100 marks 3 hours and
30 minutes
EXAMINERS:
1st Examiner: Prof TP Makgakga 2nd
Examiner: Mr MA Ngoveni
This paper consists of 5 pages. (Annexure A included).
Instructions:
1. Scan or enter the QR code (8f178a10) before you start the exam. (See page 2).
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,Question 1
1.1 Describe the theory of constructivism developed by Jean Piaget. (8)
1.2 Describe two general principles of constructivism that are largely based on Jean
Piaget's principles. (6)
1.3 Van de Walle provides seven effective suggestions to empower mathematics
teachers to teach developmentally. Name them. (7)
1.4 Teachers write lesson plans to help them structure the envisaged learning for both them
and their learners. Discuss how these lesson plans assist teachers in the teaching and
learning of Mathematics by providing six valid arguments. (12)
[33]
Question 2
2.1 Planning in the teaching of Mathematics is important. Discuss why it is important by
providing at least five valid arguments. (5)
2.2 What pre-knowledge concepts would a Grade 12 learner need to know before learning
the equation of a circle with centre (0;0) in Analytical Geometry? (6)
2.3 A circle with centre 0 and the straight line intersect at the points 𝐴(0;5) and 𝐵(4;3).
2.3.1 Sketch the two graphs on the same set of axes. (2)
2.3.2 Determine the equation of the circle. (3)
, 2.3.3 Calculate the length of chord AB. (2)
2.3.4 Determine the equation of the straight line through A and B. (4)
2.3.5 Calculate the co-ordinates of M, the midpoint of AB. (2)
2.3.6 If 𝑃(𝑥;𝑦) remains equidistant from the points A and B, prove that the equation
of the locus of P is given by 𝑦 = 2𝑥. (5)
2.4 Misconceptions are often discarded as mistakes.
2.4.1 Give four examples of misconceptions that learners might have in
response to question 2.3. (4)
2.4.2 Discuss how you would help a learner to remedy the misconceptions that you
have mentioned in question 2.4.1. (3)
[36]
Question 3
3.1 Given is the quadratic equation: 𝑚𝑥2−13𝑥−10=0 if one of the roots is 5,
3.1.1 Use the steps of Polya to solve the equation. You must explain in detail
what you are doing in each step. (8)
3.1.2 What challenges may learners experience when solving this problem? (5)
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