Your Solutions - Stage 4 & 5

Angles in Three Squares

Stage: 3 and 4 Challenge Level:

Drawing the right diagram can help you to prove a result about the angles in a line of squares.

Matching Criminals

Stage: 4 and 5 Challenge Level:

DNA profiling is an invaluable tool for the police. However, when it comes to probability, things aren't always as straightforward as they seem.

Who's the Best?

Stage: 3 and 4 Challenge Level:

Which countries have the most naturally athletic populations?

Charting Success

Stage: 3 and 4 Challenge Level:

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

Integral Chasing

Stage: 5 Challenge Level:

Can you find the missing constants from these not-quite-so-obvious definite integrals?

Designing a Polynomial

Stage: 5 Challenge Level:

Can you find a polynomial function whose first derivative is equal to the function?

Puzzling Place Value

Stage: 4 Challenge Level:

Can you explain what is going on in these puzzling number tricks?

Gabriel's Problem

Stage: 3 and 4 Challenge Level:

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Journey to School

Stage: 3 and 4 Challenge Level:

How risky is your journey to school?

Risk and Crime

Stage: 4 Challenge Level:

Are you at risk of being a victim of crime? How does your perception of that risk compare with the facts and figures?

Trusting the Tabloids

Stage: 3 and 4 Challenge Level:

Can you match the cards and figure out whether the tabloid headlines can be trusted?

Spots and Measles

Stage: 3 and 4 Challenge Level:

99% of people who have measles have spots. Ben has spots. Do you think he has measles?

Do Rare Events Happen?

Stage: 3 and 4 Challenge Level:

I'd be very surprised if I had three children all with the same birthday, but I read in the paper that it happened to one family...

The ELISA Test

Stage: 4 and 5 Challenge Level:

In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?

How Fast Does it Grow?

Stage: 5 Challenge Level:

Exponential functions grow pretty quickly...

Stage: 4 Challenge Level:

Four jewellers share their stock. Can you work out the relative values of their gems?

Stage: 5 Challenge Level:

A lune is the area left when part of a circle is cut off by another circle. Can you work out the area?

Can You Find... Trigonometry Edition

Stage: 5 Challenge Level:

What graphs can you make by transforming sine, cosine and tangent graphs?

Equation or Identity (2)

Stage: 5 Challenge Level:

Here are some more triangle equations. Which are always true?

Nested Surds

Stage: 5 Challenge Level:

Can you find values that make these surd statements true?

Can You Find... Cubic Curves

Stage: 5 Challenge Level:

Can you find equations for cubic curves that have specific features?