Algebraic operations on polynomials and rational functions.
Addition, subtraction, multiplication and division and the use of brackets and surds
Laws of indices and logarithms
The Factor Theorem for polynomials of degree two or three.
Factorisation of such polynomials (the linear and quadratic factors having integer coefficients).
Solution of cubic equations with at least one integer root.
Solution of equations e.g. f(x) = g(x)
Sums and products of roots of quadratic equations.
Unique solution of simultaneous linear equations with two or more unknowns.
Inequalities: solution of inequalities of the form g(x) < k, where g(x) = ax2+bx+c
Use of the notation |x|; solution of |x-a| < b, |x – a| >b and combinations of these

Unit 2: Euclidean geometry

Unit 3: Probability

Fundamental principle of counting
Discrete probability – simple cases – tossing coins, dice throwing, birthday distribution etc.
Outcome space, events
Addition of probabilities, conditional probability, independent events
Binomial and normal distributions
Populations and samples

Unit 4: Coordinate geometry of the straight line and circle

General equation of the line in form ax+by+c = 0
Length of perpendicular from (x1, y1) to ax+by+c = 0
Angle between two lines with slopes m1 and m2
Equation of line through the intersection of two lines a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 {form L(a1x+b1y+c1)+M(a2x+b2y+c2) = 0, L, M constant}
Division of a line segment in ratio m:n
Addition, substraction of vectors, multiplication by a scalar. Unit vectors i and j
Equation of circle centre (0,0) and radius r (x2 + y2 = r2)
General equation of circle centre (- g, - f) and radius r (x2 + y2 + 2gx + 2fy + c = 0)
Equation of tangent at (x1, y1) to x2 + y2 = r2
Intersection of line and specific circle

Unit 5: Arithmetics

Unit 6: Functions and Differential Calculus

Finding the period and range of a continuous periodic function, given its graph on scaled and labelled axis
Informal treatment of limits of functions: Rules for sums, products and quotients
Derivations from first principles of x2, x3, sin x, cos x, 1/x
First derivatives of polynomials, rational, power and trigonometric functions
First derivatives of sums
First derivatives of differences
First derivatives of products
First derivatives of quotients
Application to finding tangents to curves
Simple second derivatives
First derivatives of implicit and parametric functions
Rates of change
Maxima and minima
Curve sketching

Unit 7: Statistics

Unit 8: Number Systems

Review of numbers systems
Complex numbers: Argand diagram; addition, subtraction, multiplication, division; modulus; conjugate; conjugates of sums and products; conjugate root theorem
De Moivre’s theorem: proof by induction, applications such as nth roots of unity and identities

Unit 9: Series and Induction

Unit 10: Trigonometry

Use the radian measure of angles
Calculate the area of a sector of a circle and the length of an arc and solve problems involving these calculations
Use trigonometry to calculate the area of a triangle
Use the sine and cosine rules to solve problems 2D and 3D
Define sine A, cos A and tan A for all values of A
Graph the trigonometric function sine, cosine and tangent
Graph trigonometric functions of type a sinnA, a cosnA for an n Îµ N
Solve trigonometric equations such as sinnA = 0 and cosnA = ½ giving all solutions
Calculate the area of a sector of a circle and the length of an arc and solve problems involving these calculations
Derive the trigonometric formulae 1, 2, 3, 4, 5, 6, 7, 9
Apply the trigonometric formulae 1 - 24

Unit 11: Integral Calculus

Integration techniques (integrals of sums, multiplying constants, and substitution)
Definite integrals with applications to areas and volumes of revolution (confined to cones and spheres)