1. Numbers
* The real numbers
* Operations with zero and negative numbers
* Use of symbols to represent numbers
* Operations using algebraic numbers
2. Algebra
• Expansion, simplification and factorization
• Changing the subject of a formula
• Solving linear equations (with one variable number)
• Solving linear inequalities (with one variable number)
• Solving simultaneous linear equations (with two variable numbers)
• Word problems for linear equations, linear inequalities and simultaneous linear equations
• Solving quadratic equations by factorization and the quadratic formula
• Solving a pair of equations (with two variable numbers) where one equation is quadratic and the other linear
• Expressing numbers in exponential and logarithmic forms
• Transposition between the logarithmic and exponential forms
• Solving simple exponential equations
• Solving simple logarithmic equations (without tables or calculators)
3. Sets
• Use of set language
• Defining a set
• The null or empty set
• The universal set
• Subsets
• Set operations: union and intersection
• The complement of a set, relative complement
• Venn Diagrams
4. Geometry
* Points, Lines, Angles
* Nature of simple geometric figures
* Area of simple figures
• Area of sectors and segments of circles
• Pythagoras\' Theorem (no proof)
5. Relations and functions
• Relations
• Functions
• Ordered pairs
• Domain and range of a function
• Functional notation
• Examples of functions including constant, linear, quadratic, simple hyperbola, log and exponential functions
6. Graphs
• The Cartesian coordinate system
• The axes as real lines
• Plotting of graphs
• Representing inequalities on a number line
• General form of the quadratic function
• Graph of the quadratic function
• Roots of a quadratic function (graphical solution)
• Maximum and minimum values of a quadratic function
• Length of a straight line
• Equation of a straight line
• Parallel and perpendicular lines
• Rays, tangents, slopes, intersecting lines
• Representation of curves in space: increasing and decreasing functions, stationary points, turning points,
curvature, inflexions
• Area under a curve
7. Trigonometry
• Definition of sine, cosine and tangent
• Simple application of trigonometric ratios
• The graphs of the circular functions sine, cosine and tangent
8. Matrices
• Use of matrices to represent information
• Types of matrices
• Matrix operations and their properties
• Determinant of 2 x 2 matrices
• Singular 2 x 2 matrices
• Inverse of a non-singular 2 x 2 matrix
• Solution of simple problems in algebra using matrices
* For sections marked with an asterisk see Problem Set 0. It is assumed that students are already familiar with these ideas. They will only be touched on lightly in this course.
