# 456 - Mathematics

## Contents

## Numerical Concepts

a) Ordinary operations of arithmetic. Factors, multiples and divisors. Prime and composite numbers. Sequences and number patterns.

b) Fractions, decimals, expressions of recurring decimals as equivalent fractions. Scale and representative fractions. Ratio, percentage, Direct and inverse proportions.

c) Estimates and approximations. Significant figures; decimal places.

d) Rules of operations for indices and logarithms.

e) Simple manipulation of surds. Simple identities involving square roots.

## Algebraic symbols, expressions, and equations

a) Use of algebraic symbols to represent statements. Generalizations of arithmetical relations in symbols, the interpretation of statements given in symbolic form.

b) Equations, inequalities and identities. Solution of linear equations and inequalities in one real variable, solution in two real variables. Solution in two real variables by any algebraic method.

- WikiEducator resource: Linear Equations & Simple Linear Equations

c) Factors of expressions, including trinomials.

d) Solutions of quadratic equations and inequalities in one real variable.

## Extension of set theory, relations

a) Knowledge of Union, intersection, and complement and inverses of the elements of the set.

b) Relations, mappings and functions. Graphical representation: arrow diagrams (including papygrams), Cartesian graphs. Composite functions, e.g. fg(x), and bijective functions and etc.,

## Graphs

a) Rectangular Cartesian co-ordinates in two dimensions. Locus regarded as a set of points satisfying a given condition. The Cartesian equation of a locus in simple cases. Gradient of a line. The gradient of a curve estimated from a tangent. Use of gradient and y-intercept to determine the equation of a line. Estimation of best line through a set of points.

b) Simple application of intersection of lines and curves to the solution of simultaneous and quadratic equations.

## Vectors and Matrices

a) Notion of vectors, basic operation on vectors. Conditions for vectors to be parallel and collinear. Magnitude of a vector.

b) Addition and multiplication of matrices. Determinant and inverse of a 2 x 2 matrix.

## Geometrical Concepts

a) The transformation of reflection, rotation, translation and enlargement in two dimensions. Invariant properties under each of these transformations and the resulting ideas of symmetry, congruence, and similarity. Properties of similar and congruent figures. Combinations of transformations.

b) Simple geometric constructions. construction of a triangle, quadrilateral or other simple polygon, circumscribed and inscribed circles of a triangle from sufficient data.

c) Angle properties of parallelograms. Right-angled triangles and Pythagoras' Theorem and its converse. Sine, cosine and tangent of acute, obtuse and reflex angles.

d) Nets of the surface of solids, sketching solids. Angle between a line and a plane and between two planes.

e) The circle:

- i) symmetry properties (formal proofs not to be asked)
- ii) tangent property (formal proofs not to be asked)

f) Bearings

## Miscellaneous Application

a) Conversion from one currency to another given the relevant exchange rate.

b) Principles of taxation and insurance.

c) Mensuration of the triangles, parallelogram, circle and figures formed by combination of these. Volumes and surface areas of prism, pyramid, and sphere.

d) The application of Pythagoras' theorem. Trigonometrical methods involving simple two- and three-dimensional figures.

e) Estimation of the area under a graph and its interpretation. Application of gradient and area under a graph to easy liner kinematics involving distance-time and speed-time graphs.

f) Representation and interpretation of data in tabular or graphical form.

g) Mode, mean, and median. Modal class, estimation of mean and median from grouped data.

h) Basic concepts of probability. Simple combination of probabilities.