Eton College — 13+ Maths Scholarship 2021
Eton College set this 13+ Maths paper in 2021. Hearthprep hosts it as an interactive past paper — 8 questions worth 80 marks in 80 minutes, each marked the moment the paper is submitted 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 (2021). 8 questions, 80 marks. Answer interactively with worked solutions. Covers Algebra, Geometry — Shape, Number & Place Value, Probability, Ratio & Proportion.
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
- 2021
- Questions
- 8
- Marks
- 80
- Time
- 80 minutes
- Exam board
- ISEB
Topics in this paper
- Algebra
- Geometry — Shape
- Number & Place Value
- Probability
- Ratio & Proportion
Questions in this paper (3 of 8)
- Question 1written answer · 10 marks
(a) By considering (x + 1)(x - 1) = x^2 - 1, find two prime factors of 899. (b) Multiply out and simplify fully (x + 1)(x^2 - x + 1). (c) Using this result, prove that (i) 27001 is divisible by 31, (ii) 3376 is divisible by 211, (iii) 2^48 + 1 is divisible by 65537, (iv) 5^18 + 1 is divisible by 13.
- Question 2written answer · 10 marks
(a) I am buying musical instruments. A ukulele and a xylophone together cost £120 more than a violin. A violin and a xylophone together cost £180 more than a ukulele. How much does a xylophone cost? (b) Some of the instruments are presents for my godchildren. Because I dislike their parents, I have decided to buy each one either an accordion or a set of bagpipes. Accordions cost £80 and bagpipe…
- Question 3written answer · 10 marks
(a) Show carefully by multiplying out and simplifying that (4 + 3sqrt(5))^2 = 61 + 24sqrt(5). (b) Multiply out and simplify (sqrt(7) - 2)^2. (c) Use the pattern you have observed to find an expression for the following in the form a + b*sqrt(c), where a, b and c are integers: (i) sqrt(7 + 2*sqrt(6)), (ii) sqrt(9 - 4*sqrt(5)), (iii) sqrt(3 - 2*sqrt(2)). (d) Find an expression for sqrt(4 + sqrt(7…
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 2021?
8 questions worth 80 marks in total, written for 80 minutes. It covers Algebra, Geometry — Shape, Number & Place Value, Probability, Ratio & Proportion. Eton College set it as a 13+ Maths paper.
How long is the Eton College 13+ Maths paper?
This paper is timed at 80 minutes for 80 marks — roughly 60 seconds a mark. Hearthprep runs the same clock on screen, so your child sees how far through the time they are as they answer.
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.
Loading the interactive paper…