Grade 10 Maths · Algebra · Paper 1

Algebraic Expressions Grade 10

Real Algebraic Expressions 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: 31 past paper questions
skills: 11 skills
videos: 11 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.

Algebraic Expressions skills

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More Algebraic Expressions Grade 10 questions and answers

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4. Question 2.1.1 · June 2025 · Paper 1 · Provincial · 2 marks
2.1 Simplify the following expressions fully:
2.1.1 $4 p (2 - 5 x)$ (2)
Show the memo (1 tick)Memo
1. ✓
  Multiply the term outside the bracket with each term inside $8 p - 20 p x$
  2 marks · Multiply out a single bracket
5. Question 4.1.4 · June 2025 · Paper 1 · Provincial · 2 marks
4.1 Given: $f (x) = - x^{2} + 4$
4.1.4 Describe the transformation from $f$ to $h$ in words if $h (x) = - (x - 1) (x + 1)$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Expand the equation for h(x) $h (x) = - (x^{2} - 1)$
  $h (x) = - x^{2} + 1$
  1 mark · Multiply two binomials
2. ✓
  Describe the shiftThe graph of $f$ is shifted vertically down by $3$ units.
  1 mark · Shift a graph
6. Question 1.1.2 · November 2024 · Paper 1 · Provincial · 2 marks
1.1 Factorise the following expressions completely. Leave your answers in simplest form:
1.1.2 $a (6 a + 2 b) - 3 (3 a + b)$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Take out common factor in first term $2 a (3 a + b) - 3 (3 a + b)$
  1 mark · Take out a common factor
2. ✓
  Factorise by grouping $(3 a + b) (2 a - 3)$
  1 mark · Take out a common factor
7. Question 2.2 · November 2024 · Paper 1 · Provincial · 4 marks
2.2 How much must be added to $(x + 5) (x - 5)$ so that it will be equal to $(x + 1) (x - 25)$ ?(4)
Show the memo (3 ticks)Memo
1. ✓
  Expand first expression $(x + 5) (x - 5) = x^{2} - 25$
  1 mark · Multiply two binomials
2. ✓
  Expand second expression $(x + 1) (x - 25) = x^{2} - 24 x - 25$
  1 mark · Multiply two binomials
3. ✓
  Determine the differenceDifference is $- 24 x$
  2 marks · Collect like terms
8. Question 1.4.1 · March 2024 · Provincial · 2 marks
1.4 Factorise the following expressions fully:
1.4.1 $x^{3} - 8$ (2)
Show the memo (1 tick)Memo
1. ✓
  Apply difference of cubes $(x - 2) (x^{2} + 2 x + 4)$
  2 marks · Factorise sum or difference of cubes
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 1.5 · March 2022 · Provincial · 2 marks
Four options are provided as possible answers to the following questions. Choose the correct option.
1.5 If $(a^{3} + 27) = (a + 3) (a^{2} + ma + 9)$ , then $m$ equals:(2)
1. A -9
2. B -3
3. C 9
4. D 3
Show the memo (1 tick)Memo
1. ✓
  Sum of cubes $a^{3} + 27 = (a + 3) (a^{2} - 3 a + 9)$
  Therefore $m = - 3$
  Answer: B
  2 marks · Factorise sum or difference of cubes

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 Products : Monomial on outsideKevinmathscience

Gr 9 Products : BinomialsKevinmathscience

Gr 9 Factorisation: Common FactorKevinmathscience

Gr 9 Factorisation: Difference of Squares IntroductionKevinmathscience

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