Leaving Cert Applied Maths: the 2027 exam, the modelling project and practice

The Leaving Cert Applied Maths exam in 2027

The weightings are in the NCCA specification, and the 2027 details in the Assessment Arrangements 2027. Normally you answer all the questions. In 2027 the extra questions still cover all three content strands in roughly the usual balance, and the paper keeps its usual length.

The modelling project: the brief sets out a real-world problem with no fixed method. You work through the modelling cycle, making and justifying your own decisions, and submit a report to the SEC in the format the brief gives. The 2027 dates aren't out yet (as of 7 November 2026); in 2026 the written exams ran from 3 to 23 June (Department of Education and Youth).

What Leaving Cert Applied Maths covers

• Strand 1, Mathematical modelling: the unifying strand. Every exam question is set in a modelling context.
• Strand 2, Networks and graphs: shortest paths, spanning trees and critical path analysis.
• Strand 3, The physical world: kinematics and dynamics, including projectiles, forces, friction and momentum.
• Strand 4, A changing world: difference equations and differential equations.

Grades run from H1 to H8 and O1 to O8, in 10% bands, with CAO points from 100 for an H1 (CAO grading scale).

Leaving Cert Applied Maths practice questions

We wrote these Higher level questions for this guide, one or two from each content strand.

1. Networks: the shortest path

Question: the network shows travel times in minutes. Find the shortest route from A to E.

Answer: using Dijkstra's algorithm from A: C is 3, then B is 3 + 2 = 5 (better than 6 direct), D is 5 + 4 = 9 (better than 3 + 9 = 12), and E is 9 + 2 = 11 (better than 3 + 12 = 15). The shortest route is A, C, B, D, E, taking 11 minutes. Show the labels at each node: they carry marks.

2. Projectiles

Question: a ball is kicked from level ground at 14 m/s, 30° above the horizontal. Find its time of flight and greatest height (g = 9.8 m/s²). Answer: the vertical component is 14 sin 30° = 7 m/s. It lands when 7t − 4.9t² = 0, so t = 7 ÷ 4.9 = 1.43 s. At its highest point the ball has stopped rising, so v = 0 vertically: 0 = 7² − 2 × 9.8 × h, so h = 49 ÷ 19.6 = 2.5 m. Try a projectile question in our Laws of Motion course and press Mark.

3. Momentum

Question: a 2 kg trolley moving at 3 m/s hits a stationary 1 kg trolley and they move off together. Find their common speed. Answer: momentum is conserved: 2 × 3 = (2 + 1)v, so v = 2 m/s. Check it in the Momentum Calculator.

4. A difference equation

Question: a fish stock of 1000 grows by 5% a year, and 100 fish are caught each year, so P_n+1 = 1.05P_n − 100. Find the stock after two years. Answer: P₁ = 1.05 × 1000 − 100 = 950. P₂ = 1.05 × 950 − 100 = 897.5, so about 898 fish. The stock is falling, so the catch is too high to be sustainable.

5. A differential equation

Question: a population grows at a rate proportional to its size, dP/dt = 0.2P, with t in years. How long does it take to double? Answer: separating and integrating gives P = P₀e^0.2t. Doubling means e^0.2t = 2, so t = ln 2 ÷ 0.2 = 3.47 years. Explore solutions in the Differential Equations Calculator.

Common mistakes

• Not showing Dijkstra's working. Write the label at each node as you go.
• Using the full speed vertically in a projectile: resolve into components first.
• Leaving out assumptions in modelling answers. State them, such as ignoring air resistance.
• Not interpreting the answer. Say what the number means in context, as in the fish example.

Use a daily paper as a short timed mock

Today's Leaving Cert Applied Maths paper practises Strand 3: constant and variable acceleration, projectiles, forces and Newton's laws, friction, inclined planes, connected particles and moments. It doesn't cover networks and graphs, difference or differential equations, or the modelling project, so it can only practise part of the written exam. For when mocks happen, see our Leaving Cert mocks guide.

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