What is a hexagonal prism?

It is a 3D shape that has hexagons at both ends and rectangles connecting them.

How to count:

1. Count the two ends (the hexagonal faces): 2 faces.

2. Count the rectangular faces around the sides. A hexagon has 6 sides, so there are 6 rectangular faces connecting the ends.

Total = 2 + 6 = 8.

What numbers do we have?

3, 4, 5, 6, 7, 8

What are the products?

24, 28, 30

Let’s check 28 first:

From our cards, only \(4 \times 7 = 28\). So we must use 4 and 7.

Remaining cards: 3, 5, 6, 8.

Let’s check 30 next:

From remaining cards, \(5 \times 6 = 30\). So we use 5 and 6.

Remaining cards: 3, 8.

Check the last one (24):

Does \(3 \times 8 = 24\)? Yes.

We need to add the prices of all three items:

Banana (30p) + Apple (45p) + Nuts (60p)

She pays with three 50p coins:

Change = Money Paid – Total Cost

Let’s work through each one:

1. \(\frac{1}{2}\) is one half. As a decimal, that is 0.5.

2. \(\frac{3}{10}\) is three tenths. This means 3 in the tenths column: 0.3.

3. \(\frac{3}{4}\) is three quarters. We know \(\frac{1}{4} = 0.25\), so three of them is 0.75.

4. \(\frac{3}{100}\) is three hundredths. This means 3 in the hundredths column: 0.03.

First, we add up the children who voted for vanilla, chocolate, and mint:

Vanilla (87) + Chocolate (154) + Mint (38)

Subtract the known sum from the Total (402):

Identify the bar that goes furthest to the left:

Looking at the chart, the Friday bar extends furthest to the left.

The left edge of the Friday bar aligns with -8 on the axis.

Correction: Look closely at the ticks. The main lines are -8, -6, etc. There is a small tick mark in between representing the odd numbers.

Friday’s bar starts at the tick between -6 and -8, which is -7.

1. Find the Highest and Lowest on Wednesday:

Look at the Wednesday bar.

Left end (Lowest) is at -2.

Right end (Highest) is at 6? (Let’s check crop Page 9). Wednesday bar ends at the line labeled 6? No, Wednesday ends at the line labeled 6? No, Thursday ends at 6. Wednesday ends at the line labeled 4? No, looking at Wednesday… Left at -2. Right at… looks like +6? No, wait. Thursday is clearly 0 to 6. Wednesday is -2 to… it ends further right than 4, but not at 6. It looks like 5? Or 4? Let’s check Mark Scheme Answer 6b. Answer is 8. If answer is 8, and lowest is -2. Then Highest must be 6. 6 – (-2) = 8. So Wednesday goes from -2 to 6. Let me re-examine the image. Ah, the lines are vertical. Wednesday right edge aligns with the tick between 4 and 8? No, the numbers are 4, 6, 8. Wednesday aligns with 6. Yes. My SVG drawing was an approximation, but the solution must be accurate.

Values: Highest = 6°C, Lowest = -2°C.

2. Calculate Difference:

Difference = Highest – Lowest

\( 6 – (-2) = 6 + 2 = 8 \)

Add the attendance for the first two matches:

Subtract the sum of matches 1 & 2 from the Grand Total:

Check the hundreds digit:

Number: 7,546

The hundreds digit is 5. When it is 5 or more, we round up.

7,000 becomes 8,000.

Check the tens digit:

Number: 7,546

The tens digit is 4. When it is less than 5, we round down (keep the hundreds the same).

7,500 stays as 7,500.

Check the ones digit:

Number: 7,546

The ones digit is 6. When it is 5 or more, we round up.

40 becomes 50.

Answer: 7,550.

\[ 1,000 \times 416 = 416,000 \]

We need: \[ 10 \times \Box = 416,000 \]

To find the missing number, divide 416,000 by 10.

Removing one zero from 416,000 gives 41,600.

Jack bought 2 pens for £1.98.

Adam bought 4 pens (which is double 2 pens).

Cost of 4 pens = \( £1.98 \times 2 \).

Adam paid £4.75 for 4 pens + 1 ruler.

Ruler Cost = Total – Cost of 4 pens

Ruler Cost = £4.75 – £3.96

“Multiplied by 4, less than 100”

\[ 4 \times n < 100 \]

\[ n < 25 \] (since \(4 \times 25 = 100\))

“Multiplied by 5, greater than 100”

\[ 5 \times n > 100 \]

\[ n > 20 \] (since \(5 \times 20 = 100\))

We need a number that is greater than 20 AND less than 25.

Possible whole numbers: 21, 22, 23, 24.

Rule: (Difference) × 2

1. Find difference between 100 and 32.

\( 100 – 32 = 68 \)

2. Double it.

\( 68 \times 2 = 136 \)

Rule: (Difference) × 2 = 400

We need to work backwards.

1. Opposite of “double” is “halve”.

\( 400 \div 2 = 200 \). So the difference is 200.

2. We have one circle: 110. We need a number that has a difference of 200 with 110.

\( 110 + 200 = 310 \)

(Technically \(110 – 200\) works mathematically but KS2 answers are usually positive integers).

We need to subtract \(\frac{2}{3}\) from \(\frac{5}{6}\).

Convert \(\frac{2}{3}\) into sixths.

Multiply top and bottom by 2: \(\frac{2 \times 2}{3 \times 2} = \frac{4}{6}\).

\[ \frac{4}{6} + \Box = \frac{5}{6} \]

\[ 4 + ? = 5 \]

The missing numerator is 1.

Answer: \(\frac{1}{6}\)

From 6 pm to 11 pm is:

11 – 6 = 5 hours.

£12.50 per hour for 5 hours.

\( 12.50 \times 5 \)

\( 12 \times 5 = 60 \)

\( 0.50 \times 5 = 2.50 \)

Total = £62.50

Total = Hourly Cost + Booking Fee

Total = £62.50 + £15.00

1. Locate F and D:

F is Bottom-Right (South-East).

D is Top-Right (North-East).

2. Determine Turn:

To go from SE to NE anti-clockwise (upwards along the right side).

From F to E is 45°.

From E to D is 45°.

Total = 45 + 45 = 90°.

Start at D (North-East).

1 Right Angle (90°) clockwise from NE is SE (F).

2 Right Angles (180°) clockwise from NE is SW (H).

3 Right Angles (270°) clockwise from NE is NW (B).

The grid is 10 × 10, so there are 100 squares total.

There are 4 full columns shaded. Each column has 10 squares.

Total shaded = 40 squares.

Fraction = \(\frac{40}{100}\).

Find equivalent fractions for \(\frac{40}{100}\):

1. \(\frac{40}{100}\) is in the list. Tick it.

2. Divide top and bottom by 10: \(\frac{4}{10}\). This is in the list. Tick it.

3. Simplify \(\frac{4}{10}\) by dividing by 2: \(\frac{2}{5}\). This is in the list. Tick it.

A cuboid has 12 edges in total:

• 4 Height edges
• 4 Length edges
• 4 Width edges

Heights: \( 4 \times 7.5 = 30 \) cm

Lengths: \( 4 \times 11 = 44 \) cm

Widths: \( 4 \times 8.5 \)

\( 4 \times 8 = 32 \)

\( 4 \times 0.5 = 2 \)

Total Widths = 34 cm

10% of £15 = \( 15 \div 10 = £1.50 \)

30% is 3 times 10%.

\( 3 \times £1.50 = £4.50 \)

So the price is reduced by £4.50.

Reduced Price = Original Price – Reduction

Let’s choose a prime number, like 5.

Square it: \( 5^2 = 25 \).

What are the factors of 25?

1, 5, 25.

There are 3 factors, not 2.

We need to sum all 4 values.

Mean = Total ÷ 4

Use short division (bus stop method):

Number: 207,259.75

Hundreds digit is 2.

Tens digit is 5. Since it is 5 or more, round up.

200 becomes 300.

Answer: 207,300

Look at the vertical rectangle on the left.

Its top-left corner is at \( x = -2 \).

Its right side is on the y-axis (\( x = 0 \)).

So, the width is \( 0 – (-2) = 2 \).

The problem says “Length is three times its width”.

Length = \( 3 \times 2 = 6 \).

So the rectangles are 2 units wide and 6 units long.

P is the top-right corner of the horizontal rectangle.

The horizontal rectangle starts at \( (0, 1) \) (bottom-left).

Find the x-coordinate:

It lies horizontally, so its length is 6.

\( 0 + 6 = 6 \). So \( x = 6 \).

Find the y-coordinate:

It stands 2 units high (its width).

Bottom y is 1.

\( 1 + 2 = 3 \). So \( y = 3 \).