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Maths1,012Updated 9 Sept 20266 pages

Comprehensive GCSE AQA Maths Notes for Paper 3

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Eren Gregg@renregg_deipnwscuzce
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This collection covers essential GCSE maths topics you'll definitely encounter in your exams. From algebraic fractions to circle geometry, these concepts build on each other and appear regularly in both coursework and final assessments.
GCSE AQA Maths notes for paper 3 – page 1

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Algebraic Fractions

Working with algebraic fractions is just like handling regular fractions, but with letters thrown into the mix. The key is spotting the highest common factor and cancelling it out to simplify.

When you're adding or subtracting algebraic fractions, you need a common denominator first. If the denominators are the same, just add or subtract the numerators and keep the denominator unchanged.

For fractions with different denominators, multiply each fraction to create matching denominators. Then combine the numerators as usual.

Quick tip: Always look for common factors in brackets like m+3m+3 – they cancel out just like numbers do!

GCSE AQA Maths notes for paper 3 – page 2

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Bounds and Probability

Bounds help you understand the range of possible values when numbers are rounded. For a number rounded to the nearest 10, remember the lower bound includes the equals sign, but the upper bound doesn't.

The product rule makes counting combinations dead simple – just multiply all your options together. Restaurant menus, dice combinations, clothing choices – it works for everything.

Probability calculations often use sample space diagrams (like the dice table shown). Count your successful outcomes, divide by total possible outcomes, and you've got your answer.

Remember: When finding bounds, think about what values would round to give your number – this helps you set the correct inequalities.

GCSE AQA Maths notes for paper 3 – page 3

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Interest and Iteration

Simple interest stays constant each year – just calculate the percentage once and multiply by the number of years. Compound interest grows because you earn interest on your previous interest too.

Iteration is a clever method for solving equations that are too tricky for normal algebra. You use a formula repeatedly, plugging each answer back in until the values stop changing.

The iteration process continues until your answers stabilise to the required number of decimal places. It's like mathematical trial and improvement, but much more systematic.

Pro tip: With compound interest, each year's calculation becomes the starting amount for the next year – that's where the "compounding" happens!

GCSE AQA Maths notes for paper 3 – page 4

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Line Equations and Bearings

Parallel lines share identical gradients – that's literally all you need to remember. Change the y-intercept, keep the gradient the same, and you've got a parallel line.

Perpendicular lines use negative reciprocal gradients. If your original gradient is 2, the perpendicular gradient becomes -1/2. Flip the fraction and change the sign.

Bearings follow three strict rules: measured from North, measured clockwise, and always written with three figures (like 045° instead of 45°).

Memory trick: Perpendicular gradients multiply together to give -1, so 2 × −1/2-1/2 = -1.

GCSE AQA Maths notes for paper 3 – page 5

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Angles in Parallel Lines

When parallel lines are cut by a transversal, you get four types of angle relationships that are absolute exam favourites. Alternate angles are equal and sit in a 'Z' pattern.

Corresponding angles are equal and sit in an 'F' pattern. Vertically opposite angles are equal where two lines cross.

Co-interior angles (also called allied angles) are different – they add up to 180° and sit in a 'C' pattern between the parallel lines.

Exam hack: Learn to spot these patterns quickly – angle questions often test multiple relationships in one diagram.

GCSE AQA Maths notes for paper 3 – page 6

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