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Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
Can you work out which processes are represented by the graphs?
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
This problem challenges you to find cubic equations which satisfy different conditions.
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
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.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
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.
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
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.
This problem challenges you to sketch curves with different properties.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you draw the height-time chart as this complicated vessel fills with water?
What biological growth processes can you fit to these graphs?
The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.