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Mathematics 1
Formulae:	Trig calculus
LO1:-Use algebraic skills	Factorials Pascal’s Triangle. Binomial Theorem Partial fractions
LO2:- Use the rules of differentiation on elementary functions.	Differentiation Refresher First principles Chain rule. Product rule. Quotient rule seca coseca cota Eexponentials & Logs Higher Derivatives Rectilinear motion Extrema of functions Approximating roots
LO3:-Integrate using standard results and the substitution method.	Integration refresher e^x, 1/x, sec²x Integration by substitution. Infinite integrals (discontinuities) Areas under curves Area between curve and the x-axis Area between curve and the y-axis Volumes of revolution Distance, velocity & acceleration
LO4:- Use properties of functions.	Refresher of functions Modulus function Inverse functions Polynomials Extrema Concavity and points of inflexion Odd and Even functions Asymptotes
LO5 :- Use matrix methods to solve systems of linear equations.	Augmented matrix Gaussian elimination
Mathematics 2
LO1 :- Use further differentiation techniques	Inverse functions Inverse trig functions Implicit & explicit functions Logarithmic functions Parametric equations Equations of motion
LO2 :- Use further integration techniques	Inverse trig functions Integration by parts Integration of rational functions Differential equations Applications of differential equations
LO3:- Understand and use complex numbers	Complex numbers Argand diagrams Polar form De moivre's theorem Roots of a complex number
LO4:- Understand and use sequences and series	Recurrence relations Fixed points Arithmetic sequences n^th term of arithmetic sequence Sum to n terms of an arithmetic sequence Geometric sequences Sum to n terms of a geometric sequence Infinite series Sum to infinity - geometric series Sum first n natural numbers Sigma notation - Rules Common series - sigma notation
LO5 :-Use standard methods to prove results in elementary number theory.	Direct proof Proof by contradiction Proof by contrapositive Proof by induction
Mathematics 3
LO1:- Use vectors in three dimensions.	Vector product Scalar triple product Planes Vector equations Equations of a line Intersections
LO2:- Use matrix algebra	Matrix multiplication Determinants 2 x 2 matrix 3 x 3 matrix Cofactor of a 3 x 3 matrix Adjoint of a 3 x 3 matrix Inverse of a square matrix Transformation matrices
LO3:-Understand and use further aspects of sequences and series.	Power series D'alembert's ratio test Absolute convergence Centre of convergence Taylor's series Maclaurin's Series Maclaurin expansion Standard series Iteration Iteration - graphical method First order process Second order process Rule of false position Newton-Raphson iteration
LO4:- Solve further ordinary differential equations	First-order differential equations Second-order differential equations
LO5:- Use further number theory and direct methods of proof.	The division algorithm The euclidean algorithm Diophantine equations Number bases

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