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Achieving good results in the Leaving Certificate exam is vital to Irish students who wish to progress to university level. Undertaking the higher level Project Maths course provides the student with the maths skills which universities and employers find attractive, while simultaneously awarding the student with an extra 25 points if they achieve a D3 grade or higher. The Alison learning path in higher level project maths will introduce the students to all the major aspects of the course, and take them through the types of maths problems they can expect to see on the course. The Alison higher level project maths learning path will be of interest to any student thinking of undertaking the project maths leaving certificate exam, or to students who would like to review the main elements of the course. This learning path is also beneficial to students who are studying a maths-based university degree and who wish to review the foundational theory of the subject. This Alison learning path will cover important areas of the project maths higher level course, such as; probability, statistics, geometry, trigonometry, numbers and shapes, algebra, functions, and calculus.
Courses in this Learning Path
Strand 1 Higher Level Probability and Statistics
Probability and Statistics is one of two strands introduced in the first phase of the new Project Maths Course in the Irish curriculum. This topic covers up to half of the new Paper 2 in the Leaving Certificate Paper.
Statistics are used in real life to make sense of the information around us and how it affects us. Statistics looks at the data handling cycle and analysis of the data collected. This involves posing a question, collecting data on that question, presenting that data, analysing the data (using measures of spread and centre) and interpreting the results. In answering questions, it is essential that you can contextualise and justify your findings.
Probability is concerned with the likelihood of an event(s) happening. The information can be used to make informed decisions. The use of probability is commonly utilised in the world of finance, insurance and sport among others. Probability can also be used to infer the fairness of an event or series of events. It can be evaluated using a diagram or a rule-based approach.
A combination of Probability and Statistics can be used to prove/disprove a given conjecture or statement (Hypothesis Testing (HL only)). This Strand attempts to merge the mathematical aspects of Probability and Statistics with its real-life application. It is an interesting topic that is very accessible to all students.3-4 Hours50 Points
Strand 2 Higher Level Geometry and Trigonometry
Geometry and Trigonometry is the second of two strands introduced in the first phase of the new Project Maths Course. This topic covers up to a third of the new Paper 2 in the Leaving Certificate Paper in the Irish curriculum. Synthetic Geometry and Co-ordinate Geometry are used in real life to help us understand the dimensions and transformations of shapes and figures (lines, triangles, polygons and circles). Synthetic geometry studies shapes by means of axioms and theorems. Co-ordinate geometry studies lines and circles by reference to a fixed set of co-ordinates. Trigonometry is concerned with ‘real life’ measurements of length, angles and circular measure in both two and three dimensions. The use of trigonometry is commonly utilised in the areas of quantity surveying, building and construction, and architecture. This strand is without doubt the most applicable area of the Leaving Certificate mathematics syllabus and allows students gain experience of realistic solutions to real-world problems.
6-10 Hours50 Points
Strand 3 Higher Level Numbers and Shapes
The concepts of number and number patterns are the basic building blocks of arithmetic and algebra. Furthermore, we cannot escape the use of numbers in our everyday lives. We use clocks and watches to count through the hours and minutes of our day. We count out money to pay our bills and often take a flutter on the lottery by choosing six numbers. The application of Arithmetic and Geometric series in finance is investigated through loan repayments and investments. The use of AER (annual equivelant rate) and APR (annual percentage rate) when calculating repayments is investigated. Students are then introduced to the concept of a complex number and shown how to add, subtract, multiply and divide complex numbers. Complex numbers are used to represent the flow of current in a circuit and are also used in most areas of electronics. We use numbers to measure the perimeter and area of various shapes (triangles, rectangles, hexagons and circles) and we also use numbers to work out the volumes of solids such as cylinders, cones, spheres and hemi-spheres.
3-4 Hours50 Points
Strand 4 Higher Level Algebra
Algebra is the lifeblood and the natural language of Mathematics and provides a perfect link between number, geometry, trigonometry and functions. It would be impossible to formulate and solve real-world problems without algebraic notation.
Students are first introduced to representing numbers with letters and then they are taught how to convert problems into algebraic equations which can be solved by means of well-known techniques.
Students are taught how to solve simultaneous, quadratic and cubic equations and then extend their knowledge to the solution of inequalities. Searching for roots by trial and error and the use of synthetic division is also covered in this strand.6-10 Hours50 Points
Strand 5 Higher Level Functions and Calculus
Functions is the final strand to be introduced in phase 3 of the new Project Maths Course.
This topic provides an essential link between Algebra and Number and introduces the students to applications of calculus in the real world. Functions and Differentiation are used in real life to help us understand rates of increase and decrease.
For example, students will solve problems involving the maximum speed reached by a car and the rate of increase in the size of a raindrop as it falls to the ground. Integration is introduced as ‘anti-differentiation’ and students are given excellent examples to reinforce this theory. Applications of integration to find areas under curves and between curves are clearly demonstrated.
Finally, the concept of numerical integration is introduced through the use of the ‘Trapezoidal Rule’.3-4 Hours50 Points