KS1 2022 Mathematics Paper 2: Reasoning

💡 What do we need to find?

We need to find the total number of cars Ajay and Kemi counted.

The word “altogether” tells us we need to add their numbers together.

Ajay counted 5 cars.

Kemi counted 14 cars.

We calculate: \( 5 + 14 \)

We need a number that fits three rules:

• 1. It is a two-digit number (10 or bigger).
• 2. It is less than 20.
• 3. It is an even number (ends in 0, 2, 4, 6, or 8).

First, list two-digit numbers less than 20:

10, 11, 12, 13, 14, 15, 16, 17, 18, 19

Now, pick the even numbers from this list:

10, 12, 14, 16, 18

“1 less” means we need to count back one number.

It is the number that comes just before 60.

Start at 60 and go back one step.

\[ 60 – 1 = 59 \]

The long minute hand is pointing directly at the 9.

When the minute hand is on the 9, it means quarter to the next hour.

The short hour hand is pointing between the 3 and the 4. It is getting close to the 4.

Because the minute hand says “quarter to”, we are looking at the hour we are going towards.

We are going towards 4.

Ben has 12.

Amy has 7 more. This means we need to add 7 to Ben’s number.

We need to solve: \( 12 + 7 \)

Tuesday: This is a name of a day (like Monday, Wednesday). It is the day of the week.

April: This is a name of a month (like May, June). It is the month.

2020: This is a four-digit number. It tells us the year.

To order numbers, we look at the tens digit first (the first number).

Our numbers are:

• 76 (7 tens)
• 84 (8 tens)
• 27 (2 tens)
• 45 (4 tens)
• 18 (1 ten) – Already done

1. 18 is the smallest (1 ten).

2. Next is 27 (2 tens).

3. Next is 45 (4 tens).

4. Next is 76 (7 tens).

5. Largest is 84 (8 tens).

The word “altogether” means we need to add the numbers together.

Calculation: \( 25 + 6 \)

Quarters means 4 equal parts.

We need to draw 2 lines that split the square into 4 pieces that are the same size.

You can do this in two common ways:

1. Join the middle dots (top to bottom, left to right).
2. Join the corner dots (diagonal lines).

We need to add all three numbers together:

\[ 20 + 30 + 50 \]

Look for numbers that are easy to add first.

We know that \( 2 + 3 = 5 \), so \( 20 + 30 = 50 \).

Now we have: \( 50 + 50 \)

We know that \( 5 + 5 = 10 \), so \( 50 + 50 = 100 \).

• Hexagon (Top Left): 6 sides.
• Pentagon (Top Middle): 5 sides.
• Triangle (Top Right): 3 sides.
• Quadrilateral (Bottom Left): 4 sides.
• Star/Chevron Shape (Bottom Right): Let’s count carefully. It has 6 sides.

We need two shapes with the same number of sides.

The Hexagon has 6 sides.

The Chevron shape has 6 sides.

The boxes show:

\[ [?] + 1[?] = 18 \]

This means we are adding a single digit number to a teen number (a number starting with 1).

We know that \( 1 + 17 = 18 \). We need a different one.

Let’s check the number bonds for 8 (since the units digit is 8):

• \( 0 + 8 = 8 \) → \( 0 + 18 = 18 \)
• \( 2 + 6 = 8 \) → \( 2 + 16 = 18 \)
• \( 3 + 5 = 8 \) → \( 3 + 15 = 18 \)
• \( 4 + 4 = 8 \) → \( 4 + 14 = 18 \)
• \( 5 + 3 = 8 \) → \( 5 + 13 = 18 \)
• \( 6 + 2 = 8 \) → \( 6 + 12 = 18 \)
• \( 7 + 1 = 8 \) → \( 7 + 11 = 18 \)
• \( 8 + 0 = 8 \) → \( 8 + 10 = 18 \)

The question says the three sides are of equal length.

If one side is 3 pencils long, then every side is 3 pencils long.

Side 1: 3 pencils

Side 2: 3 pencils

Side 3: 3 pencils

\[ 3 + 3 + 3 = 9 \]

Or use multiplication: \( 3 \times 3 = 9 \)

Look at the numbers going down: 15, 20, 25.

The gap between 15 and 20 is \( 20 – 15 = 5 \).

The gap between 20 and 25 is \( 25 – 20 = 5 \).

The rule is add 5.

To find the top number (before 15), we work backwards: subtract 5.

\[ 15 – 5 = 10 \]

Look at the numbers going across: 18, 21, 24, 27.

The gap is \( 21 – 18 = 3 \).

The rule is add 3.

To find the first number (left of 18): Subtract 3.

\[ 18 – 3 = 15 \]

To find the last number (right of 27): Add 3.

\[ 27 + 3 = 30 \]

• kg (kilograms): Measures mass (how heavy something is).
• °C (degrees Celsius): Measures temperature (how hot/cold).
• cm (centimetres): Measures length.
• ml (millilitres): Measures capacity (liquid).

The number 23 has 2 digits.

The first digit is 2. This is the Tens.

The last digit is 3. This is the Ones.

So, 23 = 2 Tens and 3 Ones.

The number 5 is just a single digit.

It has no Tens column (or 0 Tens).

It has 5 Ones.

So, 5 = 0 Tens and 5 Ones.

When adding, the largest number is the answer (the total).

The numbers are 36, 42, 6.

42 is the largest.

So, \( 36 + 6 = 42 \) or \( 6 + 36 = 42 \).

When subtracting, we usually start with the largest number.

Start with 42.

If we take away 6, we get 36: \( 42 – 6 = 36 \)

If we take away 36, we get 6: \( 42 – 36 = 6 \)

The word “shares” tells us this is a division question.

We have 40 cards shared into 4 bags.

Calculation: \( 40 \div 4 \)

How many 4s go into 40?

Count in 4s: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.

That is 10 times.

\[ 40 \div 4 = 10 \]

• Top Left: 20p + 20p + 10p = 50p
• Top Right: 10p + 20p + 10p = 40p
• Bottom Left: 10p + 5p + 50p = 65p
• Bottom Right: 20p + 10p + 10p + 5p + 5p = 50p

The Top Left purse has 50p.

The Bottom Right purse has 50p.

These two have the same amount.

5 + 2 = 7

10 − 3 = 7

9 − 1 = 8

4 + 1 = 5

The answers are 7, 7, 8, and 5.

The largest number is 8.

A line of symmetry is a line that cuts a shape exactly in half, so that one side is a mirror image of the other.

If you folded the shape along the line, the two halves would match perfectly.

• Rectangle: Has 2 lines of symmetry (horizontal and vertical).
• Hexagon: Has lines of symmetry.
• Triangle: Has a line of symmetry down the middle.
• Circle: Has infinite lines of symmetry.
• L-shape: If we fold it, the sides do not match. It has no line of symmetry.

We have 6 rows.

Each row has 5 bricks.

This is 6 lots of 5.

Calculation: \( 6 \times 5 \)

In a subtraction like \( A – B = C \), the first number (\(A\)) must be the largest.

Let’s try using the largest card, 90, as the starting number.

If we start with 90, we need two other numbers that add up to 90.

Let’s look at the other cards: 20, 40, 50, 70.

Can we find two that add to 90?

• \( 20 + 70 = 90 \) — Yes!
• \( 40 + 50 = 90 \) — Yes!

So we can use the sets {90, 70, 20} or {90, 50, 40}.

But wait, we only have cards for 20, 40, 50, 70, 90.

Let’s check the first set: 90, 70, 20. Do we have all these cards? Yes.

Let’s check the second set: 90, 50, 40. Do we have all these cards? Yes.

There are 8 children.

Each child has 2 plums.

This is 8 lots of 2.

Calculation: \( 8 \times 2 \)

We are splitting 18 cards into groups of 3.

This is division: \( 18 \div 3 \).

Start with 43 people.

15 get off, so we subtract 15.

\[ 43 – 15 \]

Now 8 people get on. We need to add 8 to our new total (28).

\[ 28 + 8 \]

Look at the numbers ending in 4 (the answers): 14, 24, …, 44.

They are going up by 10 each time.

This means the starting numbers must also go up by 10: 7, 17, 27, 37.

Cost of pencil = 15p

Cost of rubber = 25p

Total cost = \( 15 + 25 \)

She pays with £1.

We know that £1 = 100p.

We need to subtract the cost from 100p.

\[ 100 – 40 \]

To find \(\frac{1}{4}\), we divide by 4.

Total strawberries = 8.

\[ 8 \div 4 = 2 \]

So, one quarter is 2 strawberries.

We want 3 quarters.

So we need 3 lots of 2.

\[ 3 \times 2 = 6 \]

We need to look at the Shoe size column.

“10 or smaller” means we need to count:

• Children with size 10.
• Children with size 9 (because 9 is smaller than 10).

Number of children with size 9: 7

Number of children with size 10: 8

We add them together:

\[ 7 + 8 = 15 \]

Rule: Multiply the two bottom numbers to get the top.

Bottom numbers: 5 and 4.

Calculation: \( 5 \times 4 \)

Top number: 70.

Bottom number we know: 10.

We need to find the missing number.

Calculation: \( 10 \times [?] = 70 \)