This is your essential maths formula sheet that covers all...
Maths268 views·Updated 20 Aug 2026·2 pagesGCSE Maths Cheat Sheets for Essential Facts and Rules
j@joyoflife
1
of 2
Essential Formulas and Calculations
Area formulas are absolutely crucial for your exams. Remember that rectangles use length × width, triangles need ½ × base × height (always use vertical height!), and circles require πr². For parallelograms, it's simply base × height, whilst trapeziums use ½ × height.
Perimeter is just the distance around any shape's edge. For circles, we call this circumference and use C = πD or C = 2πr. These circle formulas pop up constantly in exam questions.
The triangle method is brilliant for rearranging formulas like speed = distance/time. Draw a triangle, put what you're finding at the top, cover it up, and what's left shows you the calculation. For instance, to find time, you'd calculate distance ÷ speed.
Top Tip: When dealing with bearings, always measure clockwise from the north line - this catches loads of students out!
Volume calculations follow simple patterns. Cuboids use length × width × height, whilst any prism uses cross-sectional area × length. Master these basics and you'll handle most volume questions with confidence.
Percentages become easy when you remember that finding x% means multiplying by x/100. For percentage changes, work out the percentage amount first, then add or subtract from your original value.
2
of 2
Advanced Topics and Geometry
SOH CAH TOA is your best friend for right-angled triangles. Sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. But remember, this only works for right-angled triangles!
For any other triangle, you'll need the sine rule (a/sinA = b/sinB = c/sinC) or cosine rule (a² = b² + c² - 2bc×cosA). The area of any triangle can be found using ½ab×sinC when you know two sides and the included angle.
Circle geometry has key rules you must memorise. Angles in a semicircle equal 90°, and opposite angles in a cyclic quadrilateral add up to 180°. The angle at the centre is twice the angle at the circumference.
Remember: Pythagoras' theorem only works for right-angled triangles - don't use it for other triangles!
Probability follows simple rules: P(A and B) = P(A) × P(B) for independent events, and P(A or B) = P(A) + P(B) for mutually exclusive events. For "at least" problems, use 1 - P(the opposite outcome).
Graph transformations follow patterns: y = f moves the graph left by 'a' units, y = f + a moves it up by 'a' units. Percentage change always equals (change ÷ original) × 100.
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Maths268 views·Updated 20 Aug 2026·2 pagesGCSE Maths Cheat Sheets for Essential Facts and Rules
j@joyoflife
This is your essential maths formula sheet that covers all the key topics you'll need for your GCSEs. It's packed with the most important formulas, definitions, and quick methods that'll help you tackle everything from basic calculations to complex geometry...
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Essential Formulas and Calculations
Area formulas are absolutely crucial for your exams. Remember that rectangles use length × width, triangles need ½ × base × height (always use vertical height!), and circles require πr². For parallelograms, it's simply base × height, whilst trapeziums use ½ × height.
Perimeter is just the distance around any shape's edge. For circles, we call this circumference and use C = πD or C = 2πr. These circle formulas pop up constantly in exam questions.
The triangle method is brilliant for rearranging formulas like speed = distance/time. Draw a triangle, put what you're finding at the top, cover it up, and what's left shows you the calculation. For instance, to find time, you'd calculate distance ÷ speed.
Top Tip: When dealing with bearings, always measure clockwise from the north line - this catches loads of students out!
Volume calculations follow simple patterns. Cuboids use length × width × height, whilst any prism uses cross-sectional area × length. Master these basics and you'll handle most volume questions with confidence.
Percentages become easy when you remember that finding x% means multiplying by x/100. For percentage changes, work out the percentage amount first, then add or subtract from your original value.
2
of 2Sign up to see the content. It's free!
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Advanced Topics and Geometry
SOH CAH TOA is your best friend for right-angled triangles. Sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. But remember, this only works for right-angled triangles!
For any other triangle, you'll need the sine rule (a/sinA = b/sinB = c/sinC) or cosine rule (a² = b² + c² - 2bc×cosA). The area of any triangle can be found using ½ab×sinC when you know two sides and the included angle.
Circle geometry has key rules you must memorise. Angles in a semicircle equal 90°, and opposite angles in a cyclic quadrilateral add up to 180°. The angle at the centre is twice the angle at the circumference.
Remember: Pythagoras' theorem only works for right-angled triangles - don't use it for other triangles!
Probability follows simple rules: P(A and B) = P(A) × P(B) for independent events, and P(A or B) = P(A) + P(B) for mutually exclusive events. For "at least" problems, use 1 - P(the opposite outcome).
Graph transformations follow patterns: y = f moves the graph left by 'a' units, y = f + a moves it up by 'a' units. Percentage change always equals (change ÷ original) × 100.
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Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
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