Grade 10 Maths · Algebra

Write a quadratic in standard form

Expand and rearrange an equation into the form ax² + bx + c = 0 (for example x(x + 3) = 10 becomes x² + 3x − 10 = 0).

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Quadratic Equations Grade 10Kevinmathscience

Grade 10 Quadratic Equations PART 1: Step by Step explanationMiss Martins Maths and Science

Grade 10 Quadratic Equations PART 2: Gr 10 maths equationsMiss Martins Maths and Science

7) K method grade 11 | IntroKevinmathscience

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Question 6.6 · May/June 2024 · Paper 1 · National (DBE) · 5 marks

The graphs of

f (x) = x^{2} - 2 x - 3

and

g (x) = m x + c

are drawn below. D and E are the

x

-intercepts and P is the

y

-intercept of

f

. The turning point of

f

is T

(1; - 4)

. The graphs of

f

and

g

intersect at P and E. Diagram for this question

6.6 Given:

k (x) = g (x) - n

. Determine

n

k

is a tangent to

f

.(5)

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

More past paper questions: write a quadratic in standard form

Work each one out first, then open the memo and check every tick.

3. Question 1.1.5 · May/June 2025 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for $x$ :
1.1.5 $x + 3 x + 2 = 2$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Isolate the surd $3 x + 2 = 2 - x$
  1 mark · Solve a linear equation
2. ✓
  Square both sides $9 (x + 2) = (2 - x)^{2}$
  $9 (x + 2) = 4 - 4 x + x^{2}$
  1 mark · Solve a surd equation
3. ✓
  Write in standard form and factorise $x^{2} - 13 x - 14 = 0$
  $(x - 14) (x + 1) = 0$
  1 mark · Write a quadratic in standard form
4. ✓
  Solve and check for valid solutions $x = 14$ or $x = - 1$
  Check: If $x = 14$ , $14 + 316 = 14 + 12 = 26 \neq = 2$ (Reject)
  If $x = - 1$ , $- 1 + 31 = - 1 + 3 = 2$ (Accept)
  $∴ x \neq = 14$ or $x = - 1$
  1 mark · Check solutions of a surd equation
4. Question 1.1.5 · November 2024 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for $x$ :
1.1.5 $- 2 x + 4 - x = 2$ (4)
Show the memo (5 ticks)Memo
1. ✓
  Isolate the radical $- 2 x + 4 = 2 + x$
  0 marks · Solve a linear equation
2. ✓
  Square both sides $- 2 x + 4 = (2 + x)^{2}$
  $- 2 x + 4 = 4 + 4 x + x^{2}$
  1 mark · Solve a surd equation
3. ✓
  Write in standard form $x^{2} + 6 x = 0$
  1 mark · Write a quadratic in standard form
4. ✓
  Factorise and solve $x (x + 6) = 0$
  $x = 0$ or $x = - 6$
  1 mark · Solve a quadratic by factorising
5. ✓
  Validate and select correct answerCheck $x = 0$ : $4 - 0 = 2$ (Valid)
  Check $x = - 6$ : $16 - (- 6) = 10 \neq = 2$ (Invalid)
  Answer: $x = 0$ (and $x \neq = - 6$ )
  1 mark · Check solutions of a surd equation
5. Question 1.1.3 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for x:
1.1.3 $(x - 1)^{2} - 9 \geq 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Simplify to standard quadratic form $x^{2} - 2 x - 8 \geq 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Critical values $(x - 4) (x + 2) \geq 0$
  $x = 4$ or $x = - 2$
  1 mark · Solve a quadratic by factorising
3. ✓
  Solution of the inequality $x \leq - 2$ or $x \geq 4$
  2 marks · Solve a quadratic inequality
6. Question 3.1.1 · June 2025 · Paper 1 · Provincial · 3 marks
3.1 Solve for $x$ if:
3.1.1 $x - 3 = \frac{18}{x}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Write equation in standard form $x (x - 3) = 18$
  $x^{2} - 3 x - 18 = 0$
  1 mark · Write a quadratic in standard form
2. ✓
  Factorise the quadratic equation $(x + 3) (x - 6) = 0$
  1 mark · Factorise a trinomial
3. ✓
  Solve for x $x = - 3$ or $x = 6$
  1 mark · Solve a quadratic by factorising

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