Report on the 2018 Higher Level Leaving Certificate Applied Mathematics paper

by Dominick Donnelly, Bruce College, Cork

http://www.appliedmathematics.ie

Question 1(a)

Straightforward deceleration question.

Question 1(b)

Algebraic overtaking question involving velocity / time graphs. Very reasonable question, and more straightforward than many such questions.

Overall on question 1: A good question, pitched at about the right level of difficulty overall. More straightforward than many Q1s have been, which is good.

Question 2(a)

Standard enough aeroplane question.

Question 2(b)

2(b)(i) Very standard. 2(b)(ii) Absolutely diabolical question. Very difficult, involving minimisation. It is however very similar to Q2(b)(ii) in 2016, so hopefully students were able to deal with it. Many students already struggle with question 2 as it is the most vector based question, there is no need to make it this difficult. I really hope the marks get loaded into 2(a) and 2(b)(i), as I doubt there will be many succeeding with 2(b)(ii). While there is a very elegant solution using loci and not involving calculus, I would doubt many if any of the candidates would be aware of it.

Overall on question 2: Part (a) fine, part (b) awful. One of the hardest questions on the paper. Many students were shattered by this question. Hopefully most of them went elsewhere and did a different question. There is no need to make relative velocity this hard, it is hard enough already.

Question 3(a)

A novel question involving 2 colliding projectiles. Combines collisions with overtaking and meeting from Q1. Not too difficult, but the novelty may have caught students out.

Question 3(b)

Really tough and long question involving 2 particles on an inclined plane with different angles of projection and the same range. The hardest on the paper. Part (i) and the first part of (ii) standard enough. The latter part of part (ii) to find the other angle very long, and involves the use of difficult trigonometric equations. The students almost certainly won’t have solved a trig equation of this style before, and while there are various methods to solve it, this is generally a skill very few students have, as there is so little of it on the Maths course now. Hopefully the solving of the trig equation will carry very few marks.

Overall on question 3: This question is usually a banker for the vast majority of students, particularly the more moderate students. This year it was almost certainly the toughest and longest question on the paper, with the novelty in part (a) and the difficult trig in part (b). In general many of the better students will hopefully hae avoided it, but for those that did it, which is probably still a large proportion, hopefully it will be marked generously.

Question 4(a)

A standard enough question involving motion of two linked particles on an inclined plane.

Question 4(b)

A very standard moving pulley in the middle question. The main source of error in these is usually mistakes in the accelerations, and I presume it will be the same again here.

Overall on question 4: A good question, pitched at about the right level of difficulty overall. Again it is a banker for most candidates, particularly the more moderate ones, and they hopefully should have been ok here.

Question 5(a)

A standard enough 3 ball direct collision problem.

Question 5(b)

A standard enough oblique collision problem.

Overall on question 5: A good question, pitched at about the right level of difficulty overall.

Question 6(a)

A very standard 2 string Hooke’s Law problem.

Question 6(b)

A standard motion in a vertical circle problem.

Overall on question 6: A good question, pitched at about the right level of difficulty overall, for the few who have studied question 6.

Question 7(a)

A standard single ladder problem.

Question 7(b)

A tricky and difficult enough double ladder question. The fact that the two feet of the ladder are on different levels really complicates it, and I would imagine there would be very few successful attempts at it, as the distances for taking moments are complicated. Also a lot of tricky surds to deal with.

Overall on question 7: One of the hardest questions on the paper. While part (a) was straightforward, part (b) wasn’t, and I would imagine very few students will have attempted it, and for those that did, I would imagine there will be very few successful attempts at part (b).

Question 8(a)

Standard proof of moment of inertia of a disc.

Question 8(b)

A tricky enough question involving getting the moment of inertia of a disc with holes. Involves getting moment of inertia by subtraction which is relatively novel, though it was on the exam in 2017 too. Most students should have been able to have a reasonable effort at the question.

Overall on question 8: A good question, pitched at about the right level of difficulty overall, albeit at the harder end.

Question 9(a)

A very standard floating hollow sphere question.

Question 9(b)

A standard inclined rod question.

Overall on question 9: A good question, pitched at about the right level of difficulty overall. One of the shorter questions.

Question 10(a)

A standard differential equation question, going back to the old style of Q10(a) prior to 2012.

Question 10(b)

A straightforward enough question, involving population growth / decline. The question was expressed quite clearly, so the students should have been able to deal with it.

Overall on question 10: A good question, pitched at about the right level of difficulty overall, and reasonable short.

Overall impressions of whole paper

Overall a reasonable paper, pitched at about the correct level of difficulty. Most of the students I spoke to were happy with it. Eight of the ten questions (Qs. 1, 4, 5, 6, 7, 8, 9 &10) were pitched within the normal range of questions, some at the harder end, but most well within the normal range. The two more difficult questions were Qs. 2(b) and 3(b), and while Q. 2(a) was standard, Q. 3(a) was quite novel, and made this question the most difficult on the paper. Given that Q3 is generally the most frequently answered question, this may pose a problem for some candidates. Those that were able to avoid it will generally have profited, but hopefully the marking will be generous enough for those that did attempt question 3. Question 2 (b) was also very difficult, but it is very similar to the question in 2016, so that may have helped many to succeed at it.