MIP1502 Oct/Nov 2022 exam paper — questions

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Every question, by topic

  1. Question 1.1.1 · Number patterns and generalisation · 4 marks

    Three diagrams made of dotted and empty squares form a growing pattern: diagram 1 is a single square containing a dot; diagram 2 adds a square with a dot on top and two more dotted squares on either side, with the middle square left empty; diagram 3 adds a further dotted square on top and widens the base, again leaving the middle square of each row empty. A table records, for diagrams 1 to 10, the number of dots, the number of squares, and the sum of the number of dots plus the number of squares; so far only diagrams 1–3 are filled in, showing 1, 3 and 7 dots respectively, 1, 4 and 9 squares respectively, and sums of 2, 7 and 16 respectively, while the columns for diagrams 4 to 10 are still blank. Draw diagram 4 of the pattern of dotted and empty squares.Show the full question

  2. Question 1.1.2 · Number patterns and generalisation · 6 marks

    Three diagrams made of dotted and empty squares form a growing pattern: diagram 1 is a single square containing a dot; diagram 2 adds a square with a dot on top and two more dotted squares on either side, with the middle square left empty; diagram 3 adds a further dotted square on top and widens the base, again leaving the middle square of each row empty. A table records, for diagrams 1 to 10, the number of dots, the number of squares, and the sum of the number of dots plus the number of squares; so far only diagrams 1–3 are filled in, showing 1, 3 and 7 dots respectively, 1, 4 and 9 squares respectively, and sums of 2, 7 and 16 respectively, while the columns for diagrams 4 to 10 are still blank. Complete the table column entries (dots, squares and sum) for diagram 6 and for diagram 7.Show the full question

  3. Question 1.1.2 · Number patterns and generalisation · 4 marks

    Three diagrams made of dotted and empty squares form a growing pattern: diagram 1 is a single square containing a dot; diagram 2 adds a square with a dot on top and two more dotted squares on either side, with the middle square left empty; diagram 3 adds a further dotted square on top and widens the base, again leaving the middle square of each row empty. A table records, for diagrams 1 to 10, the number of dots, the number of squares, and the sum of the number of dots plus the number of squares; so far only diagrams 1–3 are filled in, showing 1, 3 and 7 dots respectively, 1, 4 and 9 squares respectively, and sums of 2, 7 and 16 respectively, while the columns for diagrams 4 to 10 are still blank. Describe in words how the number of dots and the number of squares increase from one diagram to the next.Show the full question

  4. Question 1.1.3 · Number patterns and generalisation · 6 marks

    Three diagrams made of dotted and empty squares form a growing pattern: diagram 1 is a single square containing a dot; diagram 2 adds a square with a dot on top and two more dotted squares on either side, with the middle square left empty; diagram 3 adds a further dotted square on top and widens the base, again leaving the middle square of each row empty. A table records, for diagrams 1 to 10, the number of dots, the number of squares, and the sum of the number of dots plus the number of squares; so far only diagrams 1–3 are filled in, showing 1, 3 and 7 dots respectively, 1, 4 and 9 squares respectively, and sums of 2, 7 and 16 respectively, while the columns for diagrams 4 to 10 are still blank. Find the algebraic rule, in terms of n, that determines the number of dots in diagram n. Show ALL your work.Show the full question

  5. Question 1.1.4 · Number patterns and generalisation · 2 marks

    Three diagrams made of dotted and empty squares form a growing pattern: diagram 1 is a single square containing a dot; diagram 2 adds a square with a dot on top and two more dotted squares on either side, with the middle square left empty; diagram 3 adds a further dotted square on top and widens the base, again leaving the middle square of each row empty. A table records, for diagrams 1 to 10, the number of dots, the number of squares, and the sum of the number of dots plus the number of squares; so far only diagrams 1–3 are filled in, showing 1, 3 and 7 dots respectively, 1, 4 and 9 squares respectively, and sums of 2, 7 and 16 respectively, while the columns for diagrams 4 to 10 are still blank. Show that the sum of the number of dots plus the number of squares in diagram n is given by the expression 2n² − n + 1.Show the full question

  6. Question 1.1.5 · Number patterns and generalisation · 2 marks

    Three diagrams made of dotted and empty squares form a growing pattern: diagram 1 is a single square containing a dot; diagram 2 adds a square with a dot on top and two more dotted squares on either side, with the middle square left empty; diagram 3 adds a further dotted square on top and widens the base, again leaving the middle square of each row empty. A table records, for diagrams 1 to 10, the number of dots, the number of squares, and the sum of the number of dots plus the number of squares; so far only diagrams 1–3 are filled in, showing 1, 3 and 7 dots respectively, 1, 4 and 9 squares respectively, and sums of 2, 7 and 16 respectively, while the columns for diagrams 4 to 10 are still blank. How many squares will there be in diagram 100?Show the full question

  7. Question 2.1.1 · Expressions, equations and inequalities · 2 marks

    Simplify the expression 5(3c − 4d) − 8c.Show the full question

  8. Question 2.1.2 · Expressions, equations and inequalities · 1 mark

    Factorise the expression pq − q².Show the full question

  9. Question 2.2.1 · Expressions, equations and inequalities · 1 mark

    Given the equation 10m − 3n + 2mn − 15 = 0, factorise the expression on the left-hand side.Show the full question

  10. Question 2.2.2 · Expressions, equations and inequalities · 2 marks

    Using the equation 10m − 3n + 2mn − 15 = 0, solve for m if m = n.Show the full question

  11. Question 3.1.1 · Functions and graphs · 4 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. For the catering scenario described (R1 200 budget, chicken at R30/kg and steak at R120/kg), identify what changes and what stays the same in the situation, that is, name the variables involved in the problem.Show the full question

  12. Question 3.1.2 · Functions and graphs · 4 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. Write the number sentence, in the form of an equation, that expresses the relationship between the variables you identified in 3.1.1 for the catering budget problem, and explain the reasoning behind your equation.Show the full question

  13. Question 3.1.3 · Functions and graphs · 2 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. Explain how, using the equation you wrote in 3.1.2, you could derive a function relating the two variables in the catering problem.Show the full question

  14. Question 3.1.4 · Functions and graphs · 4 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. Derive the function that relates the two variables for the catering budget problem, showing all your working.Show the full question

  15. Question 3.1.5 · Functions and graphs · 4 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. State the vertical intercept and the horizontal intercept of the function you found in 3.1.4.Show the full question

  16. Question 3.1.6 · Functions and graphs · 6 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. Draw the graph of the function you found in 3.1.4, clearly indicating both the vertical intercept and the horizontal intercept on the graph.Show the full question

  17. Question 3.1.7 · Functions and graphs · 6 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. Explain, in the context of the catering budget problem, what each intercept means and what the slope of the function represents.Show the full question

  18. Question 3.1.8 · Functions and graphs · 4 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. Using either the equation or the graph you produced, discuss the different combinations of chicken and steak (in kilograms) that you could buy for the ceremony within the R1 200 budget.Show the full question

  19. Question 3.1.9 · Functions and graphs · 4 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. Using the equation you wrote in 3.1.2, demonstrate that buying 8 kg of chicken and 8 kg of steak would cost exactly R1 200.Show the full question

  20. Question 3.2 · Functions and graphs · 8 marks

    Imagine you are catering for a ceremony and have a total budget of R1 200 to spend on meat, wanting to serve both chicken and steak, where chicken costs R30 per kilogram and steak costs R120 per kilogram. Give a brief description of the four major processes involved in algebra, providing your own original example to illustrate each process.Show the full question

  21. Question 4.1.1 · Algebraic thinking and learner misconceptions · 2 marks

    Determine how many different values the expression 6 + (7 + 3)² can take, and write down the value(s).Show the full question

  22. Question 4.1.2 · Algebraic thinking and learner misconceptions · 2 marks

    Determine how many different values the expression 6 + (x + 3)² can take.Show the full question

  23. Question 4.1.3 · Algebraic thinking and learner misconceptions · 6 marks

    For the expression 6 + (x + 3)², draw up a table showing at least six different values that the expression can produce.Show the full question

  24. Question 4.1.4 · Algebraic thinking and learner misconceptions · 4 marks

    Give the name of each of the expressions used in 4.1.1 (6 + (7 + 3)²) and 4.1.2 (6 + (x + 3)²), and describe each one.Show the full question

  25. Question 4.1.5 · Algebraic thinking and learner misconceptions · 4 marks

    Explain, with justification, the difference between the mathematical expression 4x and the mathematical statement 4x − 15.Show the full question

  26. Question 4.2 · Algebraic thinking and learner misconceptions · 6 marks

    Name at least six ideas that learners would develop if they were given an activity such as the one described in 4.1.Show the full question