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SATs Mathematics Reasoning Paper 3 in the Style of Key Stage 2 National Tests (Practice 1)

In this assessment, students will be able to complete a timed Reasoning paper in the style of Key Stage 2 SATs.

'SATs Mathematics Reasoning Paper 3 in the Style of Key Stage 2 National Tests (Practice 1)' worksheet

Key stage:  KS 2

Curriculum topic:   SATs Practice Papers

Curriculum subtopic:   Reasoning Practice Papers

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

This is a practice Reasoning paper in the style of a Key Stage 2 National Test.

 

In the real Key Stage 2 National Test, you will write your answers in a special test booklet, normally in a box or space.

 

You will also write your any working out or jottings in the booklet.

 

At EdPlace, you will use the computer to enter your answers and you should use a pencil and paper to complete your workings.

 

You must not use a calculator. 

 

This paper includes a variety of types of Reasoning questions.

 

You should work quickly and carefully through the questions. 

 

The timer is set for 40 minutes for this practice paper, although you can keep working after the timer has run out.

 

There are 23 questions. 

 

This means that you should aim for no more than 2 minutes per question and hopefully, as you become more confident, less than 1 minute.

 

Most questions are worth 1 mark and require you to type an answer in. These questions will be marked automatically.

Some questions are worth 2 marks and require you to explain your reasoning. These questions will need to be marked by an adult.

 

You may find some of the questions difficult.

 

If you are struggling to answer a question do not waste time on it, but move onto the next question.

 

Disclaimer:

We have no affiliation to the Standards and Testing Agency (STA) and these questions represent our own unique content developed by EdPlace Key Stage 2 Maths authors.

None of the content displayed here has been supplied by the STA or any other third party suppliers.

Round 36,620 to the nearest 1000.

 This four-digit number is larger than 5000, smaller than 8000 and divisible by 9.   

 

_534

 

What is the complete four-digit number?

m stands for a number.

 

'4 more than m' can be shown as the expression m + 4.

 

Match the number sentences on the left to the algebraic expressions on the right.

 

Column A

Column B

5 more than m
m - 5
2 more than three times m
m + 5
5 less than m
2m - 5
5 less than twice m
3m + 2

Order these price tags, starting with the smallest.

 

     £4.50  £4.05  £45

  

  £5.40  £40.50  £5.04

Column A

Column B

1 (smallest)
£5.40
2
£4.50
3
£4.05
4
£5.04
5
£45
6 (largest)
£40.50

Find the missing number in the calculation below:

 

7 × ? = 1288

Column A

Column B

1 (smallest)
£5.40
2
£4.50
3
£4.05
4
£5.04
5
£45
6 (largest)
£40.50

Stamps cost 52p each.

 

How many of these stamps can be bought for £10?

Here is an expression.

 

5y + 4

 

When y = 1, 5y + 4 = 9

 

9 is both odd and square.

 

For y = 3, y = 2.4 and y = 0.4, tick to show if 5y + 9 fits the criteria. 

 oddevensquareprimecube
y = 3
y = 2.4
y = 0.8

Find the missing number in the calculation below:

 

(4 × 9) - ? = 28

The table shows the cost of some maths equipment at the school shop.

 

Item Cost
Calculator £11.25
Geometry Set £6.85
Ruler 98p

 

Amy buys one calculator, one geometry set and two rulers.

How much does she spend? Show your answer in pounds and pence as a decimal. 

The pictogram shows the number of comics and books read, and the number of films watched by four children in a year.

 

How many more films did Dan watch compared to the books he read?

 

 

Look at the blue shape in the diagram below.

 

 

It is rotated 90° clockwise around the point X.

On which shape does it land?

A

B

C

How many lines of symmetry does this road sign have?

 

 

 

Select all the factors of 60.

1

2

3

4

5

6

8

9

10

12

14

15

20

30

60

Which is larger?

 

 

5/7 of 434

13% of 600

7/8 of 640

Jack's train leaves at 8.20 a.m.

 

When he arrives at the station, the clock shows:

 

          

 

For how many minutes, must Jack wait at the station before his train leaves?

Match the equivalent capacities.

Column A

Column B

1.2 litres
1.004 litres
1¼ litres
1250 ml
1400 ml
1040 ml
1.04 litres
1200 ml
1004 ml
1.4 litres

A builder uses this pie chart to work out the amount of cement, water and sand required to mix mortar.

 

 

How many kg of cement should be mixed with 8 kg of sand?

n stands for a whole number.

 

5n + 7 = 52

 

What is the value of n?

Here is a rectangle divided into identical small squares.                       

 

 

What fraction of the rectangle is shaded red?

 

Show your answer as a fraction in its simplest form. 

4/20

1/5

1/20

2/10

1/10

A bag contains 24 red beads and 10 blue beads.

 

Maria adds yellow beads to the bag.

 

The probability of picking a red bead is now 2/3.

 

How many yellow beads did Maria add to the bag?

 

Explain how you know. 

The diagram below is made of squares.

 

The area of the blue shaded square is 12 cm2.

 

Calculate the area inside the red square in cm2.

 

 

Show your working to explain how you know. 

 

 

This bar chart shows the favourite crisp flavour of some children.

 

 

Tanya says, "Slightly less than half of the children asked prefer Ready Salted or Salt and Vinegar".

 

Is Tanya correct?

 

Can you explain why?

Jane has four numbered pool balls.

 

 

She selects two balls and adds the scores together.

 

How many different totals can she get by adding the scores of two balls?

 

Show your working to prove your answer.

  • Question 1

Round 36,620 to the nearest 1000.

CORRECT ANSWER
37000
37,000
EDDIE SAYS
The answer is 37,000. When rounding to the nearest 1000, we need to check the hundreds number. If this is four or below, we round down. Five or higher means we round up. 36,620 has six hundreds, so we round up.
  • Question 2

 This four-digit number is larger than 5000, smaller than 8000 and divisible by 9.   

 

_534

 

What is the complete four-digit number?

CORRECT ANSWER
6534
6,534
EDDIE SAYS
The complete number is 6534. The number had to be larger than 5000, smaller than 8000 and divisible by 9. So, the choices were 5534, 6534 or 7534. The only one of these numbers that is divisible by 9 is 6534.
  • Question 3

m stands for a number.

 

'4 more than m' can be shown as the expression m + 4.

 

Match the number sentences on the left to the algebraic expressions on the right.

 

CORRECT ANSWER

Column A

Column B

5 more than m
m + 5
2 more than three times m
3m + 2
5 less than m
m - 5
5 less than twice m
2m - 5
EDDIE SAYS
The answers are as follows: 5 more than m = m + 5 2 more than three times m = 3m + 2 5 less than m = m - 5 5 less than twice m = 2m - 5 Top tip: In algebra, we write 3m instead of 3 × m so that we can't confuse the multiplication symbol with the letter x!
  • Question 4

Order these price tags, starting with the smallest.

 

     £4.50  £4.05  £45

  

  £5.40  £40.50  £5.04

CORRECT ANSWER

Column A

Column B

1 (smallest)
£4.05
2
£4.50
3
£5.04
4
£5.40
5
£40.50
6 (largest)
£45
EDDIE SAYS
From smallest to largest, the order is: £4.05, £4.50, £5.04, £5.40, £40.50 and £45. The digits after the decimal point show the number of pence, so £4.05 is 4 pounds and 5 pence.
  • Question 5

Find the missing number in the calculation below:

 

7 × ? = 1288

CORRECT ANSWER
EDDIE SAYS
The answer is 184. The best way to work this one out is to use the inverse (division). 1288 ÷ 7 = 184
  • Question 6

Stamps cost 52p each.

 

How many of these stamps can be bought for £10?

CORRECT ANSWER
19
EDDIE SAYS
The answer is 19. We can use mental maths to work this out. 20 stamps would cost £10.40. We can do: 10 × 52 = 520 Then double the answer: 20 × 52 = 1040 1040 pence = £10.40 This is over £10 The cost of 19 stamps is £9.88. 1040 - 52 = 988
  • Question 7

Here is an expression.

 

5y + 4

 

When y = 1, 5y + 4 = 9

 

9 is both odd and square.

 

For y = 3, y = 2.4 and y = 0.4, tick to show if 5y + 9 fits the criteria. 

CORRECT ANSWER
 oddevensquareprimecube
y = 3
y = 2.4
y = 0.8
EDDIE SAYS
When y = 3, 5y + 4 = 15 + 4 = 19 19 is is odd and prime. When y = 2.4, 5y + 4 = 12 + 4 = 16 16 is even and a square number. When y = 0.8, 5y + 4 = 4 + 4 = 8 8 is even and a cube number.
  • Question 8

Find the missing number in the calculation below:

 

(4 × 9) - ? = 28

CORRECT ANSWER
8
EDDIE SAYS
The missing number is 8. To work out the missing number, work out the brackets first. 4 × 9 = 36 Then use the inverse to calculate the missing number. 36 - 28 = 8
  • Question 9

The table shows the cost of some maths equipment at the school shop.

 

Item Cost
Calculator £11.25
Geometry Set £6.85
Ruler 98p

 

Amy buys one calculator, one geometry set and two rulers.

How much does she spend? Show your answer in pounds and pence as a decimal. 

CORRECT ANSWER
20.06
EDDIE SAYS
The answer is £20.06. Firstly, add together the two amounts of 98 pence. 2 × 98 = 196 196 pence is equal to £1.98. Next, add together in columns making sure that the decimal points are in line. 11.25 + 6.85 + 1.98 = 20.06
  • Question 10

The pictogram shows the number of comics and books read, and the number of films watched by four children in a year.

 

How many more films did Dan watch compared to the books he read?

 

 

CORRECT ANSWER
9
EDDIE SAYS
The answer is 9. Dan watched 25 films. 5 × 5 = 25 He also read 16 books. 4 × 4 = 16 To find the difference between 25 and 16 we subtract. 25 - 16 = 9
  • Question 11

Look at the blue shape in the diagram below.

 

 

It is rotated 90° clockwise around the point X.

On which shape does it land?

CORRECT ANSWER
B
EDDIE SAYS
The answer is B. When rotating, remember the corner on the point X remains fixed and the rest of the shape is turned. In this case, the shape is turned clockwise 90° (a quarter turn).
  • Question 12

How many lines of symmetry does this road sign have?

 

 

 

CORRECT ANSWER
2
EDDIE SAYS
The shape has 2 lines of symmetry. Remember that lines of symmetry divide a shape into exact halves where the two pieces are mirror images of each other. One line runs directly down the centre of the black stripe. The other line of symmetry crosses the black stripe exactly halfway. Both the lines of symmetry run across the centre of the circle.
  • Question 13

Select all the factors of 60.

CORRECT ANSWER
1
2
3
4
5
6
10
12
15
20
30
60
EDDIE SAYS
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. 1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10 Wow, sixty has so many factors! Well done if you spotted them all.
  • Question 14

Which is larger?

 

 

CORRECT ANSWER
7/8 of 640
EDDIE SAYS
The largest is 7/8 of 640. 5/7 of 434 is 310. 434 ÷ 7 = 62 62 × 5 = 310 13% of 600 is 78. 10 % of 600 = 60 1% of 600 = 6 3% of 600 = 18 60 + 18 = 78 7/8 of 640 is 560. 1/8 of 640 = 80 80 × 7 = 560
  • Question 15

Jack's train leaves at 8.20 a.m.

 

When he arrives at the station, the clock shows:

 

          

 

For how many minutes, must Jack wait at the station before his train leaves?

CORRECT ANSWER
46
EDDIE SAYS
The answer is 46 minutes. The clock shows a time of 7:34. There are 26 minutes until 8 a.m. and another 20 minutes until the train leaves at 8.20 a.m. 26 + 20 = 46
  • Question 16

Match the equivalent capacities.

CORRECT ANSWER

Column A

Column B

1.2 litres
1200 ml
1¼ litres
1250 ml
1400 ml
1.4 litres
1.04 litres
1040 ml
1004 ml
1.004 litres
EDDIE SAYS
1.2 litres is equal to 1200 ml. 1 1/4 litres is equal to 1250 ml. 1400 ml is equal to 1.4 litres. 1.04 litres is equal to 1040 ml. 1004 ml is equal to 1.004 litres. There are 1000 ml in one litre. To convert millilitres to litres, simply divide by 1000. To convert litres to millilitres we need to multiply by 1000.
  • Question 17

A builder uses this pie chart to work out the amount of cement, water and sand required to mix mortar.

 

 

How many kg of cement should be mixed with 8 kg of sand?

CORRECT ANSWER
2
EDDIE SAYS
The answer is 2 kg of cement. 60° is a quarter of 240° so the builder must use a quarter the amount of cement to sand. 8 ÷ 4 = 2
  • Question 18

n stands for a whole number.

 

5n + 7 = 52

 

What is the value of n?

CORRECT ANSWER
9
EDDIE SAYS
n stands for 9. Use inverse operations to find the missing value. 5n is worth 45. 52 - 7 = 45 5n just means five lots of n. Divide by 5 to find n. 45 ÷ 5 = 9 Check by replacing n with the number 9. (5 × 9) + 7 = 52
  • Question 19

Here is a rectangle divided into identical small squares.                       

 

 

What fraction of the rectangle is shaded red?

 

Show your answer as a fraction in its simplest form. 

CORRECT ANSWER
1/5
EDDIE SAYS
The answer is 1/5. There are 20 squares in total, 4 of which are shaded red. 4/20 can be simplified using the common factor of 4. 4/20 = 1/5
  • Question 20

A bag contains 24 red beads and 10 blue beads.

 

Maria adds yellow beads to the bag.

 

The probability of picking a red bead is now 2/3.

 

How many yellow beads did Maria add to the bag?

 

Explain how you know. 

CORRECT ANSWER
EDDIE SAYS
The answer is 2. There are 24 red beads which are 2/3 of the total. 1/3 must, therefore, be equal to 12. So, there must be 36 beads in total. 3 × 12 = 36 There are originally 34 beads. 24 + 10 = 34 Two more are needed to make a total of thirty six. 34 + 2 = 36
  • Question 21

The diagram below is made of squares.

 

The area of the blue shaded square is 12 cm2.

 

Calculate the area inside the red square in cm2.

 

 

Show your working to explain how you know. 

 

 

CORRECT ANSWER
EDDIE SAYS
The answer is 768 cm². The small blue square has an area of 12 cm². Each black outlined square can fit four of the small blue squares, so has an area of four times this. 12 × 4 = 48 cm² There are 16 black outlined squares in the shape. Total area = 16 × 48 = 768 cm²
  • Question 22

This bar chart shows the favourite crisp flavour of some children.

 

 

Tanya says, "Slightly less than half of the children asked prefer Ready Salted or Salt and Vinegar".

 

Is Tanya correct?

 

Can you explain why?

CORRECT ANSWER
EDDIE SAYS
Tanya is incorrect. Slightly more than half of the children asked prefer Ready Salted or Salt and Vinegar. There are 40 votes in total and half of this would be 20. 21 children vote for either Ready Salted or Salt and Vinegar.
  • Question 23

Jane has four numbered pool balls.

 

 

She selects two balls and adds the scores together.

 

How many different totals can she get by adding the scores of two balls?

 

Show your working to prove your answer.

CORRECT ANSWER
EDDIE SAYS
There are 5 possible totals. Possible totals are 7, 8, 9, 10 and 11. 6 + 4 = 10 6 + 5 = 11 6 + 3 = 9 4 + 5 = 9 4 + 3 = 7 5 + 3 = 8
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