# Applied Maths Exam Guide

(a) Exam Structure & Strategy

 Level Higher Time 2½ hours (150 minutes) Marks 300 Marks Structure Answer 6 out of 10 questions Each Question carries 50 marks Timing Allow 25 minutes per question NB. This time includes proofing and checking over your answers

Exam Strategy

Maximising Marks
If you answer more than six questions, they will all be corrected and you will be given the marks for the best six.

You start with all the marks.  The examiner takes marks away for mistakes.  You lose 1 mark for a numerical mistake (called a ‘slip’).  For example, if you write 2 × 1 = 3, you will lose 1 mark (out of 300).  If you say that sin 60º = 0.5, you will lose 1 mark.

You lose 3 marks for a mistake that is more serious (called a ‘blunder’).  For example, if you stated that  vAB=vB – vA  (which is wrong), you would lose 3 marks (out of 300).  This is still only  a 1% deduction – not a lot!

Of course, if you write nothing of value, you lose all the marks for that part.  This is what a good student tries to avoid.

If, as a result of making a mistake, all subsequent answers are wrong, this does not matter!  You will not lose marks again for the earlier mistake.  You are never punished twice for one mistake.  So, it is possible to get all parts of a question wrong and still get 49 out of 50.  Remember this!  It is more important to have correct methods than correct answers.

Preparation

• Most students will know before the exam what their favourite questions are and will have made a rough plan about which to answer first, which second, etc.
• Some students prepare only 6 topics.  This is fraught with danger.  The examiner might put in half a question where it doesn’t usually go.  For example, in 2002, Question 4(a) was a half question on Simple Harmonic Motion.  This stumped many students – and surprised many teachers!  Sometimes the examiner sets a fiercely difficult question, which should be avoided at all costs (1990, question 5, for example).
• It is best to prepare at least seven topics.
• To revise, it is far better to do questions than to read questions.
• If you can do all the questions from the last seven years’ papers, then you should be well prepared for the next Leaving Cert paper.
• When you are stuck and cannot work out how to solve a particular problem, check in your text-book to see if there is a question like it done out.  If not, make a note of it and ask someone: your teacher, the class genius, the family brain-box – whoever!  If you don’t, then this type of question might turn up on the exam, and the opportunity has been missed.
• Don’t stay up late the previous evening, fretting over your work.  You want your brain to perform live the next day, so give it the help it needs:  go for a walk, or play a gentle game of tennis and get a good night’s sleep.  It will pay off.

The Exam

• Do not answer Question 1 first, just because it is first on the paper.  It can be sticky, and often needs a lot of thought and a lot of time.  There are other questions which vary less from year to year (projectiles, differential equations or collisions, for example).  Try them first.
• Applied Maths exams can be a bit daunting, because you have to read and take in completely new questions.  The first few minutes are often unsettling.  Don’t fret!  It’s normal.
• Take your time.  Read questions carefully.  Don’t jump to conclusions.  You cannot assume that a particle starts from rest, unless the question actually says so.
• Remember, you do not have to get the right answers to get good marks.  If the question says, “Prove that the loss in energy is 63 J, but you get a loss of 17 J, what should you do?  The answer is , “Do nothing!  Just go on to the next question!”  You may have lost 1 or 3 marks and you might have to spend ages looking for your mistake.  (And even then you might not find it.)  You are much more likely to get a greater number of marks by starting your next question and getting on with it.
• When you are finished a problem, just glance back over the question to make sure that you have answered precisely what has been asked.  Students often leave out bits accidentally.  They also answer a question they wish they were asked, but not the one they were, in fact, asked.
• Unlike in the Physics exam, students don’t have to write units after every answer.  So, you get full marks for the correct number;  the units don’t matter.
• Don’t go back over your work, until you have done 6 questions.  Then (if there is any time left) check to see that you haven’t made any silly errors.
• If you get bogged down and don’t seem to be getting anywhere, leave that question and get on to your next one.  Leave a blank page at the end of the question which did not work out.  You can come back later. You might then be able to find a breakthrough at that point.
• Don’t panic!  Don’t hop from question to question doing only parts from each.
• Avoid over-using Tippex.  Why not just cross out a mistake and get on with it?  How long are you going to wait for the stuff to dry?
• Although there are no marks for neatness, the examiner has to try to follow your writings and your logic.  Work down the page.  Use a new line for a new step.  Try not to be all over the place.
• Do not do rough work elsewhere in your answer booklet.  All work is important and should be shown.
• It is a good idea to bring in chocolate and water, if the Superintendent allows it.  A break of routine for a few seconds can help you perform better.

(b) Walk-through the paper (Question by question)

Q1: Uniform linear acceleration.

This is a popular question, because students are familiar with the equations and time-speed graphs.  But beware!  Questions vary a lot and can be tricky.

• Do know your 4 formulae (or have Page 50 of the Maths Tables open)
• Do use the formulae only when there is constant uniform acceleration
Do draw a clear time-speed graph.
• Do define terms clearly at the beginning of your solution.
• Don’t do this question first, just because it is question 1.
• Don’t assume that the particle starts from rest, unless this is stated explicitly in the question.
• Don’t jump into the question before giving it enough clear thought.

Q2: Relative velocity

This is a question which goes very well for those who have a clear idea of what relative velocity means.  It can become unstuck for those who don’t.  It is essential to be able to find the magnitude and direction of a given vector.  It is equally important to be able to write a vector in i-j form, given its magnitude and direction.

• Do draw plenty of large clear diagrams, showing the relative path.
Do use graph paper for diagrams.
• Do know your theory of vectors well.
• Don’t mix actual paths (and angles) with relative paths (and angles).
• Don’t mix up the actual velocity of the wind with the apparent velocity of the wind.

Q3: Projectiles

This is a good question, which is very popular with students.  It is reasonably easy to master, as there is not a huge variety of different types of problem to be asked.

• Do draw diagrams for each part of the question.
• Do know your trigonometry well.
• Do be familiar with and use the Mathematical Tables.
• Don’t mix up the displacement vector with the velocity vector.

Q4: Connected Particles: Pulleys & wedges

This is another popular question.  It is all based on Newton’s Second Law:  F = ma.  This is a question where it is more important to get all the equations down on paper than to get the actual answer right.  It’s not easy to solve four simultaneous equations with four unknowns, without making a small slip.

• Do draw a force diagram for each particle separately.
• Do show the acceleration to one side of the diagram.
• Do write down the equation (F = ma) of motion for each particle.
• Do practise solving plenty of wedge questions before the exam.
• Don’t assume all accelerations are a.
• Don’t forget about relative accelerations when there is a moveable pulley.
• Don’t confuse an inclined slope with a wedge.
• Don’t fret if you get a negative acceleration: it just means the particle goes the other way.

Q5: Impacts & Collisions

This is another popular question.  It is all based on two formulae:

1. Law of Conservation of Momentum (COM):   m1u1+m2u2=m1v1+m2v2
2. Newton’s Experimental Law (NEL): • Do lay out the information clearly.
• Do remember that the j-velocities will not change (if the i-axis is the line of centres at impact).
• Do know your theory of vectors well.
Don’t forget to put the minus in front of e in NEL.
• Don’t apply NEL to both directions, just to the direction of impact.
• Don’t confuse momentum and kinetic energy.

Q6: Circular Motion and Simple Harmonic Motion

If you are going to answer this question, you must know your theory for both circular motion and Simple Harmonic Motion (SHM).  It would be foolish to study one and not the other. Questions on SHM are more common than questions on circular motion.  Half-and-half questions are also very common. It is also possible for a question about the simple pendulum to turn up.

• Do know your SHM formulae well.  They are not in the Mathematical Tables.
• Do use the radian mode on your calculator when using the trigonometry buttons.
• Don’t treat a circular motion question as a statics question.

When doing elastic band problems:
• Don’t forget that the amplitude is determined by the starting position.
• Don’t examine the forces for the starting position only; examine the forces for the general position (a distance x from the mean-centre).

Q7: Statics

This is a good question, especially for those students who have had plenty of practice with past questions on statics.

• Do draw a large clear diagram.
• Do show the forces clearly, with arrows.
• Do write down the three equations:
1. Forces up = forces down
2. Force left = forces right
3. Clockwise moments = anti-clockwise moments
• Do give the third equation extra care:  it’s the tricky one.
• Don’t worry too much about getting the correct answer.  Getting equations onto paper is the key thing here.

Q8: Moments of Inertia

This is another good question. Students must know the three proofs (rod, disc, rectangle) and variations on these themes.  Then, the student should be familiar with the Parallel Axes Theorem and the Perpendicular Axes Theorem, and how to apply them.  Finally, there are two key formulae:
1. is a constant.
2. • Do learn and practise your three proofs.
• Do be familiar with the formulae on Page 40 of the Mathematical Tables – and know the ones that are not there.
• Do know the two key formulae.
• Do draw clear, large diagrams on graph paper.
• Don’t mix up the different formulae for a disc.
• Don’t forget to put in for each part of the apparatus in the energy equation.

Q9: Hydrostatics

This is not a popular question but that doesn’t mean it is to be avoided – far from it.  Students with good knowledge of their basics can do very well here.

• Do know your definitions well.
• Do know the three different ways of calculating buoyancy.
• Don’t mix up density and relative density.
• Don’t mix up pressure and thrust.
• Don’t mix up mass and weight.

Q10: Differential Equations

This is very popular question, especially with those students who have mastered integration.  You should be able to get part (a) right.  It is the most mathematical question on the paper.  Part (b) will be trickier – but practice makes perfect!   Some students use limits of integration;  others use a constant of integration instead.  Suit yourself;  use the method you feel most comfortable with.

• Do know your integration methods (e.g. substitution) well.
• Do separate the two sides carefully.
• Do put in a scale on all force diagrams.
• Do be careful with the signs in the force equation.
• Do choose intelligently between the two possible expressions for acceleration: Don’t confuse power and force.
• Don’t put in the initial speed as a force.
Don’t put GMG’s online  Leaving Cert Applied Maths Resource Pack

Exam Guide – Leaving Cert Applied Maths This PDF outlines the structure of the Leaving Cert Applied Maths exam papers and marking scheme. It describes how you can prepare for and maximise your results in the exam. It contains advice from the Exam Commission’s Chief Examiner. It gives tips on how to study and revise in the lead up to the exam and provides a check list of what to bring on the day.