Maths GCSE

Overview of the graphs we have to learn.

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1. x squared graphs

All x squared graphs have the same symmetrical bucket shape.

If the x squared is negative then the bucket is upside down.

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2. x cubed graphs

All x cubed graphs have the same wiggle in the middle, but it can be a flat wiggle or a more pronounced wiggle.

The negative x cubed graphs always come down from the top left whereas the positive x cubed graphs go up from the bottom left

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3. 1/x graphs

These graphs are all the same basic shape, except that the negative ones are in the opposite quadrants to the positive ones.

The two halves of the graph don't touch. They're symmetrical about the lines y = x and y = -x.

This is alos the type of graph you get with inverse proportion. 


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4. k^x graphs (where k is +ve)

These graphs curve upwards when k < 1.

They are always above the x-axis and they all go through the point (0,1).

For bigger values of k, the graph trails off towards the zero end more quickly on the left and climbs more steeply on the right.

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5. Circles

The equation for a circle with centre (0,0) and radius r is :

x squared + y squared = r squared

For example, x squared + y squared = 25 is a circle with centre (0,0).

r squared = 25, so the radius is 5.

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