# Further Thinking Questions

This collection from Susan Wall, is a more comprehensive version of the resource 'Thinking Questions'. Each resource contains a number of open–ended questions which explore understanding and allow a variety of approaches. Each question is easily accessible but can be extended to make a more complex problem. Students are required to justify their answer and, where possible, generalise their answer. Students require problem solving skills and reasoning skills to tackle the problems; trial and error alone will not be sufficient.

Topics covered are: Indices and surds, sequences, logarithms, algebra, straight line graphs, quadratics, polynomials, circles, Trigonometrical functions and differentiation and integration.

## Resources

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### Straight Line Graphs

This resource contains seven problems requiring students to think, explore, explain and justify the mathematics they use in order to solve the problems presented. Students will explore the equations of straight lines, parallel lines, perpendicular lines, equations of straight lines in a variety of forms and to find...

This resource contains eleven problems requiring students to explore the graphs of quadratic equations, intersection points of quadratics and straight lines, explain what will be the same and what will be different about the graphs of two quadratic functions, transform quadratic graphs, find the odd one out,...

### Polynomials

This resource contains seven problems requiring students to explore the graphs of polynomials. Students are required to explain how they know whether a graph will cross the x axis, explain the differences and similarities of the graphs of two polynomials given just the equation, asked to devise questions that could...

### Circles

This resource contains eight problems requiring students to explore the equations of a variety of circles. Many of the problems are open-ended in so much as there is not a specific answer. These problems present the opportunity for rich discussion as students attempt to justify their solution. Students are required...