Master the essential maths formulas you'll need for your GCSE... Show more
Maths150 views·Updated May 7, 2026·2 pagesGCSE Higher Maths: Essential Formulas and Circle Theorems
brooke crotty@brookecrotty_movl
1
of 2
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 works brilliantly when you know some angles and sides. The cosine rule 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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Maths150 views·Updated May 7, 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 works brilliantly when you know some angles and sides. The cosine rule 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!
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of 2Sign up to see the content. It's free!
- Access to all documents
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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.
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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.
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