# Functions and Graphs - Stage 3

### How Far Does it Move?

##### Age 11 to 14 Challenge Level:

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

### Speeding Up, Slowing Down

##### Age 11 to 14 Challenge Level:

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

### Up and Across

##### Age 11 to 14 Challenge Level:

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.

### Route to Infinity

##### Age 11 to 14 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next?

### Parallel Lines

##### Age 11 to 14 Challenge Level:

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

### Diamond Collector

##### Age 11 to 14 Challenge Level:

Collect as many diamonds as you can by drawing three straight lines.

### Cops and Robbers

##### Age 7 to 16 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

### Maths Filler

##### Age 11 to 14 Challenge Level:

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

### Reflecting Lines

##### Age 11 to 14 Challenge Level:

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

### Translating Lines

##### Age 11 to 14 Challenge Level:

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

### How Steep Is the Slope?

##### Age 11 to 14 Challenge Level:

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

### Fill Me Up

##### Age 11 to 14 Challenge Level:

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

### Lattice Points on a Line

##### Age 11 to 14 Short Challenge Level:

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

### Graph Area

##### Age 11 to 14 Short Challenge Level:

Can you find the area between this graph and the x-axis, between x=3 and x=7?

### Point in Between

##### Age 11 to 14 Short Challenge Level:

Find the point on the line segment AB that is twice as far from B as it is from A.

### Linear Area

##### Age 11 to 14 Short Challenge Level:

Find the area of the triangle enclosed by these lines.