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Pure e-texts
An overview of pure modules Module and subsection structure
0-1-Indices & Surds Number types; indices & surds
1-1-Functions & graphs Introduction to coordinate systems; plotting of functions; transformation of functions; properties of a straight line; distance between points in the plane.
2-1-Linear & quadratic equations Finding the roots of linear and quadratic equations; discriminant function; simultaneous solutions of linear and quadratic equations
3-1-Inequalities and the modulus function Solution of linear and quadratic inequalities; definition of the modulus function and it's properties
3-2-Polynomials and the remainder theorem Multiplication of polynomials; long division; factor theorem; remainder theorem; partial fractions.
3-3-Introduction to Trigonometry Degrees; Radians; Special angles; Trig functions; General angles; Trig equations; Compound angles; asinx + bcosx; sinA+/-sinB & general solutions.
3-4-Circle Geometry Equation of circle: Equation of tangent; Circle and intersecting lines; Touching circles and Orthogonal circles
4-1-Laws of Logarithms Introduction; Laws of logarithms; Using logs to solve certain quadratic equations.
4-2-Triangle Algebra Arc length & sector area; area of triangle; area of parallelogram and trapezium; Sine rule; Cosine rule.
4-3-Binomial expansion Binomial expansion for positive integer n.
4-4-Sequences & Series Sequences; Limits; Series; Arithmetic Progressions; Geometric Progressions; Series by differencing.
4-5-Functions Properties of Functions; Domain & range; Inverse; Composite; Odd, even & bounded; Piecewise; Continuity & Asymptotes.
5-1-Differentiation Introduction; Tangents, Normals, Maxima & Minima: Points of Inflection; Product, Quotient & Chain rules; Trig functions; Implicit Diff; Ln(x); Parametric Diff; Log Diff; Technical points.
5-2-Vectors Basic rules of vectors; Unit and component vectors; Vector equation of a straight line; Dot product; Vector product; Vector equation of a plane.
5-3-Induction Mathematical Induction
6-1-Integration Introduction; Reverse of Differentiation; Substitution; Exponential and log functions; Integration by parts and reduction formulae; Further trig integration; Use of partial fractions; Arc length, surface area and volume of revolution; Numerical integration.
6-2-Finding roots numerically Intermediate Value Theorem; Iterative formulae; Newton-Raphson method; Convergence criteria.
6-3-Conic Sections Introduction; Ellipse; Parabola; Hyperbola and Translations
7-1-Differential Equations Introduction; Separable variables; First order; Second order.
7-2-Series Expansions Binomial; Taylor and Maclaurin series
7-3-Matrices Introduction, Determinants, Matrix inverse, Solving linear equations using Matrices, Solving linear equations using row reduction and transformations using Matrices.
8-1-Complex Numbers Introduction; Argand Diagram; Loci; De Moivre's Theorem; Roots of unity; Roots of polynomials.
9-1-Hyperbolic Functions Introduction; Hyperbolic Identities; Inverse Hyperbolic Functions; Differentiation and Series expansions; Integration of hyperbolic Functions
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