Eton College — 13+ Maths Scholarship 2023
Eton College set this 13+ Maths paper in 2023. 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 (2023). 8 questions, 80 marks. Answer interactively with worked solutions. Covers Algebra, Fractions, Decimals & Percentages, Geometry — Shape, Problem Solving & Logic, 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
- 2023
- Questions
- 8
- Marks
- 80
- Time
- 80 minutes
- Exam board
- ISEB
Topics in this paper
- Algebra
- Fractions, Decimals & Percentages
- Geometry — Shape
- Problem Solving & Logic
- Ratio & Proportion
Questions in this paper (3 of 8)
- Question 1written answer · 10 marks
(a) Simplify: (i) x^30 × x^10 (ii) (x^3)^20 (iii) (x^3 y^4)^5. (b) Let x = 18^2 × 19^3 × 20^4 × 21^5. (i) Find x as a product of powers of its prime factors. (ii) Find, as a product of powers of prime factors, the largest factor of x which is a square number. (iii) Find, as a product of powers of prime factors, the largest factor of x which is also a factor of y = 18^5 × 19^4 × 20^3 × 21^2.
- Question 2written answer · 10 marks
(a) The Knave of Hearts has stolen some tarts and been apprehended in turn by three guards, one after the other. To bribe them, he gave to each in turn one half of the tarts he had on him at the time, and an extra two to sweeten the deal. In this way, he eventually managed to escape with one tart for himself. How many tarts had he originally stolen? (b) Four brothers go to different towns to se…
- Question 3written answer · 10 marks
(a) 3.5% of pupils in a school hate mathematics. 80% of those that hate mathematics drink tea and 60% of those who don't hate mathematics drink tea. What percentage of tea drinkers hate mathematics? Give your answer to three significant figures. (b) Eton College has sprung a leak and rain water has already accumulated in the wine cellar. Schoolmasters are supplied with pumps to remove the water…
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 2023?
8 questions worth 80 marks in total, written for 80 minutes. It covers Algebra, Fractions, Decimals & Percentages, Geometry — Shape, Problem Solving & Logic, 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…