Grade 11 Maths · Algebra · Paper 1

Quadratic Equations Grade 11

Real Quadratic Equations 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: 95 past paper questions
skills: 8 skills
videos: 8 videos

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Question 2.1 · March 2025 · Provincial · 2 marks

Solve for x:

2.1

(x - \frac{1}{2}) (x + 2) = 0

(2)

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

Quadratic Equations skills

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More Quadratic Equations Grade 11 questions and answers

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4. Question 1.1.1 · May/June 2025 · Paper 1 · National (DBE) · 3 marks
1.1 Solve for $x$ :
1.1.1 $x^{2} - 3 x - 10 = 0$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Factorise the quadratic equation $(x + 2) (x - 5) = 0$
  1 mark · Factorise a trinomial
2. ✓
  Solve for x $x = - 2$ or $x = 5$
  2 marks · Solve a quadratic by factorising
5. Question 1.1.1 · May/June 2024 · Paper 1 · National (DBE) · 2 marks
1.1 Solve for x:
1.1.1 $3 x^{2} + 5 x = 0$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Factorize the quadratic expression $x (3 x + 5) = 0$
  1 mark · Take out a common factor
2. ✓
  State both final solutions $x = 0$ or $x = - \frac{5}{3}$
  1 mark · Solve a quadratic by factorising
6. Question 1.1.1 · March 2025 · Provincial · 3 marks
1.1 Solve for $x$ :
1.1.1 $x^{2} - 3 x - 28 = 0$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Factorise the trinomial $(x + 4) (x - 7) = 0$
  1 mark · Factorise a trinomial
2. ✓
  First answer $x = - 4$
  1 mark · Solve a quadratic by factorising
3. ✓
  Second answer $x = 7$
  1 mark · Solve a quadratic by factorising
7. Question 1.1.1 · March 2025 · Paper 1 · Provincial · 3 marks
1.1 Solve for $x$ :
1.1.1 $x^{2} - 2 x = 8$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Write in standard form $x^{2} - 2 x - 8 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Factorise the trinomial $(x + 2) (x - 4) = 0$
  1 mark · Factorise a trinomial
3. ✓
  Solve for x $x = - 2$ or $x = 4$
  1 mark · Solve a quadratic by factorising
8. Question 1.1.1 · November 2025 · Paper 1 · Provincial · 2 marks
1.1 Solve for $x$ :
1.1.1 $x (2 x + 6) = 0$ (2)
Show the memo (2 ticks)Memo
1. ✓
  First root $x = 0$ or $2 x + 6 = 0$
  $x = 0$
  1 mark · Solve a quadratic by factorising
2. ✓
  Second root $x = - 3$
  1 mark · Solve a quadratic by factorising
9. Question 2.2.2 · November 2025 · Paper 1 · Provincial · 4 marks
2.2 Solve for $x$ :
2.2.2 $x^{\frac{1}{2}} - 3 x^{\frac{1}{4}} + 2 = 0$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Write as a quadratic in $x^{\frac{1}{4}}$ $(x^{\frac{1}{4}})^{2} - 3 x^{\frac{1}{4}} + 2 = 0$
  Let $k = x^{\frac{1}{4}}$ : $k^{2} - 3 k + 2 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Factors $(k - 2) (k - 1) = 0$
  OR $(x^{\frac{1}{4}} - 2) (x^{\frac{1}{4}} - 1) = 0$
  1 mark · Factorise a trinomial
3. ✓
  Roots in terms of $x^{\frac{1}{4}}$ $x^{\frac{1}{4}} = 2$ or $x^{\frac{1}{4}} = 1$
  1 mark · Solve a quadratic by factorising
4. ✓
  Answers $x = 16$ or $x = 1$
  1 mark · Solve an equation with rational exponents
10. Question 4.2.1 · November 2025 · Paper 2 · Provincial · 2 marks
4.2 Given: $8 cos^{2} α - 2 = 0$
4.2.1 Determine the value of $cos α$ where $cos α > 0$ and $0° < α < 180°$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Simplification $8 cos^{2} α = 2$
  $cos^{2} α = \frac{1}{4}$
  1 mark · Solve a linear equation
2. ✓
  Answer $cos α = \frac{1}{2}$
  1 mark · Solve a quadratic by factorising

Quadratic Equations Grade 11 videos

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

Equations With Fractions Grade 9: IntroductionKevinmathscience

Area of Rectangle Given - Find the Length and Width - Solving Quadraticsmathtipxyz

Quadratic Equations Grade 10Kevinmathscience

1) Quadratic formula grade 11 | IntroKevinmathscience

The Nature of Roots of a Quadratic Equation Grade 11 MathsMiss Martins Maths and Science

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