This is an update on developments of our Maths Advanced database, following on from our EXT1 update in late May.
The Topic Guidance documents and sample exam questions that were released in Term1 provide a treasure trove of quality information for developing our question databases, particularly in new content areas.
The SmarterMaths platform allows us to be quick on our feet and adjust our database in real time as better information comes to light. This email aims to provide a brief summary of the database improvements that have occurred incrementally over the last few months.
One important change worth noting is that the database now includes EQ-Bank titled questions. This stands for “exemplar question bank”. If syllabus or Topic Guidance documents point to a deficiency in our database, we will use this information to create EQ-Bank questions to supplement the topic area.
To all interested Advanced teachers, recent developments are summarised below.
F1 Working With Functions
- NESA sample exam sheds some light on possible composite function question styles. This has been reflected in the database.
- NESA Adv sample exam included a challenging simultaneous equation question that was a slight surprise to us. Specific revision here is warranted and is now in the database.
- Set notation for describing the domain and range of functions is all through the NESA sample exam, a clear flag that this needs to be very well understood. Added database examples test student competence in this area.
- Algebraic Techniques – we include numerous questions with surd denominators at the expense of historical surd questions that require conjugate surds to rationalise a denominator.
- NESA sample exam is instructive in developing “transformation” revision examples. This has been a difficult area to cover and the database has been beefed up to reflect this welcome new information.
- Graphing absolute value functions is an area we thought would be important in the new syllabus. We are now even more convinced of this, especially in the “transformation of functions” space. See the EQ-Bank examples added to the database in this area.
- Past HSC questions constitute an outstanding revision set in this area although numerous examples examining the differentiation of forms a^x and log_a(x) are added to address this “new” area.
- A significant allocation in the NESA trial exam that required students to use applications of integrals caused us to sit up and pay attention.
- In response, we have created a new C4 sub-topic that is named “Other Integration Applications”. This includes motion applications among other underlying themes and warrants its upgraded status in our database.
S2 Interpretation and Bivariate Data
- Pareto Charts (common ADV content with STD2) were examined in the 2019 STD2 HSC with a shockingly low mean mark. Numerous EQ-Bank questions now cover this area, along with the 2019 STD2 example (see “S2 Other Chart Types“).
- Calculating a least squares regression line using a calculator was asked in the NESA ADV sample exam. We regard executing this (and associated calculations) efficiently as an important skill and the database within S2 Bivariate Data Analysis now reflects this view.
S3 Random Variables
- Probability Density Functions represent extremely “examinable” content and must be a revision focus in our view. Our database has grown to an hour and a half in this area, with the recent NESA topic guidance and sample exam informing the style of recently added questions.
- NESA guidance flags that finding cumulative distribution functions from probability density functions is likely to be a key element when this area is examined (departing from the Victorian experience in this topic area). EQ-Bank questions have been added to address this important information.
- Normal Distribution has a great potential overlap with STD2 and an extensive past HSC question covers this thoroughly.
- We note the syllabus dot point of combining the probability density function with the trapezoidal rule. Familiarity with this relationship and question type is clearly important in our view, and EQ-Bank questions now review this thoroughly.
M1 Modelling Financial Investments and Loans
- An interesting extension to STD2 questions in this area appeared in the NESA sample exam. M1 EQ-Bank 1 revisits this concept for revision that doesn’t exist in the past HSC question bank of STD2.