### There are 15 results

Broad Topics >

Algebra > Formulae

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

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

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

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

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

Can you find a rule which connects consecutive triangular numbers?

##### Age 11 to 14 Challenge Level:

The diagram shows a 5 by 5 geoboard with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins. What is the total number of squares that can be made on a. . . .

##### 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 11 to 14 Challenge Level:

Draw a pentagon with all the diagonals. This is called a pentagram.
How many diagonals are there? How many diagonals are there in a
hexagram, heptagram, ... Does any pattern occur when looking at. . . .

##### 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:

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

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

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

##### 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 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 11 to 14 Challenge Level:

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

##### 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:

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?