Expanding and Factorising Quadratics - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Expanding and Factorising Quadratics.

Square and Cube

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 24 - 2014
The square of a positive number is twice as big as the cube of that number. What is the number?

Relative Powers

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 10 - 2007
The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?

Divisible Expression

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 39 - 2009
Can you show this algebraic expression is divisible by 4?

Square Product

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 10 - 2011
Will this product give a perfect square?

Little Difference

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 30 - 2014
What is the value of $2006 \times 2008 - 2007 \times 2007$?