\( \DeclareMathOperator{cosec}{cosec} \)

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Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Graph Paper Flexible graph paper which can be printed or projected onto a white board as an effective visual aid.
- Deconstructing Graphs Fill in the tables of values from the information that can be read from the given graphs.
- Graph Plotter An online tool to draw, display and investigate graphs of many different kinds.
- Using Graphs Use the graphs provided and create your own to solve both simultaneous and quadratic equations.

Here are some exam-style questions on this statement:

- "
*(a) Use the red graphs to solve the simultaneous equations:*" ... more - "
*Estimate the solutions of the following simultaneous equations using their graphs as drawn on the grid below.*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Coordinates It is important that pupils become proficient at understanding coordinates at a basic level before using them in their study of graphs. Plotting points and finding the coordinates of points are the pre-requisite skills for studying a number of branches of mathematics. The Cartesian plane consists of a horizontal x-axis and a vertical y-axis that intersect at the origin (0, 0). The mathematician René Descartes developed the concept of the Cartesian plane while lying in bed one morning and observing a fly on the ceiling! Pupils should learn the conventions starting with knowing that the horizontal axis is the x-axis and the vertical axis is the y-axis (remember x is a cross so the x axis is across!). The axes meet at the origin which has coordinates (0,0). Coordinates are written as two numbers separated by a comma and contained inside brackets. For example (3,9) means the point is above 3 on the x-axis and level with 9 on the y-axis. To get to this point from origin you go along 3 and up 9 (remember to go along the hall before going up the stairs or that pole vaulter has to run along before leaping up into the air!). Coordinates can be positive or negative (remember points to the right of the origin have a positive x-coordinate – being positive is right!). The abscissa often refers to the horizontal coordinate of a point and the ordinate refers to the vertical coordinate. In three dimensions, three perpendicular lines are defined as the axes and the coordinates of each point is defined with three numbers.
- Simultaneous Equations This topic covers simultaneous equations with two different variables. The starters pose real world problems which can be solved using the techniques taught at school or by other intuitive methods. Though there are many formal strategies for solving simultaneous equations the skill of forming the equations from real life situations is a very important stage in working towards a solution. Algebraic methods are the most efficient for solving basic simultaneous equations but graphical methods, probably using a graphic display calculator or computer software package, may be more suitable for less standard sets of simultaneous equations.

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