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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Inequalities

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

HL Asked on 2 of the last 5 Higher Level papers, most recently in 2024.

OL Asked on 1 of the last 5 Ordinary Level papers, most recently in 2022.

Inequalities, Higher Level(8 marks)

Quick ones on Inequalities.

(a)Solve 3x − 4 < 11.
  1. x > 5
  2. x < 5
  3. x < 7/3
(b)Solve −2x + 3 ≤ 9.
  1. x ≥ 3
  2. x ≤ −3
  3. x ≥ −3
(c)Which of these integers is NOT a solution of 4x − 1 > 2x + 5?
  1. 3
  2. 10
  3. 4
Show the answers

(a) x < 5

(b) x ≥ −3

(c) 3

Your turn: Higher Level questions on Inequalities.

Higher Level

Asked on 2 of the last 5 Higher Level papers, most recently in 2024.

Every paper, year by year

YearWhere it came up
2026Not asked
2025Not asked
2024Q11
2023Q1
2022Not asked

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

More Inequalities questions

Inequalities, 2 marks

The graphs of f(x) and g(x) are drawn on the same axes. Where is f(x) < g(x)?

  1. Where f is above g
  2. Only where they cross
  3. Where f is below g
Show the answer

Where f is below g

f(x) < g(x) means the graph of f is lower than the graph of g. Read off the x-values where f lies under g; the crossing points mark the ends of that range.

Ordinary Level

Asked on 1 of the last 5 Ordinary Level papers, most recently in 2022.

Every paper, year by year

YearWhere it came up
2026Not asked
2025Not asked
2024Not asked
2023Not asked
2022Q8

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

More Inequalities questions

Inequalities, 2 marks

Solve the inequality 2x + 1 < 9.

  1. x < 5
  2. x > 4
  3. x < 4
Show the answer

x < 4

Treat it like an equation: take 1 from both sides, 2x < 8, then divide by 2: x < 4. The sign stays the same.

Inequalities, 3 marks

Which integers satisfy −2 < x ≤ 1?

  1. −2, −1, 0, 1
  2. −1, 0, 1
  3. −2, −1, 0
Show the answer

−1, 0, 1

−2 < x means −2 itself is NOT included. x ≤ 1 means 1 IS included. So the integers are −1, 0 and 1.

Inequalities, 3 marks

How is x ≥ 3, x ∈ ℝ, shown on a number line?

  1. Filled dot at 3, line to the right
  2. Filled dot at 3, line to the left
  3. Separate dots at 3, 4, 5, 6 and so on
Show the answer

Filled dot at 3, line to the right

x ∈ ℝ includes every real number, not just whole numbers, so draw an unbroken line. ≥ means 3 is included (filled dot) and bigger numbers are to the right.

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