Pure Math
All-New Pure Math

Study Pure Math like a Pro step by step!

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More Examples

We learn by Example, so we’ve provided over 30 examples per Chapter.

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Chapters for Download

01. Differentiation 1

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  • Gradient of a curve
  • First principles
  • The dy/dx notation
  • Tangents and Normals
  • Velocity and Acceleration

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03. Integration

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  • Reverse of differentiation
  • Velocity and Acceleration
  • Area under a curve
  • Definite integrals
  • Area cut off by a line
  • Area enclosed by two curves
  • Solids of revolution
  • Center of gravity

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05. Algebra 1

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  • Rules of Surds
  • Rules of Logarithm
  • Quadratic equations
    • Completing the square
    • The quadratic formula
    • The discriminant b²-4ac
    • Mini and maxi values
    • Sum and Product of roots
  • The Remainder and Factor theorems

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07. Algebra 2

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  • Inequalities
    • Linear inequalities
    • Quadratic inequalities
    • Rational fraction inequalities
  • Further equation methods
    • Square root equations
    • Equations reducing to quadratics
  • Simultaneous equations in 3-unknowns
    • Substitution and elimination

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09. Trigonometry 1

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  • Trigonometric ratios of angles
  • Ratios of 30°, 45°, and 60°
  • Secant, cosecant and cotangent
  • Trigonometric equations
  • Pythagoras theorem
  • Compound angle formula
  • Double angle formula
  • The t– formula
  • The form acos(x) + bsin(x)
  • The factor formula
  • Cosine and Sine rule
  • Area of a triangle

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11. Further integration 1

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  • Recognizing a function and its derivative
  • Change of variable
  • Changing limits
  • Integration using inverse trig functions
    • Using sin⁻¹(x)
    • Using tan⁻¹(x)
    • Quadratic denominators
  • Definite integrals involving trig functions

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13. Partial fractions

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  • CASE I: Denominator with only linear factors
    • Cover-up method
  • CASE II: Denominator with a quadratic factor
  • CASE III: Denominator having repeated roots
  • CASE IV: Improper fractions
  • Differentiation after Partialization
  • Integration after Partialization
  • Binomial expansion after Partialization

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15. Coordinate geometry 1

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  • The Circle
    • Cartesian equation
    • Parametric equation
    • Parametric equation
    • Circle from 3 points
    • Circle from diameter ends
    • Intersection of circle and line
    • Gradient at a point
    • Tangent from a point
    • Intersection of 2 circles
    • Orthogonal circles
  • Conics 1 [The Parabola]
    • The Parabola (e = 1)
    • Form (y – k)² = 4a(x – h)
    • Tangents / Normals
    • Parametric equation
    • Chord to parabola

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19. Complex numbers

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  • Algebra of complex numbers
  • Conjugate complex
  • Square root a complex number
  • Further complex roots
  • The Argand diagram
  • Modulus and Argument
    • Laws of Modulus
    • Rules of Arguments
  • Form r(cosθ + i sinθ)
  • De Moivre’s theorem
  • Identities in form cosθ or sinθ
  • Identities in form cosθ or sinθ
  • The nᵗʰ root of a complex number
  • Complex loci
  • Complex loci with inequalities

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