Grade 11 Maths · Paper 1

Algebra Grade 11

Real 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: 162 past paper questions
skills: 26 skills
videos: 26 videos

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Question 3.2 · March 2025 · Provincial · 5 marks

3.2 For which value(s) of k will the roots of the equation

2 x^{2} - 5 k x + \frac{25}{2} = 0

be non-real?(5)

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

What's in Algebra Grade 11

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

The Number System5 past paper questions

Exponents and Surds72 past paper questions

Quadratic Equations49 past paper questions

Simultaneous Equations13 past paper questions

Completing the Square1 past paper questions

Complete the squareRewrite a quadratic in the form a(x + p)² + q by adding and subtracting a square (for example x² + 6x + 1 = (x + 3)² − 8).2 past paper questions · 3 videos

The Quadratic Formula6 past paper questions

Inequalities17 past paper questions

Solve a quadratic inequalitySolve a quadratic inequality by finding the critical values and choosing the right interval (for example x² − 4 < 0 gives −2 < x < 2).23 past paper questions · 3 videos

Mathematical Modelling

Set up an expression or equationTurn a word problem or diagram into an equation by choosing a letter for the unknown (for example 'a number plus 5 is 12' gives x + 5 = 12).18 past paper questions · 3 videos

More Algebra Grade 11 questions and answers

Try each one on paper before you open the memo.

1. Question 1.1.3 · March 2025 · Paper 1 · Provincial · 4 marks
1.1 Solve for $x$ :
1.1.3 $x (x - 1) \geq 6$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Write in standard form $x^{2} - x - 6 \geq 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Critical values $(x - 3) (x + 2) \geq 0$
  Critical values: $- 2$ and $3$
  1 mark · Solve a quadratic by factorising
3. ✓
  Answer: lower interval $x \leq - 2$
  1 mark · Solve a quadratic inequality
4. ✓
  Answer: upper intervalor $x \geq 3$
  1 mark · Solve a quadratic inequality
2. Question 1.4.1 · March 2025 · Provincial · 2 marks
1.4 An equation is given: $\frac{1}{2} x^{2} + m x + 18 = 0$
1.4.1 Solve for $x$ in terms of $m$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Correct substitution into the quadratic formula $x = \frac{- m \pm m ^{2} - 4 ( \frac{1}{2} ) ( 18 )}{2 ( \frac{1}{2} )}$
  1 mark · Use the quadratic formula
2. ✓
  Simplified answer $x = - m \pm m^{2} - 36$
  1 mark · Use the quadratic formula
3. Question 1.3.1 · March 2025 · Provincial · 3 marks
1.3 Given the expression: $2 x^{2} + 8 x + 10$
1.3.1 Write the above expression in the form $a (x + p)^{2} + q$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Factorise a $y = 2 (x^{2} + 4 x + 5)$
  1 mark · Complete the square
2. ✓
  Complete the square $y = 2 [(x + 2)^{2} - 4 + 5]$
  1 mark · Complete the square
3. ✓
  Final form $y = 2 (x + 2)^{2} + 2$
  1 mark · Complete the square
4. Question 1.1.1 · June 2024 · Paper 1 · Provincial · 1 mark
1.1 Determine the value(s) of $x$ for which the expression $\frac{x ^{2} + 4}{9 - x}$ :
1.1.1 has real value(s).(1)
Show the memo (1 tick)Memo
1. ✓
  Determine condition for real valuesNumerator $x^{2} + 4$ is always positive.
  For real roots, denominator $> 0$ (cannot be 0 due to division).
  $9 - x > 0$
  $x < 9$
  1 mark · Find undefined or non-real values
5. Question 2.2.2 · March 2025 · Paper 1 · Provincial · 4 marks
2.2 Solve for $x$ , without using a calculator.
2.2.2 $x^{\frac{1}{2}} - 3 x^{\frac{1}{4}} - 10 = 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Factors $(x^{\frac{1}{4}} - 5) (x^{\frac{1}{4}} + 2) = 0$
  2 marks · Factorise a trinomial
2. ✓
  Restriction ( $x^{\frac{1}{4}} \neq = - 2$ ) $x^{\frac{1}{4}} = 5$ or $x^{\frac{1}{4}} = - 2$
  Reject $- 2$ (even root cannot be negative)
  1 mark · Solve an equation with rational exponents
3. ✓
  Solve for x $x = 5^{4}$
  $x = 625$
  1 mark · Solve an equation with rational exponents

Algebra Grade 11 videos

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

1) Number Types gr 10 | IntroKevinmathscience

Undefined and Non-Real expressions Grade 11 MathsMiss Martins Maths and Science

Exponents Grade 8 | All Laws CombinedKevinmathscience

Exponents Grade 10: Change to prime numberKevinmathscience

Exponential Equations grade 10Kevinmathscience

Exponents Grade 10: More than One TermKevinmathscience

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