# Expanding and Factorising Quadratics - Short Problems

### Weekly Problem 39 - 2009

##### Stage: 4 Short Challenge Level:

Can you show this algebraic expression is divisible by 4?

### Square Product

##### Stage: 4 Short Challenge Level:

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

### Two Girls

##### Stage: 4 Short Challenge Level:

Weekly Problem 45 - 2012
There are 10 girls in a mixed class. If two pupils are selected, the probability that they are both girls is 0.15. How many boys are in the class?

### Square and Cube

##### Stage: 3 and 4 Short Challenge Level:

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

### Little Difference

##### Stage: 3 and 4 Short Challenge Level:

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