Grade 10 Maths · Algebra · Paper 1

Linear Equations Grade 10

Real Linear Equations past paper questions and answers from 2015 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: 12 past paper questions
skills: 2 skills
videos: 2 videos

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Question 2.3 · March 2019 · Provincial · 5 marks

Determine, without the use of a calculator, the value of

x

in each of the following:

2.3

\frac{4 x ^{2} - 3 x - 1}{4 x + 1} + \frac{x ^{3} + 1}{x ^{2} - x + 1} = 2

(5)

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

Linear Equations skills

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

More Linear Equations Grade 10 questions and answers

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4. Question 3.1.2 · June 2024 · Paper 1 · Provincial · 4 marks
3.1 Solve for x:
3.1.2 $\frac{7}{3 - x} = \frac{5}{x + 3} + \frac{4}{x ^{2} - 9}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Factorise denominators and adjust signs $\frac{- 7}{x - 3} = \frac{5}{x + 3} + \frac{4}{( x - 3 ) ( x + 3 )}$
  2 marks · Factorise a difference of squares
2. ✓
  Multiply by LCD and solve linear equation $- 7 (x + 3) = 5 (x - 3) + 4$
  $- 7 x - 21 = 5 x - 15 + 4$
  $- 12 x = 10$
  1 mark · Clear fractions in an equation
3. ✓
  Final answer $x = - \frac{10}{12}$
  $x = - \frac{5}{6}$
  1 mark · Clear fractions in an equation
5. Question 3.1.1 · March 2022 · Provincial · 4 marks
3.1 Solve for x in each of the following equations:
3.1.1 $\frac{3}{x + 2} + \frac{5}{x - 4} = 2$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Multiply by LCD $3 (x - 4) + 5 (x + 2) = 2 (x + 2) (x - 4)$
  1 mark · Clear fractions in an equation
2. ✓
  Expand and simplify $3 x - 12 + 5 x + 10 = 2 (x^{2} - 2 x - 8)$
  $8 x - 2 = 2 x^{2} - 4 x - 16$
  $2 x^{2} - 12 x - 14 = 0$
  1 mark · Write a quadratic in standard form
3. ✓
  Factorise $2 (x - 7) (x + 1) = 0$
  1 mark · Factorise a trinomial
4. ✓
  Solve $x = 7$ or $x = - 1$
  1 mark · Solve a quadratic by factorising
6. Question 2.1.1 · March 2021 · Provincial · 2 marks
2.1 Solve for x in each of the following equations:
2.1.1 $1 - 5 x = 6$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Simplification $- 5 x = 5$
  1 mark · Solve a linear equation
2. ✓
  Solve $x = - 1$
  1 mark · Solve a linear equation
7. Question 3.1.2 · March 2021 · Provincial · 2 marks
3.1 Simplify the following expression:
3.1.2 Hence, determine the value of x if: $\frac{x - 2}{3} - \frac{x + 4}{6} = 2$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute the answer from 3.1.1 $\frac{x - 8}{6} = 2$
  1 mark · Substitute into a formula
2. ✓
  Answer $x - 8 = 12 ⟹ x = 20$
  1 mark · Clear fractions in an equation
8. Question 2.1.1 · March 2020 · Provincial · 2 marks
2.1 Solve for x:
2.1.1 $x (2 x - 5) = 0$ (2)
Show the memo (1 tick)Memo
1. ✓
  Identify roots $x = 0$ or $x = \frac{5}{2}$
  2 marks · Solve a quadratic by factorising
9. Question 2.1.2 · March 2017 · Provincial · 3 marks
2.1 Solve for x:
2.1.2 $(x + 2) (x - 3) = x (x + 1)$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Expand brackets $x^{2} - x - 6 = x^{2} + x$
  1 mark · Multiply two binomials
2. ✓
  Simplification $- 2 x = 6$
  1 mark · Solve a linear equation
3. ✓
  Final answer $x = - 3$
  1 mark · Solve a linear equation
10. Question 3.1.3.1 · March 2018 · Provincial · 1 mark
3.1 Solve for $x$ :
3.1.3 $(x - 1) (y + 3) = 0$
3.1.3.1 if $y = - 3$ (1)
Show the memo (1 tick)Memo
1. ✓
  Analyze solutionIf $y = - 3$ , then $y + 3 = 0$ . The equation becomes $(x - 1) (0) = 0$ , which is true for all $x$ .
  Answer: $x \in R$
  1 mark · Solve a quadratic by factorising

Linear Equations Grade 10 videos

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

Linear Equations Grade 9: IntroductionKevinmathscience

Equations With Fractions Grade 9: IntroductionKevinmathscience

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