### There are 18 results

Broad Topics >

Algebra > Formulae

##### Age 16 to 18 Challenge Level:

Find a quadratic formula which generalises Pick's Theorem.

##### Age 16 to 18

A introduction to how patterns can be deceiving, and what is and is not a proof.

##### Age 14 to 16 Challenge Level:

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

##### Age 14 to 16 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?

##### Age 14 to 16 Challenge Level:

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. . . .

##### Age 14 to 16 Challenge Level:

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. . . .

##### Age 14 to 16 Challenge Level:

Here are some more quadratic functions to explore. How are their
graphs related?

##### Age 14 to 16 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.

##### 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%?

##### Age 16 to 18 Challenge Level:

Crack this code which depends on taking pairs of letters and using
two simultaneous relations and modulus arithmetic to encode the
message.

##### Age 14 to 16 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

##### Age 16 to 18 Challenge Level:

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?

##### Age 14 to 16 Challenge Level:

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.

##### Age 14 to 16 Challenge Level:

Explore the two quadratic functions and find out how their graphs
are related.

##### Age 11 to 18 Challenge Level:

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

##### Age 14 to 16 Challenge Level:

Can you work out which processes are represented by the graphs?

##### Age 14 to 16 Challenge Level:

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?

##### Age 16 to 18 Challenge Level:

Which line graph, equations and physical processes go together?