Leaving Cert Maths: the papers, the 2027 changes, grades and practice questions

The Leaving Cert Maths exam in 2027

The two papers and their sections are set out in the NCCA syllabus. The 2027 changes are in the Assessment Arrangements 2027: the papers keep their usual length, Section A questions stay similar to previous years, and each Section B question will be somewhat shorter than a usual 50-mark question. Maths has no coursework, so your grade comes from the papers alone.

When is the exam? The SEC hasn't published 2027 dates yet (as of 7 November 2026). In 2026 the written exams ran from Wednesday 3 June to Tuesday 23 June, and results came out on Friday 21 August (Department of Education and Youth).

What Leaving Cert Maths covers

The syllabus has five strands. Ordinary level is a subset of Higher level, so Higher students learn both sets of outcomes.

• Statistics and Probability: counting, probability, Bernoulli trials, the normal distribution, sampling and, at Higher level, hypothesis testing.
• Geometry and Trigonometry: coordinate geometry of the line and circle, geometry proofs and constructions, and trigonometry.
• Number: complex numbers, including de Moivre's theorem at Higher level, sequences and series, financial maths and proof by induction.
• Algebra: expressions, equations, inequalities and the binomial theorem.
• Functions: graphs of functions, differentiation and integration.

Leaving Cert Maths grades and bonus points

Grades go in 10% bands, from H1 (90 to 100%, 100 points) down to H8, and from O1 (56 points) down to O8 (CAO grading scale). Higher Level Maths adds 25 bonus points at H6 or above, so an H6 (46 points) counts as 71. That bonus is why many students stay at Higher level even when it feels hard.

Leaving Cert Maths practice questions

We wrote these Higher level questions for this guide, one from each strand. Show every step: most marks are for method.

1. Number: de Moivre's theorem

Question: z = 1 + √3 i. Use de Moivre's theorem to find z⁶. Answer: the modulus is √(1 + 3) = 2 and the argument is π/3, so z = 2(cos π/3 + i sin π/3). Then z⁶ = 2⁶(cos 2π + i sin 2π) = 64. Check it in the Complex Numbers Calculator.

2. Functions: stationary points

Question: find the turning points of f(x) = x³ − 3x² − 9x + 5 and say which is which. Answer: f′(x) = 3x² − 6x − 9 = 3(x + 1)(x − 3), so f′(x) = 0 when x = −1 or x = 3. f″(x) = 6x − 6 is negative at x = −1 and positive at x = 3. So (−1, 10) is a local maximum and (3, −22) a local minimum. In the graph, x is the input and y is f(x).

3. Statistics and Probability

Question: A and B are independent events with P(A) = 0.4 and P(B) = 0.5. Find P(A ∩ B) and P(A ∪ B). Answer: independent means P(A ∩ B) = P(A) × P(B) = 0.2. Then P(A ∪ B) = 0.4 + 0.5 − 0.2 = 0.7. Practise telling independent from dependent events in our Probability course and press Mark.

4. Geometry: the circle

Question: find the centre and radius of x² + y² + 2x − 8y − 19 = 0. Answer: compare with x² + y² + 2gx + 2fy + c = 0: g = 1, f = −4 and c = −19. The centre is (−g, −f) = (−1, 4) and the radius is √(g² + f² − c) = √(1 + 16 + 19) = 6.

5. Number: financial maths

Question: €5,000 is invested at 3% a year compound interest. What is it worth after 4 years? Answer: F = P(1 + i)ᵗ = 5000 × 1.03⁴ = €5,627.54. Write i as a decimal, 0.03, not 3.

Common mistakes

• Answering all four Section B questions in 2027. You only need 3: use the time to do them well.
• Skipping the second derivative test or not stating which point is the maximum.
• Multiplying probabilities for events that aren't independent.
• Sign slips in the circle formula: the centre is (−g, −f).
• Rounding too early in financial maths. Keep full accuracy until the last line.

Use a daily paper as a short timed mock

There's a daily paper in each of four areas: Algebra and Functions (coordinate geometry, logs, sequences, trigonometry, functions), Calculus (differentiation, integration and area), Statistics and Probability (probability, the normal and binomial distributions, sampling, hypothesis testing) and Complex Numbers and Proof. They're written at Higher level, and some topics, such as partial fractions, parametric differentiation, integration by parts and differential equations, aren't on the Leaving Cert syllabus: skip those. They don't cover geometry proofs, constructions or financial maths. For when mocks happen and whether they count, see our Leaving Cert mocks guide.

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