Catalyst Academics is an ever-growing ecosystem of lessons, resources and support designed to keep improving alongside the students who use it.

On this page, you’ll find a full breakdown of the chapters and subchapters currently available in this course, as well as the content that is still in development. Students will be kept updated about upcoming releases, and your feedback will play an important role in shaping what we create next.

Where possible, we’ll use student requests and learning needs to prioritise the chapters and resources that will provide the greatest benefit!

Available Now

Explore the chapters and lessons currently available within this course:

1 MATHEMATICAL INDUCTION

A. The process of induction
B. The principle of mathematical induction
C. Proof of divisibility
D. Proofs for sequences and series
E. Proofs for products
F. Induction with matrices 

2 REAL POLYNOMIALS
A. Operations with polynomials
B. Zeros, roots, and factors
C. Polynomial equality
D. Polynomial division
E. The Remainder theorem
F. The Factor theorem
G. The Fundamental Theorem of Algebra
H. Sum and product of roots theorem (Extension)
I. Graphing real polynomials - cubics
J. Graphing real polynomials - quartics

4 COMPLEX NUMBERS
A. The complex plane
B. Modulus and argument
C. Polar form
D. Euler’s form (Extension)
E. De Moivre’s theorem
F. Roots of complex numbers

7 INTEGRATION
A. Rules for integration
B. Integrals with inverse trigonometric functions
C. Integration by substitution
D. Integration by parts
E. The area between two functions
F. Solids of revolution

Currently in Development

See the content we're working on next, with future releases shaped and prioritised using your feedback:

3 FUNCTIONS
A. Composite functions
B. Inverse functions
C. Reciprocal functions
D. The reciprocals of other functions
E. Rational functions
F. Absolute value functions 

5 VECTORS
A. Vectors in space
B. Operations with vectors in space
C. Vector algebra
D. The vector between two points
E. Parallelism
F. The scalar product of two vectors
G. The angle between two vectors
H. Proof using vector geometry
I. The vector product of two vectors 

6 VECTOR APPLICATIONS
A. Area
B. Lines in 2 and 3 dimensions
C. The angle between two lines
D. Constant velocity problems
E. The shortest distance from a point to a line
F. Intersecting lines
G. Relationships between lines
H. Planes
I. Angles in space
J. Solving 3 × 3 linear systems
K. Intersecting planes

8 RATES OF CHANGE AND DIFFERENTIAL EQUATIONS
A. Implicit differentiation
B. Related rates
C. Differential equations
D. Differential equations of the form
y’ = f(x)
E. Separable differential equations
F. Slope fields
G. Problem solving
H. Logistic growth
I. Equations of motion
J. Simple harmonic motion

9 VECTOR CALCULUS
A. Parametric equations
B. Pairs of uniformly varying quantities
C. Pairs of non-uniformly varying quantities
D. Bézier curves
E. Trigonometric parameterisation
F. Arc lengths of parametric curves