AMP STUDY NOTES
MAT1512 · CALCULUS A
Complete Module
Cheatsheet
All five chapters’ cheatsheets 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
CHEATSHEET · 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
Cheatsheet
Functions and Models — core rules, definitions, and a fast decision
guide for exam revision.
CHEATSHEET · CHAPTER 1
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 — Chapter 1 Cheatsheet
Chapter 1 Cheatsheet: Functions & Models
Core Rules
DOMAIN RESTRICTIONS
Root · Denominator · Log argument — intersect all that apply.
COMPOSITE FUNCTION
Domain: must be in 's domain and must be in 's domain.
SYMMETRY TESTS
INVERSE FUNCTION METHOD
→ solve for in terms of → swap → .
One-Line Definitions
• Domain: all valid inputs. Range: all outputs actually produced.
• One-to-one: no two inputs share an output — required for an inverse to exist.
• Domain of = range of ; range of = domain of .
Fast Decision Guide
IF THE QUESTION ASKS… REACH FOR…
"Find the domain of…" Check roots, denominators, logs separately, then intersect.
"Find and its domain" Substitute, simplify, then check both domain conditions before simplifying obscures one.
"Is this function even/odd?" Substitute , compare to and .
"Find the inverse of…" , solve for , swap variables, verify by composition.
Common Pitfalls (One Line Each)
• Domain restrictions intersect, they don't union.
• Simplifying a composite before checking its domain can hide an inherited restriction.
Page 2 of 3
MAT1512 · CALCULUS A
Complete Module
Cheatsheet
All five chapters’ cheatsheets 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
CHEATSHEET · 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
Cheatsheet
Functions and Models — core rules, definitions, and a fast decision
guide for exam revision.
CHEATSHEET · CHAPTER 1
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 — Chapter 1 Cheatsheet
Chapter 1 Cheatsheet: Functions & Models
Core Rules
DOMAIN RESTRICTIONS
Root · Denominator · Log argument — intersect all that apply.
COMPOSITE FUNCTION
Domain: must be in 's domain and must be in 's domain.
SYMMETRY TESTS
INVERSE FUNCTION METHOD
→ solve for in terms of → swap → .
One-Line Definitions
• Domain: all valid inputs. Range: all outputs actually produced.
• One-to-one: no two inputs share an output — required for an inverse to exist.
• Domain of = range of ; range of = domain of .
Fast Decision Guide
IF THE QUESTION ASKS… REACH FOR…
"Find the domain of…" Check roots, denominators, logs separately, then intersect.
"Find and its domain" Substitute, simplify, then check both domain conditions before simplifying obscures one.
"Is this function even/odd?" Substitute , compare to and .
"Find the inverse of…" , solve for , swap variables, verify by composition.
Common Pitfalls (One Line Each)
• Domain restrictions intersect, they don't union.
• Simplifying a composite before checking its domain can hide an inherited restriction.
Page 2 of 3
