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Ordinary Level Course
5th Year
Algebra
- Removing brackets and simplifying expressions.
- Solving linear equations.
- Factorising quadratic expressions.
- Further factorisation.
- Simplifying algebraic expressions involving fractions.
- Solving quadratic equations by factors.
- Solving quadratic equations involving fractions.
- Use of formula to solve quadratic equations.
- Forming a quadratic equation when given its roots.
- Working with indices.
- Manipulation of formulae.
- Simultaneous equations in two unknowns.
- Simultaneous equations - one linear, one quadratic.
- The Remainder Theorem - The Factor Theorem.
- Solving cubic equations.
- Inequalities.
Co-Ordinate Geometry of the Line
- Revision of formulae.
- Slope of a line.
- The image of a point under different transformations.
- The area of a triangle.
- The equation of a line.
- Finding the slope of a line from its equation.
- Sketching lines - Intersecting lines.
- The equation of the image of a line.
Complex Numbers
- Definition of a complex number.
- Addition and subtraction of complex numbers.
- Multiplication and division of complex numbers.
- Equality of complex numbers.
- The Argand Diagram.
- The modulus of a complex number.
- Quadratic equations with complex roots.
Co-ordinate Geometry of the Circle
- Equation of the circle with centre (0,0) and radius = r.
- Points and circles.
- Points of intersection of lines and circles.
- The equation of a tangent to a circle.
- The equation of the circle with centre (h,k) and radius = r.
- Tangents to a circle - transformations of circles.
Area and Volume
- Area and perimeter.
- Rectangular solids - prisms.
- Cylinders - spheres.
- The cone.
- Problems involving area and volume.
Statistics
- Frequency distributions.
- Histograms.
- Cumulative frequency.
- Quartiles and interquartile range.
- Weighted mean.
- Standard deviation.
Arithmetic - Simpson's Rule
- Compound interest.
- Percentages and income tax.
- Ratio and proportion - distance, speed.
- Exchange rates.
- Expressing numbers in standard form.
- Approximation - significant figures.
- Relative error - percentage error.
- Areas of irregular figures - Simpson's Rule.
6th Year
Permutations and Combinations
- Introduction to permutations and combinations.
- Permutations.
- Combinations.
Sequences and Series
- Sequences.
- Arithmetic sequences.
- Finding the values of a and d.
- Arithmetic series.
- Geometric sequences.
- Geometric series.
Functions and Graphs
- Functions.
- Inverse of a function.
- Quadratic inequalities.
- Graphs of quadratic functions.
- Graphing cubic functions.
- Using graphs of cubic functions to solve equations.
- Graph of y=1/x.
- Periodic functions.
Geometry Theorems - Enlargement
- Triangles - parallel lines.
- Proportional division - similar triangles.
- The theorem of Pythagoras.
- Triangle theorems.
Probability
- Introduction - single events.
- Two events - use of sample spaces.
- Mutually exclusive events - events A or B.
- Events A and B - the multiplication rule.
Calculus
- Slope of a line - slope of a curve.
- Rules for differentiating.
- Differentiating products and quotients.
- The Chain Rule.
- The slope of a tangent to a curve.
- Maximum and minimum turning points.
- Rates of change - speed and acceleration.
Trigonometry
- The sine, cosine and tangent ratios.
- Finding a trigonometrical ratio using a calculator or tables.
- Revision of right-angled triangles.
- Special right-angled triangles.
- Ratios of angles greater than 90 degrees.
- Compound angles.
- Area of a sector - length of arc.
- Area of a triangle - the Sine Rule.
- The Cosine Rule.
Options - one of the following topics will be studied.
Vectors
- Definition of a vector.
- Adding vectors.
- Position vectors.
- The perpendicular unit vectors.
- The modulus of a vector.
- The scalar (or dot) product of vectors.
Linear Programming
- Linear inequalities.
- Simultaneous inequalities.
- Finding the maximum and minimum of an expression.
- Linear programming.
Further Series - Binomial Theorem
- Applications of finite arithmetic series.
- Applications of finite geometric series.
- The sum to infinity of a geometric series.
- The Binomial Theorem.
Further Geometry
- Circle theorems.
- Tangents and circles.
- Intersecting chords.
- Alternative segment theorem.
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