TASC Mathematics Methods tutoring

Criteria 1 to 3 apply across all five areas and are assessed by the school. Criteria 4 to 8 are tied to one area each, and those five are also assessed in the external exam. The course document recommends an integrated approach even though the areas can be taught in any order, because so much of the content is inter-related.

The course document highly recommends that students arrive having completed Mathematics Methods Foundation Level 3, or the Australian Curriculum Mathematics 10A with some additional introductory calculus. Assumed knowledge from both is drawn on throughout.

Students must have access to CAS graphics calculators and become proficient with them. The course document also recommends computer software as an aid to learning and lists examples such as Wolfram Mathematica and Microsoft Excel.

Level 4 Methods is described as a necessary prerequisite for Mathematics Specialised Level 4, and as a foundation for tertiary study in engineering, the sciences and related technology fields. For a student who also codes, it is the mathematics behind optimisation and data science.

Every feature of the inverse is predictable from the original. The domain of f is all x except 1 and its range all y except 3; the inverse has domain all x except 3 and range all y except 1. The intercepts (0, 1) and (1/3, 0) become (1, 0) and (0, 1/3). Reflecting in the line y = x swaps everything, and a student who knows that can sketch the inverse before doing any algebra.

This function is one-to-one, so no domain needs restricting. The course document distinguishes functions from relations and asks when an inverse exists, which is why we pair this example with y = (x minus 1) squared, where an inverse exists only after the domain is cut in half.

The composition check in the table is the habit we drill. Feeding a value through the function and then the inverse must return the starting value. Two or three checks take under a minute and catch the most common error, a sign slip when rearranging.

We confirm worked examples like this with a few lines of code that evaluate both functions at many points. In lessons, students write that check themselves, which builds trust in algebra and makes the calculator in Section B a tool for confirming answers rather than finding them.