Functions and Graphs - Stage 3
How Far Does it Move?
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
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
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
Route to Infinity
Can you describe this route to infinity? Where will the arrows take you next?
Parallel Lines
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
Collect as many diamonds as you can by drawing three straight lines.
Treasure Hunt
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Maths Filler
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
Reflecting Lines
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
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?
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
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
Lattice Points on a Line
How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?
Graph Area
Can you find the area between this graph and the x-axis, between x=3 and x=7?
Point in Between
Find the point on the line segment AB that is twice as far from B as it is from A.
Linear Area
Find the area of the triangle enclosed by these lines.