### There are 16 results

Broad Topics >

Algebra > Expanding and factorising quadratics

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

Find the largest integer which divides every member of the
following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

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

The sums of the squares of three related numbers is also a perfect
square - can you explain why?

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

Explore what happens when you draw graphs of quadratic equations
with coefficients based on a geometric sequence.

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

A composite number is one that is neither prime nor 1. Show that
10201 is composite in any base.

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

Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.

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

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

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

Can you convince me of each of the following: If a square number is
multiplied by a square number the product is ALWAYS a square
number...

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

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to. . . .

##### Age 14 to 18 Challenge Level:

Find all the triples of numbers a, b, c such that each one of them
plus the product of the other two is always 2.

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

Can you find the hidden factors which multiply together to produce
each quadratic expression?

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

A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?

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

A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?

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

Can you explain the surprising results Jo found when she calculated
the difference between square numbers?

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

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .

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

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

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

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number.
(b) Prove that 11^{10}-1 is divisible by 100.