Inequalities (Copy)
IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Inequalities (Representation, Interpretation, and Number Lines)
Includes Full Worked Solutions
Paper 1 – Non-Calculator Section
Q1.
Write an inequality for:
“x is greater than –2 but less than or equal to 3”
Solution:
–2 < x ⩽ 3
Answer: –2 < x ⩽ 3
Q2.
Solve the inequality and represent it on a number line:
3x + 2 < 11
Solution:
3x < 11 – 2 → 3x < 9 → x < 3
Number Line Representation:
- Open circle at 3
- Arrow to the left from 3
Answer: x < 3
Q3.
Write the inequality shown on the number line:
●——————⭘
–4 1
Solution:
Closed circle at –4 → x ⩾ –4
Open circle at 1 → x < 1
Answer: –4 ⩽ x < 1
Q4.
Solve the inequality:
–2x + 5 ⩾ 1
Solution:
–2x ⩾ 1 – 5
–2x ⩾ –4
Now divide by –2 (flip sign):
x ⩽ 2
Answer: x ⩽ 2
Q5.
Which value satisfies the inequality:
2 < x ⩽ 6
A) 2 B) 6 C) 7 D) 1
Solution:
x must be greater than 2 and less than or equal to 6
- A) 2 → ❌ not greater than
- B) 6 → ✅
- C) 7 → ❌
- D) 1 → ❌
Answer: B) 6
Paper 2 – Calculator Allowed Section
Q6.
Solve and represent on number line:
4x – 1 ⩾ 11
Solution:
4x ⩾ 12 → x ⩾ 3
Number Line Representation:
- Closed circle at 3
- Arrow to the right from 3
Answer: x ⩾ 3
Q7.
A number x is at least –5 and less than 2.
Write an inequality and draw on a number line.
Solution:
–5 ⩽ x < 2
- Closed circle at –5
- Open circle at 2
- Line between
Answer: –5 ⩽ x < 2
Q8.
Solve:
6 – 2x < 4
Solution:
–2x < 4 – 6 → –2x < –2
Divide by –2 (flip sign):
x > 1
Answer: x > 1
Q9.
The diagram shows a number line with a single open circle at 0 and an arrow going to the left.
Write the inequality.
Solution:
Open circle = < or >
Arrow to the left = less than
Answer: x < 0
Q10.
Solve and write your answer as an inequality:
x/3 – 4 ⩽ 2
Solution:
x/3 ⩽ 6 → Multiply both sides by 3:
x ⩽ 18
Answer: x ⩽ 18
This exam covers all CORE-level outcomes for inequality understanding, solving, and number line interpretation.