How can the Internet be used to help learn Mathematics?

This page refers to topics covered in the second major State examination in Mathematics in Ireland, which is the Leaving Certificate Examination. (For visitors to Ireland: This exam is taken at age 17 or 18 (approximately) following five to six years of study in Secondary school.)

Here you will find links to Internet sites that can contribute either to the introduction, exposition or revision of the main topic headings for the Leaving Cert. Exam.

For Higher Level Mathematics

which deals with all subjects.  In the Maths area it deals with:

or some specific topics from this site:

Linear Transformations   Can you transform your photos?

Calculus Visualise the ideas of Limits, Differentiation, Integration with the help of applets

Mathematical Induction

Leaving Certificate Examination in Mathematics (Ireland)

Foundation Level

and Ordinary Level Topics

Note that much of the material is a continuation of Junior Cert. material and that the links provided are the same as those provided for the same topics at Junior Cert. level.

Note: Use of an electronic non-programmable calculator is allowed at Leaving Cert.

Paper I

Arithmetic1 (Uses Junior Cert. link) (Computation without a calculator, Use of Official Tables of Squares, Square Roots and Reciprocals, …)

Arithmetic2 (Uses Junior Cert. link) (Applications of calculations to Money, Compound Interest, Ratio, Percentages, …)

Algebra (Uses Junior Cert. link) (Simplification, Substitution, Solving equations, Factoring, Word problems, …)

Complex Numbers (not examined at Foundation Level) (As roots of a quadratic equation, Plotting, Addition, Multiplication, Division, Modulus)

Sequences and Series (not examined at Foundation Level) (Arithmetic and Geometric Sequences and Series)

Graphs/Functions (Uses Junior Cert. links) (Arrow graphs, Cartesian graphs (using the x-axis and the y-axis), Functional notation (using f(x) and variations of this notation), …)

Differential Calculus (not examined at Foundation Level) (Differentiation from First Principles, By Rule, Applications to slope of a tangent, speed, acceleration…)

Paper II

Measurement (Uses Junior Cert. links) (Length, Area, Volume, …)

Co-ordinate geometry of the Line and co-ordinate geometry formulae (Uses Junior Cert. links) (Use of formulae for measuring distance between points, area of a triangle, slope of a line, equation of a line, Transformations of points using translation and symmetries, …)

Coordinate geometry of the Circle (not examined at Foundation Level) (Basic formulae - use of centre and radius, Equation of a tangent to circle (centre (0,0) only), Images by symmetry transformations)

Geometry (Uses Junior Cert. links) (Euclidean geometry theorems and proofs, Constructions with ruler and compass, Set point transformations - symmetries, translations, rotations, …)

Trigonometry (Uses Junior Cert. links) (Right angled triangles, Direction (compass points), Sine Rule for non-right angled triangles, …)

Probability (not examined at Foundation Level) (Use of principles of counting, Use of AND and OR)

Statistics (Uses Junior Cert. links) (Bar charts, Pie charts, Mean, Mode, …)

Vectors (not examined at Foundation Level) (Addition diagrams, i and j vectors)

Linear Programming (not examined at Foundation Level) (Graphing linear inequalities, problem solving involving two variables and constraints)

Observation: The course is examined at three levels - Foundation, Ordinary, Higher. Not all the material mentioned above within each topic is examined at the first two levels although each topic is dealt with at each level.

These links cover only some of the detail which is contained within the Leaving Cert. Mathematicss course. As useful links are found they will, hopefully, be added on.

Special help pages

More homework help!

Irish Government Department of Education (find solutions to past papers)

Scoilnet with many helpful pages

Skoool  (Special site for Irish L. Cert and J. Cert )

Studyweb

History of Mathematics

Page created by Neil Hallinan

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