Grade 11 Maths · Algebra · Paper 1

Completing the Square Grade 11

Real Completing the Square 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: 6 past paper questions
skill: 1 skill
videos: 1 videos

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Question 6.1 · November 2025 · Paper 1 · Provincial · 3 marks

The graphs of

f (x) = - x^{2} - 6 x

and

g (x) = a x^{2} + b x

are drawn below.

g

is the reflection of

f

along the

x

-axis. A and B

(- 5; n)

are symmetrical on

f

along

x = - p

, i.e. the axes of symmetry. $Diagram for this question$

6.1 Write down the equation of

f

in the turning point form, i.e.

y = a (x + p)^{2} + q

(3)

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

Completing the Square skills

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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).8 past paper questions · 3 videos

More Completing the Square Grade 11 questions and answers

Try each one on paper before you open the memo.

4. 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
5. Question WE7 · Siyavula Grade 11 Mathematics, 2.2 Completing the square, Worked example 7 · 5 marks
WE7 Solve by completing the square: $2 x^{2} - 6 x - 10 = 0$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Coefficient of x squared equal to 1Divide the entire equation by $2$ :
  $x^{2} - 3 x - 5 = 0$
  1 mark · Complete the square
2. ✓
  Add and subtract the square $(\frac{- 3}{2})^{2} = \frac{9}{4}$
  $(x^{2} - 3 x + \frac{9}{4}) - \frac{9}{4} - 5 = 0$
  1 mark · Complete the square
3. ✓
  Perfect square $(x - \frac{3}{2})^{2} - \frac{9}{4} - \frac{20}{4} = 0$
  $(x - \frac{3}{2})^{2} - \frac{29}{4} = 0$
  1 mark · Complete the square
4. ✓
  Difference of two squares $(x - \frac{3}{2})^{2} - (\frac{29}{4})^{2} = 0$
  $(x - \frac{3}{2} - \frac{29}{2}) (x - \frac{3}{2} + \frac{29}{2}) = 0$
  1 mark · Factorise a difference of squares
5. ✓
  Answer $x = \frac{3}{2} + \frac{29}{2}$ or $x = \frac{3}{2} - \frac{29}{2}$ , that is $x = \frac{3 \pm 29}{2}$
  1 mark · Solve a quadratic by factorising
6. Question WE2 · Siyavula Grade 11 Mathematics, 5.1 Quadratic functions, Worked example 2 · 3 marks
WE2 Determine the turning point of $g (x) = 3 x^{2} - 6 x - 1$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Take out the coefficient $g (x) = 3 (x^{2} - 2 x) - 1$
  1 mark · Complete the square
2. ✓
  Completed square $g (x) = 3 ((x - 1)^{2} - 1) - 1 = 3 (x - 1)^{2} - 3 - 1 = 3 (x - 1)^{2} - 4$
  1 mark · Complete the square
3. ✓
  Turning pointFrom $g (x) = 3 (x - 1)^{2} - 4$ the turning point is $(1; - 4)$ .
  1 mark · Find turning point of a parabola

Completing the Square Grade 11 videos

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

Parabola Equation In Turning Point Form | Part 2 | Grade 11 FunctionsKevinmathscience

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