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Higher Level Course
5th Year
Algebra
- Working with Polynomials.
- Division and Evaluation of Polynomials.
- 2 X 2 System of Simultaneous Equations.
- 3 X 3 System of Simultaneous Equations.
- Equations, Identities and Formulae.
- Factors and the Factor Theorem.
- Rational Functions.
- Quadratic Equations.
- Non-Linear Simultaneous Equations.
- Solving Cubic Equations.
- Indices.
- Logarithms.
- Surds.
- Rules for Inequalities.
- Quadratic Inequalities.
- Modulus and Modulus Inequalities.
Trigonometry
- Radian Measure of Angles.
- Trigonometric Ratios.
- Trigonometric Functions.
- Trigonometric Identities.
- General Triangles.
- Solving Triangles.
- Compound Angle Formulae.
- Double Angle and Half-Angle Formulae.
- Sum, Difference and Factor Formulae.
- Simple Trigonometric Equations.
- Other Trigonometric Equations.
- Inverse Trigonometric Functions.
- Trigonometric Graphs.
- Periodic Functions.
Co-Ordinate Geometry of the Line
- Distance, Midpoint and Divisors.
- Slope and Angle between Two Lines.
- Translations and Area of a Triangle.
- Equation of a Line.
- Locus.
- Concurrent Lines.
- Parametric Equations of a Line.
- Positive Side of a Line.
- Perpendicular Distance.
- Bisectors of Angles.
Differential Calculus
- Limits of Functions.
- Limits of Trigonometric Functions.
- Differentiation from First Principles.
- Differentiation by Rule.
- Product and Quotient Rule.
- The Chain Rule.
- Implicit Differentiation.
- Parametric Differentiation.
- Higher Derivatives.
- Differentiation of Inverse Trigonometric Functions.
- The Exponential Function.
- The Logarithmic Function.
- Logarithmic Differentiation.
Co-Ordinate Geometry of the Circle
- Circle with Centre (0,0).
- General Equation of a Circle.
- Geometric Properties of a Circle.
- Finding the Equation of a Circle.
- Parametric Equations of a Circle.
- Two Circles.
- Intersection of Line and Circle.
- Tangent at a Point on a Circle.
- Other Tangents.
- Common Chords.
Complex Numbers
- Definition and Equality.
- Algebra of Complex Numbers.
- Conjugate and Division.
- Complex Polynomial Equations.
- The Argand Diagram.
- Modulus.
- Polar Form of a Complex Number.
- De Moivre's Theorem.
- Proving Trigonometric Identities.
- Roots of a Complex Number.
Matrices
- Matrices and Their Properties.
- Multiplication of Matrices.
- Inverse Matrices.
- Some Properties of Matrices.
6th Year
Applications of Differentiation
- Slope of a Tangent.
- Stationary Points.
- Points of Inflection.
- Asymptotes.
- Curve Sketching.
- Roots of a Cubic Equation.
- The Newton-Rhapson Method.
- Rates of Change.
Integration
- The Indefinite Integral.
- The Definite Integral.
- Integration by Substitution.
- Integration of Rational Functions.
- Trigonometric Integrals.
- Other Integrals.
- Areas by Integration.
- Volumes of Revolution.
The Binomial Theorem
- The Binomial Theorem.
- The General Term.
- Binomial Coefficients.
Proof by Induction
- Proofs by Induction.
- Proofs Involving Divisibility and Inequalities.
Probability
- Fundamental Principle of Counting.
- Permutations.
- Combinations.
- Different Groups.
- Basic Probability.
- Statistics: Mean and Weighted Mean.
- Statistics: Dispersion.
Sequences and Series
- Sequences and Their Limits.
- Monotonic Sequences.
- Finite Series.
- Telescoping Series.
- Arithmetic Sequences and Series.
- Geometric Sequences and Series.
- Infinite Series.
- Difference Equations.
- Solving Difference Equations.
Vectors and Transformation Geometry
- Vectors in the Plane.
- Vectors in the Cartesian Plane.
- Dot Product (Scalar Product).
- Linear Combinations.
- Linear Transformations.
- Properties of Linear Transformations.
- Invariance.
Further Calculus and Series
- Maximum and Minimum Problems.
- Successive Derivatives.
- Integration by Parts.
- Power Series and the Ratio Test.
- Maclaurin Series.
- Applications of Maclaurin Series.
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