Master the essential maths formulas you'll need for your GCSE...
Maths166 views·Updated 10 Aug 2026·2 pagesGCSE Higher Maths: Essential Formulas and Circle Theorems
brooke crotty@brookecrotty_movl
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Essential GCSE Maths Formulas
Trigonometry might seem intimidating, but once you've got these six key formulas down, you'll tackle any triangle problem with confidence. Start with Pythagoras' theorem - it's your foundation for right-angled triangles.
The three basic trig ratios are straightforward: sin uses opposite over hypotenuse, cos uses adjacent over hypotenuse, and tan uses opposite over adjacent. Remember the acronym SOH-CAH-TOA to keep them straight.
For more complex triangles, you've got the sine rule and cosine rule. The sine rule (a/SinA = b/SinB = c/SinC) works brilliantly when you know some angles and sides. The cosine rule (a² = b² + c² - 2bc cos A) is perfect when you're dealing with three sides or two sides and the included angle.
Quick Tip: Practice identifying which formula to use by looking at what information you're given in the question - this saves loads of time in exams!
2
of 2
Area and Volume Calculations
Area formulas are exam favourites, so nail these basics first. Rectangles use length × width, whilst triangles can be calculated using ½ × base × height or the trig version (½ab sin C) when you know two sides and the included angle.
Don't forget parallelograms (base × height) and trapeziums - the trapezium formula uses the average of the parallel sides multiplied by height: /2 × height. For circles, it's π × radius², and circumference is π × diameter.
Volume calculations follow predictable patterns that'll boost your marks. Prisms use area of cross-section × height, cylinders use π × radius² × height, and pyramids use ⅓ × base area × height. The key is identifying the shape type first.
Exam Strategy: Always write down the formula before substituting numbers - examiners often award marks for showing the correct formula even if your calculation goes wrong!
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Maths166 views·Updated 10 Aug 2026·2 pagesGCSE Higher Maths: Essential Formulas and Circle Theorems
brooke crotty@brookecrotty_movl
Master the essential maths formulas you'll need for your GCSE exams! This quick reference guide covers trigonometry, area calculations, and volume formulas that regularly appear on test papers.
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Essential GCSE Maths Formulas
Trigonometry might seem intimidating, but once you've got these six key formulas down, you'll tackle any triangle problem with confidence. Start with Pythagoras' theorem - it's your foundation for right-angled triangles.
The three basic trig ratios are straightforward: sin uses opposite over hypotenuse, cos uses adjacent over hypotenuse, and tan uses opposite over adjacent. Remember the acronym SOH-CAH-TOA to keep them straight.
For more complex triangles, you've got the sine rule and cosine rule. The sine rule (a/SinA = b/SinB = c/SinC) works brilliantly when you know some angles and sides. The cosine rule (a² = b² + c² - 2bc cos A) is perfect when you're dealing with three sides or two sides and the included angle.
Quick Tip: Practice identifying which formula to use by looking at what information you're given in the question - this saves loads of time in exams!
2
of 2Sign up to see the content. It's free!
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Area and Volume Calculations
Area formulas are exam favourites, so nail these basics first. Rectangles use length × width, whilst triangles can be calculated using ½ × base × height or the trig version (½ab sin C) when you know two sides and the included angle.
Don't forget parallelograms (base × height) and trapeziums - the trapezium formula uses the average of the parallel sides multiplied by height: /2 × height. For circles, it's π × radius², and circumference is π × diameter.
Volume calculations follow predictable patterns that'll boost your marks. Prisms use area of cross-section × height, cylinders use π × radius² × height, and pyramids use ⅓ × base area × height. The key is identifying the shape type first.
Exam Strategy: Always write down the formula before substituting numbers - examiners often award marks for showing the correct formula even if your calculation goes wrong!
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