Pure Math
All-New Pure Math

Study Pure Math like a Pro step by step!

More Examples
More Examples

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

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01. Differentiation 1

• First principles
• The dy/dx notation
• Tangents and Normals
• Velocity and Acceleration

03. Integration

• 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

05. Algebra 1

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

07. Algebra 2

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

09. Trigonometry 1

• 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

11. Further integration 1

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

13. Partial fractions

• 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

15. Coordinate geometry 1

• The Circle
• Cartesian equation
• Parametric equation
• Parametric equation
• Circle from 3 points
• Circle from diameter ends
• Intersection of circle and line
• 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

19. Complex numbers

• 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