Creating and manipulating expressions and formulae

problem
Algebraic average

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

From this sum of powers, can you find the sum of the indices?
problem
Alternating sum

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

Can you work out the value of x in this 'power-full' equation?
problem
Matchless

Age

14 to 16

Challenge level

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
problem
Gutter

Age

14 to 16

Challenge level

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
problem
Dating made easier

Age

14 to 16

Challenge level

If a sum invested gains 10% each year how long before it has doubled its value?
problem
Nicely similar

Age

14 to 16

Challenge level

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
problem
Sums of pairs

Age

11 to 16

Challenge level

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
problem
Simultaneous multiplying

Age

14 to 16

Challenge level

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 $a+b+c$?