Mathematics Extension 1

Year 12 MATHEMATICS EXTENSION 1 2027

Starting Term 4 (2026) and ending 2027, students will complete the HSC Mathematics Extension 1 

and Mathematics Advanced courses.  

It is a NESA requirement for students studying these courses to complete assessment Tasks 1 to 4 for BOTH the 

Mathematics Advanced and Mathematics Extension 1 courses. 

TERM 4 – Mathematic Induction, Further Graph Transformations and Modelling, Inverse Trigonometric Functions, Discrete Random Variables, Differentiation of Trigonometric, Exponential and Logarithmic Functions, The First and Second Derivatives, Applications of the First and Second Derivatives.

Students will begin Term 4 by completing the Extension 1 topic, Mathematical Induction. Students will examine the nature of inductive proof, including the statement to be proved, the base case and the inductive step. They will prove results for sums and prove divisibility results using mathematical induction. Identifying errors in false ‘proofs by induction’, such as cases where only one of the two required steps of a proof by induction is true, will also be looked at.

Students will then look at the Advanced topic, Further Graph Transformations and Modelling. Students will explore transformations of Trigonometric Functions, including investigating reflections, translations and dilations of these functions. Students will then Model and solve problems involving periodic phenomena using transformations of the trigonometric functions, including Modelling and solving practical problems. They will also use logarithmic scales to model and solve problems.

Following this, students will deepen their knowledge of inverse functions and begin the Extension 1 topic, Inverse Trigonometric Functions. They will define inverse trigonometric functions, graph inverse trigonometric functions, and solve problems involving inverse trigonometric functions.

The next topic to be completed will be the Advanced topic Discrete Random Variables. They will use the relative frequencies of discrete random variable datasets to estimate probabilities. The mean or expected value and variance of a probability distribution will be investigated. The topic will involve solving problems involving probabilities, expectation and variance of discrete random variables.

After this we will look at the Advanced topic, Differentiation of Trigonometric, Exponential and Logarithmic Functions. They will apply the rules of differentiation to differentiate trigonometric, exponential and logarithmic functions. This will include applying the chain rule, product rule and quotient rule to differentiate these functions. The topic will conclude with students solving problems involving equations of tangents and normals to curves involving any of the functions within the scope of the Mathematics Advanced course.

Finally, students will work through the Advanced topics The First and Second Derivatives and Applications of the First and Second Derivatives. Students will use repeated differentiation to find second derivatives, analyse stationary points of a function, interpret the second derivative and use it to find a point of inflexion. The last part of this topic looks at solving optimisation problems by using calculus.

During Term 4, students will complete their Task 1 Assessment Task in both the Advanced and Extension 1 Courses. These will contribute 15% of the overall assessment for each course.