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

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 the Key Stage 2 National Tests' 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.

From the list of numbers below, select two numbers which multiply to make 0.074.

7.4

0.1

0.2

0.37

Match each expression on the left with its simplified version on the right.

 

Column A

Column B

2(w + 3)
2w + 7
2(w - 3)
2w + 6
(w + 3) + (w + 4)
2w - 6
(w + 3) - (w + 2)
2w + 2
(w + 3) + (w - 1)
1

Calculate:

 

1329 - 457 = ?     

Column A

Column B

2(w + 3)
2w + 7
2(w - 3)
2w + 6
(w + 3) + (w + 4)
2w - 6
(w + 3) - (w + 2)
2w + 2
(w + 3) + (w - 1)
1

This pictogram shows the number of books read by some children.

 

How many more books did Jenny read than Amrita?

 

A bicycle originally costs £150.

 

 

It is reduced to £120 in the sale.

 

By what percentage has the price of the bicycle been reduced in the sale?

10%

30%

20%

15%

150%

Wishy Washy Soap Powder is sold in 2kg and 3kg packs as shown below.

 

Which pack is the better value?

 

 

 

2 kg pack

3 kg pack

Both the same

In which section will the following numbers go in this Venn Diagram?

 

14     15     32     35   

 

 

 

Column A

Column B

14
C
15
A
32
B
35
D

Look at the following price list.

 

 

Jill has a £5 note.

 

She buys 3 notepads, a ruler and 2 ballpoint pens.             

                            

How much change does she get in pence?

Daniel drives his car for a whole day.

 

He starts off with a full tank, using fuel as he drives. 

 

Which scatter graph shows this?

 

A

 

B

 

C                  

 

A

B

C

This is a right-angled triangle.

 

How many degrees is angle x?

 

 

Select the factors of 24 from this list of numbers.

 

1  2  4  8  12  16  20  24  46  48  50

1

2

4

8

12

16

20

24

46

48

50

Which two letters in the chart show where identical answers will be written?

 

  Nearest ten Nearest thousand Nearest tens of thousands.
45621 A B C
42648 D E F
48956 G H I

 

A

B

C

D

E

F

G

H

I

Select the angles which are obtuse.

 

 

(a)       (b)         (c)
 

 

 

(d)                (e)                (f)
 

 

 

(a)

(b)

(c)

(d)

(e)

(f)

Write the following time in the 24-hour clock format.

 

45 minutes before 8:35 p.m.

Charlie places 2 apples on a weighing scale.

 

The pointer shows the mass of both apples.

 

 

He takes away one apple.

 

The pointer shows the mass of the remaining apple.

 

 

What is the mass in grams of the apple that Charlie took away?

Look at this equation.

 

a - 3b = 20

 

When b = 15, what is the value of a?

 
 
  Alfie

                 

 
  
  Jaz


For every 2 toy cars that Alfie has, Jaz has 3.

 

Alfie actually has 30 toy cars.

 

How many does Jaz have?

Here is a parallelogram drawn on a graph.

 

What are the coordinates of the point at the top right?

 

 

A rectangle and its diagonal are shown below.             

 

 

Calculate the size of angle x.

Mrs Smith and Mr Newman go shopping for fruit salad. 

 

 

Mrs Smith buys 10 large cans of fruit salad. 

 

Mr Newman wants to buy a quarter of the amount of fruit salad as Mrs Smith but there are only smaller cans left. 

 

How many smaller cans does Mr Newman need to buy? Show your working. 

Lisa and Yahvin are writing lists of prime numbers between one and thirty. 

 

Yahvin's list has nine numbers and Lisa's has ten.

 

Whose list is correct? Explain your reasoning. 

 

There are several numbers which have been incorrectly placed in the Venn diagram.

 

Can you list them? Explain why they are incorrect. 

Matthew, Sian and Clare are discussing 2D shapes. 

 

Matthew says, "All quadrilaterals must contain at least one acute angle."

 

Is Matthew correct? Explain your reasoning giving examples to back up your explanation. 

  • Question 1

From the list of numbers below, select two numbers which multiply to make 0.074.

CORRECT ANSWER
0.2
0.37
EDDIE SAYS
The two correct numbers are 0.2 and 0.37 When multiplying decimals seems tricky, use whole numbers instead then use place value to find the correct decimal answer. 2 × 37 = 74 0.2 and 0.37 have 3 digits after the decimal place, so our answer must do too! 0.2 × 0.37 = 0.074
  • Question 2

Match each expression on the left with its simplified version on the right.

 

CORRECT ANSWER

Column A

Column B

2(w + 3)
2w + 6
2(w - 3)
2w - 6
(w + 3) + (w + 4)
2w + 7
(w + 3) - (w + 2)
1
(w + 3) + (w - 1)
2w + 2
EDDIE SAYS
2(w + 3) can be simplified to 2w + 6. This is because we have to multiply everything inside the brackets by 2.
2(w - 3) can be simplified to 2w - 6. This is because we have to multiply everything inside the brackets by 2.
(w + 3) + (w + 4) can be simplified as 2w + 7. This is because we add together the letters, then the numbers.
(w + 3) - (w + 2) can be simplified as 1. This is because we have to subtract: w - w = 0 3 - 2 = 1
(w + 3) + (w - 1) can be simplified as 2w + 2. This is because we add together the two sets of brackets: w + w = 2w 3 + -1 = 2
Top revision tip: Adding a negative number means our total decreases rather than increasing.
  • Question 3

Calculate:

 

1329 - 457 = ?     

CORRECT ANSWER
EDDIE SAYS
The answer is 872. Use column subtraction to do this accurately. Watch out for the tens column as you can't subtract 2 from 5!
  • Question 4

This pictogram shows the number of books read by some children.

 

How many more books did Jenny read than Amrita?

 

CORRECT ANSWER
8
EDDIE SAYS
The answer is 8.
Check the key carefully on pictogram questions. Here, one book symbol represents 2 books.
Jenny read 6 × 2 = 12 books.
Amrita read 2 × 2 = 4 books.
12 - 4 = 8
  • Question 5

A bicycle originally costs £150.

 

 

It is reduced to £120 in the sale.

 

By what percentage has the price of the bicycle been reduced in the sale?

CORRECT ANSWER
20%
EDDIE SAYS
The answer is 20%. The actual reduction in price is £30. 150 - 120 = £30 We can show this as a fraction of the whole price. 30/150 Then simplify the fraction. 30/150 = 10/50 = 1/5 We know that 1/5 is the same as 20%.
  • Question 6

Wishy Washy Soap Powder is sold in 2kg and 3kg packs as shown below.

 

Which pack is the better value?

 

 

 

CORRECT ANSWER
Both the same
EDDIE SAYS
The answer is that both the packs are the same value. The 2 kg pack costs £1.50 per kg. 3 ÷ 2 = 1.5 The 3 kg pack costs £1.50 per kg. 4.5 ÷ 3 = 1.5
  • Question 7

In which section will the following numbers go in this Venn Diagram?

 

14     15     32     35   

 

 

 

CORRECT ANSWER

Column A

Column B

14
C
15
A
32
D
35
B
EDDIE SAYS
The answers are: A = 15 B = 35 C = 14 D = 32 Use your knowledge of times tables facts to help with this question. 14 is a multiple of 7 but not 5.
15 is a multiple of 5 but not 7.
32 is neither a multiple of 5 nor 7.
35 is a multiple of both 5 and 7.
  • Question 8

Look at the following price list.

 

 

Jill has a £5 note.

 

She buys 3 notepads, a ruler and 2 ballpoint pens.             

                            

How much change does she get in pence?

CORRECT ANSWER
70
EDDIE SAYS
The answer is 70 pence. 3 notepads cost 285 pence. 3 × 95 = 285
A ruler costs 75 pence.
2 ballpoint pens cost 70 pence. 2 × 35 = 70
She spends 430 pence. 285 + 75 + 70 = 430
She starts with 500 pence and gets 70 pence change. 500 - 430 = 70
  • Question 9

Daniel drives his car for a whole day.

 

He starts off with a full tank, using fuel as he drives. 

 

Which scatter graph shows this?

 

A

 

B

 

C                  

 

CORRECT ANSWER
B
EDDIE SAYS
The answer is B. As Daniel drives further his distance travelled increases.
However, the amount of fuel in his tank decreases.
  • Question 10

This is a right-angled triangle.

 

How many degrees is angle x?

 

 

CORRECT ANSWER
57
EDDIE SAYS
The answer is 57°. Remember that angles in triangles always total 180°.
This triangle also contains a right angle (90°) marked with a square corner.
Simple subtract the known angles from 180 to calculate angle x.
180 - 90 = 90
90 - 33 = 57
  • Question 11

Select the factors of 24 from this list of numbers.

 

1  2  4  8  12  16  20  24  46  48  50

CORRECT ANSWER
1
2
4
8
12
24
EDDIE SAYS
The answers are 1, 2, 4, 8, 12 and 24. These are all the numbers which divide into 24 exactly without leaving a remainder. Watch out! 48 is a multiple of 24, not a factor.
  • Question 12

Which two letters in the chart show where identical answers will be written?

 

  Nearest ten Nearest thousand Nearest tens of thousands.
45621 A B C
42648 D E F
48956 G H I

 

CORRECT ANSWER
C
I
EDDIE SAYS
The answers are C and I (45621 and 48956 rounded to the nearest tens of thousands). Both of these numbers round up to 50000.
  • Question 13

Select the angles which are obtuse.

 

 

(a)       (b)         (c)
 

 

 

(d)                (e)                (f)
 

 

 

CORRECT ANSWER
(a)
(b)
(e)
EDDIE SAYS
The answers are A, B and E. Obtuse angles are greater than 90° but less than 180°.
  • Question 14

Write the following time in the 24-hour clock format.

 

45 minutes before 8:35 p.m.

CORRECT ANSWER
19:50
EDDIE SAYS
The answer is 19:50. 8:35 p.m. is written as 20:35 in the 24-hour clock.
35 minutes before this is 20:00
Another 10 minutes before this is 19:50.
  • Question 15

Charlie places 2 apples on a weighing scale.

 

The pointer shows the mass of both apples.

 

 

He takes away one apple.

 

The pointer shows the mass of the remaining apple.

 

 

What is the mass in grams of the apple that Charlie took away?

CORRECT ANSWER
220
EDDIE SAYS
The apple Charlie took away weighed 220 grams. Subtract the weight of the apple left on the scales from the weight of the two apples.
360 g - 140 g = 220 g
  • Question 16

Look at this equation.

 

a - 3b = 20

 

When b = 15, what is the value of a?

CORRECT ANSWER
65
EDDIE SAYS
The answer is 65. We are told that b is worth 15 so 3b is worth 45.
a - 45 = 20
Add together the two numbers to find the value of a. 45 + 20 = 65
Now check that the number works. 65 - 45 = 20
  • Question 17

 
 
  Alfie

                 

 
  
  Jaz


For every 2 toy cars that Alfie has, Jaz has 3.

 

Alfie actually has 30 toy cars.

 

How many does Jaz have?

CORRECT ANSWER
45
EDDIE SAYS
The answer is 45. Alfie has 30 cars, which is 15 lots of 2.
So Jaz has 15 lots of 3, i.e. 45 cars.
  • Question 18

Here is a parallelogram drawn on a graph.

 

What are the coordinates of the point at the top right?

 

 

CORRECT ANSWER
EDDIE SAYS
The answer is (8,7). We can use the information given to work out the missing coordinate. Look at the bottom two points, whose x coordinates differ by 3.
The top points will also have x coordinates which differ by 3.
The x coordinate will be 8. 5 + 3 = 8
The y coordinate of the missing point will be 7 as it is level in height with (5, 7).
  • Question 19

A rectangle and its diagonal are shown below.             

 

 

Calculate the size of angle x.

CORRECT ANSWER
58
EDDIE SAYS
The answer is 58°. Remember that angles in a triangle add to 180°. 90 + 32 = 122 180 - 122 = 58
  • Question 20

Mrs Smith and Mr Newman go shopping for fruit salad. 

 

 

Mrs Smith buys 10 large cans of fruit salad. 

 

Mr Newman wants to buy a quarter of the amount of fruit salad as Mrs Smith but there are only smaller cans left. 

 

How many smaller cans does Mr Newman need to buy? Show your working. 

CORRECT ANSWER
EDDIE SAYS
The answer is 5 cans. Mrs Smith buys 10 cans, which contain 4500 grams. 450 × 10 = 4500 Mr Newman wants to buy a quarter as much, which is 1125 grams. 4500 ÷ 4 = 1125 Four cans won't be enough, so he has to buy five as he can't buy half a can! 1125 ÷ 250 = 4.5
  • Question 21

Lisa and Yahvin are writing lists of prime numbers between one and thirty. 

 

Yahvin's list has nine numbers and Lisa's has ten.

 

Whose list is correct? Explain your reasoning. 

CORRECT ANSWER
EDDIE SAYS
Lisa is correct. There are 10 prime numbers between one and thirty. Prime numbers have only two factors, themselves and the number one. Well done if you spotted all the primes between one and thirty: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
  • Question 22

 

There are several numbers which have been incorrectly placed in the Venn diagram.

 

Can you list them? Explain why they are incorrect. 

CORRECT ANSWER
EDDIE SAYS
2, 3 and 12 are all placed incorrectly. They are all multiples of six and factors of twelve, so should be placed in the overlapping part of the diagram.
  • Question 23

Matthew, Sian and Clare are discussing 2D shapes. 

 

Matthew says, "All quadrilaterals must contain at least one acute angle."

 

Is Matthew correct? Explain your reasoning giving examples to back up your explanation. 

CORRECT ANSWER
EDDIE SAYS
Matthew is incorrect. Many quadrilaterals (shapes with four sides) do have at least one acute angle (angles smaller than 90 °. However, squares and rectangles are quadrilaterals and only contain right angles (90deg;).
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