MIP1502
EXAM PACK
FOR ASSISTANCE WITH THIS MODULE +27 67 171 1739
, lOMoARcPSD|22437965
UNIVERSITY EXAMINATIONS
October/November 2024
MIP1502
Mathematics for Intermediate Phase Teachers II
CONFIDENTIAL
100 marks
Duration: 3 hours and 30 minutes
Examiners:
First examiner: Mr GT Mphuthi
Second examiner: Prof TP Makgakga
EXAMINATION INSTRUCTIONS:
1. This examination question paper consists of FIVE pages, including Annexure A.
2. Read the questions carefully.
3. This question paper consists of THREE questions. Answer ALL the questions.
4. Number your answers exactly as the questions are numbered.
5. Start each question on a new page.
6. You may use a calculator.
7. Round off your answers to one decimal digit where necessary.
8. You must show ALL the working details.
9. It is your interest to write legibly and present your work neatly.
10. Please note that the diagrams are NOT necessarily drawn to scale.
11. Please note that the exam is open book. You are allowed to access your prescribed works and
the study material. You are, however, not allowed to copy verbatim from your study material.
You should provide answers in your own words. In the case of any cheating or plagiarism, no
mark will be allocated.
12. Scan or enter the QR code (page 2) before you start the exam.
13. Remember to CHECK the Honesty Declaration Box when you upload the answer script.
14. . See Appendix A on page 5 for information on how to submit your answer file.
[TURN OVER]
Downloaded by Corona Virus ()
, lOMoARcPSD|22437965
2 MIP1502 OCT/NOV 2024
[TURN OVER]
Downloaded by Corona Virus ()
, lOMoARcPSD|22437965
3 MIP1502 OCT/NOV 2024
Question 1
1.1 Name and explain the dynamic aspects of algebra. Give an example for each aspect. (12)
1.2 Explain why the sum of any two consecutive numbers cannot be even. Draw a diagram to
illustrate this. (6)
1.3 What requirements must be met for the successful development of algebraic thinking? (6)
1.4 Briefly describe the following.
1.4.1 Situational Contexts (3)
1.4.2 Mathematical Contexts. (3)
[30]
Question 2
2.1 Given the following expressions 3끫룊 + 2 and 2끫룊 + 3.
2.1.1 Which expression is bigger? Justify your reasoning. (8)
2.1.2 Draw the graphs of 끫뢦(끫룊) = 3끫룊 + 2 and 끫뢨(끫룊) = 2끫룊 + 3 on the same cartesian plane.
Show the point of intersection if the two functions do intersect. (6)
2.2 Given the equation:
끫룊 2 + 6 = 5끫룊
2
2.2.1 Show that the equation can be written as 끫룊 = 1 − (4)
x−4
2.2.2 Find the value(s) of 끫룊 that makes the statement true (4)
2.3 Evaluate the following expressions in two different ways:
3
2.3.1 16(12 − 8) − (12 − 8) + 9 (4)
4
2.3.2 3끫룂 + 끫뢾(끫룂 − 7) − 4끫뢾(끫룂 + 끫뢾 + 5) − 2끫뢾 2 when 끫뢾 = 7 끫뢜끫뢜끫뢜 끫룂 = 14. (6)
2.4 Three friends, Ace (age 16), Tracey (age 14), and Kgosi (age 9), were home alone and
hungry. They decided to buy a pizza and eat it. They chipped in their money, and it was
ninety rands in total. Ace’s contribution exceeded Tracey’s contribution by ten rands. Ace
ate twice as much as Tracey did. Kgosi contributed two-thirds as much as Tracey
contributed and ate one and a half times as much as Tracey. Ace bought a large, uncut
pizza, and they succeeded in eating it all.
2.4.1 How much did each friend contribute towards buying the pizza? (8)
2.4.2 What part of the pizza did each friend eat? Use a suitable diagram to show the
portions. (8)
[48]
[TURN OVER]
Downloaded by Corona Virus ()
EXAM PACK
FOR ASSISTANCE WITH THIS MODULE +27 67 171 1739
, lOMoARcPSD|22437965
UNIVERSITY EXAMINATIONS
October/November 2024
MIP1502
Mathematics for Intermediate Phase Teachers II
CONFIDENTIAL
100 marks
Duration: 3 hours and 30 minutes
Examiners:
First examiner: Mr GT Mphuthi
Second examiner: Prof TP Makgakga
EXAMINATION INSTRUCTIONS:
1. This examination question paper consists of FIVE pages, including Annexure A.
2. Read the questions carefully.
3. This question paper consists of THREE questions. Answer ALL the questions.
4. Number your answers exactly as the questions are numbered.
5. Start each question on a new page.
6. You may use a calculator.
7. Round off your answers to one decimal digit where necessary.
8. You must show ALL the working details.
9. It is your interest to write legibly and present your work neatly.
10. Please note that the diagrams are NOT necessarily drawn to scale.
11. Please note that the exam is open book. You are allowed to access your prescribed works and
the study material. You are, however, not allowed to copy verbatim from your study material.
You should provide answers in your own words. In the case of any cheating or plagiarism, no
mark will be allocated.
12. Scan or enter the QR code (page 2) before you start the exam.
13. Remember to CHECK the Honesty Declaration Box when you upload the answer script.
14. . See Appendix A on page 5 for information on how to submit your answer file.
[TURN OVER]
Downloaded by Corona Virus ()
, lOMoARcPSD|22437965
2 MIP1502 OCT/NOV 2024
[TURN OVER]
Downloaded by Corona Virus ()
, lOMoARcPSD|22437965
3 MIP1502 OCT/NOV 2024
Question 1
1.1 Name and explain the dynamic aspects of algebra. Give an example for each aspect. (12)
1.2 Explain why the sum of any two consecutive numbers cannot be even. Draw a diagram to
illustrate this. (6)
1.3 What requirements must be met for the successful development of algebraic thinking? (6)
1.4 Briefly describe the following.
1.4.1 Situational Contexts (3)
1.4.2 Mathematical Contexts. (3)
[30]
Question 2
2.1 Given the following expressions 3끫룊 + 2 and 2끫룊 + 3.
2.1.1 Which expression is bigger? Justify your reasoning. (8)
2.1.2 Draw the graphs of 끫뢦(끫룊) = 3끫룊 + 2 and 끫뢨(끫룊) = 2끫룊 + 3 on the same cartesian plane.
Show the point of intersection if the two functions do intersect. (6)
2.2 Given the equation:
끫룊 2 + 6 = 5끫룊
2
2.2.1 Show that the equation can be written as 끫룊 = 1 − (4)
x−4
2.2.2 Find the value(s) of 끫룊 that makes the statement true (4)
2.3 Evaluate the following expressions in two different ways:
3
2.3.1 16(12 − 8) − (12 − 8) + 9 (4)
4
2.3.2 3끫룂 + 끫뢾(끫룂 − 7) − 4끫뢾(끫룂 + 끫뢾 + 5) − 2끫뢾 2 when 끫뢾 = 7 끫뢜끫뢜끫뢜 끫룂 = 14. (6)
2.4 Three friends, Ace (age 16), Tracey (age 14), and Kgosi (age 9), were home alone and
hungry. They decided to buy a pizza and eat it. They chipped in their money, and it was
ninety rands in total. Ace’s contribution exceeded Tracey’s contribution by ten rands. Ace
ate twice as much as Tracey did. Kgosi contributed two-thirds as much as Tracey
contributed and ate one and a half times as much as Tracey. Ace bought a large, uncut
pizza, and they succeeded in eating it all.
2.4.1 How much did each friend contribute towards buying the pizza? (8)
2.4.2 What part of the pizza did each friend eat? Use a suitable diagram to show the
portions. (8)
[48]
[TURN OVER]
Downloaded by Corona Virus ()
