Stage 4 & 5 Toughnuts

Matching Criminalslive

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Picture the Process I

Stage: 5

How does the temperature of a cup of tea behave over time? What is the radius of a spherical balloon as it is inflated? What is the distance fallen by a parachutist after jumping out of a plane? After sketching graphs for these and other real-world processes, you are offered a selection of equations to match to these graphs and processes.

Two-way Functions

Stage: 5

This gives you an opportunity to explore roots and asymptotes of functions, both by identifying properties that functions have in common and also by trying to find functions that have particular properties. You may like to use the list of functions in the Hint, which includes enough functions to complete the table plus some extras.You might like to work on this problem in a pair or small group, or to compare your table to someone else's to see where you have used the same functions and where not.

Factorial Fragments

Stage: 5 Challenge Level: Challenge Level:1

Here you have an expression containing logs and factorials! What can you do with it?

Quadrature of the Lunes

Stage: 5 Challenge Level: Challenge Level:1

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:1

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

Equation or Identity (2)

Stage: 5 Challenge Level: Challenge Level:1

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

Nested Surds

Stage: 5 Challenge Level: Challenge Level:1

Can you find values that make these surd statements true?

Irrational Constructions

Stage: 5 Challenge Level: Challenge Level:1

What questions does the spiral construction prompt you to ask?

Can You Find... Trigonometric Edition Part 2live

Stage: 5 Challenge Level: Challenge Level:1

Can you find trig graphs to satisfy a variety of conditions?

How Fast Does it Grow?

Stage: 5 Challenge Level: Challenge Level:1

Exponential functions grow pretty quickly...