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:

4 TRIGONOMETRIC FUNCTIONS
A. General trigonometric functions - sine
B. General trigonometric functions - cosine
C. The general tangent function
D. Reciprocal trigonometric functions
E. Solving trigonometric equations
F. Modelling using trigonometric functions
G. Trigonometric relationships
H. Double angle identities
I. Angle sum and difference identities
J. Trigonometric equations in quadratic form (Extension)

5 MATRICES
A. Matrix structure
B. Matrix operations and definitions
C. Matrix multiplication
D. The inverse of a 2 × 2 matrix
E. Simultaneous linear equations
F. Translations and lines in 2-D
G. Linear transformations
H. Rotations about the origin
I. Reflections
J. Dilations
K. Compositions of transformations
L. The inverse of a linear transformation

6 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

7 REAL AND COMPLEX NUMBERS
A. Interval notation
B. Rational numbers
C. Division by surds
D. Irrational numbers
E. The “invention” of imaginary numbers
F. Complex numbers
G. Complex conjugates
H. Complex numbers as 2-D vectors
I. Modulus

Currently in Development

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

1 COUNTING
A. The product principle
B. Counting paths
C. Factorial notation
D. Permutations
E. Combinations
F. The inclusion-exclusion principle
G. The Pigeonhole Principle

 2 CIRCLE GEOMETRY
A. The angle in a semi-circle theorem
B. The chord of a circle theorem
C. The radius-tangent theorem
D. The angle at the centre theorem
E. Angles subtended by the same arc
F. Tangents from an external point
G. Angle between tangent and chord
H. Cyclic quadrilaterals
I. Intersecting chords and secants theorems

 3 VECTORS
A. Vectors and scalars
B. Geometric operations with vectors
C. Vectors in the plane
D. The magnitude of a vector
E. Operations with plane vectors
F. The vector between two points
G. Parallelism
H. Problems involving vector operations
I. The scalar product of two vectors
J. The angle between two vectors
K. Vector projection
L. Proof using vector geometry