Grade 11 Maths · Algebra

Solve a quadratic inequality

Solve a quadratic inequality by finding the critical values and choosing the right interval (for example x² − 4 < 0 gives −2 < x < 2).

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2) Quadratic inequalities grade 11 | IntroKevinmathscience

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Quadratic Inequalities Grade 11 and 12 Maths: Part 1Miss Martins Maths and Science

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Question 1.1.4 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

1.1 Solve for

x

1.1.4

(x - 8) (x + 2) \leq 0

(3)

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More past paper questions: solve a quadratic inequality

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3. Question 1.1.3 · November 2024 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for $x$ :
1.1.3 $x^{2} - 2 x - 3 > 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Factorise the inequality $(x - 3) (x + 1) > 0$
  1 mark · Factorise a trinomial
2. ✓
  Identify critical valuesCritical values: $x = 3$ or $x = - 1$
  1 mark · Solve a quadratic by factorising
3. ✓
  Determine the range $x < - 1$ or $x > 3$
  OR
  $x \in (- \infty; - 1) \cup (3; \infty)$
  2 marks · Solve a quadratic inequality
4. 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
5. Question 1.1.3 · November 2023 · Paper 1 · Provincial · 3 marks
1.1 Solve for $x$ in the following:
1.1.3 $2 x^{2} - 5 x + 3 < 0$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Factors $2 x^{2} - 5 x + 3 < 0$
  $(2 x - 3) (x - 1) < 0$
  1 mark · Factorise trinomials with a leading coefficient
2. ✓
  AnswerCritical values $1$ and $1 \frac{1}{2}$ ; the parabola opens upwards, so it is below the $x$ -axis between them.
  $1 < x < 1 \frac{1}{2}$
  2 marks · Solve a quadratic inequality
6. Question 1.1.3 · March 2021 · Paper 1 · Provincial · 3 marks
1.1 Solve for x:
1.1.3 $x^{2} + 8 x + 15 > 0$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Critical values $(x + 5) (x + 3) > 0$
  
  Critical values: $x = - 5$ or $x = - 3$
  1 mark · Solve a quadratic by factorising
2. ✓
  Answer $x < - 5$ or $x > - 3$
  2 marks · Solve a quadratic inequality

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