Westminster School — 13+ Maths Entrance Exam 2022
Westminster School set this 13+ Maths paper in 2022. Hearthprep hosts it as an interactive past paper — 14 questions worth 66 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 Westminster School (2022). 14 questions, 66 marks. Answer interactively with worked solutions. Covers Algebra, Arithmetic & Operations, Fractions, Decimals & Percentages, Geometry — Measurement, Problem Solving & Logic, Ratio & Proportion, Statistics & Data.
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
- Westminster School
- Entry level
- 13+
- Subject
- Maths
- Year
- 2022
- Questions
- 14
- Marks
- 66
- Time allowed
- 90 minutes
- Updated
- 3 Sept 2026
Topics in this paper
- Algebra
- Arithmetic & Operations
- Fractions, Decimals & Percentages
- Geometry — Measurement
- Problem Solving & Logic
- Ratio & Proportion
- Statistics & Data
Questions in this paper (3 of 14)
- Question 1short answer · 2 marks
If a = 6.3 and b = −1.4, use your calculator to work out (2a)² − b² − 2(a − b)².
- Question 2short answer · 3 marks
Boris completes his local Park Run in 33 minutes. Of the 5 km course, 3.7 km is tarmac, on which he was able to run at 13 kilometres per hour. The rest of the course is mud. How fast did Boris run through the mud?
- Question 3short answer · 8 marks
(a) (i) Two quantities sum to 1. If the first quantity is n/(n + 1), what is the second? (ii) By what would you divide 24w²/t to get 8w/t²? (b) Make T the subject of Q = H²/(M − T). (c) Simplify x²/(2x) − (1/2)(x − 3). (d) The solution to the equation (x + 1)/a + 3x/(2a) = 5 is x = 7. Find a.
11 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 Westminster School — 13+ Maths Entrance Exam 2022?
14 questions with 66 marks in total; Westminster School allowed 90 minutes for it. It covers Algebra, Arithmetic & Operations, Fractions, Decimals & Percentages, Geometry — Measurement, Problem Solving & Logic, Ratio & Proportion, Statistics & Data. Westminster School set it as a 13+ Maths paper.
How long is the Westminster School 13+ Maths paper?
Westminster School printed an allowance of 90 minutes on this paper. The paper carries 66 marks, roughly 82 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 11 and the marking come with a paid plan.
Where does this Westminster School 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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