Pearson Edexcel GCSE Mathematics (1MA1/1F) – May 2023

💡 What does “percent” mean?

“Percent” means “out of 100”. To convert a percentage to a decimal, we divide by 100.

📉 How to divide by 100:

When we divide by 100, the decimal point moves two places to the left.

👀 Observation:

First, count how many equal triangles make up the entire shape.

🔍 Count:

Now count how many of those sections are shaded grey.

📏 Strategy:

Look at the digit before the decimal point (the units).

💡 Reasoning:

Since 0 is smaller than 1 and 2, the number starting with 0 is the smallest. We don’t even need to check the tenths.

🚶 The Walk:

Start at \(-9\). Adding 5 means moving 5 steps to the right (towards zero and the positive numbers).

🌡️ Temperature Analogy:

If it is -9°C and it gets 5°C warmer, it is still freezing, but not as cold. It becomes -4°C.

⚖️ Inverse Operations:

We want \(p\) on its own. Currently, 2 is being subtracted from \(p\).
The opposite of subtracting 2 is adding 2.

✅ Verification:

Put 5 back into the original equation: \( 5 – 2 = 3 \). This is correct.

📖 Definitions:

• Radius: A line from the centre to the edge.
• Diameter: A line going all the way across the circle, passing through the centre.
• Circumference: The distance around the edge of the circle.

👀 Observation:

The label “Diameter” is pointing to a line that starts at the centre and goes to the edge.

This is actually a radius, not a diameter.

💡 What is a factor?

A factor is a whole number that divides into 20 without leaving a remainder. We can find them in pairs:

📐 Angles on a straight line:

Angles on a straight line always add up to 180°.

📖 Angle Types:

• Acute: Less than 90°
• Right Angle: Exactly 90°
• Obtuse: Between 90° and 180°

Since 50 is less than 90, it cannot be obtuse.

📍 Reading the grid:

Find point B. Look down to the x-axis for the first number. Look across to the y-axis for the second number.

• x-coordinate: 5
• y-coordinate: 2

✏️ Plotting:

Start at the origin (0,0). Move 4 units Right. Move 2 units Down.

Mark with a cross and label it \(C\).

📏 Midpoint Formula:

The midpoint is the average of the coordinates.

Point A is \((-3, 4)\). Point B is \((5, 2)\).

📉 Understanding the equation:

\(y = -4\) means the y-coordinate is ALWAYS -4, no matter what x is.

This creates a horizontal line crossing the y-axis at -4.

🛒 The Deal:

Max buys pairs of (1 Large + 1 Small). We need to find the price of the small plate under the offer.

📦 Bulk Buy:

He wants 6 Large and 6 Small. This means 6 of the “deal pairs”.

⚖️ Decision:

He has £15. The cost is £14.40.

➖ Method: Total tickets minus tickets sold.

We need to do \(700 – 452\). This requires borrowing (exchanging).

≈ Rounding Rules:

When estimating, round numbers to 1 significant figure (or the nearest convenient whole number) to make the maths easy.

• 297 rounds to 300
• £9.50 rounds to £10
• 399 rounds to 400
• £19.50 rounds to £20

🤔 Logic:

Look at how we rounded the numbers:

• We rounded the number of tickets UP (297→300, 399→400).
• We rounded the prices UP (9.50→10, 19.50→20).

If you round everything up, the final answer will be bigger than the real answer.

📝 Formula:

Divide the numbers, keep the letter.

\(15 \div 3 = 5\)

📦 Collect Like Terms:

Group the \(b\)’s together and the \(c\)’s together. The number 19 is on its own.

↩️ Factorise: Put back into brackets. Find the biggest number that divides into both 8 and 6.

HCF of 8 and 6 is 2.

🍕 Ratio to Fraction:

Ratio is \(2:5\).
Total parts = \(2 + 5 = 7\).
Adults are 2 parts out of 7.

✖ Rule: Top times top, bottom times bottom.

✂ Simplify: Both numbers are even, so divide by 2. Or check for bigger factors (like 6).

📐 Multiplier:

Harry wants to make 60 biscuits. The recipe is for 20.

How many times bigger is 60 than 20?

➖ Subtraction: Remove the Red and Blue counters from the total to find what’s left.

➗ Division: The remaining counters (110) are split equally between Yellow and Green.

% Formula: Percentage = \(\frac{\text{Value}}{\text{Total}} \times 100\)

🍎 Bags:

Each bag has 5 apples. If there are \(b\) bags, we multiply.

📦 Crates:

Each crate has 28 apples. If there are \(c\) crates, we multiply.

➕ Total:

Add them together and set equal to \(T\).

📈 Jump Size: How much do we add each time?

From -5 to 3 is +8.
From 3 to 11 is +8.

Since the difference is 8, the start of our formula is \(8n\).

🔙 Work Backwards: What would the term before the first one be?

Subtract 8 from the first term (-5).

✨ Simplify: It is hard to divide by a decimal. Multiply both numbers by 100 to remove the decimal points.

\( 0.15 \times 100 = 15 \)

\( 8.46 \times 100 = 846 \)

The problem becomes: \( 846 \div 15 \)

🔄 Strategy: It’s safer to turn mixed numbers into top-heavy fractions first.

Formula: \( \text{Whole} \times \text{Bottom} + \text{Top} \)

We need the bottoms to be the same. The LCM of 8 and 2 is 8.

🎲 Properties of a Cube:

A cube has 6 identical square faces.

📐 Side length:

Since each face is a square (\(\text{Area} = \text{side} \times \text{side}\)), we square root the area.

📦 Volume Formula: \( \text{Volume} = \text{side} \times \text{side} \times \text{side} \)

📍 Rule: For a frequency polygon, you must plot points at the midpoint of each interval.

Plot the points: \((2.5, 8), (7.5, 24), (12.5, 13), (17.5, 11), (22.5, 4)\).

Join them with straight lines.

📍 Placement Strategy:

1. Middle (Intersection): Numbers in BOTH lists. (1, 9)
2. Circle A only: Remaining odd numbers. (3, 5, 7)
3. Circle B only: Remaining square numbers. (4)
4. Outside: Numbers not in A or B. (2, 6, 8, 10)

🚫 Definition of B’: \(B’\) means “Not B”. Everything OUTSIDE circle B.

Set B has 3 numbers: {1, 4, 9}.

Total numbers = 10.

So “Not B” has \(10 – 3 = 7\) numbers.

📈 Trend: As the points go to the right, they go upwards.

This means as the babies get older, they get heavier.

📏 Line of Best Fit:

To estimate, we should draw a straight line that goes through the middle of the points.

Find 5.8 kg on the y-axis (weight). Go across to your line, then down to the age.

🔗 The Connection: The question tells us directly what the percentage is worth.

\( 20\% = £240 \)

📈 Scale Up: We want the full original price (100%).

How many 20s go into 100? \( 100 \div 20 = 5 \).

So, multiply the value by 5.

📦 Volume Formula: For a prism (like a cylinder), \( \text{Volume} = \text{Area of Base} \times \text{Height} \).

To find the Area, we rearrange: \( \text{Area} = \frac{\text{Volume}}{\text{Height}} \).

⬇️ Pressure Formula: We are given \( \text{Pressure} = \frac{\text{Force}}{\text{Area}} \).

❌ The Cross: The solution to simultaneous equations is simply the point where the two lines cross.

Find the coordinates of the crossing point on the grid.

➕ Multiplication Rule: When multiplying numbers with the same base, add the powers.

➖ Division Rule: When dividing numbers with the same base, subtract the powers.

Note: The bottom number is 4, which is the same as \(4^1\).

🧠 Memory: This is a standard value you need to memorise.

Imagine an equilateral triangle split in half.

🛣️ Trace the Branches:

1. First, she must work at Home on Monday (Top branch: \(0.2\)).
2. Then, she must work at the Office on Friday (Bottom branch coming from Home: \(0.3\)).

✖ AND Rule: In probability, when we want one event AND then another event, we multiply along the branches.