# Your Solutions - Stage 4 & 5

### System Speak

##### Stage: 5 Challenge Level:

Five equations... five unknowns... can you solve the system?

### Mega Quadratic Equations

##### Stage: 5 Challenge Level:

What do you get when you raise a quadratic to the power of a quadratic?

### Building Tetrahedra

##### Stage: 4 Challenge Level:

Can you make a tetrahedron whose faces all have the same perimeter?

### Of All the Areas

##### Stage: 4 Challenge Level:

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

### Area L

##### Stage: 5 Challenge Level:

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

### Graphs of Changing Areas

##### Stage: 5 Challenge Level:

Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

### Towering Trapeziums

##### Stage: 4 Challenge Level:

Can you find the areas of the trapezia in this sequence?