We have added a set of question generators on transformations of functions to TopTopics. These generate both questions that ask students to perform transformations and questions that ask them to identify transformations. Here are a few examples:
Most of the question generators on the site are focussed on procedural bread-and-butter. In order to better cater for students aiming at higher grades, we have started creating generators for longer form questions. Last month, we created resources on vectors. Over the Christmas break at the end of 2020, we added a similar resource covering functions, including composite and inverse functions. We are using compilations of these to create printable topic-focused mini exams, with worked solutions. See the Teacher Resources at A7c. As will be the case for all our mini-exams, there are two printable “fixed” mini exams in PDF, but you can also produce further versions with dynamically generated questions. Note that these dynamic versions are also printable.
A stepping-stone to factorising by inspection
Ideally, I’d like all of my students to factorise quadratic expressions by inspection, rather by using a more formal method. Before attempting to factorise by inspection, fluency in expanding brackets is essential. In particular, it is helpful if students can effortlessly expand mentally. A key hurdle in this process is finding the coefficient of the linear term, since it involves a bit more than the coefficients of the quadratic and constant terms. This applet allows students to ignore those terms and just focus on the mental arithmetic required to find the coefficients of the linear terms. Note that there are also some non-quadratic expressions here to force the students to think and prevent them from answering all of these by some kind of mindless algorithm:
Shortcut and mashup questions
We have continued to add more of these, and will continue to do so.
More behind-the-scenes work…
As previously mentioned we have been creating manylonger-form question generators, which we’ll be able to use to create more topic-based mini exams like the one on functions described above, but we have bigger plans for these question generators, which we’ll be able to release in January 2021.