Your Solutions - Stage 4 & 5

Tens

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

Giants

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

Rhombuses from Diagonals

Stage: 3 and 4

Take a look at the video showing rhombuses and their diagonals...

Getting Round the City

Stage: 3 and 4

In a city with a grid system of roads, how do you get from A to B?

Quadrilaterals in a Square

Stage: 4 Challenge Level: Challenge Level:1

What's special about the area of quadrilaterals drawn in a square?

Garden Shed

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you minimise the amount of wood needed to build the roof of my garden shed?

Powerful Quadratics

Stage: 5

This comes in two parts, with the first being less fiendish than the second. It’s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.

Summing to One

Stage: 5 Challenge Level: Challenge Level:1

This problem is a nice introduction that will give you a feeling for how logs work and what that button on your calculator might be doing.

Proving the Laws of Logarithms

Stage: 5 Challenge Level: Challenge Level:1

Here you have an opportunity to explore the proofs of the laws of logarithms.

Can You Find ... Cubic Edition

Stage: 5 Challenge Level: Challenge Level:1

Can you find cubic functions which satisfy each condition?

Can You Find ... Asymptote Edition

Stage: 5 Challenge Level: Challenge Level:1

Given a sketch of a curve with asymptotes, can you find an appropriate function?

A Tangent Is ...

Stage: 5 Challenge Level: Challenge Level:1

What do we REALLY mean when we talk about a tangent to a curve?

Transformation ... or Not?

Stage: 5 Challenge Level: Challenge Level:1

This graph looks like a transformation of a familiar function...