Key Stage 1 Mathematics Paper 2: Reasoning 2025

What are we asked? We need to find the number that comes right after 10.

“One more” means we add 1.

What do we know? There are 15 apples. 6 are sold (taken away).

What do we need to find? How many are left.

This is a subtraction sum: \( 15 – 6 \).

Look at the long rods. There are 2 rods.

Each rod is 10. So we have 2 tens.

\( 10 + 10 = 20 \)

Look at the separate cubes. There are 3 cubes.

Each cube is 1. So we have 3 ones.

The line goes from 10 to 20.

The mark is exactly in the middle (half-way).

The instruction was to write the number 9.

One-quarter (\( \frac{1}{4} \)) means 1 part out of 4 equal parts.

Or it means the shaded area is one fourth of the total area.

• Top Left: 4 equal strips. 1 is shaded. This is \( \frac{1}{4} \). (Tick)
• Top Right: 3 equal strips. 1 is shaded. This is \( \frac{1}{3} \). (Cross)
• Bottom Left: This shape is split. The top half is empty. The bottom half is split into two. The shaded part is half of the bottom half. Half of a half is a quarter. This is \( \frac{1}{4} \). (Tick)
• Bottom Right: 4 equal squares. 2 are shaded. This is \( \frac{2}{4} \) or \( \frac{1}{2} \). (Cross)

8 tens is \( 80 \).

7 ones is \( 7 \).

We have 3 sheets.

There are 4 stickers on each sheet.

This is 3 groups of 4.

The word is thirteen.

Thirteen means 1 ten and 3 ones.

It is written as 13.

• 30 is thirty.
• 13 is thirteen.
• 3 is three.
• 31 is thirty-one.

A line of symmetry works like a mirror. One side must be exactly the same as the other, just flipped.

• Top Left: Both sides match. Correct.
• Top Right: Both sides match. Correct.
• Bottom Left: Look at the sides. The left side is straight up. The right side is slanted. If you folded it, they would not meet. This is wrong.
• Bottom Right: Both sides match. Correct.

• Cylinder: 2 flat circles + 1 curved surface = 3 faces.
• Cuboid: Top, bottom, front, back, left, right = 6 faces.
• Cube: A cube is a special cuboid. Top, bottom, front, back, left, right = 6 faces.
• Square-based pyramid: 1 square base + 4 triangles = 5 faces.

The Cuboid has 6 faces.

The Cube has 6 faces.

These two numbers are the same.

We know that 1 hour has 60 minutes.

Draw a line from “1 hour” to “60 minutes”.

We know that 1 day has 24 hours.

Draw a line from “1 day” to “24 hours”.

The top number is 12 (the total).

One part is 9. We need to find the other part.

We can count on from 9 to 12.

9… 10, 11, 12. That is 3 steps.

Or subtract: \( 12 – 9 = 3 \).

We have two parts: 8 and 5.

We need to find the total on top.

Add them together: \( 8 + 5 \).

Start at 8 and count on 5: 9, 10, 11, 12, 13.

\( 8 + 5 = 13 \).

8 groups of 10.

We need to calculate \( 8 \times 10 \).

Smiley Face = 1 point

Star = 3 points

We have \( [?] + 7 + [?] = 15 \).

First, let’s take away the 7 that we know from the total.

\( 15 – 7 = 8 \).

So, the two empty boxes must add up to 8.

Kemi starts with 20.

She gives away \( ? \).

She ends with 8.

\( 20 – ? = 8 \)

We need to make 20.

We have 15.

\( 20 – 15 = 5 \).

So, 5 goes in the first box.

We need to make 20.

We have 4.

\( 20 – 4 = 16 \).

So, 16 goes in the second box.

The bottle holds half (\( \frac{1}{2} \)) a litre.

We need to make one whole litre.

• Triangle: 3 vertices. (Less than 4). Correct.
• Trapezium: 4 vertices. (Equal to 4). Correct.

• Hexagon: 6 vertices. (More than 5). Correct.
• Quadrilateral (bottom right): Count the corners. 1, 2, 3, 4.
• It has 4 vertices.
• It is in the “5 vertices or more” column.
• This is wrong.

We have 11 coins.

Each coin is £2.

Calculation: \( 11 \times 2 \).

If you use only 5p coins, the total amount must be in the 5 times table.

Multiples of 5 always end in 0 or 5.

• 20p: Ends in 0. \( 5, 10, 15, 20 \). Yes. (Tick)
• 13p: Ends in 3. Not a multiple of 5. No.
• 51p: Ends in 1. Not a multiple of 5. No.
• 15p: Ends in 5. \( 5, 10, 15 \). Yes. (Tick)
• 30p: Ends in 0. Yes. (Tick)

The numbers are 12, 5, and 7.

We know that \( 12 – 5 = 7 \).

We also know that \( 5 + 7 = 12 \) or \( 12 = 5 + 7 \).

Count the total number of equal squares: 3.

Count the number of shaded squares: 1.

The fraction is 1 out of 3.

Count the total number of small triangles: 4.

Count the number of shaded triangles: 3.

The fraction is 3 out of 4.

Three 5p coins.

\( 5 + 5 + 5 = 15 \)p.

Addition and subtraction are opposites (inverse).

If \( 12 + 7 = 19 \), then:

• \( 19 – 7 = 12 \)
• \( 19 – 12 = 7 \)

• 3cm > 3m: A metre (m) is much bigger than a centimetre (cm). Incorrect.
• 3kg > 3g: A kilogram (kg) is 1000g. So 3000g > 3g. Correct.
• 3ml > 3l: A litre (l) is bigger than a millilitre (ml). Incorrect.
• 3p > £3: £3 is 300p. 3p is not bigger than 300p. Incorrect.

• Top Left: \( 20 + 10 = 30 \)p.
• Top Right: Too many coins.
• Bottom Left: \( 20 + 5 + 2 = 27 \)p. Correct.
• Bottom Right: \( 10 + 5 + 5 = 20 \)p.

• Class A: Half past 12 (12:30).
• Class B: Half past 1 (1:30).
• Class C: Quarter past 12 (12:15).
• Class D: Quarter to 1 (12:45).

One triangle \( = \) 2 sandwiches.

We need a list with: 4 tuna, 8 cheese, 6 egg.

The bottom right list has these numbers.

We want to make 70, which ends in 0.

We need two numbers whose ones digits add to 10 (or 0).

• \( 27 \) and \( 37 \): \( 7+7=14 \) (Ends in 4). No.
• \( 35 \) and \( 45 \): \( 5+5=10 \) (Ends in 0). Let’s check: \( 30+40+10 = 80 \). Too high.
• \( 27 \) and \( 43 \): \( 7+3=10 \) (Ends in 0). Let’s check.

Ajay is on the right (at 3 o’clock).

The wheel turns clockwise.

Clockwise means going down first from the right side.

• 1 quarter turn: Ajay is at the bottom.
• 2 quarters (half) turn: Ajay is at the left.
• 3 quarters turn: Ajay is at the top.