The 34-point drop below an H6 in Maths
A Leaving Certificate student who gets 40% on the Higher Mathematics paper earns 71 CAO points for it. One who gets 39% earns 37. Every other grade boundary above 30% costs at most 12 points. This one costs 34, because of a bonus that applies on one side of the line and not the other.
The scale, read at source
The Central Applications Office publishes the common points scale for results from 2017 on. At Higher level an H1 (90 to 100%) is worth 100, and each grade below it loses 12, 11, 11, 10, 10 and 9 points down to H7 (30 to under 40%), worth 37. The last step, to an H8, loses all 37. Ordinary level runs from 56 for an O1 down through 46, 37, 28 and 20 to 12 for an O6, and an O7 or O8 earns nothing. The two scales meet four grades apart: an H5 and an O1 are both 56, an H6 and an O2 both 46, an H7 and an O3 both 37. So a mark in the 30s on a Higher paper earns what a mark in the 70s earns on the Ordinary one.
On top of that, CAO’s grid adds 25 points for Higher level Mathematics at H6 or better, which makes Higher Maths worth 125, 113, 102, 91, 81 and 71 from H1 to H6. An H7 gets no bonus. That is the 34 points: 71 at H6, 37 at H7. Your six best results from one sitting are added up, so the most anyone can score is 625.
A bonus that is not always 25
The condition matters as much as the bonus. CAO, Trinity College Dublin and the University of Galway all say the bonus counts only when Mathematics, with the bonus added, is one of the six best results. Take the example the calculator opens with, made up for the purpose: Mathematics H4 (66 plus 25 makes 91), then H2, H3, H4, H5, H6 and O2, and an LCVP Merit. The six best are 91, 88, 77, 66, 56 and 46, which is 424. Without the bonus it would be 399, so here the bonus is worth its full 25.
Now a student with H1, H1, H2, H2, H3 and H5 in six other subjects and an H6 in Higher Mathematics. Without the bonus the 46 for Mathematics does not make the six, and the total is 509. With it, Mathematics is worth 71, pushes out the H5’s 56 and makes the total 524. The bonus added 15, not 25. For this student the cliff is smaller too: an H7 in Mathematics would leave the total at 509, a loss of 15. A student whose six other results are all above 71 gets nothing from the bonus at all.
Higher or Ordinary, on points alone
An H6 in Higher Mathematics (71) beats an O1 (56) by 15. An H7 (37) loses to it by 19. If the choice were between a sure O1 and a Higher paper that you pass at H6 or better with probability p, the Higher paper earns more on average once p is above 19 in 34, about 56%. Against a sure O2 the line falls to 9 in 34, about 26%. That arithmetic ignores everything except points, it only applies when Mathematics will be one of the six, and a course’s Mathematics requirement can settle the question before points do.
Foundation Maths: 20 points, or none
CAO’s grid lists 20 points for an F1 and 12 for an F2 in Foundation Mathematics, awarded “by certain institutions”, and CAO’s own points calculator adds them. Three of the five universities whose pages were read for this guide say the opposite for themselves: Galway, Maynooth University and the University of Limerick award no points for it, and Trinity accepts it for minimum entry only. The calculator leaves Foundation points out by default and shows the other total. Even where they count, they are often worth less than they look: with an F1 and six other results whose lowest is an O6 (12), the F1 replaces that 12, so the total moves from 313 to 321, a gain of 8.
LCVP, and one sitting
The Leaving Certificate Vocational Programme Link Modules earn 66 for a Distinction, 46 for a Merit and 28 for a Pass, the same as an H4, an H6 and an O4, and CAO says every institution counts them in place of a sixth subject. In the example above the Merit ties with two other results at 46; a Distinction would add 20, the largest single gain on that list. University College Cork and the others are clear that the Link Modules count for points but not toward minimum entry requirements.
Finally, CAO scores one sitting only, so repeating the Leaving Certificate gives you a second score, not a combined one. Trinity is an exception of its own: it lets applicants add the Trinity Matriculation examination of the same year to their Leaving Certificate for scoring.