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IGCSE Edexcel Maths Formula Sheet (Visual Guide)
IGCSE Edexcel 4MA1/4MB1

The Ultimate IGCSE Maths Formula Sheet (2026)

Your definitive visual guide for exam success. Synthesizing critical concepts in Geometry, Mensuration, Algebra, and Trigonometry. These high-definition revision cards pair visual learning with text-based formulas to ensure you master every equation.

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GetYourTutors infographic: 'The Ultimate IGCSE Maths Formula Sheet (2026).' Visualizes the definitive revision guide covering 4 core domains. 1. Algebra: Features graphs and the Quadratic Equation (ax^2+bx+c=0). 2. Geometry: visualizes polygon and circle theorems. 3. Mensuration: Displays 3D volume and surface area formulas for prisms and cones. 4. Trigonometry: Visualizes SOH CAH TOA right-angled triangles and sine/cosine wave graphs. Badges: Explicitly covers Edexcel and Cambridge IGCSE curricula.

Part 1: Mensuration (Area & Volume)

Master the essential 3D shapes and 2D area calculations required for the higher paper.

GetYourTutors infographic: 'SURFACE AREA FORMULAS.' Visualizes key IGCSE/GCSE geometry formulas for 3D shapes. 1. Cylinder: Shows the formula for Curved Surface Area as A = 2πrh (where r=radius, h=height). 2. Cone: Shows the formula for Curved Surface Area as A = πrl (where r=radius, l=sloping edge/slant height). 3. Sphere: Shows the formula for Total Surface Area as A = 4πr^2. Note: Distinguishes between curved surface and total surface area for exam accuracy.

Cylinder, Cone & Sphere

CylinderSA = 2πrh + 2πr²
ConeCSA = πrl
SphereSA = 4πr²
GetYourTutors infographic: 'VOLUME FORMULAS.' Visualizes key IGCSE/GCSE formulas for 3D shapes. 1. Prism: V = Al (Cross-sectional Area times length). 2. Cylinder: V = pi r^2 h (Circular base area times height). 3. Pyramid: V = 1/3 Ah (Note: Volume is 1/3 of the corresponding prism). 4. Cone: V = 1/3 pi r^2 h (Note: Volume is 1/3 of the corresponding cylinder). 5. Sphere: V = 4/3 pi r^3. The guide highlights the relationship between 'straight' shapes and 'pointed' shapes for easier memorization.

Volume Formulas

SphereV = 4/3πr³
ConeV = 1/3πr²h
PyramidV = 1/3 × Base × H
GetYourTutors infographic: 'Quick Guide: 3D Geometric Formulas.' Visualizes key IGCSE/GCSE formulas. 1. Cuboid: Defined by length (l), width (w), and height (h). Formulas: Volume = l x w x h; Surface Area = 2(lw + lh + wh). 2. Cube: Defined by side length (s). Formulas: Volume = s^3; Surface Area = 6s^2. 3. Triangular Prism: Defined by base area (A), length (l), and base perimeter (P). Formulas: Volume = A x l; Surface Area = 2A + (P x l). Note: Highlights the use of 'Base Area' method for prisms.

Cuboids & Prisms

CuboidV = l × w × h
PrismV = Area × Length
GetYourTutors infographic: 'Advanced 3D Geometry Formulas.' Visualizes complex IGCSE/GCSE shapes. 1. Square-based Pyramid: Defined by base side (s), vertical height (h), and slant height (l). Formulas: Volume = 1/3 s^2 h; Surface Area = s^2 + 2sl. 2. Triangular Pyramid: Defined by Base Area (A) and height (h). Formula: Volume = 1/3 Ah. 3. Hemisphere: Defined by radius (r). Formulas: Volume = 2/3 pi r^3; Total Surface Area = 3 pi r^2 (includes the flat circular base). Note: Highlights the critical difference between vertical height (h) for volume and slant height (l) for surface area.

Advanced 3D

HemisphereV = 2/3πr³
Total SASA = 3πr²
GetYourTutors infographic: 'GEOMETRIC AREA FORMULAS.' Visualizes key formulas for advanced shapes. 1. Trapezium: Defined by parallel sides a and b and vertical height h. Formula: Area = 1/2(a+b)h. 2. Circle Sector: Shows a slice of a circle with angle theta (in Degrees). Formula: Area = (theta/360) * pi * r^2. 3. Circle Segment: Shows the chord-cut region with radius r and angle theta (in Radians). Formula: Area = 1/2 r^2 (theta - sin theta). Note: Explicitly highlights the switch from Degrees (Sector) to Radians (Segment) for exam accuracy.

Geometric Area Formulas

Trapezium Area = ½(a + b)h
Circle Sector Area = (θ/360) × πr2
(Angle θ in degrees)
Circle Segment Area = ½r2(θ - sin θ)
(Angle θ in radians)
GetYourTutors infographic: 'Geometric Formulas.' Visualizes Area and Perimeter rules for 4 key quadrilaterals. 1. Rectangle: Formulas for Area (l x w) and Perimeter (2(l+w)). 2. Square: Formulas for Area (s^2) and Perimeter (4s). 3. Parallelogram: Formulas for Area (b x h) and Perimeter (2(a+b)). 4. Rhombus: Visualizes two distinct Area methods: Standard (s x h) and Diagonal Method (Area = 1/2 d1 d2, using diagonals d1 and d2). Note: Highlights the critical difference between the slant height (a) and vertical height (h) for parallelograms.

Quadrilaterals

TrapeziumA = ½(a + b)h
ParallelogramA = b × h
Part 2

Geometry & Circle Theorems

GetYourTutors infographic: 'Key Angle Rules in Geometry.' Visualizes essential theorems for parallel lines and polygons. 1. Exterior Angles of a Regular Polygon: Shows the formula Exterior Angle = 360 degrees / n (where n is the number of sides). 2. Parallel Line Rules: Visualizes three key angle relationships formed by a transversal intersecting parallel lines: Alternate Angles (Z-shape) are equal. Corresponding Angles (F-shape) are equal. Co-interior Angles (C-shape/Consecutive) sum to 180 degrees.

Angle Theorems

LineSum = 180°
PointSum = 360°
GetYourTutors infographic: 'Geometry Essentials: Understanding Polygon Angles.' Visualizes key IGCSE/GCSE theorems. 1. Quadrilaterals: States that angles in any four-sided shape sum to 360°. 2. Exterior Angle of a Triangle: Visualizes the rule that an exterior angle equals the sum of the two opposite interior angles. 3. Sum of Interior Angles: Displays the universal formula Sum = (n-2) * 180 degrees (where n = number of sides). 4. Regular Polygons: Shows how to find a single interior angle of a regular polygon using the formula ((n-2) * 180) / n.

Polygons

Interior(n - 2) × 180°
Exterior360° / n
GetYourTutors infographic: 'Advanced 3D Geometry Formulas.' Visualizes complex IGCSE/GCSE shapes. 1. Square-based Pyramid: Defined by base side (s), vertical height (h), and slant height (l). Formulas: Volume = 1/3 s^2 h; Surface Area = s^2 + 2sl. 2. Triangular Pyramid: Defined by Base Area (A) and height (h). Formula: Volume = 1/3 Ah. 3. Hemisphere: Defined by radius (r). Formulas: Volume = 2/3 pi r^3; Total Surface Area = 3 pi r^2 (includes the flat circular base). Note: Highlights the critical difference between vertical height (h) for volume and slant height (l) for surface area.

Volume & Surface Area of 3D Solids

Square-based Pyramid Volume = (1/3)s2h
Surface Area = s2 + 2sl
Triangular Pyramid Volume = (1/3)Ah
(Where A = base area)
Hemisphere Volume = (2/3)πr3
Surface Area = 3πr2
GetYourTutors infographic: 'Key Circle Geometry Theorems.' Visualizes 3 advanced IGCSE/GCSE angle rules involving tangents. 1. Cyclic Quadrilateral (Exterior): Visualizes the rule that the exterior angle of a cyclic quadrilateral is exactly equal to the opposite interior angle (alpha = alpha). 2. Tangent-Radius Theorem: Shows that a tangent line is always perpendicular (90 degrees) to the radius at the point of contact. 3. Alternate Segment Theorem: Visualizes the angle between a tangent and a chord being equal to the angle in the alternate segment (beta = beta). Note: Highlights the 'Tangent-Chord' relationship critical for solving high-level geometry proofs.

Advanced Circle Theorems

Tangent90° to Radius
Alt SegmentAngle = Opp Interior
Cyclic QuadOpposite Sum = 180°
GetYourTutors infographic: 'Understanding Circle Theorems.' Visualizes 4 critical IGCSE/GCSE geometry rules. 1. Angle at the Center: Shows that the angle at the center (2 theta) is double the angle at the circumference (theta). Formula: Angle at Center = 2 x Angle at Circumference. 2. Angles in the Same Segment: Visualizes the 'bowtie' shape, showing that angles subtended by the same arc are equal (30 degrees = 30 degrees). 3. Angle in a Semicircle: Shows a triangle built on the diameter always has a 90 degree (right angle) at the circumference. 4. Cyclic Quadrilateral: Shows a four-sided shape with all vertices touching the circle. Rule: Opposite angles sum to 180 degrees.

Core Circle Properties

CenterAngle = 2 × Circumference
SegmentSame Arc Angles Equal
SemicircleTriangle = 90°

Part 3: Algebra & Tricky Topics

GetYourTutors infographic: 'Quadratic Formula.' Visualizes the universal method for solving quadratics. 1. The Problem (Standard Form): Displays the equation ax^2 + bx + c = 0 with the critical condition that coefficient a ≠ 0. 2. The Solution (The Formula): clearly presents the formula x = (-b ± √(b^2 - 4ac)) / 2a. 3. Purpose: Explains that this formula calculates the 'values of x' (roots) for any quadratic equation, particularly those that cannot be easily factored.

Quadratic Formula

ax²+bx+c=0Use when you can't factorise
GetYourTutors infographic: 'The Golden Rule of Substitution.' Visualizes a critical algebra technique to avoid calculator errors. 1. The Rule: When substituting a number (especially a negative one like -3), always enclose it in brackets: {-3}. 2. The Example: Substituting x = -3 into the equation y = x^2 - 4x. 3. Correct Method: y = (-3)^2 - 4(-3) = 21. Explains that brackets ensure the entire negative number is squared. 4. Common Mistake: y = -3^2 - 4 - 3 = -16. Explains that without brackets, calculators square the number before applying the negative sign, leading to a wrong answer.

Golden Rule of Substitution

Rule Always put negative numbers in brackets: (-3)
Example y = (-3)2 - 4(-3) = 21
GetYourTutors infographic: 'Unwrapping Variables: Your Guide to Inverse Operations.' Visualizes the 4 essential algebraic pairs used to isolate variables. 1. Foundational: Shows Addition (+) is the inverse of Subtraction (-); they cancel each other out. 2. Multiplicative: Shows Multiplication (x) is the inverse of Division (÷). 3. Exponents: Visualizes that taking the nth Root (n√x) is the inverse of raising to the nth Power (x^n). 4. Reciprocals: Shows that the Reciprocal (1/x) is its own inverse (flipping both sides). Note: Highlights the strategy of 'unwrapping' an equation to make a specific letter the subject.

Unwrapping Variables: Your Guide to Inverse Operations

Foundational Inverse Pairs
Addition (+) ↔ Subtraction (-) These two basic operations directly cancel each other out.
Multiplication (x) ↔ Division (÷) Use one operation to reverse the effect of the other.
Advanced Inverse Pairs
Power (xn) ↔ Root (n√x) Taking the nth root is the inverse of raising to the nth power.
Reciprocal (1/x) ↔ Reciprocal
(Flip Both Sides)		 To undo a reciprocal, simply take the reciprocal again.
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