**Applied Maths – what’s it all about?**

Unlike most other subjects there is no *Applied Maths* option for Junior Cert so for you the student it is quite difficult to know just what the subject is like at Leaving Cert level.

It is a fascinating subject which deals with solving real-life problems using mathematical models. In particular since it is a problem solving subject Project Maths will benefit from Applied Maths. The emphasis is on using different mathematical models to solve everyday problems.

Applied Maths will instil skills which will last a lifetime; how to analyse a problem, how to represent the problem mathematically, how to solve the maths, and then how to interpret your answer so that it makes sense when applied to real life situations.

**Why study Applied Maths?**

- If you like (and are good at) Maths

- If you are thinking about studying Engineering in college

- It complements the Maths Course and enables students to obtain the bonus points.

- Looks good on your CV

**Do I need to be good at Maths to study Applied Maths?**

You do need to be reasonably good at maths if you intend taking it at Higher Level, but you certainly don’t need to be an ‘A’ student. If you are a comfortable ‘B’ student then you should have little difficultly lasting the pace.

In studying Applied Maths you will improve on your mathematical skills in areas such as trigonometry, geometry, vectors, differentiation and integration.

**I want to do Business; wouldn’t I be just wasting my time doing Applied Maths?**

It mightn’t seem obvious but employers in Business and Finance are always looking for graduates from the field of Applied Maths – they already have lots of employees who know about business, what they don’t have is enough people who can offer solutions to unusual problems.

Many Applied Mathematicians get jobs in the business world because they have analytical and problem-solving skills which can be applied to the money markets and/or the stock-exchange.

It is also (relatively) straightforward to get a business (or business management) degree once you have an Science/Engineering degree if you so choose. It is not however straightforward to do it the other way around

**Who shouldn’t study Applied Maths? **This subject doesn’t suit students who just like learning things off by heart.

In fact the questions are designed to catch out those very students and whether that is fair or not is a moot point - you are being warned about it now so if you don’t like it you know what to do.

So Applied Maths suits people who like solving puzzles. This means being able to think for yourself, and because almost all of your secondary-school education encourages you to ‘learn the right answer off by heart’ it can make a lot of students uncomfortable. The ability to problem-solve is however a very important skill and is highly-valued by many employers. It is one of the reasons why you often see politicians and business people on the news saying that the country needs more scientists and engineers.

As the name suggests, the course is mathematical in nature, and you do need to be very good at maths to be successful at higher level. In general you should be averaging a ‘B’ or higher, and just because you got an ‘A’ in Maths in the Junior Cert does not necessarily mean that you will be comfortable with the subject.

The material itself is similar to that which you would study in Engineering in university, so even if you are not great at maths but want to be an engineer you should consider taking up the subject. Even if you end up taking the Ordinary Level exam at the end it will still stand to you at third level.

**How long is the course?**

The course itself is fairly short.

There are ten topics but only six questions to do on the exam itself so there is enormous choice.

In fact normally we only cover about 8 topics, and try to ensure we know them very well rather than trying to cover too much.

**What is the format of the paper in the leaving cert exam?**

Time: 2½ hours

We generally aim to cover 8 (or at most 9) topics (where each topic corresponds to a different question); it’s more advisable to spend your time becoming competent in 8 questions rather than spending time on others and this still allows for ample choice on the day itself.

There are 10 questions on the paper and the candidate has only to answer six questions.

NO other paper offers this much choice.

**What is the paper like at Ordinary Level?**

Applied Maths at the Ordinary Level is probably the easiest subject on the leaving cert curriculum. It is very short and can easily be covered in one year or less. The questions vary very little from year to year so with a just a little practice it should be easy to nail the A.

**How likely is it that I will get A at Higher Level?**

27% of students on average receive an A in the Leaving Cert. Don’t be fooled by this number however as the students who do Applied Maths are of a very high calibre.

Any student who can get an A in Maths should certainly be getting an A in Applied Maths

**Is it possible to study Applied Maths in college.**

You can study Applied Maths itself at third level. It is known as ‘Mathsphysics’ in NUI universities and as ‘Theoretical Physics’ in Trinity College.

**I want to study Maths in college – should I take Applied Maths now?**

Applied Maths is an invaluable subject for those who plan to study pure maths in university. Indeed many of those who have studied maths at university say that Applied Maths was a more important preparation than Maths itself!

**I want to study Engineering in college – should I take Applied Maths now?**

If you are considering studying **any kind of engineering** in college, Applied Maths is very important; all engineering students have to study Applied Maths in first year in college and you will have a head start if you have the Leaving Cert course done beforehand.

**Do I need to be doing Physics to study Applied Maths?**

It is not necessary to take Physics as a Leaving Cert subject in order to do Applied Maths. There is an overlap, but it’s not as great as you might think. If anything, doing Applied Maths will help you in Physics much more than the other way around in that you will develop a deeper understanding of many of the concepts which only get covered superficially in Physics.

**Reasons you should consider doing applied maths**

- Many students study Applied Maths for the benefit of their future maths results.

These are students who are chasing the bonus 25 points in honours Maths and who will find maths easier as a result of studying Applied Maths.

- Apart from being a terrific subject about of 3 in every 10 students will achieve an A1.

- Some universities (like UCC) are accepting a C1 in either Maths OR Applied Maths.

- Many students study Applied Maths to improve their problem solving skills and so produce better HPAT results to ensure they get into medicine.

- The single greatest obstacle for engineering students is passing Applied Maths in college - not a problem for those who studied it in school.

The text in Italics is taken from quotes given to *The Irish Applied Maths Teachers Association (iamta.ie)*

*As few schools offer Applied Maths as a scheduled class, most that take it on do so outside of school hours. This can be stressful and tiring at first but the end result is worth any hardships suffered.*

*Getting the actual correct answer only gives you a small amount of the marks.*

*Applied Maths was my favourite subject at school. It was a course completely unlike any other. Lateral and logical thinking are needed for it and solving problems is something I have always been interested in. The subject doesn’t involve enormous amounts of theory that you have to learn off by heart, like in biology, but just encourages you to think and apply principles.*

*Although no points in the Leaving Cert ever come easy, the Applied Maths examiners love to give away marks for writing down basic information and applying simple rules. Applied Maths may seem like a tough subject at first, but given a little time and a good bit of practice it becomes a tremendously satisfying and rewarding subject.*

*I soon discovered that Applied Maths is a hugely under-rated subject with a lot of benefits. Firstly, for those people who, like me, have lazy tendencies, and can think of better ways to spend an afternoon than memorising dates until you can’t even remember what year it is any more, Applied Maths is the ideal subject. There is almost no theory and very little writing involved, which is something I greatly appreciated when trying to write *poetry* essays every weekend. *

*If you are doing Higher Level Maths, this course compliments it! The Points may be the same but the amount of equations, topics, theorems and methods to recall is less. *

*Applied Maths allows the student to solve real life problems through logical reasoning and creative thought, and in my opinion that is something that no other Leaving Cert subject offers. As a student it seems daunting to take on another subject when school is already difficult and hectic as it is. However, Applied Maths added very little to my work load. Subjects such as Maths and Physics overlap with Applied Maths in many areas such as integration, vectors and mechanics.*

*If you are doing Physics then this will sort out about 40% of the entire physics paper for you! *

*If you are doing both ..... *

*Applied Maths also made life easier on a number of levels. Whole sections of Maths seemed easier having covered them the year before. Quadratic equations, integration and trigonometry benefited purely because we were using them so often. The mechanics section of physics posed little difficulty for many of us as we knew our UVAST inside and out and in other ways Applied Maths always encouraged you to look outside the box for an easier way of doing things – which is invaluable whatever you’re doing. Although it needed attention, with a little effort it’s definitely a manageable course with relatively little learning off. In short it’s a gift to anyone mathematically inclined who enjoys a challenge*

*It will help you if you want to pursue a career in Engineering, Architecture or any other technical subject. *

*I am currently studying Engineering in U.C.D. one of the core modules of the course is Mechanics, which is little more than Leaving Certificate Applied Maths*

*Applied Maths has advantages which I really came to appreciate in those last few days and weeks before the exam, *

*There was very little theory to be learned*

*It was a predictable subject with lots of choice.*

*And most importantly I had two days off after having finished all my other exams in which to try and learn everything.*

**In conclusion**

Applied Maths is not an easy subject, but it is a wonderfully rewarding subject to take on if you are good at maths and enjoy challenging yourself. It is interesting, challenging, educational, and it is good for careers.

**Related Careers**

Who would want to employ somebody who has studied Applied Maths?

In short, anybody who would like an employee who can solve problems, so basically everybody.

Studying Applied Maths enables students achieve employment and career prospects at the top end of the market in very diverse areas.

The following represent just some of the areas which students end up in after studying Applied Maths.

- Actuary
- Architecture
- Astronomy
- Business
- Chemistry
- Computer Programming...animated films, computer games
- Currency Exchange companies
- Economics
- Education
- Engineering
- environmental studies
- Forensics
- Hardware design...iphones, speakers etc
- Information Technology
- Investment banking
- Maths
- Medicine
- Metereology
- Pharmaceuticals
- Physics
- Planning traffic flow systems for big cities
- Political studies
- Robotics
- Science
- Statistician in the Central Statistics Office or in a casino
- The army ballistics division

**APPLIED MATHEMATICS Syllabus**

**Ordinary and Higher Level Courses**

Knowledge of the relevant parts of the Mathematics course is assumed.

N.B. Those parts of the syllabus which are printed in *italics *belong to the Higher Level course only.

The Higher Level course includes the Ordinary Level course treated in greater depth.

1. Motion of a particle. Displacement, velocity as vectors. Applications of the vector addition law. Description of vectors in terms of unit perpendicular vectors. Elementary treatment of relative motion.

2. Newton’s laws. Mass, momentum. Acceleration and force as vectors. Units and dimensions.

3. Motion in a straight line under uniform acceleration e.g. motion under gravity, motion on smooth and rough inclined planes. Work, potential energy, kinetic energy, power. Application of energy conservation. Motion of connected particles.

4. Equilibrium of a particle under concurrent forces, including friction.

5. Centre of gravity of simple bodies and systems of particles Moments and couples. Equilibrium of a rigid body or bodies.

6. Liquid pressure. Thrust on a horizontal surface. Archimede’s Principle.

7. Angular velocity. Uniform motion in a circle without gravitational forces. Conical pendulum. Circular orbits.

8. Conservation of momentum. Collisions. Direct collisions, elastic (0 < e ≤ 1) and inelastic (e = o). Oblique collisions of smooth elastic spheres in two dimensions.

9. Simple harmonic motion of a particle in a straight line. (Application of simple harmonic motion to include the simple pendulum.)

10. Motion of a rigid body about a fixed axis:

11. Calculation of moments of inertia for a rod, rectangular lamina, circular lamina and compound bodies formed of those. (Sphere is excluded). Application of parallel and perpendicular axes theorems, with proofs done as classwork. Idea of radius of gyration. Application of the conservation of energy principle to a rotating body.

12. Ordinary differential equations and applications:

- a. first order, variables separable

- b. Second order reducing to type