small mistake that leads to wrong answer.
2 marks
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18 This pie chart shows how children in the whole of Year 6travel into school:
There are 52 children in the whole of Year 6.
a) How many children come to school by car?
b) 5 children come to school by taxi. How many children cycle?
c) 17 children come to school by bus. How many children walk?
1 mark
1 mark
1 mark
Car
Cycle
Taxi
Walk
Bus
13
8
9
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19
20
Two litres of sparking water costs £1.68.
What does 750ml of sparkling water cost?
Award 2 marks for correct answer of 63p
Award 1 mark for an incorrect answer, if evidence ofappropriate method is shown, for example:
168 ÷ 2 = 84p (cost of 1 litre)84 ÷ 4 = wrong answer (cost of 250ml)Wrong answer x 3 = 63p (cost of 750ml)
OR:168 ÷ 8 = 21p21 x 3 = wrong answer
Award 2 marks for correct answer of 250
Award 1 mark for an incorrect answer, if evidence ofappropriate method is shown, for example:175 ÷ 7 = wrong answerWrong answer x 10 = wrong answer
I have read of my book.
I have 175 pages left to read.
How many pages are in my book altogether?
2 marks
2 marks
3
10
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21
22
A rectangle has an area of 45cm².
One of its sides is 9cm long.
What is its perimeter?
A cube has edges of 7cm.
What is the volume of the cube?
1 mark
1 mark
cm
cm 3
28
343
END OF TEST
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National curriculum tests
Key Stage 2
Mathematics
PRACTICE TEST E
Paper 3: reasoning
First name
Middle name
Last name
Total marks
It is illegal to make or distribute
unauthorised printed or digital
copies of copyrighted material.!
TheSchoolRun’s practice tests are similar in format and style to atypical KS2 SATs paper. They do not include any ofcial questions
and they are not endorsed by any ofcial examining body. © TheSchoolRun
-
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It is illegal to make or distribute
unauthorised printed or digital
copies of copyrighted material.!
Give your child the test paper along with a blue / black pen or dark pencil, a rubber (optional), aruler (showing cm and mm), a protractor (angle measurer) and a mirror.
They may use a rubber, but they can cross out instead of rubbing out if preferred.
Your child is not allowed a calculator or tracing paper.
Give your child 40 minutes to do the test.
Encourage them to leave out any questions they are not sure of.
Remind them to check their work at the end if they have time.
Do not help your child with any of the questions.
Explain to your child that most questions on this Paper are worth one mark,but some questions are worth two marks. Even if the answer of a two-mark questionis incorrect, one mark may be awarded for doing some of the working out correctly,so it is important to show your working clearly in the space provided.
There are a total of 35 marks on this paper.
KS2 SATs
Maths reasoning
TheSchoolRun practice papers
Paper 3: instructions
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1 mark
1
2
Here is a diagram for sorting numbers.
Put one number into each of the two empty sections.
It is - 4°C in the middle of the night.
By morning, the temperature is 2°C.
How much has the temperature risen in this time?
Prime number Above 10
5
°C 1 mark
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1 mark
1 mark
1 mark
3 Look at this number:
Write the digit that is in the tenths place
If you added 10,000 to this number, which digitwould change?
Write the digit that is in the tens place
479,382.651
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4This bar chart shows the eye colour of the children in the wholeof Year 5:
Esme says: “Over half the children in Year 5 havegreen eyes.”
Explain why she is wrong.
1 mark
Blue Green Brown
20
25
30
35
15
10
5
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5 These potatoes weigh 500g.
Put an arrow on the scales to show this amount.
1 mark
1 mark
1 k g
gram
0 g
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6
7
What do I have to add to 0.007 to make 1?
Write this number in words:
3,892,859
1 mark
1 mark
8 Danny got 86% in an exam.
He got 43 marks in total.
What was the total possible number of marks he couldhave got?
1 mark
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9
What are the co-ordinates for point A?
What are the co-ordinates for point B?
A ( , )
( , )B
( , )
( , )
1 mark
1 mark
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10 Together, these four bags weigh 1 kg.
They are all of identical weight.
a) What is the weight of each bag?Give your answer in grams.
b) What would the weight of 8 bags be?
1 mark
1 mark g
kg
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11 Write in the four missing digits to make this subtraction correct:
2 marks
- 4
2
8
5
5
1
5
4
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12
13
What do you multiply 7 by to make 2.1?
Simplify this fraction:
1860
749
1 mark
1 mark
1 mark
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14 Claire has eaten a third of her dinner.
Tanya has eaten half this amount.
How much has Tanya eaten?
1 mark
15 What is the area of this triangle?
1 mark
5cm
6 c m
cm2
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16 Robert starts with a number and multiplies it by 3.
He then halves the result.
He adds ten to this.
He ends up with 26.5.
What number did he start with?
2 marks
Show your
method
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17 There are 1000 cars in a multi-storey car park.
600 of these are staying in the car park for the whole day.
What percentage are NOT staying in the car park for the
whole day?
2 marks
Show your
method
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18 Here are the ingredients for vegetable lasagne:
90g carrots90g courgettes90g mushrooms150g cheese300ml milk30g flour15 pasta sheets
Daniel has only 100g of cheese, so he will have to makea smaller lasagne than the one in the recipe.
1 mark
1 mark
a) What weight of mushrooms should he use?
b) How many pasta sheets should he use?
g
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19Mr Potter wants to make a border of square stone slabsaround the edge of his pond like this:
The pond is a square.
Its perimeter is 6 metres.
Each stone square has sides of 25cm.
How many stone squares will he need to go all the wayaround the outside of the pond?
Hint: Don’t forget the corners!
2 marks
Show your
method
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20 This line graph shows the grades a boy got on each of hissix maths tests:
a) Roughly what mark did he get for Test 5?
b) Roughly what is the difference in marks between hishighest and lowest score?
1 mark
1 mark
20
1
M a r k o u t o f 2 0
2 3 4 5 6
40
60
80
100
120
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10100
30100
48
30%
60%
0.1
0.6
0.5
21 Match each card on the left to an equivalent card on theright, by drawing lines.
2 marks
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22 What number needs to go in the gap to make thisnumber sentence correct?
x 7 = 50 - 81 mark
END OF TEST
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ANSWERS
1 mark
1 mark
1
2
Here is a diagram for sorting numbers.
Put one number into each of the two empty sections.
Middle section to have any prime number above 10:11, 13, 17, 19, 23, 29 etc.Right-hand section to have any number above 10 thatis NOT prime: 12, 14, 15, 16, 18, 20, 21, 22 etc.
It is - 4°C in the middle of the night.
By morning, the temperature is 2°C.
How much has the temperature risen in this time?
Prime number Above 10
5
°C
6
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1 mark
1 mark
1 mark
3 Look at this number:
Write the digit that is in the tenths place
If you added 10,000 to this number, which digitwould change?
Write the digit that is in the tens place
479,382.651
8
6
7
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4This bar chart shows the eye colour of the children in the wholeof Year 5:
Esme says: “Over half the children in Year 5 havegreen eyes.”
Explain why she is wrong.
There are 60 children altogether and only 20 havegreen eyes.OROne third of the children have green eyes.
1 mark
Blue Green Brown
20
25
30
35
15
10
5
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5 These potatoes weigh 500g.
Put an arrow on the scales to show this amount.
1 mark
1 mark
1 k g
gram
0 g
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6
7
What do I have to add to 0.007 to make 1?
Write this number in words:
Three million, eight hundred and ninety-two thousand,eight hundred and fifty-nine.
3,892,859
1 mark
1 mark 0.993
8 Danny got 86% in an exam.
He got 43 marks in total.What was the total possible number of marks he couldhave got?
501 mark
-
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75/86
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unauthorised printed or digital
copies of copyrighted material.!
9
What are the co-ordinates for point A?
What are the co-ordinates for point B?
A ( , )
( , )B
( , )
( , )2 7
7 3
1 mark
1 mark
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unauthorised printed or digital
copies of copyrighted material.!
10 Together, these four bags weigh 1 kg.
They are all of identical weight.
a) What is the weight of each bag?Give your answer in grams.
b) What would the weight of 8 bags be?
1 mark
1 mark g
kg
250
2
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11 Write in the four missing digits to make this subtraction correct:
Award 2 marks for all four correct.Award 1 mark for three correct.
2 marks
- 4 3 9
1 4
2
8
5
5
1
5
4
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copies of copyrighted material.!
12
13
What do you multiply 7 by to make 2.1?
Simplify this fraction:
18 360 10
7 149 7
1 mark
1 mark
1 mark
0.3
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unauthorised printed or digital
copies of copyrighted material.!
14 Claire has eaten a third of her dinner.
Tanya has eaten half this amount.
How much has Tanya eaten?
1 mark
15 What is the area of this triangle?
1 mark
5cm
6 c m
cm2
16
15
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16 Robert starts with a number and multiplies it by 3.
He then halves the result.
He adds ten to this.
He ends up with 26.5.
What number did he start with?
Award 2 marks for correct answer of 11.
Award 1 mark for an incorrect answer, if evidence ofappropriate method is shown, for example:
26.5 - 10 = 16.5, 16.5 x 2 = wrong answer,wrong answer ÷ 3 = wrong answer.
2 marks
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17 There are 1000 cars in a multi-storey car park.
600 of these are staying in the car park for the whole day.
What percentage are NOT staying in the car park for the
whole day?
Award 2 marks for correct answer of 40%.
Award 1 mark for an incorrect answer, if evidence of
appropriate method is shown, for example:
600 / 1000 = 60 / 100So those NOT staying in car park = wrong answer / 100= wrong percentage
2 marks
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unauthorised printed or digital
copies of copyrighted material.!
18 Here are the ingredients for vegetable lasagne:
90g carrots90g courgettes90g mushrooms150g cheese300ml milk30g flour15 pasta sheets
Daniel has only 100g of cheese, so he will have to makea smaller lasagne than the one in the recipe.
1 mark
1 mark
a) What weight of mushrooms should he use?
b) How many pasta sheets should he use?
g60
10
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19Mr Potter wants to make a border of square stone slabsaround the edge of his pond like this:
The pond is a square.
Its perimeter is 6 metres.
Each stone square has sides of 25cm.
How many stone squares will he need to go all the wayaround the outside of the pond?
Hint: Don’t forget the corners!
Award 2 marks for correct answer of 28.
Award 1 mark for an incorrect answer, if evidence ofappropriate method is shown, for example:
Each side - 150cm, so can fit 6 squares6 x 4 = 24(child forgets to add corner stones to make total of 28).
2 marks
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copies of copyrighted material.!
20 This line graph shows the grades a boy got on each of hissix maths tests:
a) Roughly what mark did he get for Test 5?
90 (but accept between 88 and 92)
Accept between 22 and 27
b) Roughly what is the difference in marks between hishighest and lowest score?
1 mark
1 mark
20
1
M a r k o u t o f 2 0
2 3 4 5 6
40
60
80
100
120
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unauthorised printed or digital
copies of copyrighted material.!
10100
30100
48
30%
60%
0.1
0.6
0.5
21 Match each card on the left to an equivalent card on theright, by drawing lines.
Award 2 marks for all four correct.
Award 1 mark for two correct.
2 marks
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22 What number needs to go in the gap to make thisnumber sentence correct?
x 7 = 50 - 81 mark
END OF TEST
6