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Mathematics and statistics
The University has developed a number of resources and workbooks to help develop your skills in maths and stats.
The University has developed a number of workbooks, that are made freely available for your use. If you reproduce any part of these documents, please ensure that the University of Sydney’s copyright is appropriately acknowledged.
Resources are grouped into topics and can be downloaded individually, or as a zip file containing all resources for the topic area. You can also download of all the resources featured on this page (zip, 14.4MB).
- General mathematical resources (pdf, 74KB)
- Introductory algebra for social sciences (pdf, 2MB)
- Revising algebra skills (pdf, 108KB)
Maths 2 Unit Bridging Course
- Study guide (pdf, 52KB)
- Exercise book (pdf, 331KB)
- Exercise book solutions (pdf, 380KB)
- Audiovisual modules (YouTube videos)
Extension 1 Bridging Course
Download all general mathematical resources (zip, 1.8MB)
- Miscellaneous topics study guide (pdf, 87KB)
- Absolute values (pdf, 83KB)
- Exponents (pdf, 117KB)
- Mathematical induction (pdf, 165KB)
- Sigma notation (pdf, 83KB)
- Solving inequalities (pdf, 125KB)
- Solving simultaneous equations (pdf, 77KB)
- Trigonometric identities (pdf, 668KB)
- Polynomials (pdf, 110KB)
Download all miscellaneous resources (zip, 1.3MB)
- Probability and statistics study guide (pdf, 68KB)
- Basic concepts in probability (pdf, 147KB)
- Counting techniques (pdf, 1.9MB)
- Introduction to probability theory (pdf, 2MB)
- Further probability theory (pdf, 2MB)
- Introduction to descriptive statistics (pdf, 2MB)
- The binomial distribution (pdf, 2.1MB)
- The normal distribution (pdf, 2.1MB)
Download all probability and statistics resources (zip, 4.2MB)
- Functions and graphs study guide (pdf, 67KB)
- Functions and their graphs (pdf, 2.3MB)
- Functions: the domain and range (pdf, 119KB)
- Functions and straight line graphs (pdf, 113KB)
- Graphs of polynomials (pdf, 93KB)
- Exponential functions (pdf, 136KB)
- Logarithmic functions and log laws (pdf, 167KB)
- Introduction to exponentials and logarithms (pdf, 2.1MB)
- Working with quadratics and exponential graphs (pdf, 131KB)
- Introduction to trigonometric functions (pdf, 2.3MB)
Download all function and graph resources (zip, 3.4MB)
- Calculus study guide (pdf, 157KB)
- Mathematical modelling recordings (YouTube video)
- Introduction to calculus tutorial recordings (YouTube video)
Differential calculus
- Introduction to calculus (pdf, 78KB)
- Introduction to differential calculus (pdf, 2.1MB)
- The rules of calculus (pdf, 89KB)
- Composite function rule (the chain rule) (pdf, 88KB)
- Derivatives of exponential and logarithmic functions (pdf, 81KB)
- Differentiation of trigonometry (pdf, 78KB)
- The first derivative and stationary points (pdf, 99KB)
- Second derivative and points of inflection (pdf, 95KB)
Integral calculus
- Introduction to integration part 1: the anti-derivative (pdf, 191KB)
- Introduction to integration part 2: the definite integral (pdf, 281KB)
Applications of calculus
- Curve sketching using calculus (pdf, 119KB)
- Optimisation using calculus (pdf, 115KB)
- Exponentials and logarithms: applications and calculus (pdf, 845KB)
- Modelling and calculus (pdf, 544KB)
Download all calculus resources (zip, 3.3MB)
An introduction to matrix algebra
- Introduction to matrices (pdf, 195KB)
- Addition, subtraction and scalar multiplication (pdf, 178KB)
- Matrix multiplication (pdf, 304KB)
- Elementary row operations (pdf, 72KB)
- Using elementary row operations to solve a system of equations (pdf, 202KB)
- The inverse matrix (pdf, 80KB)
- Finding the inverse of a matrix (pdf, 84KB)
- Solving systems of linear equations using the inverse (pdf, 70 KB)
- Determinants (pdf, 82KB)
- Properties of determinants (pdf, 82KB)
- Using matrix algebra in linear regression (pdf, 83KB)
Download all linear algebra resources (zip, 985KB)
More assistance
If you’re enrolled in a mathematics, statistics or related unit of study, visit our Canvas site for information on how to best use these materials.
The Learning Hub (Mathematics) also offers face-to-face support, including a Drop-in Centre and unit of study workshops.
New students
If you're a new student, we suggest visiting the University's Maths learning support page where you can chat to our maths bot to determine which units to enrol in based on your program of study and receive personalised advice for learning support.
Last updated: 11 April 2025