Grade 11 Maths · Algebra · Paper 1

Quadratic Formula Grade 11

Real Quadratic Formula past paper questions and answers from 2018 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: 14 past paper questions
skills: 4 skills
videos: 4 videos

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Question 6.5 · November 2024 · Paper 1 · Provincial · 5 marks

Sketched below is the graph of

f (x) = x^{2} - 4 x - 5

for

x \in (- \infty; 6]

.

A and B are the

x

-intercepts and C the

y

-intercept of

f

. $Diagram for this question$

6.5 Suppose

h

is a tangent, to the curve

f

at a certain point, with a gradient of

- 2

. Calculate the

y

-intercept of

h

.(5)

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

Quadratic Formula skills

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

More Quadratic Formula Grade 11 questions and answers

Try each one on paper before you open the memo.

4. 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
5. Question 2.2.2 · March 2025 · Provincial · 2 marks
Solve for x:
2.2 Given: $3 x^{2} - 5 x - 17 = 0$
2.2.2 Use the quadratic formula to calculate the value(s) of x. (Correct to TWO decimal places).(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution $x = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 ( 3 ) ( - 17 )}{2 ( 3 )}$
  1 mark · Use the quadratic formula
2. ✓
  Final answers $x = 3, 36$ or $x = - 1, 69$
  1 mark · Use the quadratic formula
6. Question 1.1.2 · November 2025 · Paper 1 · Provincial · 4 marks
1.1 Solve for $x$ :
1.1.2 $4 x^{2} = 9 - 3 x$ (correct to TWO decimal places)(4)
Show the memo (4 ticks)Memo
1. ✓
  Standard form $4 x^{2} + 3 x - 9 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Substitution into the formula $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$
  $x = \frac{- 3 \pm ( 3 ) ^{2} - 4 ( 4 ) ( - 9 )}{2 ( 4 )}$
  1 mark · Use the quadratic formula
3. ✓
  First root $x = \frac{- 3 \pm 153}{8}$
  $x = 1, 17$
  1 mark · Use the quadratic formula
4. ✓
  Second root $x = - 1, 92$
  1 mark · Use the quadratic formula
7. Question 1.1.2 · November 2024 · Paper 1 · Provincial · 4 marks
1.1 Solve for $x$ :
1.1.2 $2 x^{2} - 3 x = 7$ (answers correct to TWO decimal places)(4)
Show the memo (4 ticks)Memo
1. ✓
  Standard form $2 x^{2} - 3 x - 7 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Substitution $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$
  $x = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 ( 2 ) ( - 7 )}{2 ( 2 )}$
  1 mark · Use the quadratic formula
3. ✓
  First $x$ -value $x = 2, 77$
  1 mark · Use the quadratic formula
4. ✓
  Second $x$ -value $x = - 1, 27$
  1 mark · Use the quadratic formula
8. Question 1.1.2 · November 2023 · Paper 1 · Provincial · 4 marks
1.1 Solve for $x$ in the following:
1.1.2 $x (3 x + 1) = 5$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Standard form $x (3 x + 1) = 5$
  $3 x^{2} + x - 5 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Substitution $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$
  $= \frac{- 1 \pm 1 ^{2} - 4 ( 3 ) ( - 5 )}{2 ( 3 )}$
  $= \frac{- 1 \pm 61}{6}$
  1 mark · Use the quadratic formula
3. ✓
  First answer $x = 1, 14$
  1 mark · Use the quadratic formula
4. ✓
  Second answer $x = - 1, 47$
  1 mark · Use the quadratic formula
9. Question 1.1.1 · March 2019 · Provincial · 3 marks
1.1 Solve for x:
1.1.1 $7 x^{2} - 2 x - 3 = 0$ (correct to TWO decimal places)(3)
Show the memo (2 ticks)Memo
1. ✓
  Quadratic formula substitution $x = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 ( 7 ) ( - 3 )}{2 ( 7 )}$
  1 mark · Use the quadratic formula
2. ✓
  Final answers $x = - 0, 53$ or $x = 0, 81$
  2 marks · Use the quadratic formula
10. Question 1.1.1 · March 2018 · Provincial · 4 marks
1.1 Solve for x in each of the following:
1.1.1 $3 x^{2} + 10 x - 5 = 0$ (correct to TWO decimal places)(4)
Show the memo (2 ticks)Memo
1. ✓
  Substitute into quadratic formula $x = \frac{- 10 \pm 1 0 ^{2} - 4 ( 3 ) ( - 5 )}{2 ( 3 )}$
  1 mark · Use the quadratic formula
2. ✓
  Calculate final values $x = 0, 44$ or $x = - 3, 77$
  3 marks · Use the quadratic formula

Quadratic Formula Grade 11 videos

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

1) Quadratic formula grade 11 | IntroKevinmathscience

The Nature of Roots of a Quadratic Equation Grade 11 MathsMiss Martins Maths and Science

How to find the discriminant and label the solutions of a quadraticBrian McLogan

Nature of the roots Grade11: L2 Find a value for kOnline Maths by Miss Pythagoras

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