Grade 10 Maths · Algebra · Paper 1

Simplifying Algebraic Expressions Grade 10

Real Simplifying Algebraic Expressions past paper questions and answers from 2023 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: 79 past paper questions
skills: 9 skills
videos: 9 videos

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Question 1.3 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

1.3 Show that

(1 + x^{m} + x^{- n})^{2} - (1 - x^{m} - x^{- n})^{2}

is divisible by

2

for all real values of

m

and

n

.(3)

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

Simplifying Algebraic Expressions skills

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More Simplifying Algebraic Expressions Grade 10 questions and answers

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4. Question 1.3.1 · March 2025 · Provincial · 2 marks
1.3 Simplify the following fully:
1.3.1 $(x - 2 y) (x^{2} + 2 x y + 4 y^{2})$ (2)
Show the memo (1 tick)Memo
1. ✓
  Expand or apply rule $x^{3} - 8 y^{3}$ (Difference of cubes)
  2 marks · Multiply out larger brackets
5. Question 3.1.1 · March 2025 · Provincial · 2 marks
3.1 Given: $f (x) = \frac{2 x + 3}{- x - 3}$

Given: $f (x) = \frac{2 x + 3}{- x - 3}$
3.1.1 Show that $f (x)$ can also be written as $f (x) = \frac{3}{x + 3} - 2$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Manipulate expression $f (x) = \frac{2 x + 3}{- ( x + 3 )} = \frac{- ( 2 x + 3 )}{x + 3}$
  $= \frac{- ( 2 x + 6 - 3 )}{x + 3} = \frac{- [ 2 ( x + 3 ) - 3 ]}{x + 3}$
  1 mark · Simplify an algebraic fraction
2. ✓
  Separate terms $= \frac{- 2 ( x + 3 )}{x + 3} + \frac{3}{x + 3} = - 2 + \frac{3}{x + 3}$
  1 mark · Simplify an algebraic fraction
6. Question 2.1.1 · June 2024 · Paper 1 · Provincial · 2 marks
2.1 Simplify the following:
2.1.1 $2 b (b - 5 c)^{2}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Square the binomial $= 2 b (b^{2} - 10 b c + 25 c^{2})$
  1 mark · Square a binomial
2. ✓
  Distribute 2b $= 2 b^{3} - 20 b^{2} c + 50 b c^{2}$
  1 mark · Multiply out a single bracket
7. Question 1.2.2 · November 2024 · Paper 1 · Provincial · 4 marks
1.2 Simplify the following expressions completely:
1.2.2 $\frac{x + 3}{x - 3} \times \frac{x ^{3} - 27}{x ^{2} - 9} \div \frac{x ^{2} + 3 x + 9}{x - 3}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Change division to multiplication and invert $\frac{x + 3}{x - 3} \times \frac{x ^{3} - 27}{x ^{2} - 9} \times \frac{x - 3}{x ^{2} + 3 x + 9}$
  1 mark · Simplify an algebraic fraction
2. ✓
  Factorise numerators and denominators $\frac{x + 3}{x - 3} \times \frac{( x - 3 ) ( x ^{2} + 3 x + 9 )}{( x - 3 ) ( x + 3 )} \times \frac{x - 3}{x ^{2} + 3 x + 9}$
  2 marks · Simplify an algebraic fraction
3. ✓
  Cancel common factors to simplify $1$
  1 mark · Simplify an algebraic fraction
8. Question 1.5.1 · March 2024 · Provincial · 2 marks
1.5 Simplify the following expressions fully:
1.5.1 $(2 x - 1) (x^{2} - 2 x + 1)$ (2)
Show the memo (1 tick)Memo
1. ✓
  Distribute and simplify $2 x^{3} - 4 x^{2} + 2 x - x^{2} + 2 x - 1$
  $= 2 x^{3} - 5 x^{2} + 4 x - 1$
  2 marks · Multiply out larger brackets
9. Question 10.2.5 · November 2024 · Paper 2 · Provincial · 3 marks
10.2 In the diagram, PAT is the common tangent of the smaller and larger circles at A. AMB is the diameter of the larger circle with M on the circumference of the smaller circle. ASC and BC are chords of the larger circle and MS chord of the smaller circle. M is the centre of the larger circle.

It is also given that, the length of AM $= p$ units, AS $= (p - 1)$ units and BC $= 6$ units.

Answer the questions that follow. $Diagram for question 10.2$
10.2.5 Calculate the value of $p$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Apply Pyth theorem $p^{2} = (p - 1)^{2} + 3^{2}$ [Pyth. theorem]
  1 mark · Use the theorem of Pythagoras
2. ✓
  Simplification $p^{2} = p^{2} - 2 p + 1 + 9$
  $2 p = 10$
  1 mark · Square a binomial
3. ✓
  Answer $p = 5$
  1 mark · Use the theorem of Pythagoras
10. Question 1.2.1 · March 2023 · Provincial · 2 marks
1.2 Expand the following expressions:
1.2.1 $(a - 2) (a^{2} + 2 a + 4)$ (2)
Show the memo (2 ticks)Memo
1. ✓
  $a^{3}$ $(a - 2) (a^{2} + 2 a + 4) = a^{3} \dots$
  1 mark · Multiply out larger brackets
2. ✓
  $- 8$ $= a^{3} - 8$
  1 mark · Multiply out larger brackets

Simplifying Algebraic Expressions Grade 10 videos

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

Algebra Grade 9: Add and Subtract like termsKevinmathscience

Gr 9 Factorisation: Common FactorKevinmathscience

Gr 9 Factorisation: Difference of Squares IntroductionKevinmathscience

11) Multiply algebraic fractions grade 10 Part 1Kevinmathscience

2) Binomial x trinomial | products grade 10Kevinmathscience

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