GCSE 2024 Edexcel Foundation Paper 3

💡 What does “percent” mean?

The word “percent” literally means “per 100” or “out of 100”. The symbol % is a shorthand for writing a fraction with a denominator of 100.

💡 How many centimetres in a metre?

There are 100 centimetres in 1 metre. To convert from centimetres (small unit) to metres (large unit), we divide by 100.

💡 Look at the position of the digit

Let’s break down the number 62 837 into its place value columns:

• 6 is in the Ten Thousands place (60,000)
• 2 is in the Thousands place (2,000)
• 8 is in the Hundreds place (800)
• 3 is in the Tens place
• 7 is in the Units/Ones place (7)

💡 Remember the hidden coefficient

The term \( a \) is the same as \( 1a \). We can add and subtract the coefficients (numbers in front) just like normal numbers because all terms contain \( a \).

💡 Strategy: Convert to decimals or common denominators

It’s hard to compare fractions with different denominators. Let’s convert them to decimals or use a common denominator of 12.

💡 Arrange from smallest to largest

Compare the values we calculated:

0.25 is the smallest (1/4)

0.5 is in the middle (1/2)

0.666… is the largest (2/3)

💡 Why we multiply:

The scale tells us that every single centimeter on the map equals 4 kilometers in reality. Since we have 8 centimeters, we have 8 groups of 4 km.

💡 Why we divide:

Now we are going backwards from reality to the map. We need to find how many “4 km chunks” fit into 10 km. Each chunk will represent 1 cm on the map.

💡 Identify the height of each bar

By tracing the top of each bar across to the y-axis, we find:

• Bus: 9
• Car: 7
• Cycle: 3
• Walk: 8
• Other: 1

💡 What is the mode?

The mode is the most common value, or the one with the highest frequency. In a bar chart, this is simply the tallest bar.

💡 Find the difference

We need to subtract the number of students who cycle from the number who walk.

💡 Find 18th birthday year

We add 18 to her birth year.

💡 Add 5 years repeatedly

We need to list the election years starting from 2011 to see if 2030 is included.

💡 Multiply rate by duration

We calculate the cost for each component separately.

💡 Sum the costs

Add the three amounts together and check if it is less than £500.

💡 Definition of a Radius

A radius is a straight line drawn from the center of the circle to any point on the edge (circumference).

💡 Definition of a Chord

A straight line connecting two points on the circumference of a circle, which does not pass through the center, is called a chord.

(Note: A chord that passes through the center is called a diameter).

💡 Multiply episodes by duration

We need to find the total duration in minutes first.

💡 How many minutes in an hour?

There are 60 minutes in 1 hour. To convert minutes to hours, we divide by 60.

💡 What is a prime number?

A prime number has exactly two factors: 1 and itself. It cannot be divided evenly by any other number.

Let’s check numbers between 20 and 40:

• 21 (divisible by 3, 7) ❌
• 22 (even) ❌
• 23 (prime) ✅
• 25 (divisible by 5) ❌
• 27 (divisible by 3, 9) ❌
• 29 (prime) ✅
• 31 (prime) ✅
• 33 (divisible by 3, 11) ❌
• 35 (divisible by 5, 7) ❌
• 37 (prime) ✅
• 39 (divisible by 3, 13) ❌

💡 Strategy: Use Row and Column Totals

We can find missing numbers by subtracting known numbers from totals.

💡 Formula for Pie Chart Angle

\[ \text{Angle} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 360^\circ \]

💡 Use decimals for percentages

15% = 0.15 and 20% = 0.20

💡 Multiplying terms

When we multiply a variable by itself multiple times, we use an index (power) to show how many times it appears.

💡 Multiply games by points

Points from wins = 5 × (number of wins)

Points from draws = 2 × (number of draws)

💡 How many times more?

She needs 30 biscuits, and the recipe is for 20.

💡 Rotate about the origin (0,0)

A 180° rotation changes the sign of both coordinates: \( (x, y) \rightarrow (-x, -y) \).

• Point (2, 2) becomes (-2, -2)
• Point (4, 2) becomes (-4, -2)
• Point (1, 4) becomes (-1, -4)
• Point (5, 4) becomes (-5, -4)

💡 Check the line of reflection

The question asked to reflect in \( x = 3 \) (a vertical line passing through 3 on the x-axis).

Mike’s shape is a reflection of Shape A in the line \( y = 3 \) (a horizontal line passing through 3 on the y-axis).

💡 Substitute x values into y = 3x – 2

💡 Use isosceles triangle properties

Since \( AB = BC \), triangle \( ABC \) is isosceles with base \( AC \).

Base angles are equal, so \( \angle BCA = \angle CAB = 81^\circ \).

Angles in a triangle add to \( 180^\circ \).

💡 Use the given ratio

We are told \( \angle BCD = 4 \times \angle ABC \).

Since \( BC = CD \), triangle \( BCD \) is isosceles. The vertex is at \( C \), so the base is \( BD \).

Base angles \( \angle CBD \) and \( \angle CDB \) are equal.

💡 Find the highest common factor (HCF)

Look for a number that divides into both 6 and 15.

HCF of 6 and 15 is 3.

💡 Look for a common variable

Both terms contain \( m \).

Factor out \( m \).

💡 Break down numbers into primes

We can use factor trees or listing method.

💡 Identify the intersection

Find the numbers that appear in both lists.

63: 3, 3, 7

105: 3, 5, 7

💡 Move the decimal point

Positive power: move right (make bigger). Negative power: move left (make smaller).

💡 Make powers the same or use calculator

This is a calculator paper, so you can type it in directly. However, understanding the method helps check your answer.

Method: Convert to ordinary numbers, add, then convert back.

💡 What is a side elevation?

It’s the view from the side (arrow direction). The arrow points at the slanted rectangular face.

Wait, typically “side elevation” means the view from the side perpendicular to the front. The arrow points at the right side.

Usually, side elevation is a rectangle. The dimensions should be Length x Height.

Rana drew 7cm x 4cm.

The height of the prism is 4cm (vertical). The length is 7cm.

However, from the side, the view is projected. The height of the rectangle should be the vertical height of the prism (4cm). The width should be the length of the prism (7cm).

Rana drew a 7×4 rectangle. Why is it wrong?

Let’s look at the arrow direction carefully. The arrow points at the slant face.

If looking perpendicular to the length, you see a rectangle of height 4cm and width 7cm.

Rana drew 7 width and 4 height. This seems correct? Unless…

Let’s check the mark scheme for acceptable reasons.

Acceptable: “The height of the rectangle should be less than 4 cm” (if viewing the slant face directly? No).

Usually side elevation is a rectangle. Is the height 4?

The vertical height is 4cm. The side elevation is a rectangle 7cm by 4cm.

Wait, Rana drew a 7×4 rectangle. Why is it wrong?

Ah, the “side elevation” might imply the view of the triangle face if the arrow was pointing there? No, arrow is side.

Maybe the vertical height is NOT 4? The diagram labels the left slant edge as 4cm. And a vertical dashed line as 4cm? No, usually one or the other.

Let’s re-examine diagram in PDF page 20.

Left slant edge is 4cm. Base is 6cm. Vertical dashed height is… NOT LABELLED 4cm. The 4cm label points to the top vertex height? Or the slant edge?

There is a line pointing to the vertical height labelled 4cm. AND a label “4 cm” on the left slant edge.

Actually, looking at the PDF crop: The “4 cm” is on the left slant edge. The vertical dashed line has a “4 cm” label too? No, only one 4cm label on the diagram top.

Wait, there are two “4 cm” labels. One on left slant edge. One for vertical height.

If vertical height is 4cm, then side elevation is 7×4 rectangle.

Let’s check the mark scheme for Q24.

Mark scheme says: “The height of the rectangle / it should be less than 4 cm”

“The 4 cm sides are wrong / too long”

“The height of the rectangle should be 2.6… / sqrt(7)”

AHA! This implies the vertical height is NOT 4cm.

The diagram shows the SLANT HEIGHT is 4cm. The BASE is 6cm.

If the slant edge is 4cm and half-base is 3cm (assuming isosceles), then vertical height \( h = \sqrt{4^2 – 3^2} = \sqrt{16-9} = \sqrt{7} \approx 2.65 \) cm.

So the vertical height is ~2.65cm, not 4cm.

Rana drew it 4cm high.

💡 What is a plan view?

The view from directly above (bird’s eye view).

You see the two sloping rectangular faces.

The total width is the base of the triangle (6 cm).

The length is the length of the prism (7 cm).

There will be a line in the middle representing the top ridge.

💡 Increase means 100% + 6%

Total percentage = 106%

Multiplier = 1.06

💡 Use the formula: Amount × Multiplier^years

💡 Use Density Formula

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

The flour fills the tin completely, so the volume of the flour equals the volume of the tin.

💡 Subtract empty space

The tin volume is 1000 cm³. There is 700 cm³ of empty space.

💡 Use Density Formula

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Mass of salt is 600 g.

💡 Probabilities sum to 1

For any branch split, the probabilities must add up to 1.

Coin A (heads) = 0.6 → Coin A (not heads) = 1 – 0.6 = 0.4

Coin B (heads) = 0.55 → Coin B (not heads) = 1 – 0.55 = 0.45

💡 Multiply along branches

We want “Heads on A” AND “Heads on B”.

💡 Formula: \( V = \pi r^2 h \)

💡 Divide volume by rate

Rate is 250 cm³/s.

💡 Divide by 60

💡 Be careful with squaring negatives

\( (-5)^2 \) means \( -5 \times -5 \), which is positive 25.

💡 Isolate h

We need to perform inverse operations to get \( h \) on its own.

1. Multiply by 3 to remove division.
2. Add 5 to remove subtraction.