Applied Maths Predictions Leaving Cert Higher Level

Updated in January 2024

A note about 2024

The course has completely changed recently. This means that past papers lack their normal relevance as far as the prediction process is concerned. This means we’re not able to make predictions for 2024.

What we predicted in 2022

Please exercise caution with all predictions and don’t take too many risks. Please refer to official guidance from SEC and DoE for Covid-19 related assessment change updates.

Outline:

There are ten questions on the applied maths paper every year.

In 2022, candidates will be required to answer five questions from ten. Each question carries 50 marks, as in previous years. The total mark allocation for the paper will be 250 marks, instead of the usual 300 marks.

Each question refers to the same respective topic(s) each year. For example Q2 is always on the topic relative velocity. There are generally several different areas of the topic that can be asked.

Q1-Linear Acceleration

Q1 part (a) is generally straightforward and uses the manipulation of the motion formulas.

2021 had a very standard (a) part whereas 2018 and 2019 included the likes of inclined planes and friction. It is likely that in 2022 this part will include an element such as inclined planes,forces or frictional forces so the best advice would be to know Q4 material well if you plan on answering Q1.

Q1 part (b) can also be straightforward but is often longer than part (a). It may ask: train track/common start, overtaking, motion under gravity,greatest gap or multistage problems.

Of course you must be familiar with all these type of scenarios and as long as you can do the exam papers for the last 15 or so years you should be well covered with them.

There is a decent chance that a multistage problem like that of 2013 or 2011 may appear.These usually include the average speed for the journey and information on 3 different stages. It has not appeared since 2013 so it is worth practicing a few of these types of questions.

Q2-Relative velocity

Part (a) and part (b) can include any area of this topic such as wind questions,river questions,the typical two boats/planes traveling questions or shortest distance between two vehicle questions (among others).

There isn’t much ability to predict what will come up in either part given this question does not follow any clear trends but there hasn’t been a wind question (see 2019 Q2a) since 2019 and it tends to come up frequently so it may be worth putting in extra practice on those.

Q3-Projectiles

Part (a) of this question is generally a standard projectile scenario where the plane is not inclined. For these questions it generally asks you to find the likes of range,angle of projection,max height or speed of particle.

For part (b) it is almost guaranteed to be an inclined plane scenario. It is also crucial that you consider whether the particle is traveling up or down the plane as this affects your motion equations. The types of problems asked can be any of the following: Particle striking plane at right angle, particle striking plane horizontally, a bouncing question(restitution), a max range question or a question where landing angle is given.

2021 had a bouncing question so that is unlikely to appear. A horizontal landing or right angle landing has a good chance of appearing as they haven’t come up in a number of years. It is also important that you are comfortable with the differentiation needed to answer a max range question as it could appear.

Q4-Pulleys/wedges

A wedge question appeared in 2021 and it generally does not come up in consecutive years so is unlikely to appear in 2022. Practically every year one of the parts is a type of pulley question so it is important you are comfortable with all movable and fixed pulley past exam questions.

Given wedges are unlikely to appear , there may be an inclined plane question such as the one asked in 2018 (a).

Q5-Collisions

Part (a) of this question is generally always a direct collision/ non-oblique collision. 2021 and 2020 both involved two balls colliding. It is likely that 2022 may include a third ball colliding like in 2019 or else it may have a wall involved in the problem.

Part (b) is usually some kind of oblique collision. In 2022 It is likely that in either part (a) or part (b) there will be kinetic energy involved so it is worth knowing the formula for KE and how to get the percentage loss in KE. There is also a good chance that in part (b) you may be asked to find the angle of deflection given it wasn’t asked the last two years.

Q6- Circular Motion/ Simple Harmonic Motion

Part (a) usually relates to simple harmonic motion , although it can also be swapped and end up in part (b). For this part you almost always need to show it moves with simple harmonic motion. After that there are a few questions they can ask involving the amplitude, max speed or time taken among others. You must be familiar with all the formulas and methods for simple harmonic motion.

The other part is generally related to circular motion. It can be circular motion in a vertical circle or in a horizontal circle. It is risky to bank on only one of these appearing as they don’t seem to alternate each year. You must be comfortable with both vertical and horizontal circular motion.

Q8-Rigid body motion

Part (a) is always a proof. You are required to prove the moment of inertia of a rod/disc is a certain amount. These are straightforward proofs that guarantee you full marks if you know them. It generally tends to switch between a rod and disc each year so in 2022 it is likely to ask you to prove the moment of inertia of a disc. That being said you should know how to prove it for a rod as well as there’s no guarantee it will ask for inertia of a disc.

Part (b) is usually a more complex question requiring you to find the MOI(moment of inertia) of a system as well as further information on the system. The system could be a set of rods, various discs or a combination of systems. After it makes you find the MOI you are generally asked to find at least one of : angular speed, period of oscillations, length of equivalent simple pendulum or kinetic energy among others. It is relatively likely that they ask you to find kinetic energy in 2022 as it hasn’t been asked in the last few years. This may involve the system moving or perhaps a wheel rolling on a surface. It is also important you can find all other elements of the system mentioned above.

Q9-Hydrostatics

The main types of questions asked in this section are floating,fixed,pressure and mixture questions. Unfortunately there are no guaranteed questions for this topic like in q8. Consequently it is difficult to predict what would come up. Generally students who choose to answer q9 in the exam have a good understanding of all the physics and concepts involved with hydrostatics and are therefore able to answer all possible problems.

Q10-Differential equations

Question 10 ,while always involving types of differential equations , can involve several types of problems. The problems are not unique to part (a) or (b). There can be Force based questions, acceleration/movement questions,various rates of change questions,population/bacteria growth or decay as well as purely equation based differential equations like 2018 (a). Acceleration/ velocity questions are popular in this section and there is a good chance one may appear in 2022 given past trends. A purely equation based differential question last appeared in 2018 so it is worthwhile practicing a few of those as well (e.g 2013 (a), 2018 (a) ).

Note: Make sure you are aware that these questions regarding movement of a particle are not linear acceleration problems like Q1. Acceleration changes over time so you must integrate/differentiate depending on what you are trying to find.