Grade 11 Maths · Algebra · Paper 1

Inequalities Grade 11

Real Inequalities past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 24 past paper questions
skill: 1 skill
videos: 1 videos

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Question 2.3 · March 2025 · Provincial · 4 marks

Solve for x:

2.3

x^{2} + 4 x \leq 5

(4)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Inequalities skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

Solve a quadratic inequalitySolve a quadratic inequality by finding the critical values and choosing the right interval (for example x² − 4 < 0 gives −2 < x < 2).28 past paper questions · 3 videos

More Inequalities Grade 11 questions and answers

Try each one on paper before you open the memo.

4. Question 1.1.3 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for x:
1.1.3 $(x - 1)^{2} - 9 \geq 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Simplify to standard quadratic form $x^{2} - 2 x - 8 \geq 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Critical values $(x - 4) (x + 2) \geq 0$
  $x = 4$ or $x = - 2$
  1 mark · Solve a quadratic by factorising
3. ✓
  Solution of the inequality $x \leq - 2$ or $x \geq 4$
  2 marks · Solve a quadratic inequality
5. Question 1.1.3 · March 2025 · Provincial · 4 marks
1.1 Solve for $x$ :
1.1.3 $2 x^{2} + x - 3 \geq 0$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Correct factors $(2 x + 3) (x - 1) \geq 0$
  1 mark · Factorise trinomials with a leading coefficient
2. ✓
  Critical values $x = - \frac{3}{2}$ or $x = 1$
  1 mark · Solve a quadratic by factorising
3. ✓
  Answer: lower interval $x \leq - \frac{3}{2}$
  1 mark · Solve a quadratic inequality
4. ✓
  Answer: upper intervalor $x \geq 1$
  1 mark · Solve a quadratic inequality
6. Question 1.1.3 · March 2025 · Paper 1 · Provincial · 4 marks
1.1 Solve for $x$ :
1.1.3 $x (x - 1) \geq 6$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Write in standard form $x^{2} - x - 6 \geq 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Critical values $(x - 3) (x + 2) \geq 0$
  Critical values: $- 2$ and $3$
  1 mark · Solve a quadratic by factorising
3. ✓
  Answer: lower interval $x \leq - 2$
  1 mark · Solve a quadratic inequality
4. ✓
  Answer: upper intervalor $x \geq 3$
  1 mark · Solve a quadratic inequality
7. Question 1.1.3 · November 2025 · Paper 1 · Provincial · 4 marks
1.1 Solve for $x$ :
1.1.3 $x (x - 4) + 2 (4 - x) > 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Rewrite $2 (4 - x)$ as $- 2 (x - 4)$ $x (x - 4) + 2 (4 - x) > 0$
  $x (x - 4) - 2 (x - 4) > 0$
  1 mark · Take out a common factor
2. ✓
  Critical values $(x - 4) (x - 2) > 0$
  Critical values: $x = 4$ or $x = 2$
  1 mark · Solve a quadratic by factorising
3. ✓
  Solution interval $x < 2$ or $x > 4$
  2 marks · Solve a quadratic inequality
8. Question 1.3.2 · June 2024 · Paper 1 · Provincial · 4 marks
1.3 Solve for $x$ :
1.3.2 $x^{2} + 4 > 3 x + 2$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Standard form $x^{2} - 3 x + 2 > 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Factorise $(x - 2) (x - 1) > 0$
  1 mark · Factorise a trinomial
3. ✓
  Determine critical valuesCritical values: 1 and 2
  1 mark · Solve a quadratic by factorising
4. ✓
  Solve inequality $x < 1$ or $x > 2$
  OR
  $x \in (- \infty; 1) \cup (2; \infty)$
  1 mark · Solve a quadratic inequality
9. Question 1.2.1 · March 2024 · Paper 1 · Provincial · 3 marks
1.2 Given: $x^{2} - x - 20 < 0$
1.2.1 Solve for $x$ if $x^{2} - x - 20 < 0$ .(3)
Show the memo (2 ticks)Memo
1. ✓
  Determine critical values (factors) $(x + 4) (x - 5) < 0$
  Critical values: $- 4$ and $5$
  1 mark · Solve a quadratic by factorising
2. ✓
  Determine solution range $- 4 < x < 5$
  OR
  $x \in (- 4; 5)$
  2 marks · Solve a quadratic inequality
10. Question 1.1.3 · November 2024 · Paper 1 · Provincial · 3 marks
1.1 Solve for $x$ :
1.1.3 $(x + 1) (4 - x) > 0$ ; where $x \in N$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Critical values $(x + 1) (4 - x) > 0$
  $(x + 1) (x - 4) < 0$
  critical values: $x = - 1$ or $x = 4$
  1 mark · Solve a quadratic by factorising
2. ✓
  Interval $- 1 < x < 4$ , but $x \in N$
  1 mark · Solve a quadratic inequality
3. ✓
  Natural numbers in the interval $∴ x \in {1; 2; 3}$
  1 mark · Write or draw a solution set

Inequalities Grade 11 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

2) Quadratic inequalities grade 11 | IntroKevinmathscience

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