## Leaving Certificate Project Maths - Ordinary Level Learning Path

The Leaving Certificate is the highest level of qualification in the Irish secondary school system, good results in its examinations can secure students a place on their dream university course. An understanding of the project maths ordinary level course is appealing to universities and future employers, particularly if the student is looking to find work in a mathematics-based field. The Alison learning path in Leaving Certificate project maths to ordinary level provides an understanding of the standard expected at ordinary level. The Alison ordinary level project maths course is of interest to all students hoping to undertake the ordinary level paper of project maths, or to students who are considering taking up the subject but wish to gain a better understanding of what is expected. It is also beneficial to professionals who wish to improve their understanding of the subject, or who are considering entering a related field of work. This Alison learning path will cover important areas of the project maths ordinary level course, such as; probability, statistics, geometry, trigonometry, numbers and shapes, algebra, functions, and calculus.

### Courses in this Learning Path

1. #### Strand 1 Ordinary Level Probability and Statistics

Probability and Statistics is one of two strands introduced in the first phase of the new Project Maths Course. This topic covers up to half of the new Paper 2 in the Leaving Certificate Paper in the Irish curriculum.

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.

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.

1.5-3 Hour
50 Points
2. #### Strand 2 Ordinary Level Geometry and Trigonometry

Synthetic geometry is also known as axiomatic or pure geometry and is the study of geometry without the use of coordinates or formulae. It studies shapes by means of axioms and theorems. This course begins by teaching you the different concepts of synthetic geometry. You will look into the different properties of shapes and learn about geometric reasoning which is the use of critical thinking, logical arguments, and spatial reasoning to solve problems and find new relationships.

Coordinate geometry is also known as analytic geometry or cartesian geometry. It is the study of geometry using a coordinate system, in contrast to synthetic geometry. This course will teach you the different concepts of coordinate geometry. You will learn its usefulness in physics and engineering, and also in aviation and space science. You will also cover trigonometry and study the relations of the sides and angles of triangles and the relevant functions of any angles.

Synthetic Geometry and Coordinate Geometry are used in real life to help us understand the dimensions and transformations of shapes and figures such as lines, triangles, polygons, and circles. Upon the completion of this course, you will have a better understanding of key geometry axioms and theorems. So, check out the course today and learn how to properly solve for the slope and equation of a line passing through two given points, find distances and angles using Sine and Cosine Rules, and more.

3-4 Hours
50 Points
3. #### Strand 3 Ordinary 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.

1.5-3 Hour
50 Points
4. #### Strand 4 Ordinary Level Algebra

This course begins by showing you how to factor quadratics. You will learn how to factor the difference of two squares and expand brackets using the grid method and FOIL method. In addition, you will also learn how to expand any two brackets and rearrange simple formulae. You will study the two steps of rearranging simple formulae, rearrange formulae with squares and square roots, and rearrange formulae where subjects appear twice.

An equation is a statement that asserts the equality of two expressions. This course will teach you the steps in solving equations. You will look into inequality which is an equation that uses symbols for "less than"(<) and "greater than"(>) where an equation uses a symbol for "is equal to" (=). You will also learn how to solve complex numbers which are the building blocks of algebra and can be applied to different aspects of real life.

This course will show you how to represent numbers with letters and convert problems into equations among other algebraic concepts. Upon the completion of this course, you will have a better understanding of the steps involved in solving linear simultaneous equations with two unknowns, solving basic inequalities, interpreting the solutions of simple simultaneous equations, forming quadratic equations with given roots, and more. Check out the course and start expanding your algebra skills today!

1.5-3 Hour
50 Points
5. #### Strand 5 Ordinary Level Functions and Calculus

Functions was 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. Use of differentiation to find the slope of a tangent to a curve at a specified point is introduced. This is then extended to the study of increasing and decreasing functions. 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 highest point reached by a firework or rocket. Finally, the concept of numerical integration is introduced through the use of the ‘Trapezoidal Rule’ to find areas under specific curves.

1.5-3 Hour
50 Points