Entrance exams to UK schools usually want to get an idea of a child's underlying intelligence as well as overall academic ability. A school wants to find out not just what the student knows now, but also how quickly they are likely to learn in the future. One happy consequence is that they tend to get creative with their maths questions. Although you'll get your usual straightforward questions early on, the later questions can be downright fiendish, especially considering the age group. I've collected some of the best ones here.

11+ questions

The first two are from the London girls' school consortium, which includes schools such as City of London, Francis Holland, South Hampstead and Channing. The third question is from an entrance exam for Hokkien school in Singapore. The final question is one of my own devising (which relies on prime numbers).

Question 1: London Consortium 11+

quiz show red car

Question 2: London Consortium 11+

ABCD is a 4 digit number

Question 3: London Consortium 11+


Question 4: written by me

Find the dimensions of a rectangle which has an area of 4800cm² and a perimeter of 320cm.

Question 5 & 6: London Consortium 11+

equilateral triangle shaded & secret fruit gums.png



13+ questions

Scholarship papers are always great for a challenge - these questions are from King's School Canterbury, Sevenoaks and Eton.

Question 1: King's School Canterbury

Martini glass Kings 13+

Question 2: Sevenoaks School

13+ Q

Question 3: King's School Canterbury

Monty q

Question 4: Eton College 2012

Eton 13+ Maths Scholarship Question Factors

16+ / GCSE

Unfortunately GCSE papers very rarely get that creative with their questions. However, some textbook authors still throw some interesting ones in there. In addition, there are plenty of intriguing questions to be found on 16+ papers. 

Question 1: from GCSE Mathematics: Revision and Practice: Higher: Students' Book by David Rayner

Fishtank p304

Question 2: St Paul's Girls' School 16+ question reproduced from memory by a student

cube dipped in paint

Question 3: De Leys Cambridge Scholarship 16+ 

De Leys Cambridge Scholarship Paper

Since I frequently set these questions for homework, I will not publish the answers. However, you can always send me an email and ask for some guidance. You can also find more 11+ exam papers here, and 13+ exam papers here.