GCSE Maths Cheat Sheets for Essential Facts and Rules

08/12/2025

Maths

gcse maths cheat sheets

Subjects

Maths

141

•

8 Dec 2025

•

2 pages

GCSE Maths Cheat Sheets for Essential Facts and Rules

@joyoflife

This is your essential maths formula sheet that covers all... Show more

$# AREAS $\text{cm}^2$ or $\text{m}^2$ - RECTANGLE $\text{A = L \times W}$ - TRIANGLE $\text{A = }\frac{1}{2}\text{b \times h}_v$ (vertical$

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 $a+b$ × 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.

$# AREAS $\text{cm}^2$ or $\text{m}^2$ - RECTANGLE $\text{A = L \times W}$ - TRIANGLE $\text{A = }\frac{1}{2}\text{b \times h}_v$ (vertical$

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 $h² = a² + b²$ 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 $x + a$ moves the graph left by 'a' units, y = f(x) + a moves it up by 'a' units. Percentage change always equals (change ÷ original) × 100.

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Subjects

Maths

•

141

•

8 Dec 2025

•

2 pages

GCSE Maths Cheat Sheets for Essential Facts and Rules

@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... Show more

$# AREAS $\text{cm}^2$ or $\text{m}^2$ - RECTANGLE $\text{A = L \times W}$ - TRIANGLE $\text{A = }\frac{1}{2}\text{b \times h}_v$ (vertical$

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Essential Formulas and Calculations

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.

Top Tip: When dealing with bearings, always measure clockwise from the north line - this catches loads of students out!

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.

$# AREAS $\text{cm}^2$ or $\text{m}^2$ - RECTANGLE $\text{A = L \times W}$ - TRIANGLE $\text{A = }\frac{1}{2}\text{b \times h}_v$ (vertical$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Topics and Geometry

Remember: Pythagoras' theorem $h² = a² + b²$ only works for right-angled triangles - don't use it for other triangles!

Graph transformations follow patterns: y = f $x + a$ moves the graph left by 'a' units, y = f(x) + a moves it up by 'a' units. Percentage change always equals (change ÷ original) × 100.

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4.9/5

App Store

4.8/5

Google Play

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user