MIP1502
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Recent exam questions and answers
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DISCLAIMER & TERMS OF USE
1. Educational Aid: These study notes are designed to serve as educational aids and should not be considered as a
substitute for individual research, critical thinking, or professional guidance. Students are encouraged to
conduct their own extensive research and consult with their instructors or academic advisors for specific
assignment requirements.
2. Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the
information provided in these study notes, the seller cannot guarantee the completeness or correctness of all
the content. It is the responsibility of the buyer to verify the accuracy of the information and use their own
judgment when applying it to their assignments.
3. Academic Integrity: It is crucial for students to uphold academic integrity and adhere to their institution's
policies and guidelines regarding plagiarism, citation, and referencing. These study notes should be used as a
tool for learning and inspiration, but any direct reproduction of the content without proper acknowledgment and
citation may constitute academic misconduct.
4. Limited Liability: The seller of these study notes shall not be held liable for any direct or indirect damages,
losses, or consequences arising from the use of the notes. This includes, but is not limited to, poor grades,
academic penalties, or any other negative outcomes resulting from the application or misuse of the information
provide
]
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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.
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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]
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EXAM PACK
Recent exam questions and answers
Summarised study notes
Exam tips and guidelines
+27 81 278 3372
DISCLAIMER & TERMS OF USE
1. Educational Aid: These study notes are designed to serve as educational aids and should not be considered as a
substitute for individual research, critical thinking, or professional guidance. Students are encouraged to
conduct their own extensive research and consult with their instructors or academic advisors for specific
assignment requirements.
2. Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the
information provided in these study notes, the seller cannot guarantee the completeness or correctness of all
the content. It is the responsibility of the buyer to verify the accuracy of the information and use their own
judgment when applying it to their assignments.
3. Academic Integrity: It is crucial for students to uphold academic integrity and adhere to their institution's
policies and guidelines regarding plagiarism, citation, and referencing. These study notes should be used as a
tool for learning and inspiration, but any direct reproduction of the content without proper acknowledgment and
citation may constitute academic misconduct.
4. Limited Liability: The seller of these study notes shall not be held liable for any direct or indirect damages,
losses, or consequences arising from the use of the notes. This includes, but is not limited to, poor grades,
academic penalties, or any other negative outcomes resulting from the application or misuse of the information
provide
]
, 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]
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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]
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