Eton College — 13+ Maths Scholarship 2018 (Paper B)
Eton College set this 13+ Maths paper in 2018. Hearthprep hosts it as an interactive past paper — 8 questions worth 80 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 (2018). 8 questions, 80 marks. Answer interactively with worked solutions. Covers Algebra, Fractions, Decimals & Percentages, Geometry — Shape.
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
- 2018
- Questions
- 8
- Marks
- 80
- Time allowed
- 90 minutes
- Updated
- 3 Sept 2026
Topics in this paper
- Algebra
- Fractions, Decimals & Percentages
- Geometry — Shape
Questions in this paper (3 of 8)
- Question 1short answer · 10 marks
a) Solve for x: 1 / (3 + 1/x) = 3/16 b) Solve for x: 1 / (1 + 1/(1 + 1/x)) = 5/7 Notice that 5/11 = 1/(11/5) = 1/(2 + 1/5). c) Find positive integers a, b, and c such that 1 / (a + 1/(b + 1/c)) = 7/17
- Question 2short answer · 10 marks
OPQR is a square of side length 3 cm. PU = QT = RS = x cm, where 0 < x < 3. The shaded region OSTU has area A. (S lies on side OR, T lies on side RQ, U lies on side QP — each x cm from R, Q, P respectively.) a) Show that A = x² − (9/2)x + 9 b) Expand (x − 9/4)², simplifying fully. c) Hence find a number d such that A = (x − 9/4)² + d d) For what value of x is A smallest, and what is this area?
- Question 3short answer · 10 marks
Parallel lines A and B are 120 m apart on flat ground. Jeff and Will both run back and forth between line A and line B, following parallel straight lines, without bumping into each other. Jeff starts at line A. When a whistle is blown at time t = 0, he runs towards line B at 4 m/s. When he reaches line B he instantaneously turns and runs at the exact same speed back towards line A. He then inst…
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 2018 (Paper B)?
8 questions with 80 marks in total; Eton College allowed 90 minutes for it. It covers Algebra, Fractions, Decimals & Percentages, Geometry — Shape. 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 80 marks, roughly 68 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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