Essential Formulas You Need to Know for Edexcel GCSE Higher Maths

For Edexcel GCSE Higher Maths students, knowing these formulas is crucial for tackling a range of problems, from algebra to trigonometry and geometry.

This cheat sheet is designed to give you quick access to all the key formulas you need to succeed in your exam.

Keep this guide handy for quick reference during your revision sessions.

1. Algebra

👉 Quadratic Formula:

Used to solve quadratic equations of the form 

👉 Difference of Two Squares:

👉 Completing the Square:

👉 Laws of Indices:

👉 nth Term of an Arithmetic Sequence:

Where a is the first term and d is the common difference.

👉 Inequalities 

When multiplying or dividing an inequality by a negative number, remember to flip the inequality sign.

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2. Number

👉 Surds:
 

When dealing with surds, you may need to rationalise the denominator:

👉 Percentage Increase/Decrease:

👉 Compound Interest:

Where A is the amount, P is the principal, r is the rate, and n is the time.

👉 Estimation:

When estimating, round numbers to 1 significant figure. This can simplify calculations:

👉 Unit conversions:

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3. Geometry

👉 Area of a Triangle:

👉 Area of a Circle:

👉 Circumference of a Circle:

👉 Pythagoras' Theorem:

For a right-angled triangle:

where c is the hypotenuse.

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4. Ratio, proportion and rates of change

👉 Direct Proportion:

If y is directly proportional to x:

👉 Inverse Proportion:

If y is inversely proportional to x:

👉 Gradient of a line: 

To find the gradient between two points 

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5. Geometry and Measures

👉 Volume of a Prism:

👉 Volume of a Cylinder:

👉 Surface Area of a Sphere:

👉 Volume of a Sphere:

👉 Surface Area of a Cone:

Where l is the slant height. 

👉 Volume of a Cone:

👉 Transformations:

Translations: Move shapes using vectors, e.g

Rotations: Always state the centre of rotation, angle, and direction (clockwise or counterclockwise).

Reflections: State the equation of the mirror line.

Enlargements: State the scale factor and centre of enlargement.

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6. Trigonometry

👉 Trigonometry (Right-Angled Triangle):

👉 Sine Rule:
👉 Cosine Rule:

👉 Area of a Triangle (Sine Rule):

👉Trigonometric Values to Memorise

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7. Probability and Statistics

👉 Probability:

👉 Mean (Average):

👉 Median:

Middle value when data is ordered.

👉 Mode:

Most frequently occurring value.

👉 Range:

Difference between the highest and lowest values.

 

⭐️ Quick Revision Tips:

• Understand: Make sure you understand when and how to use each formula.
• Practice: Regularly practice applying these formulas to a variety of problems.
• Memorise: Some formulas are given in the exam, but it's vital to memorize others that aren't provided.

This cheat sheet is tailored to the Edexcel GCSE Higher Maths syllabus, ensuring you have all the key formulas you need to tackle your exam with confidence.