GCSE Nov 2021 Edexcel Foundation Paper 1

💡 What are we doing? To change a fraction to a percentage, we need to make the denominator 100 or multiply the fraction by 100.

Per-cent means “out of 100”.

💡 Strategy: Negative numbers are smaller than zero. The “bigger” the negative number looks (like 10 vs 2), the smaller it actually is (further to the left on a number line).

Let’s separate negatives and positives:

• Negatives: -7, -10, -2
• Zero: 0
• Positives: 8, 1

💡 Why we do this: The denominator 100 tells us the number ends in the “hundredths” column.

Place value columns: Units . Tenths Hundredths

💡 Strategy: We want the nearest “ten”.

Number: 327

The tens digit is 2 (representing 20). The next digit (units) is 7.

💡 What does squared mean? It means multiplying the number by itself.

It does NOT mean \( 7 \times 2 \).

💡 Analysis: The shape has four sides (quadrilateral). It has one pair of parallel sides (marked with arrows).

A quadrilateral with exactly one pair of parallel sides is called a Trapezium.

💡 Analysis: The shape has a circular top and bottom, and straight sides connecting them (like a tin of beans).

This shape is called a Cylinder.

💡 Strategy: “Shared equally” means division.

We need to calculate \( 42 \div 3 \).

💡 Strategy: Check the height of each bar against the table.

• Blue: Table says 10. Graph shows 10. (Correct)
• Green: Table says 4. Graph shows 4. (Correct)
• Brown: Table says 15. Graph shows 16. (Incorrect)

Danny thinks he should get £3.30.

The correct change is £3.50.

So, Danny is incorrect.

We need the difference between Monday (5°C) and Wednesday (-2°C).

Difference means subtraction (highest – lowest).

💡 What this tells us: The key shows that one full square represents 8 games.

Monday has 2 full squares.

If 1 square = 8, we can divide the square into 4 quarters. Each quarter = \( 8 \div 4 = 2 \).

• Tuesday: 2 full squares + 3 quarters (L-shape).
• Wednesday: 1 full square + 1 quarter.

We are told \( \frac{3}{7} \) are boys.

This means for every 7 students, 3 are boys.

Number of girls = Total – Boys = \( 7 – 3 = 4 \).

Group 1 ratio is 3:4.

Group 2 ratio is 3:4.

They are the same.

Let’s look at the differences between the numbers.

\( 2 – 1 = 1 \)

\( 4 – 2 = 2 \)

If the pattern of differences increases by 1 each time (+1, +2, +3…), then the next difference is +3.

Triangle numbers are formed by adding consecutive integers (+2, +3, +4…).

Terms given: 1, 3, 6, 10

💡 Strategy: Multiply the term outside by EACH term inside.

💡 Strategy: Find the highest common factor of both terms.

Terms: \( 6y^2 \) and \( -5y \)

Both contain \( y \).

💡 Strategy: Isolate \( x \) by doing the inverse operations in reverse BIDMAS order.

💡 Strategy: Substitute \( x = 0.5 \) into the expression for length \( AB \).

Length \( AB = 4x – 2 \)

A kite has two pairs of equal sides.

• \( AB = BC = 4x – 2 \)
• \( AD = CD = 3AB = 3(4x – 2) \)

Perimeter = \( AB + BC + CD + AD \)

💡 Strategy: Find how many “batches” of 12 biscuits she can make with each ingredient by dividing what she has by what she needs.

She can make 4 batches with butter, 5 with sugar, but only 3.5 with flour.

The flour limits her to 3.5 batches.

💡 Reasoning: Flour is the limiting ingredient (only enough for 3.5 batches). Sugar was already sufficient for 5 batches.

Having even more sugar won’t help because she still runs out of flour.

💡 Strategy: Substitute values of \( x \) into \( y = 2x – 2 \).

💡 Formula: \( \frac{\text{Change}}{\text{Original}} \times 100 \)

💡 Strategy: Ignore decimal points first. Multiply \( 367 \times 42 \), then put the decimal point back.

Total decimal places = 2 (from 3.67) + 1 (from 4.2) = 3.

💡 Strategy: Make the divisor a whole number by multiplying both sides by 10.

\( \mathcal{E} \) contains even numbers less than 19:

\( \{ 2, 4, 6, 8, 10, 12, 14, 16, 18 \} \)

Which numbers are in BOTH A and B?

\( A = \{ \mathbf{6}, 12, \mathbf{18} \} \)

\( B = \{ 2, \mathbf{6}, 14, \mathbf{18} \} \)

Intersection (Middle): 6, 18

A only: 12 (since 6 and 18 are already in middle)

B only: 2, 14 (since 6 and 18 are already in middle)

Check the universal set list. What hasn’t been used?

Used: \( \{ 2, 6, 12, 14, 18 \} \)

Remaining: 4, 8, 10, 16

The denominators are 5 and 3. The lowest common multiple is 15.

Rahim (£208,000) > Tamara (£176,000)

Ibrahim (15 parts) has 24 more stickers than Matilda (7 parts).

Difference in parts = \( 15 – 7 = 8 \) parts.

Difference in stickers = 24.

We need “How many more does Ibrahim have than Rosie”.

Ibrahim = 15 parts.

Rosie = 4 parts.

Difference = \( 15 – 4 = 11 \) parts.

💡 Formula: \( \text{Volume} = \text{Area of Cross Section} \times \text{Length} \)

The cross section is a triangle.

\( \text{Area of Triangle} = \frac{\text{base} \times \text{height}}{2} \)

A cube has 6 identical square faces.

Area of one face = \( x \times x = x^2 \)

Total Surface Area = \( 6x^2 \)

💡 Strategy: “Correct to 1 decimal place” means the value is rounded to the nearest 0.1.

The “gap” is 0.1.

The error is half of this gap: \( 0.1 \div 2 = 0.05 \).

💡 Strategy: Rearrange the equation into the standard form \( y = mx + c \).

Given: \( y = 3 – 4x \)

Rearranged: \( y = -4x + 3 \)