Pearson Edexcel GCSE Foundation Paper 2 (June 2024)

💡 What are we asked to do?

We need to arrange the numbers from smallest (lowest) to largest.

Remember: Negative numbers are smaller than zero. The “bigger” the negative number looks, the smaller its value actually is (e.g., -10 is smaller than -1).

💡 Key Fact:

There are 1000 millilitres (ml) in 1 litre (l).

To convert from millilitres to litres, we divide by 1000.

💡 How do we convert fractions over 100?

A fraction over 100 represents “hundredths”.

\( \frac{31}{100} \) is 31 hundredths.

In decimal place value:

• The first digit after the decimal point is tenths.
• The second digit after the decimal point is hundredths.

💡 What is a multiple?

Multiples of 7 are numbers in the 7 times table.

We need to find one that fits in the range \(30 < x < 40\).

💡 What does \(2m\) mean?

In algebra, when a number is written next to a letter, it means multiplication.

\( 2m \) means \( 2 \times m \).

💡 Interpreting the Key:

One full square = 4 houses.

Half a square = \(4 \div 2 = 2\) houses.

Quarter of a square = \(4 \div 4 = 1\) house.

💡 Strategy:

We need to represent 11 houses.

\( 11 = 4 + 4 + 3 \)

So we need 2 full squares (8) and we have 3 left over.

3 is three-quarters of 4.

💡 Strategy:

Total = Jan + Feb + Mar + Apr + May = 60.

We need to find the values for Feb and Mar from the pictogram, add them to Jan and Apr, and subtract from 60.

💡 Method:

Use a ruler. Place the 0 mark at one end of the line and read the value at the other end.

💡 Method:

Use a protractor. Place the center on the vertex (corner). Align the zero line with one arm of the angle. Read the scale where the other arm passes.

Looking at the diagram, it is an acute angle (less than 90°).

💡 Definition:

A hexagon is a polygon with 6 sides.

It does not have to be regular (equal sides). Any closed shape with 6 straight sides counts.

💡 Method:

Coordinates are written as \((x, y)\).

Find the position on the horizontal x-axis, then the vertical y-axis.

💡 Formula:

Midpoint = \( (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) \)

Point A is \((2, 1)\).

Point B is \((-2, -5)\) (Read from graph: Left 2, Down 5).

💡 Action:

Coordinates \((-4, 2)\) mean:

x = -4 (Left 4)

y = 2 (Up 2)

💡 Strategy:

Subtract the start reading from the end reading to find the distance travelled.

💡 Strategy:

Multiply the miles by the rate (47p). Note that the rate is in pence.

💡 Strategy:

There are 100p in £1. Divide by 100.

💡 Strategy:

Add the fixed expenses (£80) to the driving pay.

💡 Strategy:

Be systematic to ensure you don’t miss any.

Total outcomes = \(2 \times 2 \times 2 = 8\).

💡 Observation:

Look closely at section 2. There is a square symbol at the center.

This symbol indicates a right angle (90°).

💡 Formula:

Probability is based on the fraction of the total circle.

Total angles in a circle = 360°.

Angle for section 2 = 90°.

💡 Reasoning:

Majid assumes that because there are 3 sections, the probability is \( \frac{1}{3} \).

This is only true if the sections are equal in size.

Since the sections are different sizes (one is 90°, the others are larger), Majid is wrong.

💡 Strategy:

If \( \frac{2}{3} \) are white, then \( 1 – \frac{2}{3} = \frac{1}{3} \) are milk chocolate.

Alternatively, find the number of white bars first and subtract from the total.

💡 Strategy:

Multiply the number of milk chocolate bars by the weight of one bar.

💡 Rule:

Multiply the numbers first, then write the letters alphabetically.

💡 Strategy:

Replace \( x \) with 3 and \( y \) with -4 in the formula.

Remember that \( 2y \) means \( 2 \times y \).

💡 Formula:

\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)

💡 Formula:

\( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)

💡 Key Conversion:

0.25 hours is not 25 minutes!

To convert decimal hours to minutes, multiply by 60.

💡 Comparison:

Add Monday’s time (3 hours) to Tuesday’s time.

💡 Method:

Find 2.5% of £3500.

Using a calculator multiplier: \( 2.5\% = 0.025 \).

💡 Simple Interest:

Simple interest means the amount is the same every year.

Multiply the annual interest by the number of years (6).

💡 Method:

Go to 6 on the ounces (horizontal) axis.

Go up to the line, then go across to the grams (vertical) axis.

💡 Strategy:

First, convert 1 kg to grams because the graph uses grams.

\( 1 \text{ kg} = 1000 \text{ grams} \).

The graph doesn’t go up to 1000g. We need to find a value we can scale up.

💡 Locus Rule:

The set of points a fixed distance from a point is a circle.

Since it’s “less than”, we want the inside of the circle.

💡 Locus Rule:

The set of points equidistant from two points is the perpendicular bisector of the line joining them.

💡 Combine the Conditions:

We need the area that satisfies BOTH rules:

1. Inside the arc from A.

2. To the left of the perpendicular bisector.

💡 Strategy:

If the school pays 56%, the rest is paid by the children.

Total percentage = 100%.

💡 Strategy:

Find 44% of £1800.

Using a calculator multiplier: \( 0.44 \).

💡 Strategy:

Divide the total children’s cost by 66.

💡 Tip:

Calculate the top (numerator) and bottom (denominator) separately if you aren’t confident with using fraction buttons.

💡 Significant Figures:

The first significant figure is the first non-zero digit.

In 0.5170…, the first sig fig is 5.

The second sig fig is 1.

Look at the next digit (7) to decide whether to round up.

💡 Pythagoras’ Theorem:

In a right-angled triangle: \( a^2 + b^2 = c^2 \)

\( c \) is always the hypotenuse (the longest side opposite the right angle).

Here, the hypotenuse is \( AC = 19 \).

We are finding a shorter side \( CB \).

💡 Rearranging for a shorter side:

\( \text{side}^2 = \text{hypotenuse}^2 – \text{other side}^2 \)

\( CB^2 = 19^2 – 10^2 \)

💡 3 Significant Figures:

1st sig fig: 1

2nd sig fig: 6

3rd sig fig: 1

The next digit is 5, so round the 1 up to 2.

💡 Strategy:

Divide 90 by prime numbers (2, 3, 5, 7…) until you only have primes left.

💡 Rule:

To find the LCM from prime factors, take the highest power of each prime factor present in either list.

\( A = 2^2 \times 3^1 \)

\( B = 2^1 \times 3^2 \)

💡 Substitute n=6:

\( n = 6 \) machines.

💡 Substitute n=9:

\( n = 9 \) machines.

💡 Strategy:

We know 24 yellow discs represent a probability of 0.16.

\( \text{Total} = \frac{\text{Number of items}}{\text{Probability}} \)

💡 Strategy:

Subtract the yellow discs from the total.

💡 Ratio 5:4

Total parts = \( 5 + 4 = 9 \) parts.

These 9 parts represent the 126 discs.

💡 Strategy:

Substitute the x values into \( y = x^2 – x \).

Remember that squaring a negative number gives a positive result.

💡 Action:

Plot the points: \( (-2,6), (-1,2), (0,0), (1,0), (2,2), (3,6) \).

Join them with a smooth curve. Do NOT use a ruler.

The bottom of the curve should dip slightly below the x-axis between 0 and 1.

💡 Strategy:

The equation is \( x^2 – x = 4 \).

This means we want to find where our curve (\( y = x^2 – x \)) meets the line \( y = 4 \).

Draw a horizontal line across at \( y = 4 \). Read the x-values where it crosses the curve.

💡 Strategy:

We don’t know the total number of sweets, but we can work with the ratio parts directly as if they were the number of sweets (or multiples of them).

Ratio: \( A : L : T = 1 : 6 : 14 \)

Let’s assume there are \( 1 + 6 + 14 = 21 \) sweets (or 21 parts).

💡 Calculation:

Tina starts with 14 parts.

She gives \( \frac{3}{7} \) of 14.

💡 Calculation:

Tina gives \( 12.5\% \) of the rest (8 parts).

Note: \( 12.5\% = \frac{1}{8} \).

💡 Rule:

The sum of angles in a quadrilateral is 360°.

💡 Definition:

A trapezium has one pair of parallel sides.

If two lines are parallel, the co-interior angles (angles on the same side inside the parallel lines) sum to 180°.

Check pairs: A + B or C + D?

💡 Similar Triangles:

Identify corresponding sides.

The base of ABC is 6 cm.

The base of DEF is 1.5 cm.

Scale Factor = \( \frac{\text{Large}}{\text{Small}} = \frac{6}{1.5} \).

💡 Strategy:

\( DE \) corresponds to \( AB \) (the side length).

\( AB = 8 \) cm.

Divide by the scale factor.

💡 Strategy:

Total frequency = 120.

The median is at position \( \frac{120+1}{2} = 60.5 \) (or roughly the 60th value).

Use cumulative frequency.

💡 Strategy:

To estimate mean from grouped data, assume all items are at the midpoint of the interval.

💡 Formula:

\( \text{Mean} = \frac{\text{Total Sum}}{\text{Total Frequency}} \)