Step 1: Understanding the constraints

We need to make a 3-digit number using the digits 4, 8, 2, 7.

The 4 is fixed in the tens place: [ ] [ 4 ] [ ]

We have digits 8, 2, 7 remaining.

Step 2: Finding the lowest number

To make the number as small as possible:

• Put the smallest available digit in the Hundreds place (the most valuable place).
• Put the next smallest digit in the Ones place.

Available digits: 2, 7, 8.

Smallest is 2. So put 2 in the hundreds place.

Next smallest is 7. So put 7 in the ones place.

Step 1: Break down the words

“Eighty thousand” = 80,000

“Three hundred” = 300

“Six” = 6

Step 2: Combine

80,000 + 300 + 6 = 80,306

Step 1: Understanding Reflection

Reflecting in the \(y\)-axis (the vertical line) means the shape flips horizontally.

Every point on the left moves to the same distance on the right.

Step 2: Reflecting Coordinates

• Point C is 1 square left of the axis. It moves to 1 square right.
• Point B is 3 squares left of the axis. It moves to 3 squares right.
• Point A is 3 squares left of the axis. It moves to 3 squares right.

Step 1: Identify the rule

\(1,880 – 1,780 = 100\)

\(1,980 – 1,880 = 100\)

The sequence is increasing by 100 each time.

Step 2: Apply the rule

\(1,980 + 100 = 2,080\)

\(2,080 + 100 = 2,180\)

Step 1: Round each number

• 13.2 rounds to 13 (down)
• 14.7 rounds to 15 (up)
• 15.9 rounds to 16 (up)
• 16.3 rounds to 16 (down)
• 17.6 rounds to 18 (up)

Step 2: Identify the pair

15.9 and 16.3 both round to 16.

Step 1: Partition the number

\(1,300,450\) represents:

• 1,000,000 (One million)
• 300,000 (Three hundred thousand)
• 400 (Four hundred)
• 50 (Fifty)

Step 2: Compare with equation

We have 1,000,000, 400, and 50.

The missing part is 300,000.

Step 1: Analyze the pattern

Looking at the first row: \(\frac{1}{2}, 1, 1\frac{1}{2}, \dots\)

The numbers increase by \(\frac{1}{2}\) (0.5) each step.

Step 2: Find the vertical jump

Look at the first number in Row 1: 0.5

Look at the first number in Row 2: 3

The difference is \(3 – 0.5 = 2.5\).

This means each row starts 2.5 higher than the row above it.

Step 3: Calculate down to the bottom-left corner

We need to find the number in the first column of the 5th row.

• Row 1: 0.5
• Row 2: 3.0 (0.5 + 2.5)
• Row 3: 5.5 (3.0 + 2.5)
• Row 4: 8.0 (5.5 + 2.5)
• Row 5: 10.5 (8.0 + 2.5)

Step 1: Identify Sides and Regularity

• Shape 1: 6 sides, not all equal. -> Irregular Hexagon.
• Shape 2: 5 sides (house shape), not all angles equal. -> Irregular Pentagon.
• Shape 3: 5 sides, looks equal. -> Regular Pentagon.
• Shape 4: 6 sides, looks equal (or irregular in sketch, but marked as Hexagon). -> Regular Hexagon.

Step 1: Check multiples of 3

We know that \(10 \times 3 = 30\).

The next multiple is \(11 \times 3 = 33\).

Step 2: Conclusion

32 is between 30 and 33, so it is not in the 3 times table.

Step 1: Calculate \(8^2\)

\(8 \times 8 = 64\)

Step 2: Find the missing value

\(64 + \text{something} = 73\)

\(73 – 64 = 9\)

Step 3: Convert to a square number

The question asks for the base of the square: \(\_\_^2 = 9\).

Which number squared makes 9? \(3 \times 3 = 9\).

Step 1: Calculate total sold

  7918
+ 4624
-------
 12542
-------

Step 2: Subtract from starting amount

  15000
- 12542
-------
   2458
-------

Working: \(0-2\) can’t do, borrow… becomes \(10-2=8\), \(9-4=5\), \(9-5=4\), \(4-2=2\).

Step 1: Visualize folding

A cuboid net typically needs 4 rectangular faces in a row (for the sides) and two square/end faces on opposite sides of the strip.

Step 2: Identify valid nets

The Mark Scheme accepts two nets:

• The 2nd net shown (often a T-shape or similar arrangement where faces don’t overlap).
• The 4th net shown (Standard cross or 1-4-1).

Step 1: Use the Distributive Law

We have 6 lots of 754 plus 3 lots of 754.

\(754 \times (6 + 3)\)

Step 2: Add the multipliers

\(6 + 3 = 9\)

So, \(754 \times 9\).

Part A: 25%

25% is equal to \(\frac{1}{4}\).

Do we have cards 1 and 4? Yes.

Answer: \(\frac{1}{4}\)

Part B: 0.4

0.4 is equal to \(\frac{4}{10}\) or \(\frac{2}{5}\).

Do we have cards 2 and 5? Yes.

Answer: \(\frac{2}{5}\)

Part A: Leaving Home

Arrival: 7:10 (Ten past seven).

Travel time: 1 hour 20 minutes.

Subtract 1 hour: 6:10.

Subtract 20 minutes: 6:10 – 10 mins = 6:00, – 10 mins = 5:50.

Answer: 5:50 pm (or 17:50).

Part B: Duration

Start: 7:20 pm.

Finish: 9:05 pm.

7:20 to 8:20 = 1 hour.

8:20 to 9:00 = 40 minutes.

9:00 to 9:05 = 5 minutes.

Total minutes = 40 + 5 = 45 minutes.

Total time: 1 hour 45 minutes.

Step 1: Find mass of eggs only

Total mass – Box mass = Eggs mass

\(870 – 30 = 840\) grams.

Step 2: Divide by number of eggs

We need to do \(840 \div 24\).

    35
   ----
24|840
  -720 (30 x 24)
   ---
   120
  -120 (5 x 24)
   ---
     0

Calculation: \(24 \times 3 = 72\), so \(24 \times 30 = 720\). Remainder 120.

\(24 \times 5 = 120\).

Total = 35.

Step 1: Add the fractions

We need to add \(\frac{1}{2} + \frac{1}{3}\).

Step 2: Find common denominator

Common denominator is 6.

\(\frac{1}{2} = \frac{3}{6}\)

\(\frac{1}{3} = \frac{2}{6}\)

Step 3: Calculate sum

\(\frac{3}{6} + \frac{2}{6} = \frac{5}{6}\)

Part A: Graphing

Locate 2012 Rainfall in table: 700.

Draw a bar up to the 700 line on the graph.

Part B: Calculating Mean

We need sunshine hours for 2013, 2014, and 2015.

2013: 1,452

2014: 1,669

2015: 1,508

Step 2: Add them up

 1452
 1669
+1508
-----
 4629
-----

Step 3: Divide by 3

\(4629 \div 3\)

\(4000 \div 3 = 1333\)… easier to use bus stop.

4 div 3 = 1 r 1.

16 div 3 = 5 r 1.

12 div 3 = 4.

9 div 3 = 3.

Result: 1,543.

Step 1: Cost of Mushrooms

500g is half a kg.

\(3.20 \div 2 = £1.60\).

Step 2: Cost of Carrots

\(1\frac{1}{4}\) kg is 1.25 kg.

1 kg = 60p.

\(\frac{1}{4}\) kg = \(60 \div 4 = 15\)p.

Total for carrots = \(60p + 15p = 75\)p (or £0.75).

Step 3: Total Cost

\(£1.60 + £0.75 = £2.35\).

Step 4: Change

\(£5.00 – £2.35 = £2.65\).

Step 1: Understand Perimeter

Perimeter is distance around the outside: \(w + 6 + w + 6\).

This simplifies to \(2w + 12\) or \(2 \times (w+6)\).

Step 2: Check each option

• \(w \times 6\) = Area (Incorrect)
• \(w \times 2 + 12\) = \(2w + 12\) (Correct, as \(2 \times 6 = 12\))
• \(2 \times (w + 6)\) = Correct formula
• \(6 + w + 6 + w\) = Correct sum

Step 1: Total pupils

\(25 \times 34\).

\(25 \times 4 = 100\). \(34 = 4 \times 8 + 2\). Or just long multiply.

\(34 \times 100 = 3400\). \(3400 \div 4 = 850\).

Total = 850 pupils.

Step 2: Percentage NOT playing sport

\(100\% – 62\% = 38\%\).

Step 3: Calculate 38% of 850

\(10\% = 85\).

\(30\% = 85 \times 3 = 255\).

\(1\% = 8.5\).

\(8\% = 8.5 \times 8 = 68\).

Total: \(255 + 68 = 323\).

Step 1: Identify the pattern

Input 3 \(\to \times 0\) (3-3)

Input 4 \(\to \times 1\) (4-3)

Input 5 \(\to \times 2\) (5-3)

Rule: Multiply by (Number – 3), then divide by 2.

Step 2: Apply to Octagon (8)

Multiply by: \(8 – 3 = 5\).

Second step is always: \(\div 2\).

Calculate: \(8 \times 5 = 40\). \(40 \div 2 = 20\).

Row 2: \(\frac{3}{20}\)

To convert to decimal, make denominator 100.

\(\frac{3}{20} \times 5 = \frac{15}{100}\).

Decimal: 0.15

Row 3: \(\frac{5}{8}\)

Memorize that \(\frac{1}{8} = 0.125\).

\(5 \times 0.125 = 0.625\).