Working systematically

problem
Put out

Age

16 to 18

Challenge level

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?
problem
Spread

Age

16 to 18

Challenge level

Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?
problem
Towards Maclaurin

Age

16 to 18

Challenge level

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.
problem
Over-booking

Age

16 to 18

Challenge level

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 2% of flights are over-booked?
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.