Eton College — 13+ Maths Scholarship 2016
Eton College set this 13+ Maths paper in 2016. Hearthprep hosts it as an interactive past paper — 8 questions worth 88 marks in a 90-minute timed mode, each marked on submission and backed by a step-by-step worked solution. Most 13+ entrance exams are sat between November and January of the year of entry.
Real 13+ Maths paper from Eton College (2016). 8 questions, 88 marks. Answer interactively with worked solutions. Covers Algebra, Geometry — Shape, Number & Place Value, Problem Solving & Logic.
This is the school's own past paper, reproduced here with worked solutions by Hearthprep. Most 13+ entrance exams are sat between November and January of the year of entry, so a timed attempt at this paper is worth doing early enough to leave room for the topics it exposes. Work through it on screen with instant marking, or print the PDF and sit it under exam conditions.
- School
- Eton College
- Entry level
- 13+
- Subject
- Maths
- Year
- 2016
- Questions
- 8
- Marks
- 88
- Time allowed
- 90 minutes
- Updated
- 3 Sept 2026
Topics in this paper
- Algebra
- Geometry — Shape
- Number & Place Value
- Problem Solving & Logic
Questions in this paper (3 of 8)
- Question 1short answer · 11 marks
(a) Solve the equation: 0.78(65 - x) + 0.22x = 2.4. (b) In a certain country, there are two political parties, Crimson and Scarlet. However, a quarter of Scarlet voters are embarrassed they vote Scarlet and pretend they vote Crimson in surveys, and similarly a fifth of Crimson voters pretend they vote Scarlet in surveys. In a very large survey, 51.4% of those asked said they would vote Crimson,…
- Question 2short answer · 11 marks
A marathon was due to start at midday, but Mr Tortoise was allowed to start at 7am as he can only walk, which he does at a constant speed of 3 mph. At midday, Mr Hare sets off running at a constant speed of 10 1/2 mph. (a) At what time does he overtake Mr Tortoise? (b) At what time is he exactly two miles ahead of Mr Tortoise?
- Question 3written answer · 11 marks
(a) Expand the brackets and simplify: (i) (x^2 + y^2)^2; (ii) (x^2 - y^2)^2. (b) A right-angled triangle has a hypotenuse of length x^2 + y^2 and another side of length x^2 - y^2 where x and y are positive numbers with x greater than y. Use algebra and your results from above to find the length of the third side. Give your answer in simplified form in terms of x and y. (c) I am trying to draw a…
5 further questions in this paper open with any paid plan, along with marking and the worked solutions. See plans.
Frequently asked questions
What is in the Eton College — 13+ Maths Scholarship 2016?
8 questions with 88 marks in total; Eton College allowed 90 minutes for it. It covers Algebra, Geometry — Shape, Number & Place Value, Problem Solving & Logic. Eton College set it as a 13+ Maths paper.
How long is the Eton College 13+ Maths paper?
Eton College printed an allowance of 90 minutes on this paper. The paper carries 88 marks, roughly 61 seconds a mark.
Can my child answer this paper online?
Yes. Every question on this page can be answered in the browser and is marked the moment the paper is submitted — multiple choice, short answers and written responses alike. Answers are matched leniently, so a correct value written a different way (units, fractions, word numbers) still scores.
Are worked solutions included?
Every question has a step-by-step worked solution and an AI tutor that will talk through it after the paper is submitted. The first 3 questions of this paper are free to try; the remaining 5 and the marking come with a paid plan.
Where does this Eton College paper come from?
This is the school's own past paper, reproduced here with worked solutions by Hearthprep. Use it to time a full mock attempt, then drill whichever topics your child drops marks on.
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