---
title: "13 Plus Scholarship Maths Preparation | CASE and Additional"
description: "13 plus scholarship maths preparation: what ISEB's CASE maths paper is, how it builds on the Additional specification, the topics, and original practice."
canonical: https://learn.modernagecoders.com/13-plus-scholarship-maths-preparation
source: src/pages/13-plus-scholarship-maths-preparation.html
---
> 13 plus scholarship maths preparation: what ISEB's CASE maths paper is, how it builds on the Additional specification, the topics, and original practice.

What is the 13 plus scholarship maths paper?

For many independent senior schools it is the maths paper of ISEB's Common Academic Scholarship, CASE. ISEB's mathematics specification describes it as one paper of 90 minutes and 100 marks, "based on the 13+ CE specification for the Additional Paper", the harder optional level of Common Entrance. ISEB says senior schools enter pupils for CASE, choose the papers and mark them, usually at the senior school, in sessions in February and May. Some schools instead pick scholars from Common Entrance results or set papers of their own. The Additional topics include Pythagoras' theorem, simultaneous and simple quadratic equations, algebraic proof, reverse percentages and standard form. Modern Age Coders teaches this maths live online with original practice.

Where to begin

## Three courses for 13 plus scholarship maths

Scholarship maths sits on top of a secure Key Stage 3. Pick by what your child needs first. Each card opens the syllabus.

[![Maths Olympiad & Competition Course course thumbnail](/images/olympiad-competition-maths.webp)  SCH / 01 Competition maths The closest match to scholarship style: unfamiliar problems, proof and puzzles that reward thinking over recall. Open the syllabus →](/courses/olympiad-competition-mathematics-mastery)[![Middle School Mathematics Mastery course thumbnail](/images/middle-school-maths.webp)  SCH / 02 Lower secondary maths The Core and Additional ground of Years 7 and 8: number, algebra, geometry and data, made secure. Open the syllabus →](/courses/comprehensive-middle-school-mathematics-mastery)[![Algebra Foundations course thumbnail](/images/algebra-foundations.webp)  SCH / 03 Algebra foundations Rearranging, simultaneous equations and expanding brackets, the algebra the Additional level leans on. Open the syllabus →](/courses/algebra-foundations-masterclass)

What CASE is

## What is the ISEB Common Academic Scholarship exam?

A set of scholarship papers from ISEB in nine subjects, maths among them, which senior schools choose, enter pupils for and mark themselves. The questions rest on the Common Entrance 13+ specifications.

ISEB's page for schools puts it simply: "We offer a series of Common Academic Scholarship (CASE) assessments in English, mathematics, science, history, geography, theology, philosophy and religion, French and Latin." It goes on: "Pupils sitting CASE assessments are entered by the senior schools they have applied to, who choose which papers pupils will sit and also mark the papers. Pupils will usually sit the exam at the senior school." That division of roles matters. ISEB writes the paper, but there is no national scholarship pass mark: each senior school reads its own candidates' scripts and decides on its own awards.

### Not every school uses CASE

ISEB itself notes that "Some senior schools select their scholars from candidates who sit CE in the autumn or spring term." In those schools the Common Entrance papers, often including the optional Additional maths paper, do double duty.

Other schools write their own scholarship papers, or buy a computer test such as Cambridge Select Insight, which Cambridge offers in versions for 11+ and 13+ entry. The school's own admissions page is the only reliable guide.

### How CASE fits the year

ISEB runs "two CASE sessions each year, in February and May". Common Entrance at 13+ has three sessions, in November, January and May or June.

ISEB asks senior schools to tell prep schools CASE results "as soon as possible, so that decisions can be made about whether a candidate still needs to be entered for the CE examinations". For some pupils a scholarship result settles the place before Common Entrance is sat.

Sources: [ISEB, CASE at 13+ information for schools](https://www.iseb.co.uk/assessments/common-entrance/case-information-for-schools/); [ISEB, CE at 13+ information for schools](https://www.iseb.co.uk/assessments/common-entrance/at-13-for-schools/); [Cambridge Insight, entrance assessments](https://www.cem.org/entrance-assessments); all read 31 October 2026. Modern Age Coders is not connected with ISEB, Cambridge or any school.

The papers

## How does the scholarship paper compare with Common Entrance maths?

It is longer per mark, harder in content and lighter on help. The table sets ISEB's 13+ maths papers side by side, as its specification lists them.

| Paper | Marks | Time | Who sits it |
| --- | --- | --- | --- |
| Foundation non-calculator and calculator | 100 each | 60 minutes each | For support in individual circumstances, by agreement with senior schools |
| Core non-calculator and calculator | 100 each | 60 minutes each | Suggested for all candidates |
| Mental arithmetic test | 40 | 10 minutes | Foundation and Core candidates, the same test |
| Additional Paper | 100 | 60 minutes, calculators allowed | Optional, "to offer challenge to the more able" |
| Common Academic Scholarship | 100 | 90 minutes | Scholarship candidates entered by a senior school |

Two lines of the specification define the scholarship paper. First, its content: "The Common Academic Scholarship Examination (90 minutes) will be based on the 13+ CE specification for the Additional Paper." Second, its time. By our own arithmetic, 90 minutes for 100 marks gives about 54 seconds a mark, against 36 seconds a mark on a 60-minute, 100-mark Common Entrance paper. That extra half again of time per mark is not a gift. It is room for longer chains of reasoning, and the specification says so in its list of changes: "Expectation of greater quality of thought and working, rather than quantity of questions".

### Less scaffolding

The specification promises "Questions with less scaffolding": candidates "will less often be led through problems, step by step". A scholarship question may ask for the final result and leave the route entirely to the pupil.

### More puzzles

It also lists "An increased number of thought-provoking puzzles", with "More unfamiliar problems" placed "towards the end of papers to encourage candidates to explore and experiment".

### Units and working

Under the same heading, ISEB adds "Writing units in answers" and "Increased testing of core skills (with fewer words)". Marks follow the working, so a bare answer is a risk.

Source: [ISEB CE and CASE Mathematics specification](https://www.iseb.co.uk/wp-content/uploads/Syllabus-CE-CASE-Mathematics-Helvetica-_V7.1-2.pdf) (for teaching from September 2021, examinations from November 2022), read 31 October 2026. ISEB sells past papers through its own shop; we do not reproduce any.

Topics

## What maths topics are on the 13 plus scholarship paper?

Everything at Core level plus a list of further topics ISEB reserves for the Additional level. A scholarship candidate should know both lists well enough to use them without prompting.

| Area | Additional topic | ISEB guidance |
| --- | --- | --- |
| Geometry | Pythagoras' theorem | Listed as a further topic |
| Algebra | Simultaneous equations | "2 equations and 2 variables, may be in context", "solved algebraically or graphically" |
| Algebra | Quadratic equations | "Simple examples or solved graphically" |
| Algebra | Algebraic proof | "Candidates should use (a box) or Q.E.D. to conclude a proof" |
| Algebra | Rearranging formulae; equations with more than one denominator; factorising by a variable | Listed as further topics |
| Graphs | Plotting curves | "May be parabolic or reciprocal" |
| Measure | Volume and surface area of prisms and cylinders | Listed as a further topic |
| Number | Reverse percentages | "Finding the original value" |
| Number | Standard form; HCF and LCM; significant figures | Standard form "With positive indices" |
| Sequences and rates | nth term; multi-part journeys | "Find average speed over multi-part journeys" |
| Transformations | Enlargement by fractional scale factor | Listed as a further topic |

### What is out

The specification's "What's OUT" list removes some things at Core and Foundation, among them bearings with map scale drawing, accurate constructions and drawing pie charts.

At Additional level it removes all of those except significant figures, and adds one more removal: "Solving inequalities". A scholarship candidate should not spend hours on inequalities for this paper.

### Calculators

The specification says: "A simple scientific calculator is recommended. Calculators with more advanced features, such as graph plotting and solving equations, are not permitted." The Additional Paper allows calculators.

For the scholarship paper itself, check the instructions each senior school gives with the entry; we do not assume a rule ISEB's specification does not state.

Worked examples, written by us

## What does a strong scholarship answer look like?

Three original problems at Additional level, each answered the way a marker hopes to read it: every step written, units given, proofs closed with Q.E.D. None comes from an ISEB paper.

### 1. A short algebraic proof

Prove that the sum of any three consecutive whole numbers is a multiple of 3. Let the numbers be n, n + 1 and n + 2. Their sum is 3n + 3, which equals 3(n + 1). Since n + 1 is a whole number, the sum is 3 times a whole number, so it is a multiple of 3. Q.E.D. The marks are in the second-to-last sentence: saying why 3(n + 1) is a multiple of 3, not just writing it.

### 2. Simultaneous equations in context

Four apples and three pears weigh 1 kg; two apples and five pears weigh 920 g. Find each weight. Let a and p be grams: 4a + 3p = 1000 and 2a + 5p = 920. Double the second: 4a + 10p = 1840. Subtract the first: 7p = 840, so a pear is 120 g. Then 2a = 920 minus 600, so an apple is 160 g. Check in the first equation: 640 plus 360 is 1000. Working in grams keeps every number whole.

### 3. Average speed is not the average of speeds

A cyclist rides 12 km at 24 km/h, then 12 km at 12 km/h. What is the average speed? Times first: 0.5 hours and 1 hour, so 24 km takes 1.5 hours. Average speed is 24 divided by 1.5, which is 16 km/h, not 18. Multi-part journeys are on the Additional list precisely because the tempting answer is wrong.

| Question (ours) | Answer | The reasoning |
| --- | --- | --- |
| After a 15 per cent rise, a club has 391 members. How many did it have before? | 340 | 391 is 115 per cent of the original, so divide by 1.15. The trap is taking 15 per cent of 391 off. |
| A right-angled triangle has legs 9 cm and 12 cm. How long is the hypotenuse? | 15 cm | 81 plus 144 is 225, and the square root is 15. Recognising 9, 12, 15 as 3, 4, 5 scaled by 3 saves the calculation. |
| Find the nth term of 7, 11, 15, 19, ... | 4n + 3 | The difference is 4, so start with 4n; 4 times 1 is 4, and the first term is 7, so add 3. Test it on the fourth term: 19. |
| Express 34,000,000 in standard form. | 3.4 times 10 to the power 7 | Move the decimal point seven places. The specification limits standard form to positive indices, so this is the expected kind. |
| Solve x squared equals 49. | x equals 7 or minus 7 | Both signs. Leaving out minus 7 is the most common lost mark on simple quadratics. |
| A cylinder has radius 3 cm and height 10 cm. Give its volume in terms of pi. | 90 pi cubic centimetres | Area of the circle, 9 pi, times the height. Leaving pi in keeps the answer exact. |

We set these as full written solutions, never as answer-only drills. A scholarship marker is reading for the chain of reasoning ISEB's specification asks for, so in lessons a correct answer with a missing step is treated as unfinished, and a proof without its closing sentence is sent back.

A plan

## How should a pupil prepare for 13 plus scholarship maths?

Secure Core first, then Additional, then practise writing full solutions to unfamiliar problems. Our plan below runs across Years 7 and 8; adjust it to the senior school's dates.

1. Find out how the senior school chooses scholars: CASE, Common Entrance with the Additional paper, its own paper, or a computer test. Note the session, February or May for CASE.
2. Check Core level is secure with ISEB's specification as a checklist, because scholarship questions assume it without warning.
3. Teach each Additional topic from the ISEB list, starting with algebra (rearranging, simultaneous equations, brackets), since it feeds proof and graphs.
4. Add proof early. Short "show that" and "prove that" questions, closed with a box or Q.E.D. as the specification asks, build the habit of justifying.
5. Work unscaffolded problems weekly: a question with the final demand only, no parts (a), (b), (c) to guide the route.
6. In the final term, sit full 90-minute papers under time, then review the working line by line rather than just the score.

### Where competition maths helps

Problems from junior maths challenges ask for the same willingness to explore and experiment that ISEB describes. They train pupils to try a small case, spot a pattern and then prove it.

Our [UK competitions calendar](/uk-coding-maths-and-ai-competitions-calendar) lists the challenges open to Years 7 and 8.

### What we will not do

Reproduce ISEB papers or a school's scholarship paper, or present our questions as theirs. ISEB sells its past papers; families can buy them from ISEB.

Promise an award. Scholarships are decided by each senior school on its own marking, and often on interview and other papers too.

For pupils sitting Common Entrance rather than a scholarship paper, our [Common Entrance maths page](/common-entrance-maths-tuition) covers the Core papers and mental arithmetic test. For pupils who will meet GCSE maths soon after, our [GCSE maths page](/gcse-maths-tuition-online) shows where the Additional topics lead.

Timeline

## From Year 7 to a scholarship session

CASE runs in February and May, often in Year 8. Our stages work back from the session the senior school names.

| When | Stage | Secure when |
| --- | --- | --- |
| Year 7 | 1. Core level | Fractions, percentages, ratio, linear equations and angle facts used without prompting |
| Year 7 to early Year 8 | 2. Additional topics | Every item on ISEB's Additional list taught and practised |
| Year 8, autumn | 3. Proof and unscaffolded work | Full written solutions to problems with no guiding parts |
| Weeks before the session | 4. Ninety minutes | Timed papers finished with working a marker can follow |

### Short on time

With one term to go, stage 3 matters more than covering the last Additional topic. Method shown well scores on unfamiliar questions.

After a first lesson we say plainly what is realistic.

### After the scholarship

The same algebra and proof carry straight into GCSE and beyond. Some pupils try [maths through coding](/courses/maths-through-coding) next.

Pupils who enjoyed the puzzles often keep going with competition maths.

All related courses

## Courses for 13 plus scholarship maths

From secure foundations to stretch. Each card opens a syllabus.

I

### Foundations

Years 6 and 7

UK / PSP / 01

#### Lower secondary maths

Key Stage 3 number, algebra, geometry and data.

[Open the syllabus](/courses/comprehensive-middle-school-mathematics-mastery)

UK / PSP / 02

#### Algebra foundations

Expressions, equations and graphs from first principles.

[Open the syllabus](/courses/algebra-foundations-masterclass)II

### Stretch

Years 7 and 8

UK / PSP / 03

#### Competition maths

Proof, puzzles and problems without a set route.

[Open the syllabus](/courses/olympiad-competition-mathematics-mastery)

UK / PSP / 05

#### Middle school competitions

Contest problems at the right age.

[Open the syllabus](/courses/middle-school-math-competitions-course)III

### Next steps

Year 9 onwards

UK / PSP / 06

#### GCSE maths

Foundation and Higher for AQA, Edexcel and OCR.

[Open the syllabus](/courses/gcse-mathematics-mastery)

UK / PSP / 07

#### IGCSE maths

Core, Extended and Additional Mathematics.

[Open the syllabus](/courses/igcse-mathematics-mastery)

UK / PSP / 08

#### Maths through coding

Python for exploring patterns and testing proofs.

[Open the syllabus](/courses/maths-through-coding)

How lessons run

## Live lessons built around written reasoning

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Our teachers are based in India, which has no daylight saving, so they sit four and a half hours ahead of the UK in summer and five and a half in winter. We give you every time in UK time.

After school

The usual slot for Years 7 and 8.

Weekend morning

Long enough for a full 90-minute paper.

Holidays

Extra sessions before February or May.

### Whole solutions

Every answer written as a chain a marker can follow.

### Proof habits

Show-that questions closed properly, with Q.E.D.

### Unscaffolded problems

Final demand only, the route left to the pupil.

### Our own questions

No ISEB or school paper copied.

### Group or one to one

A class of 15 to 20 at one level, or a private teacher.

### No award promises

Senior schools decide scholarships, not tutors.

Student work

## Projects from students at our school

Work our older students built, several of them strong mathematicians too. More on [student labs](/student-labs).

![NutriLife AI nutrition coach project screenshot](/images/projects/nutrilife.webp)

AI and ML

#### NutriLife

An AI nutrition coach that reads what you eat and works you toward a target.

by Bhavya · [Open it](https://nutrilife-bhavya.lovable.app)

![Misti AI chatbot for maths and coding screenshot](/images/projects/misti.webp)

AI and ML

#### Misti

A chatbot that answers mathematics and programming questions, built and deployed by a student.

by Harshit · [Open it](https://misti.modernagecoders.com)

![GuardianX AI internet safety assistant screenshot](/images/projects/guardianx.webp)

AI and ML

#### GuardianX

An assistant that helps a young person recognise unsafe situations online.

by Vivaan · [Open it](https://guardianx-cybersaver.lovable.app)

![SkyCast weather forecast application screenshot](/images/projects/skycast.webp)

Web app

#### SkyCast

A weather forecasting site with live conditions for any location.

by Krish

Fees

## Fees for 13 plus scholarship maths lessons

A monthly fee, shown in the currency used for UK families. The first lesson is free and there is no fee to join.

Free first class

USD 0

no card required

- A full Additional-level lesson
- A clear note of what to work on
- Only a phone number to book

Book it

Group batch

USD 100

a month, billed in US dollars

- A class of 15 to 20 at a similar level
- The same teacher each month
- Proof and problem-solving practice
- Quieter weeks in exam season

Start here

One to one

USD 150

a month, billed in US dollars

- A teacher for one pupil
- Built around one school's session
- Good for closing a specific gap

Enquire

What families say

## Rated 4.9 across 547 Google reviews

Parent reviews from our Google profile, unchanged.

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Parent

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"Modern Age Coders has been a game-changer for me. I struggled to grasp IT concepts and coding before joining, but their classes transformed everything. I can now confidently write complex programs with ease."

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Scholarship questions

## What parents ask about 13 plus scholarship maths

### What is the CASE exam?

CASE is ISEB's Common Academic Scholarship, a set of scholarship papers in nine subjects including mathematics. Senior schools enter pupils, choose which papers they sit and mark them.

### How long is the 13 plus scholarship maths paper?

ISEB's specification lists the Common Academic Scholarship maths paper as one paper of 90 minutes worth 100 marks. Schools that set their own scholarship papers may use different lengths.

### What is on the scholarship maths paper?

ISEB says it is based on the 13+ Common Entrance specification for the Additional Paper. That adds topics such as Pythagoras' theorem, simultaneous equations, simple quadratics, algebraic proof, reverse percentages and standard form to Core level.

### When are CASE exams sat?

ISEB runs two CASE sessions each year, in February and May. Pupils usually sit them at the senior school that entered them.

### Is scholarship maths harder than Common Entrance?

Yes. It uses the harder Additional content, and ISEB's specification promises less scaffolding and more thought-provoking puzzles. By our arithmetic it also gives about half as much time again per mark as a Core paper.

### Do all schools use CASE for scholarships?

No. ISEB notes that some senior schools select scholars from pupils who sit Common Entrance, and others set their own papers or use a computer test. Check each school's admissions page.

### Can I use a calculator?

ISEB recommends a simple scientific calculator and bans graph-plotting and equation-solving models. The Additional Paper allows calculators; for the scholarship paper, follow the senior school's instructions.

### Where can I find past scholarship papers?

ISEB sells past Common Entrance and CASE papers through its own shop. We do not copy them; our lessons use problems we write at the same level.

### When are lessons held?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. We confirm each time in UK time.

### Can you guarantee a scholarship?

No one honestly can. Senior schools mark their own candidates and decide awards, often with interviews and other subjects too. We teach the maths and the written reasoning.

Related pages

## More on independent school entry

Other papers and next steps.

### [Common Entrance maths](/common-entrance-maths-tuition)

Core papers and the mental arithmetic test at 11+ and 13+.

### [11 plus maths tuition](/11-plus-maths-tuition)

Entry at 11, before scholarship age.

### [GCSE maths tuition](/gcse-maths-tuition-online)

Where the Additional topics lead.

### [IGCSE maths tuition](/igcse-maths-tuition-online)

The course many independent schools teach next.

### [UK competitions calendar](/uk-coding-maths-and-ai-competitions-calendar)

Challenges that build scholarship-style thinking.

### [Coding classes in the UK](/coding-classes-in-united-kingdom)

Every UK page we publish.

## Related pages in this guide

Part of the guide: [UK selective school maths tests: 7+, 11+, 13+ and 16+](/uk-selective-school-maths-tests-guide)

### Tests by provider and entry point

- [GL Assessment 11 plus maths practice](/gl-assessment-11-plus-maths-practice)
- [CEM 11 plus maths practice](/cem-11-plus-maths-practice)
- [Quest Assessments 11 plus maths practice](/quest-assessments-11-plus-maths-practice)
- [ISEB Common Pre-Test maths practice](/iseb-common-pre-test-maths-practice)
- [UKiset maths reasoning practice](/ukiset-maths-reasoning-practice)
- [Independent school 11 plus maths in London](/independent-school-11-plus-maths-london)
- [7 plus maths preparation](/7-plus-maths-preparation)
- [16 plus sixth form entrance maths](/16-plus-sixth-form-entrance-maths)
- [11 plus maths tuition](/11-plus-maths-tuition)

### 11+ by area

- [11 plus maths tuition in Barnet](/11-plus-maths-tuition-barnet)
- [11 plus maths tuition in Bexley](/11-plus-maths-tuition-bexley)
- [11 plus maths tuition in Birmingham](/11-plus-maths-tuition-birmingham)
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- [11 plus maths tuition in Gloucestershire](/11-plus-maths-tuition-gloucestershire)
- [11 plus maths tuition in Hertfordshire](/11-plus-maths-tuition-hertfordshire)
- [11 plus maths tuition in Kent](/11-plus-maths-tuition-kent)
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- [11 plus maths tuition in Lancashire](/11-plus-maths-tuition-lancashire)
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- [11 plus maths tuition in Reading](/11-plus-maths-tuition-reading)
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- [11 plus maths tuition in Wiltshire](/11-plus-maths-tuition-wiltshire)
- [11 plus maths tuition on the Wirral](/11-plus-maths-tuition-wirral)
- [11 plus maths tuition in Wolverhampton and Walsall](/11-plus-maths-tuition-wolverhampton-and-walsall)

### Northern Ireland transfer test

- [Transfer test maths tuition Belfast](/transfer-test-maths-tuition-belfast)
- [Transfer test maths practice, Northern Ireland](/transfer-test-maths-practice-northern-ireland)

More guides: [UK maths exam boards and specification codes](/uk-maths-exam-boards-and-specification-codes) · [UK maths year by year, Reception to Year 11](/uk-maths-year-by-year-guide) · [UK university admissions: maths tests and computing applications](/uk-university-admissions-maths-and-computing-guide) · [UK maths enrichment, competitions and able pupils](/uk-maths-enrichment-and-competitions-guide)

Start here

## Book a free maths lesson

Tell us your child's year and the senior schools in view. We will check how each one picks scholars, teach a real Additional-level lesson and tell you what we noticed.

Prefer reading first? The [competition maths course](/courses/olympiad-competition-mathematics-mastery) lists its topics, and [how we teach](/how-we-teach) explains the approach.

[WhatsApp us](https://wa.me/919123366161?text=Hello%20Modern%20Age%20Coders%2C%20I%20would%20like%20a%20free%20maths%20lesson%20for%20a%2013%20plus%20scholarship.) · [+91 91233 66161](tel:+919123366161) · [connect@modernagecoders.com](mailto:connect@modernagecoders.com)

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- [KS2 and 11 Plus Maths Tutor Cost UK 2026: What to Budget](/ks2-and-11-plus-maths-tutor-cost-uk)
- [GCSE Maths Calculator vs Non-Calculator Papers Explained](/gcse-maths-calculator-vs-non-calculator-papers)

### From the blog

- [Maths Learning Guides](/blog/topic/maths)
- [10 Mental Maths Tricks for Kids, With Worked Examples](/blog/mental-maths-tricks-for-kids)
- [Abacus vs Vedic vs Mental Maths: A Clear Comparison](/blog/abacus-vs-vedic-vs-mental-maths)
- [How to Help a Child with Maths Anxiety: A 2026 Parent Guide](/blog/help-child-with-maths-anxiety)

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