Algorithms
Students will be able to follow an algorithm given by a flow chart or text; know the meaning of the order of an algorithm; solve bin packing problems using the first-fit algorithm and first-fit decreasing algorithm and sort lists using bubble sort or quick sort. Assessment will be via continuous scrutiny of class and homework.
Networks
Students will know what is meant by a graph and by a network; that a network can be represented by a matrix; what is meant by a complete graph, a planar graph and isomorphic graphs; what is meant by a tree, a spanning tree and a minimum spanning tree; be able to find a minimum spanning tree using Prim’s algorithm (from a network or a matrix) or Kruskal’s algorithm (from a network); use Dijkstra’s algorithm to find a shortest path; what is meant by the order of a vertex; what is meant by an Eulerian graph and a semi-Eulerian graph and be able to solve route inspection problems to find the shortest distance required to travel along every edge of a network, starting and finishing at the same vertex. Assessment will be via continuous scrutiny of class and homework.
Critical Path Analysis
Students will be able to construct an activity network from a precedence table to model a project; know about the use of dummy activities; to be able to find earliest event times and latest event times; to find earliest start times, latest start times, earliest finish times and latest finish times for an activity; to identify critical activities and the critical path; to find the float associated with an activity; to construct Gantt charts (cascade charts) and to find the lower bound for the number of workers needed to complete a project in the shortest possible time. Assessment will be via continuous scrutiny of class and homework.
Linear Programming
Students will be able to illustrate linear inequalities in two variables graphically; formulate simple maximisation and minimisation problems; use graphs to solve 2-D linear programming problems and interpret the solution to a linear programming problem. Assessment will be via continuous scrutiny of class and homework.
Complex Numbers
Students will be able to solve any quadratic equation with real coefficients; add, subtract, multiply and divide complex numbers in the form x+iy𝑥+i𝑦; to use the terms ‘real part’ and ‘imaginary part’ about the complex conjugate; know that non-real roots of quadratic equations form a conjugate pair; know about the modulus and argument of a complex number; be able to convert between the Cartesian form and the modulus-argument form of a complex number; to multiply and divide complex numbers in modulus-argument form; to use and interpret Argand diagrams; be able to represent the sum or difference of two complex numbers on an Argand diagram and to construct and interpret simple loci in the Argand diagram. Assessment will be via continuous scrutiny of class and homework.
Sequences and Series
Students will be able to use the standard series formulae. Assessment will be via continuous scrutiny of class and homework.
Roots of Polynomials
Students will know about the relationships between roots and coefficients of quadratic equations, cubic equations and quartic equations; be able to form a new equation whose roots are related to the roots of a given equation by a linear transformation; that non-real roots of polynomial equations with real coefficients occur in conjugate pairs and be able to solve cubic equations or quartic equations with real coefficients. Assessment will be via continuous scrutiny of class and homework.
Volumes of Revolution
Students will be able to calculate the volume of revolution formed by rotating a plane region about both the x and y axis. Assessment will be via continuous scrutiny of class and homework.
Matrices and their Inverses
Students will be able to add, subtract and multiply conformable matrices, and to multiply a matrix by a scalar; know about the zero matrix and identity matrix; be able to calculate the determinant of a 2×2 matrix, and to use the matrix facility on a calculator to find the determinant of a 3×3 matrix; know that the magnitude of the determinant of a 2×2 matrix gives the area scale factor of the associated transformation, and that the sign of the determinant indicates whether the orientation of the image is preserved or reversed; know that the magnitude of the determinant of a 3×3 matrix gives the volume scale factor of the associated transformation, and that the sign of the determinant indicates whether the orientation of the image is preserved or reversed; know about the significance of a zero determinant in terms of transformations; know what is meant by a singular matrix and a non-singular matrix; be able to find the inverse of a 2×2 matrix, and to use the matrix facility on a calculator to find the inverse of a 3×3 matrix; know about how an inverse matrix relates to transformations; be able to find the determinant and inverse of a 3×3 matrix without using a calculator; know how to solve three linear simultaneous equations in three variables by use of the inverse matrix and be able to interpret geometrically the solution and failure of solution of three simultaneous linear equations. Assessment will be via continuous scrutiny of class and homework.