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:

2 QUADRATICS
A. Solving quadratic equations
B. The discriminant of a quadratic
C. The sum and product of the roots
D. Quadratic functions
E. Finding a quadratic from its graph
F. Where functions meet
G. Problem solving with quadratics
H. Quadratic optimisation

 4 POLYNOMIALS
A. Polynomials
B. Zeros, roots, and factors
C. Factorising cubic polynomials
D. Solving cubic equations
E. Graphing cubic functions
F. Quartic functions

 5 THE UNIT CIRCLE AND RADIAN MEASURE
A. Radian measure
B. Arc length and sector area
C. The unit circle and the trigonometric ratios
D. Applications of the unit circle
E. Exact values
F. The gradient of a straight line

 7 TRIGONOMETRIC FUNCTIONS
A. Periodic behaviour
B. The sine function
C. The cosine function
D. The tangent function
E. Trigonometric equations
F. Using trigonometric functions
G. Angle sum and difference identities

Currently in Development

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

1 RELATIONSHIPS BETWEEN VARIABLES
A. Linear relationships
B. Inverse proportion
C. Reciprocal functions
D. Rational functions

3 RELATIONS AND FUNCTIONS
A. Relations and functions
B. Function notation
C. Domain and range
D. Composite functions
E. Sign diagrams
F. Transforming y = f(x)
G. Graphs of circles

6 NON-RIGHT ANGLED TRIANGLE TRIGONOMETRY
A. Areas of triangles
B. The cosine rule
C. The sine rule
D. Problem solving

8 COUNTING AND THE BINOMIAL EXPANSION
A. The product and sum principles
B. Permutations
C. Factorial notation
D. Combinations
E. Binomial expansions
F. The binomial theorem

9 PROBABILITY
A. Experimental probability
B. Sample space
C. Theoretical probability
D. Compound events
E. Tree diagrams
F. Sets and Venn diagrams
G. The addition law of probability
H. Conditional probability
I. Independent events

10 NUMBER SEQUENCES
A. Number sequences
B. Arithmetic sequences
C. Geometric sequences
D. Series
E. Arithmetic series
F. Geometric series

11 STATISTICS
A. Key statistical concepts
B. Measuring the centre of data
C. Measuring the spread of data
D. Variance and standard deviation
E. The normal distribution

12 SURDS, INDICES, AND EXPONENTIALS
A. Surds
B. Indices
C. Index laws
D. Scientific notation
E. Rational indices
F. Algebraic expansion and factorisation
G. Exponential equations
H. Exponential functions
I. Growth and decay
J. The natural exponential

13 LOGARITHMS
A. Logarithms in base 10
B. Logarithms in base a
C. Laws of logarithms
D. Natural logarithms
E. Solving exponential equations using logarithms
F. Growth and decay

 14 INTRODUCTION TO DIFFERENTIAL CALCULUS
A. Rates of change
B. Instantaneous rates of change
C. Finding the gradient of the tangent
D. The derivative function

15 PROPERTIES AND APPLICATIONS OF DERIVATIVES
A. Simple rules of differentiation
B. Tangents and normals
C. Increasing and decreasing functions
D. Stationary points
E. Kinematics
F. Optimisation