CHAPTER 01
Mathematical Foundations
The mathematical language and ideas needed to understand calculus.
FOUNDATIONS
Mathematical ideas before calculus
Number Systems
Natural numbers, integers, rational numbers, irrational numbers and the real number line.
Learn → 02Algebraic Expressions
Variables, constants, coefficients, terms and what an algebraic expression represents.
Learn → 03Equations and Identities
Equality, equations, identities and why algebraic operations preserve equality.
Learn → 04Inequalities
Ordering numbers, interval notation and the logic behind manipulating inequalities.
Learn → 05Powers and Roots
Index laws, negative powers, fractional powers and roots as inverse operations.
Learn → 06Algebraic Manipulation
Expanding, factorising, rearranging and simplifying expressions without changing their mathematical value.
Learn → 07Coordinates and Graphs
Cartesian coordinates, ordered pairs, axes and graphs as geometric representations of mathematical relationships.
Learn → 08Mathematical Change
Initial and final values, finite change, \(\Delta x\), \(\Delta y\), and change in one quantity relative to another.
Learn → 09Mathematical Notation
Symbols, brackets, subscripts, superscripts, sets and how mathematical expressions are read.
Learn →Where this is leading
These ideas provide the mathematical language needed to understand functions, limits, derivatives and integrals.