Ceist Eile

Ceist Eile is in development. Features, questions and prices may change while we refine it.

Subjects · Leaving Cert Maths

Leaving Cert Maths: Algebra

How often Algebra comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker

OL Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker

FL Asked on 4 of the last 7 Foundation Level papers, most recently in 2025.

Algebra, Higher Level(6 marks)

Quick ones on Algebra.

(a)Solve: 3x − 7 = 11
  1. x = 4/3
  2. x = 6
  3. x = 18
(b)Factorise: x² − 9
  1. (x − 9)(x + 1)
  2. (x − 3)²
  3. (x − 3)(x + 3)
(c)Roots of x² − 5x + 6 = 0?
  1. 2 and 3
  2. 1 and 6
  3. −2 and −3
Show the answers

(a) x = 6

(b) (x − 3)(x + 3)

(c) 2 and 3

Your turn: Higher Level questions on Algebra.

Higher Level

Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Paper 1, Q1, Paper 1, Q8, Paper 1, Q9
2025Paper 1, Q1, Paper 1, Q5, Paper 1, Q6
2024Paper 1, Q1, Paper 1, Q6, Paper 1, Q9
2023Paper 1, Q1
2022Paper 1, Q1, Paper 1, Q2, Paper 1, Q5
2021Paper 1, Q2, Paper 1, Q3, Paper 1, Q5, Paper 2, Q5
2019Paper 1, Q1, Paper 1, Q3, Paper 1, Q4, Paper 1, Q6
2018Paper 1, Q1, Paper 1, Q2
2017Paper 1, Q1, Paper 1, Q5
2016Paper 1, Q2, Paper 1, Q5

Links open the State Examinations Commission’s paper for that year.

More Algebra questions

Algebra, 2 marks

Sum of the roots of x² − 7x + 10 = 0?

  1. −7
  2. 10
  3. 7
Show the answer

7

For ax² + bx + c = 0, the sum of the roots is −b/a = 7. Check: the roots are 2 and 5.

Algebra, 2 marks

Product of the roots of 2x² + 3x − 8 = 0?

  1. −1.5
  2. −4
  3. −8
Show the answer

−4

For ax² + bx + c = 0, the product of the roots is c/a = −8/2 = −4.

Algebra, 2 marks

Simplify: (x² − 4)/(x − 2)

  1. x + 2
  2. x − 2
  3. x² − 2
Show the answer

x + 2

Factorise the top: (x − 2)(x + 2). Cancel (x − 2), which is valid when x ≠ 2.

Ordinary Level

Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q2, Q3, Q7, Q8, Q10
2025Q3, Q4, Q5, Q10
2024Q3, Q4, Q5, Q9
2023Q3, Q6, Q7
2022Q2, Q8
2021Q3, Q4
2019Q4, Q6, Q8
2018Q1, Q3, Q6, Q9
2017Q3, Q4, Q9
2016Q1, Q3

Links open the State Examinations Commission’s paper for that year.

More Algebra questions

Algebra, 2 marks

Solve 2x + 7 = 19.

  1. x = 13
  2. x = 12
  3. x = 6
Show the answer

x = 6

Take 7 from both sides: 2x = 12. Then divide by 2: x = 6.

Algebra, 2 marks

Simplify 3(x + 4) + 2x.

  1. 6x + 12
  2. 5x + 12
  3. 5x + 4
Show the answer

5x + 12

3(x + 4) = 3x + 12. Adding 2x gives 3x + 2x + 12 = 5x + 12.

Algebra, 2 marks

Factorise x² + 5x.

  1. x(x + 5)
  2. (x + 5)(x − 5)
  3. x²(1 + 5x)
Show the answer

x(x + 5)

x is common to both terms, so take it outside: x² + 5x = x(x + 5).

Foundation Level

Asked on 4 of the last 7 Foundation Level papers, most recently in 2025.

Every paper, year by year

YearWhere it came up
2026Not asked
2025Q2
2024Q11
2023Not asked
2022Not asked
2021Q8, Q10
2019Q1

Links open the State Examinations Commission’s paper for that year.

More Algebra questions

Algebra, 2 marks

Solve x + 7 = 12.

  1. x = 19
  2. x = 12
  3. x = 5
Show the answer

x = 5

Take 7 from both sides: x = 12 − 7 = 5. Check: 5 + 7 = 12.

Algebra, 2 marks

Find the value of 3a + 2 when a = 4.

  1. 9
  2. 14
  3. 34
Show the answer

14

3a means 3 × a. So 3 × 4 + 2 = 12 + 2 = 14.

Algebra, 2 marks

Solve 2x = 18.

  1. x = 9
  2. x = 16
  3. x = 36
Show the answer

x = 9

2x means 2 × x. Divide both sides by 2: x = 18 ÷ 2 = 9.

Other Maths topics

All of Leaving Cert Maths