Find a quadratic formula which generalises Pick's Theorem.
Crack this code which depends on taking pairs of letters and using
two simultaneous relations and modulus arithmetic to encode the
A moveable screen slides along a mirrored corridor towards a
centrally placed light source. A ray of light from that source is
directed towards a wall of the corridor, which it strikes at 45
degrees. . . .
Given the mean and standard deviation of a set of marks, what is
the greatest number of candidates who could have scored 100%?
Explore the two quadratic functions and find out how their graphs
A introduction to how patterns can be deceiving, and what is and is not a proof.
Here are some more quadratic functions to explore. How are their
Prove that 3 times the sum of 3 squares is the sum of 4 squares.
Rather easier, can you prove that twice the sum of two squares
always gives the sum of two squares?
Can you find a rule which relates triangular numbers to square numbers?
Rotate a copy of the trapezium about the centre of the longest side
of the blue triangle to make a square. Find the area of the square
and then derive a formula for the area of the trapezium.
Let a(n) be the number of ways of expressing the integer n as an
ordered sum of 1's and 2's. Let b(n) be the number of ways of
expressing n as an ordered sum of integers greater than 1. (i)
Calculate. . . .
Write 100 as the sum of two positive integers, one divisible by 7 and the other divisible by 11.
Then find formulas giving all the solutions to
7x + 11y = 100
where x and y are integers.
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
Can you work out which processes are represented by the graphs?
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
Which line graph, equations and physical processes go together?
Show that all pentagonal numbers are one third of a triangular number.
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Can you find a rule which connects consecutive triangular numbers?