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Can you work out the equations of the trig graphs I used to make my pattern?

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Can you deduce which Olympic athletics events are represented by the graphs?

Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

Class 5 were looking at the first letter of each of their names. They created different charts to show this information. Can you work out which member of the class was away on that day?

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Can you find trig graphs to satisfy a variety of conditions?

Draw graphs of the sine and modulus functions and explain the humps.

Can you adjust the curve so the bead drops with near constant vertical velocity?

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has. . . .

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Be playful with graphs and networks, and see what theorems you can discover!

Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x

If you can sketch y=f(x), there are several related functions you can also sketch...

What graphs can you make by transforming sine, cosine and tangent graphs?

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

Look for the common features in these graphs. Which graphs belong together?

You can get a great feel for functions by sketching their graphs or using graph plotting software...

Can you work out which processes are represented by the graphs?

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

This module looks at some of the things you need to understand about polar coordinates.

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Can you find sets of sloping lines that enclose a square?

A collection of short problems on straight line graphs.

How does the temperature of a cup of tea behave over time? What is the radius of a spherical balloon as it is inflated? What is the distance fallen by a parachutist after jumping out of a plane?. . . .

What can you say about this graph? A number of questions have been suggested to help you look at the graph in different ways. Use these to help you make sense of this and similar graphs.

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.