MAT1512 MATHEMATICS I (PDF) | 2026 EXAM QUESTIONS
AND ANSWERS + RATIONALES | STUDY GUIDE | 100%
CORRECT
1. What is the purpose of the MAT1512 module?
A) To develop advanced skills in abstract algebra and topology
B) To develop basic skills in differential and integral calculus essential for the physical, life and
economic sciences
C) To provide a historical overview of mathematical discoveries
D) To focus exclusively on the theory of linear algebra
Correct Answer: B) To develop basic skills in differential and integral calculus essential for the
physical, life and economic sciences
Rationale: According to the official module description, MAT1512 is designed to help students
develop basic skills in differential and integral calculus which are essential for the physical, life
and economic sciences. Students credited with the module will have a firm conceptual grasp of
limits, continuity, differentiation and integration.
2. What is the NQF level and credit value of MAT1512?
A) NQF level 4 with 8 credits
B) NQF level 5 with 12 credits
C) NQF level 6 with 16 credits
D) NQF level 7 with 24 credits
Correct Answer: B) NQF level 5 with 12 credits
Rationale: MAT1512 is registered as an undergraduate degree module at NQF level 5 with 12
credits. It is a year module presented in English and is fully online at the University of South
Africa.
3. Which of the following is NOT a core topic covered in MAT1512?
A) Limits and continuity
B) Differentiation and its applications
C) Integration and the Fundamental Theorem of Calculus
D) Vector spaces and linear transformations
Correct Answer: D) Vector spaces and linear transformations
Rationale: The purpose of MAT1512 clearly states that the module covers limits, continuity,
differentiation and integration. Vector spaces and linear transformations are topics from linear
algebra, not from calculus A.
4. According to the MAT1512 tutorial letter, what is the prescribed textbook for this module?
A) Stewart's Calculus, 9th edition
B) Thomas' Calculus, 14th edition
, C) Calculus by Anton, Bivens and Davis
D) The textbook is not specified in the tutorial letter
Correct Answer: A) Stewart's Calculus, 9th edition
Rationale: The tutorial letter for MAT1512 indicates that the prescribed textbook is "Calculus,
Stewart, 9th edition". Students are expected to use this textbook for their studies and
assessments.
5. What is the exam duration for the MAT1512 January/February 2025 examination?
A) 1 hour
B) 2 hours
C) 3 hours
D) 4 hours
Correct Answer: B) 2 hours
Rationale: The MAT1512 January/February 2025 exam paper specifies that the exam is 2 hours
long. The examination paper consists of 5 pages and is worth a total of 100 marks.
6. Which of the following limit evaluation techniques is specifically mentioned for use in
MAT1512 exam questions?
A) L'Hôpital's Rule
B) The Squeeze Theorem
C) Integration by parts
D) The Mean Value Theorem
Correct Answer: B) The Squeeze Theorem
Rationale: The January/February 2025 exam paper explicitly includes a question to use the
Squeeze Theorem to evaluate a limit. Past exam papers also reference the Squeeze Theorem for
evaluating limits of functions that are difficult to evaluate directly.
7. Determine the following limit: lim_{x→-3⁻} (x² - 9) / |x - 3|
A) 0
B) -6
C) 6
D) The limit does not exist
Correct Answer: A) 0
Rationale: The limit is evaluated by direct substitution. When x approaches -3 from the left, the
expression (x² - 9)/(|x - 3|) becomes ((-3)² - 9)/(|-3 - 3|) = (9 - 9)/(|-6|) = 0/6 = 0. The limit is well-
defined and exists.
8. Evaluate the limit: lim_{y→0} (sin 5y) / (sin 8y)
A) 0
AND ANSWERS + RATIONALES | STUDY GUIDE | 100%
CORRECT
1. What is the purpose of the MAT1512 module?
A) To develop advanced skills in abstract algebra and topology
B) To develop basic skills in differential and integral calculus essential for the physical, life and
economic sciences
C) To provide a historical overview of mathematical discoveries
D) To focus exclusively on the theory of linear algebra
Correct Answer: B) To develop basic skills in differential and integral calculus essential for the
physical, life and economic sciences
Rationale: According to the official module description, MAT1512 is designed to help students
develop basic skills in differential and integral calculus which are essential for the physical, life
and economic sciences. Students credited with the module will have a firm conceptual grasp of
limits, continuity, differentiation and integration.
2. What is the NQF level and credit value of MAT1512?
A) NQF level 4 with 8 credits
B) NQF level 5 with 12 credits
C) NQF level 6 with 16 credits
D) NQF level 7 with 24 credits
Correct Answer: B) NQF level 5 with 12 credits
Rationale: MAT1512 is registered as an undergraduate degree module at NQF level 5 with 12
credits. It is a year module presented in English and is fully online at the University of South
Africa.
3. Which of the following is NOT a core topic covered in MAT1512?
A) Limits and continuity
B) Differentiation and its applications
C) Integration and the Fundamental Theorem of Calculus
D) Vector spaces and linear transformations
Correct Answer: D) Vector spaces and linear transformations
Rationale: The purpose of MAT1512 clearly states that the module covers limits, continuity,
differentiation and integration. Vector spaces and linear transformations are topics from linear
algebra, not from calculus A.
4. According to the MAT1512 tutorial letter, what is the prescribed textbook for this module?
A) Stewart's Calculus, 9th edition
B) Thomas' Calculus, 14th edition
, C) Calculus by Anton, Bivens and Davis
D) The textbook is not specified in the tutorial letter
Correct Answer: A) Stewart's Calculus, 9th edition
Rationale: The tutorial letter for MAT1512 indicates that the prescribed textbook is "Calculus,
Stewart, 9th edition". Students are expected to use this textbook for their studies and
assessments.
5. What is the exam duration for the MAT1512 January/February 2025 examination?
A) 1 hour
B) 2 hours
C) 3 hours
D) 4 hours
Correct Answer: B) 2 hours
Rationale: The MAT1512 January/February 2025 exam paper specifies that the exam is 2 hours
long. The examination paper consists of 5 pages and is worth a total of 100 marks.
6. Which of the following limit evaluation techniques is specifically mentioned for use in
MAT1512 exam questions?
A) L'Hôpital's Rule
B) The Squeeze Theorem
C) Integration by parts
D) The Mean Value Theorem
Correct Answer: B) The Squeeze Theorem
Rationale: The January/February 2025 exam paper explicitly includes a question to use the
Squeeze Theorem to evaluate a limit. Past exam papers also reference the Squeeze Theorem for
evaluating limits of functions that are difficult to evaluate directly.
7. Determine the following limit: lim_{x→-3⁻} (x² - 9) / |x - 3|
A) 0
B) -6
C) 6
D) The limit does not exist
Correct Answer: A) 0
Rationale: The limit is evaluated by direct substitution. When x approaches -3 from the left, the
expression (x² - 9)/(|x - 3|) becomes ((-3)² - 9)/(|-3 - 3|) = (9 - 9)/(|-6|) = 0/6 = 0. The limit is well-
defined and exists.
8. Evaluate the limit: lim_{y→0} (sin 5y) / (sin 8y)
A) 0
