Chancing upon this tweet from Transum proved fortunate. Hidden gems indeed, I had not noticed the Advanced Starters before, some of which I think could be useful for students aiming at the highest GCSE grades as well as for Advanced Level students.
The problem, Find the Radius, illustrated in the tweet is very neat!

Looking at the Main Transum Starters page I see at the foot of the page we have various categories of starters including the Advanced Starters.
I recommend exploring!
The Custom Starter allows teachers to select the number questions and the topics to include; scroll down the page and choose the topics you want from the Concept Selection.

It is possible to save a particular selection of topics as the URL for your selection will be generated. It is also possible to drag the panels so your questions are displayed in the desired order. The beginning of a lesson can be an ideal time to review previous learning, starters like this can be ideal.

(The excellent MathsBot site also provides Starters which can be customised.)

To find exact solutions we could review trigonometric equations. A reminder here of the Quadratic Equation calculator from Math Warehouse, something I use regularly as full working is shown when using the quadratic formula.

Math Warehouse – Quadratic Equation Calculator

Some further problems which caught my eye, we could try Average Cycling speed with GCSE students aiming for the highest grades. I think I’ll try Algebraic Product with all my classes next week!

Transum – Advanced Starters

A problem such as Reverse Connection could be used with a variety of students, older students could look at an algebraic proof.