Grade 10 Maths · Algebra · Paper 1

Quadratic Equations Grade 10

Real Quadratic Equations past paper questions and answers from 2022 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: 19 past paper questions
skills: 4 skills
videos: 4 videos

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Question 5.2 · June 2025 · Paper 1 · Provincial · 6 marks

Given:

f (x) = - x + 1

and

g (x) = \frac{- 2}{x} + 2

, which are not drawn to scale. R and S are points of intersection of the graphs.

DBQ is a line perpendicular to the x-axis with D and B on

g

and

f

respectively. The coordinates of Q are

(- 1; 0)

5.2 Determine the coordinates of R and S.(6)

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

Quadratic Equations skills

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

More Quadratic Equations Grade 10 questions and answers

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4. Question 3.1.1 · June 2025 · Paper 1 · Provincial · 3 marks
3.1 Solve for $x$ if:
3.1.1 $x - 3 = \frac{18}{x}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Write equation in standard form $x (x - 3) = 18$
  $x^{2} - 3 x - 18 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Factorise the quadratic equation $(x + 3) (x - 6) = 0$
  1 mark · Factorise a trinomial
3. ✓
  Solve for x $x = - 3$ or $x = 6$
  1 mark · Solve a quadratic by factorising
5. Question 3.1.1 · June 2024 · Paper 1 · Provincial · 2 marks
3.1 Solve for x:
3.1.1 $3 x^{2} = 2 x$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Standard form and factorise $3 x^{2} - 2 x = 0$
  $x (3 x - 2) = 0$
  1 mark · Take out a common factor
2. ✓
  Solve for x $x = 0$ or $x = \frac{2}{3}$
  1 mark · Solve a quadratic by factorising
6. Question 2.1.3 · November 2024 · Paper 1 · Provincial · 4 marks
2.1 Solve for $x$ :
2.1.3 $2 x^{2} - x - 10 = 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Factorise the quadratic $(2 x - 5) (x + 2) = 0$
  1 mark · Factorise trinomials with a leading coefficient
2. ✓
  Set factors to zero $2 x - 5 = 0$ or $x + 2 = 0$
  1 mark · Solve a quadratic by factorising
3. ✓
  State final solutions $x = \frac{5}{2}$ or $x = - 2$
  2 marks · Solve a quadratic by factorising
7. Question 2.1.1 · March 2024 · Provincial · 2 marks
2.1 Solve for $x$ :
2.1.1 $(x + 3) (x - 1) = 0$ (2)
Show the memo (1 tick)Memo
1. ✓
  Solve for x $x = - 3$ or $x = 1$
  2 marks · Solve a quadratic by factorising
8. Question 2.1.1 · March 2023 · Provincial · 3 marks
2.1 Solve for x:
2.1.1 $x^{2} = 5 x$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Set equation to zero $x^{2} - 5 x = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Factorise $x (x - 5) = 0$
  1 mark · Take out a common factor
3. ✓
  Solve $x = 0$ or $x = 5$
  1 mark · Solve a quadratic by factorising
9. Question 2.1.1 · March 2023 · Provincial · 3 marks
2.1 Solve for x:
2.1.1 $3 x^{2} = 5 x + 12$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Standard form $3 x^{2} - 5 x - 12 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Factorise $(3 x + 4) (x - 3) = 0$
  1 mark · Factorise trinomials with a leading coefficient
3. ✓
  Solve $x = - \frac{4}{3}$ or $x = 3$
  1 mark · Solve a quadratic by factorising
10. Question 3.1.1 · March 2022 · Provincial · 2 marks
3.1 Solve for x:
3.1.1 $(2 x + 1) (x - 3) = 0$ (2)
Show the memo (2 ticks)Memo
1. ✓
  First root $2 x + 1 = 0 \Rightarrow x = - \frac{1}{2}$
  1 mark · Solve a quadratic by factorising
2. ✓
  Second root $x - 3 = 0 \Rightarrow x = 3$
  1 mark · Solve a quadratic by factorising

Quadratic Equations Grade 10 videos

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

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

Quadratic Equations Grade 10Kevinmathscience

8) Factorising trinomials grade 10 | Part 2Kevinmathscience

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