Graph sketching

problem
Guess the function

Age

16 to 18

Challenge level

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.
problem
Area L

Age

16 to 18

Challenge level

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?
problem
Spot the difference

Age

16 to 18

Challenge level

If you plot these graphs they may look the same, but are they?
problem
Brimful

Age

16 to 18

Challenge level

Can you find the volumes of the mathematical vessels?
problem
Folium of Descartes

Age

16 to 18

Challenge level

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
problem
Polar flower

Age

16 to 18

Challenge level

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.
problem
Rational request

Age

16 to 18

Challenge level

Can you make a curve to match my friend's requirements?
problem
Interpolating polynomials

Age

16 to 18

Challenge level

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.