Creating and manipulating expressions and formulae

problem

Square Ratio

Age

14 to 16

Challenge level

2 out of 3

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?
problem

Big Fish

Age

14 to 16

Challenge level

2 out of 3

Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces in order to weigh it...
problem

Simultaneous Multiplying

Age

14 to 16

Challenge level

2 out of 3

If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?
problem

Alternating Sum

Age

14 to 16

Challenge level

2 out of 3

Given that the number 2008 is the correct answer to a sum, can you find n?
problem

Algebraic Mean

Age

14 to 16

Challenge level

2 out of 3

The mean of three numbers x, y and z is x. What is the mean of y and z?
problem

Three Fruits

Age

14 to 16

Challenge level

2 out of 3

Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?
problem

Average Surroundings

Age

14 to 16

Challenge level

2 out of 3

Can you work out Ali's age based on the diagram?
problem

Divisible Expression

Age

14 to 16

Challenge level

2 out of 3

Can you show this algebraic expression is divisible by 4?
problem

How Do You React?

Age

14 to 16

Challenge level

2 out of 3

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
problem

Robert's Spreadsheet

Age

14 to 16

Challenge level

2 out of 3

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?