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Exam Review

Key Facts: LC Applied Maths Exam

2.5 hours

Duration of the Leaving Certificate Applied Mathematics written examination

NCCA Applied Mathematics specification

80% + 20%

Written examination weighting and modelling project weighting

NCCA Applied Mathematics specification

4 strands

Modelling; networks and graphs; physical world; changing world

NCCA Applied Mathematics specification

Higher and Ordinary

Applied Mathematics is offered at two levels, H1-H8 and O1-O8

State Examinations Commission grading scale

EUR 116

2026 Leaving Certificate exam fee for a school-based candidate (covers all subjects)

Citizens Information - Examination fees

SEC project brief

The modelling project uses a common annual brief issued by the SEC for both levels

NCCA Applied Mathematics specification

Written not MCQ

The official SEC paper uses structured written answers; this bank is an MCQ study adaptation

State Examinations Commission paper format

100

Free original multiple-choice practice questions in this bank

OpenExamPrep

Leaving Certificate Applied Mathematics is an Irish senior-cycle modelling subject set by the SEC at Higher (H1-H8) or Ordinary (O1-O8) Level. Assessment is 20% modelling project plus 80% written paper (2 hours 30 minutes) across networks, particle dynamics and difference/differential equations under the four-strand NCCA specification. This free bank provides 100 original English MCQ study items — an adaptation of the real structured-written format — with substantial numeric calculation practice.

Sample LC Applied Maths Practice Questions

Try these sample questions to review concepts for the LC Applied Maths exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A particle moves in a straight line with constant acceleration 3 m/s² from rest. What is its speed after 4 s?
A.12 m/s
B.7 m/s
C.3 m/s
D.48 m/s
Explanation: Use v = u + at with u = 0, a = 3 m/s² and t = 4 s: v = 0 + 3 × 4 = 12 m/s.
2A particle starts with speed 8 m/s and accelerates at 2 m/s² for 5 s. How far does it travel in that time?
A.65 m
B.50 m
C.40 m
D.90 m
Explanation: s = ut + (1/2)at² = 8×5 + (1/2)×2×5² = 40 + 25 = 65 m.
3A car slows from 20 m/s to 8 m/s in 6 s with constant acceleration. Taking the direction of the initial velocity as positive, what is the acceleration?
A.-2 m/s²
B.2 m/s²
C.-12 m/s²
D.4 m/s²
Explanation: a = (v − u)/t = (8 − 20)/6 = −12/6 = −2 m/s².
4On a velocity–time graph, a straight line runs from (0 s, 0 m/s) to (10 s, 20 m/s). What is the constant acceleration?
A.2 m/s²
B.0.5 m/s²
C.20 m/s²
D.200 m/s²
Explanation: Acceleration is the slope of the v–t graph: a = Δv/Δt = 20/10 = 2 m/s².
5A particle starts from rest and accelerates at 4 m/s² over a distance of 18 m. Using v² = u² + 2as, what is its final speed?
A.12 m/s
B.6 m/s
C.√18 m/s
D.72 m/s
Explanation: v² = 0 + 2(4)(18) = 144, so v = 12 m/s (taking the positive root for speed).
6A particle has displacement s = 3t² − 2t (s in metres, t in seconds). What is its velocity at t = 2 s?
A.10 m/s
B.8 m/s
C.12 m/s
D.4 m/s
Explanation: v = ds/dt = 6t − 2. At t = 2, v = 12 − 2 = 10 m/s.
7Take g = 10 m/s². A stone is dropped from rest from a height of 45 m. How long does it take to reach the ground?
A.3 s
B.4.5 s
C.9 s
D.√45 s
Explanation: s = (1/2)gt² with u = 0: 45 = 5t² ⇒ t² = 9 ⇒ t = 3 s.
8A projectile is launched with speed 20 m/s at 30° above the horizontal. Take g = 10 m/s². What is the initial vertical component of velocity?
A.10 m/s
B.20 m/s
C.10√3 m/s
D.20√3 m/s
Explanation: u_y = u sin θ = 20 sin 30° = 20 × 0.5 = 10 m/s.
9For a launch of 20 m/s at 30° (g = 10 m/s²), what is the initial horizontal component of velocity?
A.10√3 m/s
B.10 m/s
C.20 m/s
D.5 m/s
Explanation: u_x = u cos θ = 20 cos 30° = 20 × (√3/2) = 10√3 m/s.
10A force of 15 N acts on a particle of mass 3 kg. Ignoring all other forces, what is the magnitude of the acceleration?
A.5 m/s²
B.45 m/s²
C.0.2 m/s²
D.18 m/s²
Explanation: Newton’s second law: F = ma ⇒ a = F/m = 15/3 = 5 m/s².

About the LC Applied Maths Exam

Leaving Certificate Applied Mathematics is a senior-cycle subject in the Irish second-level system that develops mathematical modelling of real-world problems. Under the NCCA specification it is examined by the State Examinations Commission (SEC) at Higher Level or Ordinary Level through two components: a Mathematical Modelling Project worth 20% (common annual brief; report marked by the SEC) and a written examination worth 80% lasting 2 hours 30 minutes. The course is organised in four strands: Strand 1 Mathematical modelling (unifying); Strand 2 Mathematical modelling with networks and graphs (adjacency matrices, minimum spanning trees, shortest paths, project scheduling); Strand 3 Mathematically modelling the physical world — kinematics and dynamics (1D/2D motion, vectors, projectiles, forces, friction, connected particles, collisions, work-energy, momentum, circular motion, dimensional analysis); and Strand 4 Mathematically modelling a changing world (recurrence relations, difference equations and differential equations). This free bank gives 100 original English single-best-answer multiple-choice questions as a calculation-focused study adaptation — not the official SEC item format — covering core techniques from the specification.

Exam sponsor: State Examinations Commission (SEC), Ireland. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Two components at Higher and Ordinary Level under the NCCA specification: Mathematical Modelling Project (20%, annual SEC brief, completed in sixth year, marked by SEC) and written examination (80%, 2 hours 30 minutes) assessing Strand 2 networks/graphs, Strand 3 kinematics and dynamics, and Strand 4 difference/differential equations, with Strand 1 modelling skills embedded throughout.

Time Limit

Written examination: 2 hours 30 minutes. Modelling project: completed in sixth year against the annual SEC brief (submission date set each year by the SEC).

Passing Score

No single pass mark. Results use the eight-point scale: Higher Level H1-H8 and Ordinary Level O1-O8, each a percentage band (H1/O1 90-100%, H2/O2 80 to under 90%, down to H8/O8 below 30%).

Exam / Certification Fees

In 2026 the Leaving Certificate examination fee is EUR 116 for a school-based candidate (EUR 301 for a school-going repeat candidate); full medical card holders are exempt. The fee covers all subjects entered, not Applied Mathematics alone.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

10%

Mathematical modelling (Strand 1)

Practice covers the modelling cycle (formulate, translate, compute, evaluate and iterate), identifying variables and assumptions, choosing representations, and using dimensional analysis to check whether results are reasonable.

25%

Networks and graphs (Strand 2)

Practice covers network terminology, adjacency matrices and matrix products, Prim and Kruskal minimum spanning trees, Dijkstra and dynamic-programming shortest paths, and project networks with earliest/latest times, critical path and floats.

45%

Kinematics and dynamics (Strand 3)

Practice covers constant-acceleration motion, velocity-time graphs, 2D vectors, projectiles, free-body diagrams, friction, Newton's laws, connected particles, direct and oblique collisions with restitution, work-energy, impulse-momentum and circular motion of a particle.

20%

Changing world (Strand 4)

Practice covers recurrence relations, first- and second-order linear difference equations (homogeneous and inhomogeneous) for growth, finance and discrete systems, and first-order separable differential equations for continuous growth, decay and related models.

Preparing for the LC Applied Maths Exam

What You Need to Know

  • Passing score: No single pass mark. Results use the eight-point scale: Higher Level H1-H8 and Ordinary Level O1-O8, each a percentage band (H1/O1 90-100%, H2/O2 80 to under 90%, down to H8/O8 below 30%).
  • Assessment: Two components at Higher and Ordinary Level under the NCCA specification: Mathematical Modelling Project (20%, annual SEC brief, completed in sixth year, marked by SEC) and written examination (80%, 2 hours 30 minutes) assessing Strand 2 networks/graphs, Strand 3 kinematics and dynamics, and Strand 4 difference/differential equations, with Strand 1 modelling skills embedded throughout.
  • Time limit: Written examination: 2 hours 30 minutes. Modelling project: completed in sixth year against the annual SEC brief (submission date set each year by the SEC).
  • Exam / certification fees: In 2026 the Leaving Certificate examination fee is EUR 116 for a school-based candidate (EUR 301 for a school-going repeat candidate); full medical card holders are exempt. The fee covers all subjects entered, not Applied Mathematics alone. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

LC Applied Maths: Suggested Study Strategy

1Drill network algorithms until automatic: Prim/Kruskal for MSTs, Dijkstra for shortest paths, and critical-path early/late times with free and total float.
2Master the constant-acceleration (SUVAT) formulae and the links s, v = ds/dt, a = dv/dt using calculus when acceleration is not constant.
3For projectiles, resolve into horizontal (constant velocity) and vertical (constant acceleration) components; track time of flight, range and maximum height carefully.
4Always draw free-body diagrams for dynamics: resolve parallel and perpendicular to planes, include friction μR, and apply F = ma or energy methods as appropriate.
5For collisions, apply conservation of momentum and Newton's experimental law (coefficient of restitution e) along the line of impact; treat oblique impacts by resolving components.
6Practise solving first-order difference equations and separable differential equations with initial conditions, then interpret the solution back in the real-world context.
7Work past SEC papers against official marking schemes so you show method, units and interpretation — partial credit is a major feature of the written paper.
8Treat the modelling project as a full cycle: research, assumptions, mathematical model, computation, evaluation and refinement, with clear citation of sources.

Frequently Asked Questions

Is the Leaving Certificate Applied Maths exam multiple choice?

No. The official assessment is a written examination of structured multi-part questions (80%) plus a Mathematical Modelling Project (20%). These multiple-choice items are an original English study adaptation for calculation and concept practice, not the real exam format.

How is Leaving Cert Applied Mathematics assessed?

There are two SEC-set components at Higher and Ordinary Level: a modelling project worth 20% based on an annual brief completed in sixth year, and a written paper worth 80% lasting 2 hours 30 minutes.

What topics are on the Applied Mathematics specification?

Four strands: (1) mathematical modelling; (2) networks and graphs (matrices, MSTs, shortest paths, project scheduling); (3) physical world kinematics and dynamics (motion, forces, projectiles, collisions, energy, circular motion); (4) modelling a changing world with difference and differential equations.

What is the modelling project?

It is a 20% component based on a brief issued annually by the SEC. Candidates define a problem, translate it to mathematics, compute a solution, analyse and iterate, then submit a written report of their own work for SEC marking.

How is Leaving Cert Applied Maths graded?

There is no single pass mark. Results use the eight-point scale (Higher Level H1-H8, Ordinary Level O1-O8), where each grade is a percentage band, for example H1/O1 is 90-100% and H4/O4 is 60 to under 70%.

Are these official SEC practice questions?

No. These are original OpenExamPrep English single-best-answer questions modelled on the NCCA Applied Mathematics specification. The State Examinations Commission publishes official past papers and marking schemes separately on examinations.ie.