Year 11+ Being resourceful

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

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

Can you find the area of a parallelogram defined by two vectors?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Can you work out the probability of winning the Mathsland National Lottery?

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?

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Use the differences to find the solution to this Sudoku.

The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Find the sum of this series of surds.

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

Can you work out the equations of the trig graphs I used to make my pattern?