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KS2 Mathematics 2016 Paper 2: Reasoning
Exam Guide
- Paper Type: Reasoning (Non-Calculator)
- Total Marks: 35 Marks
- Instruction: You may not use a calculator to answer any questions in this test.
- Requirement: Show all working out for full marks.
Table of Contents
- Question 1 (Number Order)
- Question 2 (House Prices)
- Question 3 (Missing Digits)
- Question 4 (Population Table)
- Question 5 (Venn Diagram)
- Question 6 (Reflection)
- Question 7 (Equivalent Fractions)
- Question 8 (Decimal Addition)
- Question 9 (Cost Calculation)
- Question 10 (Shading Fractions)
- Question 11 (Usage Rate)
- Question 12 (Algebra Substitution)
- Question 13 (Stack Height)
- Question 14 (Common Multiples)
- Question 15 (Thermometer Scale)
- Question 16 (Place Value)
- Question 17 (Geometry Angles)
- Question 18 (Missing Number)
- Question 19 (Total Cost)
- Question 20 (Coordinates Reflection)
Question 1 (2 marks)
Ali puts these five numbers in their correct places on a number line.
511 499 502 555 455
Write the number closest to 500.
Write the number furthest from 500.
Question 2 (1 mark)
Put these houses in order of price starting with the lowest price.
One has been done for you.
Answer: _______ B _______ _______ _______
Worked Solution
Step 1: Listing the Values
💡 Why we do this: We need to compare the values carefully, looking at the thousands first.
✏ Working:
- A: 135,300
- B: 119,125 (Already placed: 2nd lowest)
- C: 130,500
- D: 131,500
- E: 91,500
Step 2: Ordering
💡 Why we do this: Sort from smallest to largest.
✏ Working:
- £91,500 (E) – Smallest (only 5 digits)
- £119,125 (B) – Given
- £130,500 (C) – 130k is smaller than 131k
- £131,500 (D)
- £135,300 (A) – Largest
🏁 Final Answer:
E, B, C, D, A
✓ Total: 1 mark
Question 3 (2 marks)
Write the three missing digits to make this addition correct.
+ 4 4
1 5
Worked Solution
Step 1: The Units Column
💡 Why we do this: Start from the right. We need a number that adds to 4 to end in 5.
Calculation: \( ? + 4 = 5 \)
Answer: \( 1 \)
So the top right digit is 1.
Step 2: The Tens Column
💡 Why we do this: Move to the middle column. We have \( 5 + ? \) ending in 1.
Calculation: \( 5 + ? = 11 \) (It must be 11 because 5 is larger than 1)
\( ? = 11 – 5 = 6 \)
So the middle box is 6.
Don’t forget the carry over of 1 to the hundreds column!
Step 3: The Hundreds Column
💡 Why we do this: Add the digits plus the carry over.
Calculation: \( 1 \text{ (top)} + 4 \text{ (bottom)} + 1 \text{ (carry)} = 6 \)
So the bottom left box is 6.
🏁 Final Answer:
1 5 [1]
+ 4 [6] 4
-------
[6] 1 5
✓ Total: 2 marks
Question 4 (2 marks)
This table shows the number of people living in various towns in England.
| Town | Population |
|---|---|
| Bedford | 82,448 |
| Carlton | 48,493 |
| Dover | 34,087 |
| Formby | 24,478 |
| Telford | 166,640 |
What is the total of the numbers of people living in Formby and in Telford?
What is the difference between the numbers of people living in Bedford and in Dover?
Worked Solution
Step 1: Total for Formby and Telford
💡 Why we do this: “Total” means addition. We find the values for Formby and Telford and add them using column addition.
166640 (Telford)
+ 24478 (Formby)
--------
191118
11
Step 2: Difference between Bedford and Dover
💡 Why we do this: “Difference” means subtraction. We calculate Bedford minus Dover.
781234148 (Bedford) - 34087 (Dover) -------- 48361
🏁 Final Answer:
Total: 191,118
Difference: 48,361
✓ Total: 2 marks
Question 5 (2 marks)
Write each number in its correct place on the diagram.
16 17 18 19
Worked Solution
Step 1: Analyze Number 16
💡 Why we do this: Check properties: Is it Prime? Square? Even?
16 is \( 4 \times 4 \), so it is Square.
16 ends in 6, so it is Even.
It is not Prime.
Placement: Intersection of Square and Even.
Step 2: Analyze Number 17
17 has only factors 1 and 17. It is Prime.
It is not Square. It is not Even (Odd).
Placement: Prime circle only.
Step 3: Analyze Number 18
18 ends in 8. It is Even.
Factors: 1, 2, 3, 6, 9, 18. Not Prime.
Not a square number (\(4^2=16, 5^2=25\)).
Placement: Even region only (bottom oval, outside other circles).
Step 4: Analyze Number 19
19 has only factors 1 and 19. It is Prime.
Not Square. Not Even.
Placement: Prime circle only.
🏁 Final Answer:
- 17, 19: In ‘prime numbers’ only.
- 16: In overlap of ‘square numbers’ and ‘even numbers’.
- 18: In ‘even numbers’ only.
✓ Total: 2 marks
Question 6 (1 mark)
This diagram shows a shaded shape inside a border of squares.
Draw the reflection of the shape in the mirror line.
Use a ruler.
Question 7 (2 marks)
Write the two missing values to make these equivalent fractions correct.
Question 8 (1 mark)
Circle two numbers that add together to equal 0.25
0.05 0.23 0.2 0.5
Question 10 (2 marks)
Each diagram below is divided into equal sections.
Shade three-quarters of each diagram.
Question 11 (2 marks)
A packet contains 1.5 kg of oats.
Every day Maria uses 50 g of oats to make porridge.
How many days does the packet of oats last?
Question 12 (2 marks)
a) \( n = 22 \)
What is \( 2n + 9 \)?
b) \( 2q + 4 = 100 \)
Work out the value of \( q \).
\( q = \)
Question 13 (2 marks)
A stack of 20 identical boxes is 140 cm tall.
Stefan takes three boxes off the top.
How tall is the stack now?
Question 15 (2 marks)
This thermometer shows temperatures in both °C and °F.
Work out what 25°C is in °F.
Question 16 (2 marks)
Write the number that is five less than ten million.
Write the number that is one hundred thousand less than six million.
Question 17 (2 marks)
Calculate the size of angles \(a\) and \(b\) in this diagram.
\( a = \) °
\( b = \) °
Question 19 (3 marks)
Miss Mills is making jam to sell at the school fair.
- 🍓 Strawberries cost £7.50 per kg
- 🍬 Sugar costs 79p per kg
- 🫙 10 glass jars cost £6.90
She uses 12 kg of strawberries and 10 kg of sugar to make 20 jars full of jam.
Calculate the total cost to make 20 jars full of jam.
Question 20 (1 mark)
Here are two triangles drawn on coordinate axes.
Triangle B is a reflection of triangle A in the x-axis.
Two of the new vertices of triangle B are (10, -10) and (20, -30).
What are the coordinates of the third vertex of triangle B?
( , )