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Maths928Updated 12 Oct 202624 pages

GCSE Maths Revision Notes for Pearson Edexcel

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Maths can feel overwhelming, but these key topics are actually quite manageable once you break them down. This collection covers essential GCSE maths concepts from exponential equations and indices to trigonometry and graphs - all the stuff you'll need to nail your exams.
GCSE Maths Pearson Edexcel notes – page 1

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Solving Exponential Equations

Ever wondered how to tackle those tricky equations with x in the power? The secret is making sure both sides have the same base number.

When the bases match, you can ignore them completely and just solve the powers. For example, if you have 3^x−4x-4 = 3^2, then x-4 = 2, so x = 6. It's that simple!

Sometimes you'll need to convert different bases first. Like changing 25 to 5² so everything matches. Once the bases are identical, drop them and solve the equation that's left.

Quick Tip: Always check if you can rewrite numbers as powers of the same base - 81 = 3⁴, 27 = 3³, etc.

GCSE Maths Pearson Edexcel notes – page 2

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Indices Rules

Think of indices (or powers) like a mathematical shortcut - they tell you how many times to multiply a number by itself.

The power of a power rule says xax^a^b = x^(ab). Just multiply the powers together. When multiplying with the same base, add the powers: x^a × x^b = x^a+ba+b. For division, subtract them: x^a ÷ x^b = x^a−ba-b.

Negative and fractional indices might look scary, but they're not. A negative power means "one over": x^−a-a = 1/x^a. Fractional powers are roots - x^1/21/2 is the square root, x^1/31/3 is the cube root.

Memory Trick: BIDMAS applies to indices too - always sort out the powers before other operations!

GCSE Maths Pearson Edexcel notes – page 3

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Surds

Surds are just square roots that can't be simplified to whole numbers - think √2 or √3.

Adding surds works like adding fractions - you need the same "denominator" (the number under the root). So 3√8 + 4√8 = 7√8. If they're different, simplify first: √18 = 3√2, so you can then add them properly.

Multiplying surds is easier - just multiply everything together. √4 × √2 = √8. To rationalise the denominator (get rid of surds on the bottom), multiply top and bottom by the same surd.

Pro Tip: Always look for perfect square factors when simplifying - √20 = √(4×5) = 2√5.

GCSE Maths Pearson Edexcel notes – page 4

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Exact Trig Values

You absolutely need to memorise the exact trigonometric values for 30°, 45°, 60°, and 90°. These pop up everywhere in exams!

The key angles give you exact fractions instead of messy decimals. For 30°: sin = 1/2, cos = √3/2, tan = 1/√3. For 45°: sin = cos = √2/2, tan = 1. For 60°: sin = √3/2, cos = 1/2, tan = √3.

Using exact values makes calculations much cleaner. If you need to find a side length and you know an angle is 30°, you can work with exact fractions throughout your solution.

Memory Aid: Draw a right-angled triangle with angles 30°, 60°, 90° and sides 1, 2, √3 to remember the ratios!

GCSE Maths Pearson Edexcel notes – page 5

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Bearings and Trigonometry

Bearings always start from North, go clockwise, and use three figures (like 045° or 270°). They're just a way of describing direction precisely.

For any triangle problem, ask yourself: "Is it right-angled?" If yes, use SOHCAHTOA. If no, you need either the sine rule or cosine rule. Use sine rule when you know a side and its opposite angle. Use cosine rule for everything else.

The sine rule is a/sin A = b/sin B = c/sin C. The cosine rule is a² = b² + c² - 2bc cos A. These formulas will be on your exam paper, so don't panic about memorising them perfectly.

Decision Tree: Right angle? → SOHCAHTOA. Not right angle + know side/opposite angle? → Sine rule. Everything else? → Cosine rule.

GCSE Maths Pearson Edexcel notes – page 6

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Solving Equations Graphically

Graphical solutions mean drawing a curve and reading off where it crosses certain lines or points.

Start by making a table of values - pick x-values in your given range and work out the corresponding y-values. Plot these points carefully, then draw a smooth curve through them (no ruler for curves!).

To solve equations like x³ - x² - 4x + 4 = 2, draw a horizontal line at y = 2 and see where it crosses your curve. The x-coordinates of these crossing points are your answers.

Graph Rules: Curves should be smooth, pass through every plotted point exactly, and have no gaps or jagged bits.

GCSE Maths Pearson Edexcel notes – page 7

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Estimating from Graphs

Reading values from curved graphs requires careful plotting and smooth curve drawing.

When solving equations graphically, you might need to draw additional lines. For x³ - x² - 4x + 4 = 0, look for where your curve crosses the x-axis (where y = 0).

Estimation means reading approximate values from your graph. Don't worry about being perfectly precise - examiners expect some small errors when reading from graphs. Just make sure your curve is as accurate as possible.

Quality Check: Your curve should look like it belongs in a maths textbook - smooth, continuous, and passing exactly through your plotted points.

GCSE Maths Pearson Edexcel notes – page 8

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HCF, LCM and Histograms

HCF (Highest Common Factor) and LCM (Lowest Common Multiple) problems start with prime factorisation - break numbers down to their prime factors.

Use a Venn diagram approach: put common factors in the middle, unique factors on the sides. HCF = product of middle section, LCM = product of everything. For 25 and 40: 25 = 5², 40 = 2³ × 5, so HCF = 5, LCM = 200.

Histograms show frequency density (height) against class width. Remember: frequency = frequency density × class width. The area of each bar represents the actual frequency.

Key Formula: In histograms, it's all about area - frequency density × class width = frequency.

GCSE Maths Pearson Edexcel notes – page 9

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Interest Calculations

Simple interest is straightforward - you earn the same amount each year. Formula: Interest = Principal × Rate × Time, then add to your starting amount.

Compound interest is where your interest earns interest too. Use the multiplier method: Final Amount = Start Amount × 1+rate1 + rate^time. If the rate is 5% increase, multiply by 1.05. If it's 5% decrease, multiply by 0.95.

These percentage problems pop up everywhere - population growth, depreciation, inflation. The compound interest formula handles them all.

Memory Tip: Simple = same each year. Compound = grows faster because interest earns interest.

GCSE Maths Pearson Edexcel notes – page 10

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Tangent to a Circle

A tangent line touches a circle at exactly one point and meets the radius at that point at 90°.

To find a tangent's equation, first work out the gradient of the radius from the centre to the point of contact. The tangent's gradient is the negative reciprocal of this (if radius gradient = 1/2, tangent gradient = -2).

Use y = mx + c to find the tangent equation. You know the gradient mm and a point it passes through, so substitute to find c. Remember that perpendicular gradients multiply to give -1.

Circle Basics: For a circle centred at origin with radius r, the equation is x² + y² = r².

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