Grade 10 Maths · Algebra · Paper 1

Mathematical Modelling Grade 10

Real Mathematical Modelling past paper questions and answers from 2015 to 2024, 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
skills: 2 skills
videos: 2 videos

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Question 2.4 · March 2024 · Provincial · 4 marks

2.4 The difference between two numbers is 5. Six times the smaller number is equal to four times the greater number. Find the numbers.(4)

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Mathematical Modelling skills

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

More Mathematical Modelling Grade 10 questions and answers

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4. Question 4.3 · March 2019 · Provincial · 4 marks
4.3 The mean of three numbers is 25. The second number is four less than twice the first. The third number is two more than four times the first. (Hint: Let the smallest number be $x$ ). Calculate the numerical value of the smallest number.(4)
Show the memo (3 ticks)Memo
1. ✓
  Define variablesFirst number: $x$
  Second number: $2 x - 4$
  Third number: $4 x + 2$
  1 mark · Set up an expression or equation
2. ✓
  Set up equation $\frac{x + ( 2 x - 4 ) + ( 4 x + 2 )}{3} = 25$
  $7 x - 2 = 75$
  2 marks · Calculate the mean
3. ✓
  Solve for x $7 x = 77$
  $x = 11$
  1 mark · Calculate the mean
5. Question 2.5 · March 2016 · Provincial · 4 marks
2.5 The length of a rectangle is 40 cm longer than its breadth. If the area of the rectangle is 1200 cm², calculate the length of the rectangle.(4)
Show the memo (4 ticks)Memo
1. ✓
  Set up equationLet breadth $= x$ , then length $= x + 40$
  $x (x + 40) = 1200$
  1 mark · Set up an expression or equation
2. ✓
  Factorise the left-hand side $x^{2} + 40 x - 1200 = 0$
  $(x + 60) (x - 20) = 0$
  1 mark · Factorise a trinomial
3. ✓
  Both answers and reject $x = - 60$ $x = - 60$ (reject) or $x = 20$
  1 mark · Solve a quadratic by factorising
4. ✓
  Calculate lengthLength $= 20 + 40 = 60$ cm
  1 mark · Solve a quadratic by factorising
6. Question 3.4 · March 2015 · Provincial · 4 marks
3.4 Whilst on holiday, a family of 2 adults and 4 children stay at a hotel for 7 days. The hotel charges R300 less per day for a child than an adult. The bill for the 7-day holiday is R21 000. How much does the hotel charge for an adult? Show all your working details.(4)
Show the memo (4 ticks)Memo
1. ✓
  Set up expressions for daily costAdult cost = $x$
  Child cost = $x - 300$
  1 mark · Set up an expression or equation
2. ✓
  Set up equation for total bill $7 (2 x + 4 (x - 300)) = 21000$ OR $2 x + 4 (x - 300) = 3000$
  1 mark · Set up an expression or equation
3. ✓
  Simplify $2 x + 4 x - 1200 = 3000$
  $6 x = 4200$
  1 mark · Solve a linear equation
4. ✓
  Solve for x $2 x + 4 (x - 300) = 21000$
  $6 x = 22200$
  $x = 3700$
  1 mark · Solve a linear equation

Mathematical Modelling Grade 10 videos

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Translating Words To Algebraic Expressions Explained!The Organic Chemistry Tutor

Area of Rectangle Given - Find the Length and Width - Solving Quadraticsmathtipxyz

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