📐 IGCSE Maths Formula Sheet 2025
Complete Cambridge IGCSE Mathematics (0580/0607/0980) Formula Reference Guide
Cambridge IGCSE Extended Papers Free Download
Essential IGCSE Mathematics Formulas
Master your IGCSE Mathematics exams with our comprehensive formula sheet covering all essential formulas for Cambridge IGCSE (0580/0607/0980) Extended papers. This reference guide includes area, volume, trigonometry, algebra, and more.
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Cambridge IGCSE™ Mathematics (0580, 0607, and 0980)
List of formulas for Extended papers
Area and Circumference
Area, A, of triangle, base b, height h.
A = (1/2)bh Area, A, of circle of radius r.
A = πr² Circumference, C, of circle of radius r.
C = 2πr Surface Area
Curved surface area, A, of cylinder of radius r, height h.
A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l.
A = πrl Surface area, A, of sphere of radius r.
A = 4πr² Volume
Volume, V, of prism, cross-sectional area A, length l.
V = Al Volume, V, of pyramid, base area A, height h.
V = (1/3)Ah Volume, V, of cylinder of radius r, height h.
V = πr²h Volume, V, of cone of radius r, height h.
V = (1/3)πr²h Volume, V, of sphere of radius r.
V = (4/3)πr³ Quadratic Equation
For the equation ax² + bx + c = 0, where a ≠ 0.
x = (-b ± √(b² - 4ac)) / 2a Triangle Formulas
For the triangle shown,
Sine Rule:
a / sin A = b / sin B = c / sin C Cosine Rule:
a² = b² + c² - 2bc cos A Area of triangle:
Area = (1/2)ab sin C Geometric Formulas
Rectangle - length l, width w
Area = lw, Perimeter = 2(l + w) Square - side s
Area = s², Perimeter = 4s Parallelogram - base b, height h
Area = bh, Perimeter = 2(a + b) Rhombus - side s, height h
Area = sh = (1/2)d₁d₂, Perimeter = 4s Trapezium - parallel sides a,b, height h
Area = (1/2)(a + b)h Sector of Circle - radius r, angle θ (degrees)
Area = (θ/360) × πr², Arc length = (θ/360) × 2πr Segment of Circle - radius r, angle θ
Area = (1/2)r²(θ - sin θ) where θ is in radians 3D Geometric Formulas
Cuboid - length l, width w, height h
Volume = lwh, Surface Area = 2(lw + lh + wh) Cube - side s
Volume = s³, Surface Area = 6s² Triangular Prism - base area A, length l
Volume = Al, Surface Area = 2A + perimeter × l Square-based Pyramid - base side s, height h
Volume = (1/3)s²h, Surface Area = s² + 2sl Triangular Pyramid - base area A, height h
Volume = (1/3)Ah Hemisphere - radius r
Volume = (2/3)πr³, Surface Area = 3πr² Angle Theorems in Geometry
Angles on a straight line
Sum = 180° Angles around a point
Sum = 360° Vertically opposite angles
Are equal Angles in a triangle
Sum = 180° Angles in a quadrilateral
Sum = 360° Exterior angle of triangle
= Sum of opposite interior angles Angles in a polygon (n sides)
Sum = (n - 2) × 180° Interior angle of regular polygon
= (n - 2) × 180° / n Exterior angle of regular polygon
= 360° / n Corresponding angles (parallel lines)
Are equal Alternate angles (parallel lines)
Are equal Co-interior angles (parallel lines)
Sum = 180° Angle at center of circle
= 2 × angle at circumference Angles in same segment
Are equal Angle in semicircle
= 90° Opposite angles in cyclic quadrilateral
Sum = 180° Exterior angle of cyclic quadrilateral
= Opposite interior angle Tangent perpendicular to radius
Angle = 90° Angle between tangent and chord
= Angle in alternate segment Additional Essential Formulas
Pythagoras' Theorem (for right-angled triangles):
a² + b² = c² Distance between two points (x₁, y₁) and (x₂, y₂):
d = √[(x₂ - x₁)² + (y₂ - y₁)²] Midpoint of line segment:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2) Gradient of line:
m = (y₂ - y₁)/(x₂ - x₁) Equation of straight line:
y = mx + c Arithmetic sequence nth term:
aₙ = a₁ + (n-1)d Geometric sequence nth term:
aₙ = a₁ × r^(n-1) Sum of arithmetic sequence:
Sₙ = n/2[2a₁ + (n-1)d] Sum of geometric sequence:
Sₙ = a₁(1 - rⁿ)/(1 - r) 📚 How to Use This Formula Sheet
Practice Regularly
Use these formulas in practice problems to build muscle memory and confidence for your exams.
Understand, Don't Memorize
Learn the logic behind each formula rather than just memorizing. This helps in problem-solving.
Time Management
Know which formulas to apply quickly during exams. Practice identifying formula patterns in questions.
Review Consistently
Regular revision of formulas ensures they stay fresh in your memory when you need them most.
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