AMP STUDY NOTES
MAT1512 · CALCULUS A
Complete Module
Additional Practice Problems
All five chapters’ practice problems combined into a single volume, in
order, for the full module.
Chapter 1 — Functions and Models
Chapter 2 — Limits and Derivatives
Chapter 3 — Differentiation Rules
Chapter 4 — Integrals
Chapter 5 — Differential Equations, Growth/Decay & Partial Derivatives
PRACTICE PROBLEMS · ALL CHAPTERS
Independent study material. Independently authored revision aid, not affiliated with, endorsed by, or sourced
from UNISA or any official assessment body. © AMP Study Notes.
,AMP STUDY NOTES
MAT1512 · CALCULUS A
Chapter 1
Additional Practice Problems
Six practice problems in the style commonly seen in MAT1512
assessments, spanning domain-finding, composite functions,
symmetry, inverses, and piecewise functions — each with a
complete, independently worked solution.
PRACTICE PROBLEMS · CHAPTER 1
Independent study material. These are original practice problems, written to match the style and difficulty of
typical MAT1512 assessments. They are not reproductions of any specific past exam, assignment, or memo, are
not affiliated with, endorsed by, or sourced from UNISA or any official assessment body, and include
independently worked, verified solutions. © AMP Study Notes.
, AMP Study Notes — MAT1512 — Chapter 1 Practice Problems
Chapter 1: Additional Practice Problems
Six problems covering the full spread of Chapter 1's exam-relevant skills, each with a complete solution. Attempt
each problem before reading its solution.
Problem 1 — Domain With a Log and a Fraction
Find the domain of .
Solution. The logarithm requires a strictly positive argument:
The fraction requires a non-zero denominator:
Answer: intersecting both, the domain is .
Problem 2 — Composite Function
Let and . Find and its domain.
Solution.
itself has domain all reals, so the only restriction comes from : its input, , must be non-
zero.
Answer: , domain all reals except .
Problem 3 — Even, Odd, or Neither
Classify as even, odd, or neither.
Solution.
Compare to and : matches neither.
Answer: is neither even nor odd.
Page 2 of 3
MAT1512 · CALCULUS A
Complete Module
Additional Practice Problems
All five chapters’ practice problems combined into a single volume, in
order, for the full module.
Chapter 1 — Functions and Models
Chapter 2 — Limits and Derivatives
Chapter 3 — Differentiation Rules
Chapter 4 — Integrals
Chapter 5 — Differential Equations, Growth/Decay & Partial Derivatives
PRACTICE PROBLEMS · ALL CHAPTERS
Independent study material. Independently authored revision aid, not affiliated with, endorsed by, or sourced
from UNISA or any official assessment body. © AMP Study Notes.
,AMP STUDY NOTES
MAT1512 · CALCULUS A
Chapter 1
Additional Practice Problems
Six practice problems in the style commonly seen in MAT1512
assessments, spanning domain-finding, composite functions,
symmetry, inverses, and piecewise functions — each with a
complete, independently worked solution.
PRACTICE PROBLEMS · CHAPTER 1
Independent study material. These are original practice problems, written to match the style and difficulty of
typical MAT1512 assessments. They are not reproductions of any specific past exam, assignment, or memo, are
not affiliated with, endorsed by, or sourced from UNISA or any official assessment body, and include
independently worked, verified solutions. © AMP Study Notes.
, AMP Study Notes — MAT1512 — Chapter 1 Practice Problems
Chapter 1: Additional Practice Problems
Six problems covering the full spread of Chapter 1's exam-relevant skills, each with a complete solution. Attempt
each problem before reading its solution.
Problem 1 — Domain With a Log and a Fraction
Find the domain of .
Solution. The logarithm requires a strictly positive argument:
The fraction requires a non-zero denominator:
Answer: intersecting both, the domain is .
Problem 2 — Composite Function
Let and . Find and its domain.
Solution.
itself has domain all reals, so the only restriction comes from : its input, , must be non-
zero.
Answer: , domain all reals except .
Problem 3 — Even, Odd, or Neither
Classify as even, odd, or neither.
Solution.
Compare to and : matches neither.
Answer: is neither even nor odd.
Page 2 of 3
