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Reasoning Mathematics Paper 2 in the Style of 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.

'Reasoning Mathematics Paper 2 in the Style of 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 Arithmetic paper in the style of a Key Stage 2 National Test.

 

This is an assessment with a variety of arithmetic questions.

Some are multiple-choice and some will require you to type in an answer.

 

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 choose an answer or 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.

In which of these 5 numbers, does the digit 5 have the greatest value?

4.356     4.635     4.365     4.536     4.257

4.356

4.635

4.365

4.536

4.257

Which number comes next in this sequence?

3.51, 3.72, 3.93, ?

Which numbers are missing from this multiplication grid?

 

 

If the quadrilateral is reflected in the mirror line, where will the centre of the shape be?

 

(8,5)

(10,5)

(9,5)

(5,5)

Oliver has written 3 equivalent fractions.

Match the letters and numbers to show how each fraction should be completed.

Column A

Column B

a
15
b
3
c
20

Ben has drawn a right-angled triangle.

 

 

Ben says "angle a must be more than 55°".

Angie says "angle a must be less than 55°".

Who is correct? Explain your answer.

Ann is shopping for vegetables.

She buys 3/4 of a kilogram of carrots and weighs them on the digital scales.

The digital scales show the mass of the carrots in grams and kilograms.

What number do the scales show on their display?

0.75 kg

75 g

750 g

0.075 kg

Ben and Sita go shopping.

 

Fruit Price per kg
Oranges £3.40
Bananas £2.60
Apples £1.25

 

Ben has a five-pound note and Sita has 4 £2 coins.

They buy 2 kg of oranges and 3 kg of apples.

How much do they spend altogether?

How much change do they get?

 

Write your answer in numbers without the £ sign.

0.75 kg

75 g

750 g

0.075 kg

Match these numbers to the number they will round to.

Column A

Column B

34,589 rounded to the nearest thousand
35,000
34,589 rounded to the nearest hundred
30,000
34,589 rounded to the nearest ten
34,590
34,589 rounded to the nearest tens of thousand
34,600

5.14 × 2.89 × 3.51

Which of the following options would be the most sensible way to estimate the answer to this calculation?

5 x 2 x 3

5 x 3 x 4

5 x 3 x 3

6 x 3 x 4

Aimen thinks of a number.

She doubles it and adds 60.

Then she divides it by 5.

Her answer is 60.

 

Which number did Aimen start with?

5 x 2 x 3

5 x 3 x 4

5 x 3 x 3

6 x 3 x 4

Type the missing number in the box to make the calculation correct.

4.5 ÷ ? = 0.0045

5 x 2 x 3

5 x 3 x 4

5 x 3 x 3

6 x 3 x 4

Steve has drawn a trapezium.

 

 

Match the statements below with true and false to show your understanding.

Column A

Column B

Has 2 acute, and 2 obtuse angles.
True
Has 1 pair of parallel sides.
False
Has perpendicular sides.
True
Has angles which total 270°
False

Pair of dice

Ruth rolls 2 fair six-sided dice and then adds together the 2 numbers rolled. 

She says that she will never get a prime number total, no matter how many times she rolls the dice.

Is Ruth correct?

Explain your reasoning with an example.

These 2 shapes both have the same perimeter.

 

 

The octagon has sides of 6 cm.

What is the area of the square? Write your answer in numbers.

Fred wants to order the numbers from largest to smallest.

 

0.126

0.315

0.132

0.306

Column A

Column B

0.306
2nd
0.126
4th
0.132
3rd
0.315
1st

Christopher is using a rule to make a sequence.

The rule is to subtract 3, then multiply by 2.

Fill in the missing number in the sequence.

 

 

Column A

Column B

0.306
2nd
0.126
4th
0.132
3rd
0.315
1st

Which of the following statements are true and which are false?

Lucy and Ben are making cuboids from blocks.

Lucy makes a cuboid which is 2 cubes high, 3 cubes wide and 3 cubes deep.

 

 

 

Ben makes a cuboid double the height, width and depth and says that the volume will also be doubled. 

Is Ben correct?

 

Class 5 have been voting for their favourite fruit. 

Use the pie to answer the following questions.

 

a. What fraction of students prefer fruits beginning with p? Show your answer in it's simplest form.

 

b. What was the mean number of votes per fruit in the survey?

What number is missing from this calculation?

24 ÷ ? + 37 = 45

 

Match the numbers and letters below to show the missing numbers in these 2 calculations.

Column A

Column B

a
9
b
1
c
4
d
0

Mrs Smith has a dripping tap. 

Every 10 seconds, the tap drips twice.

Each drip contains 2.5 ml of water.

 

How much water does Mrs Smith waste in one day to the nearest litre?  Write your answer as a number without the units.

  • Question 1

In which of these 5 numbers, does the digit 5 have the greatest value?

4.356     4.635     4.365     4.536     4.257

CORRECT ANSWER
4.536
EDDIE SAYS
The answer is 4.536. In this number, the digit 5 is worth five-tenths. In the other numbers, the digit 5 is in the hundredths or thousandths place so it is worth less.
  • Question 2

Which number comes next in this sequence?

3.51, 3.72, 3.93, ?

CORRECT ANSWER
4.14
EDDIE SAYS
The missing number will be 4.14. The rule of the sequence is to add 0.21.
  • Question 3

Which numbers are missing from this multiplication grid?

 

 

CORRECT ANSWER
EDDIE SAYS
The missing numbers are as follows: a = 6 b = 63 c = 15 d = 5
  • Question 4

If the quadrilateral is reflected in the mirror line, where will the centre of the shape be?

 

CORRECT ANSWER
(9,5)
EDDIE SAYS
The answer is (9,5). The centre of the shape is (5,5) and when reflected over the mirror the centre will be 4 squares to the right at point (9,5).
  • Question 5

Oliver has written 3 equivalent fractions.

Match the letters and numbers to show how each fraction should be completed.

CORRECT ANSWER

Column A

Column B

a
3
b
15
c
20
EDDIE SAYS
The equivalent fractions are: 3/5, 9/15 and 12/20.
  • Question 6

Ben has drawn a right-angled triangle.

 

 

Ben says "angle a must be more than 55°".

Angie says "angle a must be less than 55°".

Who is correct? Explain your answer.

CORRECT ANSWER
EDDIE SAYS
Angle a is 52° so Angie is correct. All triangles have angles which add up to 180°. This triangle is right angled, so must contain one angle of 90°. To find the size of angle a, subtract 90° and 38° from 180°.
  • Question 7

Ann is shopping for vegetables.

She buys 3/4 of a kilogram of carrots and weighs them on the digital scales.

The digital scales show the mass of the carrots in grams and kilograms.

What number do the scales show on their display?

CORRECT ANSWER
0.75 kg
750 g
EDDIE SAYS
The scales will show 750g and 0.75kg. This is because there are 1000 grams in 1 kilogram and 3/4 of this is 750.
  • Question 8

Ben and Sita go shopping.

 

Fruit Price per kg
Oranges £3.40
Bananas £2.60
Apples £1.25

 

Ben has a five-pound note and Sita has 4 £2 coins.

They buy 2 kg of oranges and 3 kg of apples.

How much do they spend altogether?

How much change do they get?

 

Write your answer in numbers without the £ sign.

CORRECT ANSWER
EDDIE SAYS
They spend £6.80 on oranges and £3.75 on apples, so £10.55 in total. They have £13 to spend and will have £2.45 left.
  • Question 9

Match these numbers to the number they will round to.

CORRECT ANSWER

Column A

Column B

34,589 rounded to the nearest tho...
35,000
34,589 rounded to the nearest hun...
34,600
34,589 rounded to the nearest ten
34,590
34,589 rounded to the nearest ten...
30,000
EDDIE SAYS
34,589 rounded to the nearest thousand is 35,000. 34,589 rounded to the nearest hundred is 34,600. 34,589 rounded to the nearest ten 34,590. 34,589 rounded to the nearest tens of thousand 30,000.
  • Question 10

5.14 × 2.89 × 3.51

Which of the following options would be the most sensible way to estimate the answer to this calculation?

CORRECT ANSWER
5 x 3 x 4
EDDIE SAYS
5 × 3 × 4 is the most sensible option using rounding. 5.14 rounds down to 5. 2.89 rounds up to 3. 3.51 rounds up to 4.
  • Question 11

Aimen thinks of a number.

She doubles it and adds 60.

Then she divides it by 5.

Her answer is 60.

 

Which number did Aimen start with?

CORRECT ANSWER
EDDIE SAYS
Aimen starts with 120. 120 doubled is 240. 240 + 60 = 300 300 ÷ 5 = 60
  • Question 12

Type the missing number in the box to make the calculation correct.

4.5 ÷ ? = 0.0045

CORRECT ANSWER
EDDIE SAYS
The missing number is 1000. When dividing by 1000, each digit in a number moves 3 places to the right. Zero is used to hold the place of the ones, tenths and hundreds in this number.
  • Question 13

Steve has drawn a trapezium.

 

 

Match the statements below with true and false to show your understanding.

CORRECT ANSWER

Column A

Column B

Has 2 acute, and 2 obtuse angles.
True
Has 1 pair of parallel sides.
True
Has perpendicular sides.
False
Has angles which total 270°
False
EDDIE SAYS
A trapezium does have 2 acute and 2 obtuse angles. It also has one pair of parallel sides. There are no lines which meet at a right angle so there are no perpendicular lines. Angles in a quadrilateral (4 sided shape) always add up to 360°, not 270°.
  • Question 14

Pair of dice

Ruth rolls 2 fair six-sided dice and then adds together the 2 numbers rolled. 

She says that she will never get a prime number total, no matter how many times she rolls the dice.

Is Ruth correct?

Explain your reasoning with an example.

CORRECT ANSWER
EDDIE SAYS
Ruth is not correct. There are many ways she could roll a prime number total e.g. 1 + 1 = 2 (the only even prime). 1 + 2 = 3 1 + 4 = 5
  • Question 15

These 2 shapes both have the same perimeter.

 

 

The octagon has sides of 6 cm.

What is the area of the square? Write your answer in numbers.

CORRECT ANSWER
EDDIE SAYS
The square has an area of 144 cm². The octagon has 8 sides, each 6 cm. 6 × 8 = 48. Therefore, the square also has a perimeter of 48cm. Each side of the square must be 12cm. The area of the square can be found by multiplying the length of 2 sides. 12 × 12 = 144
  • Question 16

Fred wants to order the numbers from largest to smallest.

 

0.126

0.315

0.132

0.306

CORRECT ANSWER

Column A

Column B

0.306
2nd
0.126
4th
0.132
3rd
0.315
1st
EDDIE SAYS
The numbers in order from largest to smallest are: 0.315 0.306 0.132 0.126
  • Question 17

Christopher is using a rule to make a sequence.

The rule is to subtract 3, then multiply by 2.

Fill in the missing number in the sequence.

 

 

CORRECT ANSWER
EDDIE SAYS
The sequence will be as follows: 40, 72, 138, 270. To find the first missing number, divide by 2 and add 3. To find the last missing number, simply subtract 3 and multiply by 2.
  • Question 18

Which of the following statements are true and which are false?

CORRECT ANSWER
EDDIE SAYS
4/5 = 70% is not correct. 4/5 is equivalent to 8/10 or 80%. 2/3 > 60% is correct. 2/3 is eqivalent to 66.6%. 9/20 < 40% is not correct. 9/20 is equivalent to 45%. 6/5 > 90% is correct. 6/5 is an improper fraction, so is worth 1 1/5 or 120%. 3/4 < 70% is incorrect. 3/4 is equivalent to 75%.
  • Question 19

Lucy and Ben are making cuboids from blocks.

Lucy makes a cuboid which is 2 cubes high, 3 cubes wide and 3 cubes deep.

 

 

 

Ben makes a cuboid double the height, width and depth and says that the volume will also be doubled. 

Is Ben correct?

CORRECT ANSWER
EDDIE SAYS
Ben is not correct. Volume is found by multiplying the three dimensions of the cuboid. Length × Width × Depth Lucy's cuboid has a volume of 18 cm³ whereas Ben's has a volume of 144 cm³.
  • Question 20

 

Class 5 have been voting for their favourite fruit. 

Use the pie to answer the following questions.

 

a. What fraction of students prefer fruits beginning with p? Show your answer in it's simplest form.

 

b. What was the mean number of votes per fruit in the survey?

CORRECT ANSWER
EDDIE SAYS
The fraction of students who prefer fruits beginning with p is 10 out of 36. This can be simplified to 5/18. The mean number of votes per fruit is 9. To find the mean, add the numbers from the data, then divide by the number of pieces of data.
  • Question 21

What number is missing from this calculation?

24 ÷ ? + 37 = 45

CORRECT ANSWER
3
EDDIE SAYS
The missing number is 3. 24 ÷ 3 + 37 = 45
  • Question 22

 

Match the numbers and letters below to show the missing numbers in these 2 calculations.

CORRECT ANSWER

Column A

Column B

a
4
b
0
c
1
d
9
EDDIE SAYS
The calculations are as follows: 45 × 23 = 1035 1152 ÷ 12 = 96
  • Question 23

Mrs Smith has a dripping tap. 

Every 10 seconds, the tap drips twice.

Each drip contains 2.5 ml of water.

 

How much water does Mrs Smith waste in one day to the nearest litre?  Write your answer as a number without the units.

CORRECT ANSWER
43
EDDIE SAYS
The answer is 43 litres. In 10 seconds, the tap wastes 5ml. In 1 minute, the tap wastes 30ml. In 1 hour, the tap wastes 1,800ml. In 1 day (24 hours) the tap wastes 43,200ml. There are 1000ml in 1 Litre so this is 43.2 litres, which rounds to 43 litres.
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