Your Solutions - Stage 4 & 5

Angles in Three Squares

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Integral Chasing

Stage: 5 Challenge Level: Challenge Level:1

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

Designing a Polynomial

Stage: 5 Challenge Level: Challenge Level:1

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

Do Rare Events Happen?

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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...

How Fast Does it Grow?

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Exponential functions grow pretty quickly...

Gift of Gems

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

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

Rationals Between...

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

What fractions can you find between the square roots of 65 and 67?

Unit Interval

Stage: 5 Short Challenge Level: Challenge Level:1

Can you prove our inequality holds for all values of x and y between 0 and 1?

Quadrature of the Lunes

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Equation or Identity (2)

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Nested Surds

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you find values that make these surd statements true?

Can You Find... Cubic Curves

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

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