Grade 11 Maths · Algebra · Paper 1

Mathematical Modelling Grade 11

Real Mathematical Modelling past paper questions and answers from 2023 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: 7 past paper questions
skill: 1 skill
videos: 1 videos

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Question 2.3 · November 2025 · Paper 1 · Provincial · 4 marks

2.3 Given: The area of a rectangle is

(1 6^{x} - 100)

^{2}

and the breadth is

(4^{x} + 10)

cm.
Determine the length of the rectangle in terms of

x

.(4)

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

Mathematical Modelling skills

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

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).25 past paper questions · 3 videos

More Mathematical Modelling Grade 11 questions and answers

Try each one on paper before you open the memo.

4. Question 3.2 · November 2024 · Paper 1 · Provincial · 5 marks
In a linear number pattern the first term is $x$ and a common difference is 5 less than the first term.
3.2 Calculate the value of the first term if it is given that the sum of the first three terms of the linear number pattern is 63.(5)
Show the memo (5 ticks)Memo
1. ✓
  $d = x - 5$ $T_{1} = x$
  $d = x - 5$
  1 mark · Set up an expression or equation
2. ✓
  $T_{2}$ and $T_{3}$ Sequence: $x$ ; $x + (x - 5)$ ; $x + 2 (x - 5)$
  1 mark · Find a linear general term
3. ✓
  Equating to 63Equation:
  $x + x + (x - 5) + x + 2 (x - 5) = 63$
  1 mark · Set up an expression or equation
4. ✓
  Simplification $4 x - 5 + 2 x - 10 = 63$
  $6 x = 78$
  1 mark · Collect like terms
5. ✓
  Value of $x$ $x = 13$
  1 mark · Solve a linear equation
5. Question 10 · November 2023 · Paper 1 · Provincial · 4 marks
10 A bag contains $x$ balls of which 5 are red and the rest are green. One ball is taken out of the bag randomly and it is not replaced. A second ball is taken out of the bag. The probability of picking both green balls is $\frac{3}{11}$ . Show that the probability of picking both green balls can be represented by the equation: $4 x^{2} - 59 x + 165 = 0$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  $\frac{x - 5}{x} \times \frac{x - 6}{x - 1}$ Tree diagram (see image): first pick G with $\frac{x - 5}{x}$ ; second pick G with $\frac{x - 6}{x - 1}$ .
  $P (GG) = P (G) \times P (G)$
  $= \frac{x - 5}{x} \times \frac{x - 6}{x - 1}$ $Memo diagram$
  1 mark · Calculate from a tree diagram
2. ✓
  Equating to $\frac{3}{11}$ $\frac{x - 5}{x} \times \frac{x - 6}{x - 1} = \frac{3}{11}$
  1 mark · Set up an expression or equation
3. ✓
  Getting rid of fractions $11 (x - 5) (x - 6) = 3 x (x - 1)$
  1 mark · Clear fractions in an equation
4. ✓
  Standard form $11 (x^{2} - 11 x + 30) = 3 x^{2} - 3 x$
  $11 x^{2} - 121 x + 330 = 3 x^{2} - 3 x$
  $8 x^{2} - 118 x + 330 = 0$
  $4 x^{2} - 59 x + 165 = 0$
  1 mark · Write a quadratic in standard form

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