How is Leaving Certificate Higher Level Maths examined?

It is examined by two written papers, each lasting 2 hours 30 minutes and worth 300 marks (600 marks in total). Each paper has Section A (Concepts and Skills) and Section B (Contexts and Applications).

What is the difference between Paper 1 and Paper 2?

Paper 1 mainly covers Number, Algebra and Functions including calculus. Paper 2 mainly covers Geometry and Trigonometry, and Statistics and Probability. Both papers include short-answer and longer applied questions.

What are the five strands of the syllabus?

The Project Maths syllabus has five strands: Strand 1 Statistics and Probability, Strand 2 Geometry and Trigonometry, Strand 3 Number, Strand 4 Algebra, and Strand 5 Functions (including differential and integral calculus).

What are the bonus points for Higher Level Maths?

A grade of H6 (40-49%) or higher in Higher Level Mathematics earns 25 bonus CAO points, which are added to the points from the candidate's best six subjects for third-level admission.

How are the grades reported?

Higher Level results use the H1-H8 scale: H1 is 90-100%, H2 is 80 to under 90%, and so on in 10% bands down to H8 (below 10%). H7 (30-39%) is the lowest grade that still awards CAO points at Higher Level.

Are these official State Examinations Commission questions?

No. These are original OpenExamPrep single-best-answer concept questions modelled on the syllabus strands. The State Examinations Commission publishes official past papers and marking schemes separately, and you should also practise full long-form questions.

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Key Facts: LC Higher Maths Exam

2 papers

Higher Level Maths is assessed by two written papers, each 2 hours 30 minutes

State Examinations Commission

300 marks

Each paper is worth 300 marks, giving 600 marks in total

State Examinations Commission examination papers

5 strands

The Project Maths syllabus has five strands across Papers 1 and 2

NCCA Leaving Certificate Mathematics syllabus

25 bonus points

A grade of H6 or higher in Higher Level Maths earns 25 bonus CAO points

Central Applications Office (CAO)

H1-H8

Higher Level grades range from H1 (90-100%) to H8 (below 10%)

State Examinations Commission grading scale

2 sections

Each paper has Section A (Concepts and Skills) and Section B (Contexts and Applications)

State Examinations Commission examination papers

June sitting

Higher Level Maths papers are sat during the annual June Leaving Certificate examinations

State Examinations Commission timetable

100

Free original single-best-answer practice questions here

OpenExamPrep

Leaving Certificate Higher Level Mathematics is the top of three levels in the Irish State exam, set by the State Examinations Commission and built on the five-strand Project Maths syllabus. It is assessed by two written papers, each 2 hours 30 minutes and 300 marks (600 marks total), each split into Section A (Concepts and Skills) and Section B (Contexts and Applications). Paper 1 covers Number, Algebra and Functions including calculus; Paper 2 covers Geometry and Trigonometry and Statistics and Probability. Results use the H1-H8 scale, and a grade of H6 (40-49%) or higher earns 25 bonus CAO points. This 100-question bank provides original single-best-answer concept practice across all five strands.

Sample LC Higher Maths Practice Questions

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

1Solve the equation 2x^2 - 7x + 3 = 0.

A.x = 3 or x = 1/2

B.x = -3 or x = -1/2

C.x = 3 or x = 2

D.x = 7 or x = 3

Explanation: Factorise: 2x^2 - 7x + 3 = (2x - 1)(x - 3) = 0, so x = 1/2 or x = 3. You can confirm by the quadratic formula with a = 2, b = -7, c = 3, giving x = (7 ± 5)/4.

2For the quadratic 3x^2 - 4x + 2 = 0, what does the discriminant tell you about the roots?

A.Two distinct real roots

B.One repeated real root

C.No real roots (two complex roots)

D.Exactly one real root and one complex root

Explanation: The discriminant is b^2 - 4ac = (-4)^2 - 4(3)(2) = 16 - 24 = -8. A negative discriminant means there are no real roots; the two roots are complex conjugates.

3Simplify (x^2 - 9)/(x^2 - x - 6) for x not equal to 3 or -2.

A.(x - 3)/(x - 2)

B.(x + 3)/(x + 2)

C.(x - 3)/(x + 2)

D.(x + 3)/(x - 2)

Explanation: Factorise numerator and denominator: (x^2 - 9) = (x - 3)(x + 3) and (x^2 - x - 6) = (x - 3)(x + 2). Cancelling the common factor (x - 3) leaves (x + 3)/(x + 2).

4Solve the inequality x^2 - 5x + 6 < 0.

A.x < 2 or x > 3

B.2 < x < 3

C.x < -3 or x > -2

D.-3 < x < -2

Explanation: Factorise: (x - 2)(x - 3) < 0. The product is negative between the roots, so the solution is 2 < x < 3. The parabola opens upward and dips below zero between its roots.

5Simplify (2 + 3i)(4 - i), where i^2 = -1.

A.11 + 10i

B.8 - 3i

C.5 + 14i

D.11 - 10i

Explanation: Expand: (2 + 3i)(4 - i) = 8 - 2i + 12i - 3i^2 = 8 + 10i - 3(-1) = 8 + 3 + 10i = 11 + 10i.

6What is the modulus of the complex number z = 5 - 12i?

A.7

B.13

C.17

D.169

Explanation: The modulus is |z| = sqrt(a^2 + b^2) = sqrt(5^2 + (-12)^2) = sqrt(25 + 144) = sqrt(169) = 13.

7Using De Moivre's theorem, evaluate (cos 30 degrees + i sin 30 degrees)^3.

A.cos 90 degrees + i sin 90 degrees

B.cos 10 degrees + i sin 10 degrees

C.cos 33 degrees + i sin 33 degrees

D.3 cos 30 degrees + 3i sin 30 degrees

Explanation: De Moivre's theorem gives (cos theta + i sin theta)^n = cos(n theta) + i sin(n theta). With theta = 30 degrees and n = 3, the result is cos 90 degrees + i sin 90 degrees, which equals i.

8Solve the simultaneous equations 2x + y = 7 and x - y = 2.

A.x = 3, y = 1

B.x = 1, y = 5

C.x = 2, y = 3

D.x = 4, y = -1

Explanation: Adding the equations: (2x + y) + (x - y) = 7 + 2 gives 3x = 9, so x = 3. Substituting into x - y = 2 gives 3 - y = 2, so y = 1.

9Simplify the surd expression sqrt(50) + sqrt(8).

A.7 sqrt(2)

B.sqrt(58)

C.10 sqrt(2)

D.5 sqrt(10)

Explanation: sqrt(50) = sqrt(25 x 2) = 5 sqrt(2) and sqrt(8) = sqrt(4 x 2) = 2 sqrt(2). Adding gives 5 sqrt(2) + 2 sqrt(2) = 7 sqrt(2).

10If log_2(x) = 5, what is the value of x?

A.10

B.25

C.32

D.7

Explanation: By the definition of a logarithm, log_2(x) = 5 means 2^5 = x. Since 2^5 = 32, x = 32.

About the LC Higher Maths Practice Questions

Verified exam format metadata for Leaving Certificate Higher Level Mathematics is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.