Winchester College — 13+ Maths Entrance Exam 2023
Winchester College set this 13+ Maths paper in 2023. Hearthprep hosts it as an interactive past paper — 9 questions worth 74 marks in 74 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 Winchester College (2023). 9 questions, 74 marks. Answer interactively with worked solutions. Covers Algebra, Geometry — Shape, Number & Place Value.
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
- Winchester College
- Entry level
- 13+
- Subject
- Maths
- Year
- 2023
- Questions
- 9
- Marks
- 74
- Time
- 74 minutes
- Exam board
- ISEB
Topics in this paper
- Algebra
- Geometry — Shape
- Number & Place Value
Questions in this paper (3 of 9)
- Question 1short answer · 10 marks
Evaluate: a) 0.2 / 0.05 b) 2 * sqrt(0.25) c) 0.00002 x 50000 d) 116 + 9 x 116 + 116 e) (sqrt(43) x sqrt(43)) / (sqrt(129))^2 f) Find 15% of 20% of 25% of 6000. g) Put the following numbers in ascending order: 2^14 x 7^2, 2^13 x 7^3, 2^11 x 7^5, 2^12 x 7^4.
- Question 2written answer · 19 marks
Solve: a) 36 / (2x + 1) = 4 b) 7(2x + 1) - 3(6 - 3x) = -57 c) cube_root(9^2 / x) + 3 = 6 d) 3 / (2x + 7) = 5 / (x + 21) e) (2x - 2/3) / (4/5 - x) = 0 f) Expand and simplify: (a^2 + b)(a^2 - b). g) Expand and simplify: 3x(x + 2) - 2(x - x^2). h) Make x the subject of the formula: y = (x/4)^5 + 6. (Currently y is the subject.) i) Solve cube_root(3 * sqrt((3x+3)/(1/3))) = 3.
- Question 3written answer · 6 marks
A formula for p is p = n^2 - n + 11. a) Complete this table by finding the value of p when n = 1, n = 3, n = 6, n = 9 and n = 11 (other values given: n=2 p=13, n=4 p=23, n=5 p=31, n=7 p=53, n=8 p=67, n=10 p=101). b) Circle the values of p in the table that are prime. c) Holly thinks that when n is any positive whole number the formula q = n^2 - n + 41 always gives values of q that are prime. (i…
6 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 Winchester College — 13+ Maths Entrance Exam 2023?
9 questions worth 74 marks in total, written for 74 minutes. It covers Algebra, Geometry — Shape, Number & Place Value. Winchester College set it as a 13+ Maths paper.
How long is the Winchester College 13+ Maths paper?
This paper is timed at 74 minutes for 74 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 6 and the marking come with a paid plan.
Where does this Winchester 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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