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Leaving Certificate: Applied Maths

Applied Maths is a subject which is ideally suited to any student who has a keen interest in maths and physics. Students are introduced to practical techniques which can be employed to solve various interesting problems.

Students are introduced to practical techniques which can be employed to solve various interesting problems. Students are trained to analyse a problem written in English, translate it into suitable mathematical language, solve it and then translate the result back into English. During this process students see the true power of maths and how it can be used. Taking applied maths vastly improves a student's chance of achieving a higher grade in both pure maths and physics.

For any student considering entry into any of the fields of engineering at university, applied maths is a must. The Leaving Certificate syllabus forms the foundations required for first-year college mathematical physics, and would therefore be of great benefit.

> Exam Layout

The exam in June has a very straightforward layout.

There are 10 questions and students need to complete any six correctly to obtain full marks. The key to success is to revise the whole course as students who only cover six/seven topics from the syllabus can struggle to complete the paper.

> Timing and Technique

Approximately 22 mins should be allocated for the completion of each question. This gives students in the region of 10-15 mins to read the paper and choose their questions, as well as time to check over answers at the end of the exam.

Like maths, it is all about technique so students should draw very neat force diagrams where required and explain clearly all steps taken in the completion of questions. It is the technique which is being marked more than the answer.

The content of the Leaving Cert applied maths course is as follows:

>Linear Motion This section covers the use of familiar formulae such as v=u+at etc. It focuses on motion in a straight line under a constant acceleration. The concepts of power and force may also make an appearance.

>Relative Velocity In this topic students learn how to effectively use vectors to solve problems involving winds, currents and relative motion in general. This section has many applications in navigation.

>Projectiles Firstly students are introduced to projectiles on a horizontal plane before this is extended to projectiles on an inclined plane. The main questions which would be asked would include calculating times of flight, maximum range, velocity after ‘t' seconds as well as landing angles and many other similar calculations.

>Newton’s Laws and Connected Particles The main emphasis of this chapter is the analysis of Newton's three laws of motion, in particular his second Law, which implies that Force is proportional to Acceleration.

>Impacts and Collisions This section centres on the Law of Conservation of Momentum. It also studies how ‘bouncy’ the objects are by applying Newton’s Law of Restitution. We also study collisions which are oblique (at an angle).

>Circular Motion At the beginning of this section we are introduced to the concept of centripetal force and its applications in motion of a circle in a horizontal plane. We move on to look at circular motion in a vertical plane and the Law of Conservation of Energy in the vertical case.

>Simple Harmonic Motion The motion of a particle on a spring or elastic string is studied in depth with many other applications looked into. It is quite a challenging topic and is dealt with from a very ‘mathematical’ perspective.

>Statics Statics is a very popular topic as it is very straightforward to visualise the kind of forces which occur in structures. It begins with a straightforward study of ladders which may be resting against a wall or which may be self-supporting. We then go on to look at things such as, what is the greatest load we could place on a ladder before slipping would occur, or what would be the forces acting on a particular joint in a structure.

>Hydrostatics The concepts of density, pressure and the principle of Archimedes are studied. The level of detail is significantly higher than that studied in physics.

>Moments of Inertia This section looks at the motion of complex systems involving several components rather than simple one-body problems. It uses integration to find the moments of inertia of a system, uses this to calculate the kinetic energy of the system and then uses this to study its motion. It also takes an interesting look at rolling objects such as wheels and pulleys and incorporates the concept of angular momentum into spinning objects.

>Differential Equations This is perhaps the most exciting area of the course. It begins with an introduction to first-order differential equations with separable variables before taking the next step into basic second-order differential equations. It is this topic which truly teaches students the power of maths and how it can be applied in situations that previously had to be drastically simplified before being approached. The main example would be the introduction of the idea of “air resistance”, which is almost ignored in other areas of the course. Integration again forms the backbone of this topic. In short, applied maths is a challenging but extremely rewarding subject which gives a firm understanding of the usefulness of mathematics in many different situations.

It is also proving popular as an eighth “insurance subject” protecting again possible disappointment should something go wrong in another subject.