Pathway 01 · Foundation
University Foundations
The algebra, functions, trigonometry and exponential reasoning that university calculus assumes from the first lecture. It ends with an informal but careful introduction to limits, so the first formal course starts on solid ground.
- Audience
- Students preparing for a first university mathematics course, or returning to mathematics after a break, who want their prerequisites to be reliable rather than approximate.
- Modules
- 5, in order
- Level
- Foundation
Prerequisites
- Secondary-school arithmetic with fractions, powers and roots
- Basic algebraic manipulation: expanding, factoring and solving linear equations
- Familiarity with coordinates and graphs in the plane
You will be able to
- Solve linear, quadratic and absolute-value equations and inequalities and state the solution sets in interval notation
- Find the domain, range, composition and inverse of a function and sketch its graph by transformations of a known graph
- Solve exponential and logarithmic equations using the laws of exponents and logarithms
- Evaluate trigonometric functions at standard angles in radians and derive identities such as
- Explain in words what means and evaluate simple limits by factoring or rationalizing
Modules
Work through these in order.
- 01
Algebra and equations
Rebuild fluency with algebraic manipulation and with solving equations and inequalities exactly.
- 02
Functions and graphs
Treat functions as objects with domains and rules, and read their behavior from graphs.
- 03
Exponentials and logarithms
Understand exponential growth and decay and the logarithm as its inverse.
- 04
Trigonometry
Work in radians on the unit circle and use identities as tools rather than facts to memorize.
- 05
Readiness for limits
Meet limits informally through tables, graphs and algebra, and read the formal definition for the first time.