Why use Review Questions?

Unlike the other resources on the site, which were designed specifically for classroom use, Review questions were originally designed for summative assessment (they are past examination questions, reproduced almost verbatim – see below). The questions we have selected allow for a variety of uses in the classroom, and though the questions have a single correct final answer, many of them can be approached in more than one way.

Among other things, these questions can support students to:

  • Develop their problem-solving and proof skills
  • Recognise where and how prior learning applies to a question that they have never seen before
  • Identify areas in which their understanding is less well-formed
  • Reflect on where and how connections between mathematical ideas could be made
  • Draw on mathematical behaviours and problem solving strategies to see a way into a problem, and to help them to become “unstuck” when necessary
  • Reflect on whether there are more efficient approaches to particular problems (or parts of problems), making use of alternative representations where possible

Typically, the original exam questions have little scaffolding, so students are not told how to go about reaching a solution. We have provided a Suggestion section for some Review questions, offering ideas for how to think about the problem. Each Review question is also accompanied by a complete solution, which contains the thinking behind at least one approach to the problem, and may offer links to related ideas.

Possible approaches

These questions can be used in a variety of ways. Here are a few possible ones.

  • Using a question to introduce an idea

    Sometimes a question can be used as a stimulus to introduce a new idea or to develop a new skill. The question could then be revisited later to reflect on what has been learnt. For example R7433 could be used to introduce stationary points, second derivatives and/or points of inflection.

  • Using a question to develop understanding

    Our other resources often suggest ways of working which are equally applicable to these Review questions. For example, students could…

    • … share and reflect on the different approaches used.

    • … be asked to “Say what you see” if the question contains a diagram. This offers a way to develop awareness of significant features of the question and encourage students to reflect on the tools they already have that may help them here.

    • … explore the question further by asking questions such as “What happens if …?” This might mean thinking about different representations, or generalising a problem. An example of this can be seen in R7350, where the Solution section includes a challenge to generalise the problem from a quadratic to a cubic.

  • Using a question to consolidate and review material

    Questions could be used at the end of a topic, or at a later date, as a way to bring different concepts together and to observe what prior learning students can apply. It could be enhanced by asking students to justify their answer (if the question does not ask for this), or to recall the key results from the relevant topic or topics, or to present their reasoning to the class. Question R5276 brings together polynomials and arithmetic series, for example.

Examples of some other Review questions and ideas on how they could be used are offered in the remaining sections.

Selecting Review questions

A number of Review questions are featured at each station, while more are available at some stations by clicking “Include additional \(N\) questions” at the end of the list.

Review questions can also be browsed by clicking on the “Browse” button at the top-right of the page: Copy of the browse button. Through this mechanism, the source of the question can easily be seen, and questions can be filtered by type (O/AO-level papers, A-level papers, STEP papers, Oxford MAT papers, and so on).

The source of the Review questions

The Review questions all come from past examinations. We have reproduced the wording as accurately as possible, though we have not made any attempt to preserve the style of question part numbering. (Some papers used (a), (b), (c), while others used (i), (ii), (iii), for example.) We have made some light editorial changes to clarify instructions, for example “Without the use of tables” now has “[or calculators]” added, and some multiple choice questions have an added instruction to choose the correct option. We have not used questions written in Imperial units (in, lb, …) if the question requires detailed knowledge of these units.