2019 Key Stage 1 Mathematics Paper 2: Reasoning

What is the question asking?

We need to identify which day of the week comes after Tuesday, or specifically, fill in the blank or check the correct day based on the order of the week.

The order of days is: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.

The question asks us to tick “Wednesday”. We simply need to find the box that says Wednesday.

What are we looking for?

We need a number that fits in the gap. The number must be:

• Bigger than 52
• Smaller than 57

Let’s count up from 52 to 57:

52, 53, 54, 55, 56, 57.

Any of the numbers in bold are correct.

What is a vertex?

A vertex is a corner where sides or edges meet.

Let’s count the corners (vertices) on the outer shape:

• Hexagon: 6 corners (Too many)
• Square (rotated): 4 corners (Correct)
• Triangle (Pyramid base): 3 corners on the face we see, but the question implies the 2D shape or the visible corners. The square shape clearly has 4.
• Square with cross: 4 corners (Correct)
• Circle: 0 corners

Note: The question asks for shapes with 4 vertices. The two square-like shapes (one plain rotated square, one with a cross pattern) both have 4 outer corners.

What does the equals sign mean?

It means “the same as”. The value on the left (12) must be the same as the value on the right.

So, something times 6 equals 12.

Let’s count in 6s until we reach 12:

• \( 1 \times 6 = 6 \)
• \( 2 \times 6 = 12 \)

So the missing number is 2.

The question asks for “96” (Ninety-six).

Ninety means 9 tens.

Six means 6 ones.

So we write 9 followed by 6.

Let’s look at the properties of each shape listed:

• Square: A box shape. It has 4 equal sides and 4 corners that are “L” shapes (right angles).
• Octagon: “Oct” means 8 (like octopus). It has 8 sides and 8 vertices.
• Circle: A round shape. It has 1 curved side and 0 corners (vertices).

• Square matches “has 4 right angles”.
• Octagon matches “has 8 vertices”.
• Circle matches “has no vertices”.

We need to see if the number gets bigger (add +) or smaller (subtract -).

• 23 to 22: The number went down by 1.
  So, \( 23 – 1 = 22 \).
• 40 to 39: The number went down by 1.
  So, \( 40 – 1 = 39 \).
• 19 to 20: The number went up by 1.
  So, \( 19 + 1 = 20 \).

First, let’s write down the value of each dice:

• Dice 1: 6
• Dice 2: 5
• Dice 3: 1
• Dice 4: 4
• Dice 5: 2

We need a total of 13. Let’s try starting with the biggest number, 6.

• \( 6 + 5 = 11 \). We need \( 13 – 11 = 2 \). Do we have a 2? Yes!
• Check: \( 6 + 5 + 2 = 13 \).

We interpret “A × B” as “A rows of B” or “A columns of B”.

• Box 1: 6 eggs in a row, 2 rows. \( 6 \times 2 \). (Matches top box).
• Box 2: 5 eggs in a row, 3 rows deep. \( 5 \times 3 \).
• Box 3: 3 eggs in a row, 2 rows deep. \( 3 \times 2 \).
• Box 4: 5 eggs in a row, 2 rows deep. \( 5 \times 2 \).

The question says Sam has cards numbered 1 to 8.

So the full set is: 1, 2, 3, 4, 5, 6, 7, 8.

• We see 1.
• We see 2.
• We see 4.
• We see 5.
• We see 7.
• We see 8.

The numbers we cannot see are 3 and 6.

Finding \(\frac{1}{2}\) of a number means splitting it into two equal parts.

Another way to think about it is working backwards: if half of a number is 3, then the whole number must be double 3.

We know that: \[ ? \div 2 = 3 \]

So: \[ 3 \times 2 = 6 \]

Let’s check: Is half of 6 equal to 3? Yes.

Look at the numbers we have:

• 16 to 14: Subtract 2
• 14 to 12: Subtract 2

The rule is: Count backwards in 2s.

Starting from 12:

• \( 12 – 2 = 10 \)
• \( 10 – 2 = 8 \)
• \( 8 – 2 = 6 \)

We need two numbers that add up to 70.

It helps to think about number bonds to 7 (like \( 5 + 2 = 7 \)) and then multiply by 10.

We have 10 and need to reach 70.

Calculation: \( 70 – 10 = \mathbf{60} \).

Check: \( 10 + 60 = 70 \).

We have 30 and need to reach 70.

Calculation: \( 70 – 30 = \mathbf{40} \).

Check: \( 40 + 30 = 70 \).

Look at the main numbers: 45, 50, 55, 60.

They are going up in 5s.

Now look at the small marks between 55 and 60. There are 4 marks, creating 5 spaces.

This means each small mark represents 1.

Start at 55 and count the small ticks:

• 1st tick: 56
• 2nd tick: 57
• 3rd tick: 58
• 4th tick: 59 (This is where the arrow points)
• Next is 60.

The arrow points to 59.

Amy starts with 50p and spends 30p.

Calculation: \[ 50\text{p} – 30\text{p} = 20\text{p} \]

She has 20p left.

• Top Left: \(5 + 5 + 5 = 15\text{p}\) (Incorrect)
• Top Right: A single 50p coin. This is what she started with, not what she has left. (Incorrect)
• Bottom Left: \(10 + 10 + 5 = 25\text{p}\) (Incorrect)
• Bottom Right: \(10 + 5 + 5 = 20\text{p}\) (Correct!)

The shape is a Triangular Prism.

It is made of:

• Two triangles (one at each end).
• Three rectangles (connecting the triangles).

Look at the options provided:

• Square: No squares on this prism.
• Rectangle: Yes, the long sides are rectangles.
• Trapezium: No.
• Pentagon: No.
• Triangle: Yes, the ends are triangles.

• Top Clock: Minute hand is on the 5. \(5 \times 5 = 25\). This is 25 past.
• Middle Clock: Minute hand is on the 9. This means 45 minutes, or quarter to the next hour.
• Bottom Clock: Minute hand is on the 3. This means 15 minutes, or quarter past.

• Top Clock: Hour hand is past 4. Time is 4:25. Matches twenty-five past four.
• Middle Clock: Hour hand is almost at 4 (it is coming from 3). Time is 3:45. Matches quarter to four.
• Bottom Clock: Hour hand is just past 4. Time is 4:15. Matches quarter past four.

A line of symmetry is a mirror line. If you fold the shape along the line, both halves must match exactly.

• Shape 1 (Triangle): One side is straight up, the other is sloped. No mirror line.
• Shape 2 (Quadrilateral): The top is sloped, the bottom is flat. No mirror line.
• Shape 3 (M-shape): If you draw a vertical line right down the middle, the left side is a reflection of the right side. It has a line of symmetry.
• Shape 4 (Parallelogram): If you fold it in half, the corners don’t meet. It has rotational symmetry but no line of symmetry.

Look at the first number in each row:

• Row 1 starts with 1
• Row 2 starts with 2
• Row 3 starts with 3
• Row 4 starts with 4

So the next row must start with 5.

Each row adds three consecutive numbers (numbers that follow each other).

If we start with 5, the next numbers are 6 and 7.

So the calculation is: \( 5 + 6 + 7 \).

Now add them up:

\( 5 + 6 = 11 \)

\( 11 + 7 = 18 \)

Also, notice the answers go up by 3 each time: 6, 9, 12, 15… so the next is 18.

Imagine Sam is facing the Triangle (Top).

A half turn means turning 180 degrees. This is like turning all the way around to face the opposite direction.

If you face North and do a half turn, you face South.

Sam starts pointing up at the Triangle.

The shape directly opposite (at the bottom) is the Pentagon.

Equation: \( 27 + \square = 67 \)

Look at the tens digit. It changes from 20 to 60. That is an increase of 4 tens (40).

Calculation: \( 67 – 27 = 40 \).

Do we have a 40 card? Yes.

Equation: \( 54 – \square = 34 \)

Look at the tens digit. It goes down from 50 to 30. That is a decrease of 2 tens (20).

Calculation: \( 54 – 34 = 20 \).

Do we have a 20 card? Yes.

Equation: \( \square + 88 = 98 \)

The number goes up from 88 to 98. That is an increase of 1 ten (10).

Calculation: \( 98 – 88 = 10 \).

Do we have a 10 card? Yes.

Look at the height of the bars:

• Pizza: The bar goes up to the line for 6.
• Burger: The bar goes up to the line for 8.

“How many fewer” means we need to find the difference (subtract).

\[ 8 – 6 = 2 \]

“Seven times that number” means we need to multiply Ben’s number by 7.

Ben has 5 marbles.

Calculation: \( 5 \times 7 \)

Using our 5 times table: 5, 10, 15, 20, 25, 30, 35.

The question tells us one acorn = 2 points.

There are two acorns in the sum.

So, \( 2 + 2 = 4 \) points for the acorns.

The whole sum is 10.

We know: \( \text{Leaf} + 4 = 10 \).

To find the missing number, we subtract 4 from 10:

\[ 10 – 4 = 6 \]

We need to make 30p first. We can use:

• 20p + 10p
• Or 10p + 10p + 10p

Let’s try 20p and 10p. That’s 2 coins used so far.

We need 7p using 3 more coins (to make 5 coins total).

We can make 7p with: 5p, 1p, 1p.

Does this work? \( 20 + 10 + 5 + 1 + 1 = 37 \).

Total coins: 5. This works!

We could also do: 10p, 10p, 10p, 5p, 2p.

\( 10 + 10 + 10 + 5 + 2 = 37 \). Total coins: 5. This also works.

The total number of pencils is 30. This goes first in the division sentence.

He shares them into 3 pots. This is what we are dividing by.

So far: \( 30 \div 3 \)

How many 3s go into 30?

\( 3 \times 10 = 30 \)

So, \( 30 \div 3 = 10 \).

• Ben: 4 blocks = 4 books
• Kemi: 5 blocks = 5 books
• Ajay: 7 blocks = 7 books
• Sita: 3 blocks = 3 books

“Fewer than 5” means numbers that are smaller than 5. It does NOT include 5.

• Ben (4): Yes, 4 is less than 5.
• Kemi (5): No, 5 is not fewer than 5.
• Ajay (7): No, 7 is more than 5.
• Sita (3): Yes, 3 is less than 5.

The calculation ends in 9.

We have \( \square + 3 = 9 \).

What number adds to 3 to make 9?

\( 9 – 3 = 6 \). So the first missing number is 6.

The answer starts with 20 (2 tens).

We have \( 10 + \square = 20 \) (looking at the tens column: \( 1 + ? = 2 \)).

\( 2 – 1 = 1 \). So the second missing number is 1.

Let’s check: \( 16 + 13 \).

\( 16 + 10 = 26 \)

\( 26 + 3 = 29 \)

It works!

First, let’s work out how much Sita and Ben used altogether.

\( 25\text{g} + 35\text{g} \)

\( 20 + 30 = 50 \)

\( 5 + 5 = 10 \)

\( 50 + 10 = 60\text{g} \) used.

The bag started with 100g.

We need to subtract what was used.

\( 100 – 60 = 40 \)

You can subtract one by one:

\( 100 – 25 = 75 \)

\( 75 – 35 = 40 \)

Finding \(\frac{1}{4}\) means splitting the total into 4 equal groups.

We need to share 12 bags into 4 groups.

Calculation: \( 12 \div 4 \).

Using multiplication facts: \( 4 \times 3 = 12 \).

So, one quarter of 12 is 3.

Look at the diagram. There are 4 columns. Each column is a quarter.

How many bags in one column? 3.

“Gives away” means we need to subtract.

Calculation: \( 63 – 37 \)

We can use column subtraction, but we need to exchange (borrow) because we can’t do \( 3 – 7 \).

Detail:

• Exchange a ten from the 60. Now we have 5 tens and 13 ones.
• \( 13 – 7 = 6 \)
• \( 5 – 3 = 2 \)

Ben buys 2 tickets. Each ticket is 35p.

We need to find \( 35 + 35 \) or \( 35 \times 2 \).

• \( 30 + 30 = 60 \)
• \( 5 + 5 = 10 \)
• \( 60 + 10 = 70\text{p} \)

Total cost is 70p.

Ben started with 90p.

We need to subtract the cost from the total.

\[ 90 – 70 = 20 \]