# A Level Geometry

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### Geometry

Mathcentre provide these resources which cover aspects of geometry and are suitable for students studying mathematics at A Level, those for whom mathematics is an integral part of their course and some apply to GCSE Higher Level students. **The topics covered include the geometry of a circle, polar coordinates, the gradient and intercept of straight lines and properties of straight line segments.**

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of geometry will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided.

### Geometry

Mathcentre provide these resources which cover aspects of geometry often used in the field of engineering. **They include the gradient and intercept of straight line graphs, polar coordinates and converting degrees and radians**.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of geometry will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided.

### Geometry

Mathcentre provide this resource which covers the slope intercept form, an aspect of geometry that involves** the gradient and vertical intercept of a graph, which can be established from the terms of a linear equation.**

Comprehensive notes, with clear descriptions are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of gradients and intercepts will find it useful, as there are a selection of questions to be completed, for which answers are provided.

### Hyperbolic Geometry

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation introduces Euclid's axioms and theorems and provides historic information on the development of geometric principles, as well as discussing hyperbolic geometry. A link to Non-Euclid software, from Joel Castellanos's site at the university of New Mexico, is also available.

The activity is designed to explore aspects of the subject which may not normally be encountered, to encourage new ways to approach a problem mathematically and to broaden the range of tools that an A Level mathematician can call upon if necessary.

### Could Pi Be 3?

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation investigates the value of π in different types of geometry and provides a link for students to experiment with Hyperbolic geometry. The classic definition of a distance function, or metric, is given and a version of the Manhattan metric provides an interesting outcome.

The activity is designed to explore aspects of the subject which may not normally be encountered, to encourage new ways to approach a problem mathematically and to broaden the range of tools that an A Level mathematician can call upon.

### Coordinate Geometry

Seven RISP activities covering a range of topics, each one having some activity which explores coordinate geometry.**Circle Property:** Students generate two coordinates. The coordinates form the end points of the diameter of a circle. Students have to find the equation of the circle formed, compare their results with colleagues and explain their findings.**Circles or Not?:** Students use a graph plotter to alter the coefficients of the equation of a circle and explore which values produce a circle and why.**Tangents:** Explores the equation of a tangent to a quadratic. Students are asked to use a graph plotter to draw a quadratic graph of the form y=x^{2} + a^{2}, then draw a line y=kx altering the value of k until the line is a tangent to the curve. Students then form a relationship between k and a.**More Venn diagrams:** A Venn diagram is given with the three sets defined. Students have to generate a pair of straight lines for each region. The activity is repeated for quadratic equations.**Six Parabolas:** Students explore the properties of six quadratic graphs using a graph plotter.**Advanced Arithmogons**: Extends the idea of numerical arithmogons to coordinate geometry, algebraic fractions, product rule and quotient rule.**Parabolic Clues:** Students have to identify the equation of a parabola given four properties. The twist to this activity is that a quadratic can be found which has any three properties but in each case not the fourth

### Circle Geometry

Three advanced level lesson ideas from Susan Wall designed to explore the properties of circles and their equations. Each activity is accompanied by teacher notes suggesting how the activity could be delivered and possible extension ideas.

The first activity requires students to match the equations of circles to statements cards. There is not a unique solution to this problem thus requiring students to explain the mathematics used to justify their solution.

The second activity asks students to determine whether each of a number of statements is true or false. Once again students are required to justify their answer showing the mathematics they have used. In this exercise students are required to complete the square to rearrange the equation of the circle into a form that can be used to determine whether the statement is true or false.

The third activity contains a miscellany of probing questions which can be used in a variety of ways in the classroom in order to assess student understanding.