A. Math: Levels and Topics Covered

Additional Mathematics

                                                   

Upper Secondary Level/ Middle School (Grade 9&10)

• Simultaneous Equations (Quadratic-Linear simultaneous eqns., pts. of intersection)
• Polynomials, Remainder and Factor Theorem, Cubic Equations (Identities, long division)
• Partial Fractions (Proper & Improper fractions)
• Quadratic Equations and Inequalities (Sum & Product of roots, Discriminant)
• Modulus Functions (Solving Modulus eqns, sketch graphs) 
• Indices, Surds
• Logarithms
• Coordinate Geometry (Distance, gradient, perpendicular/ parallel lines, eqn of straight lines, area, midpoint)
• The Linear Law
• Equations of Circles
• Trigonometry (Solve trigo. eqn, sketch sin/cos/tan graphs, proving identities)
• Further Trigonometry (Compound angle, double angle, factor formula, R-formula)
• The Binomial Theorem (General term formula, binomial expansions)
• Matrices (Solve simultaneous equation using matrix method) 
• Differentiation (Power, chain, product and quotient law, gradient)
• Applications of Differentiation (Eqn of tangent/normal, stationary points, max./min. pt./pt. of inflection)
• Further Applications of Differentiation (Rates of change, increasing/decreasing function/maxima/minima)
• Differentiation of Trigonometry (Diff. sine, cosine, tangent related expressions and its applications)
• Differentiation of Logarithmic and Exponential Functions (Sketching of ln and expo. graphs, diff of ln, expo. related expressions, and its applications)
• Integration (Integration of algebraic, trigo., ln, expo. expressions) 
• Kinematics (Displacement, velocity, acceleration relating to diff. & integration)
• Applications of Integration (Area under graphs)
• Geometrical Proofs (Midpoint, intercept, tangent.-secant, intersecting chords, alternate segment theorems)

Note: the list above might not be exhaustive, kindly leave a comment should you require coaching with topics not in the above list.