Simultaneous equations

problem

Escriptions

Age

16 to 18

Challenge level

1 out of 3

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
problem

Battery Modelling

Age

16 to 18

Challenge level

1 out of 3

Find out how to model a battery mathematically
problem

Coffee

Age

14 to 16

Challenge level

2 out of 3

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?
problem

All Square

Age

11 to 14

Challenge level

2 out of 3

Solve the system of equations xy = 1 yz = 4 zx = 9
problem

Double Time

Age

16 to 18

Challenge level

2 out of 3

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.
problem

Pareq Calc

Age

14 to 16

Challenge level

3 out of 3

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.
problem

Nine, Ten and One

Age

11 to 14

Challenge level

1 out of 3

Can you find the value of t in these equations?
problem

Colour Islands Sudoku

Age

11 to 14

Challenge level

1 out of 3

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
problem

Addition Equation Sudoku

Age

11 to 14

Challenge level

1 out of 3

You need to find the values of the stars before you can apply normal Sudoku rules.
problem

In Sum-Mary

Age

11 to 14

Challenge level

1 out of 3

What does the sum of these three numbers tell us about their product?