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The cyclic trimer of formaldehyde, . Acid-catalysed acetal cleavage can regenerate formaldehyde, which is strongly hydrated in water.
A shallow acceptor can bind an electron hole through the screened Coulomb potential of a negatively charged impurity. A scalar band effective mass approximation gives a hydrogen-like bound-state ladder. Actual valence-band degeneracy and anisotropy can split levels and limit that approximation.
Dengue virus exposure can be investigated through antibodies in serum, but antibody detection must be distinguished from identification of current infection. Cross-reactivity with antibodies to other related viruses can limit interpretation.[ref]
A retrovirus replicates through reverse transcription of its RNA into DNA, followed by a DNA stage that can integrate into the host genome. Viral gene expression can then use cellular transcription machinery.
Rous sarcoma virus is a transforming avian retrovirus used to dissect the relationship between viral replication, Src-dependent transformation and cellular growth-control genes.
The retroviral life cycle includes entry, RNA-to-DNA copying by reverse transcriptase, a DNA intermediate and gene expression followed by particle production. Integration as a provirus can make the genetic change persistent across cell divisions.
A poxviral disease important in some red squirrel declines. Differential susceptibility and field exposure both matter when attributing population change. [ref]
Parapoxvirus causes a deleterious disease in red squirrels associated with UK population declines by Daniel M. Tompkins and others. Proceedings of the Royal Society B 269, pp. 529–533; contrasting experimental susceptibility of red and grey squirrels
An infection caused by a virus. Entry, genome expression and production of infectious particles are distinct stages; detecting viral nucleic acid does not alone measure all of them.
Exam sources held for the University of Cambridge, checked on 18 October 2026. Each year range means at least one held paper in every listed year; it does not promise every paper or module for that year. Links lead to existing course or exam articles; bold course names have no dedicated article yet. Download links lead to public originals, sometimes inside larger releases.
Solutions: officially advertised student answers are sufficient to skip new solutions, including suggested answers on Moodle or in a departmental library; access may require sign-in or payment. “Unverified” means that availability or exact-year coverage has not been established, rather than that no answers exist. Marking schemes, selected answers and examiner reports are distinguished where that is all the evidence establishes. Existing wiki drafts are retained and are separate from University answer availability.
For Physics courses, the official past-paper search requires University sign-in; its exact-year solution holdings remain unverified except for the public sets identified below.
- Past exam of the computer science course of the University of Cambridge. Download official papers; read the solution-note access policy.
- 2025–2026: the newest two years’ solution notes are restricted to supervisors and teaching staff; students may be shown them during supervisions. Complete worked coverage is unverified.
- 1993–2024: solution notes for many questions require Raven sign-in. Complete worked coverage of every held paper is unverified.
- Past exam of the mathematics course of the University of Cambridge. Download official Parts IA, IB and II papers; download official Part III papers. Public model-answer and mark-scheme release with download links advertises academic-year ranges; completeness and working depth of those bundles remain unverified. The official undergraduate index also links selected 2011 IA solutions and draft marking schemes.
- 2021–2026 (Part III): Complete worked solutions: availability unverified.
- 2019–2026 (Part IA): Complete worked solutions: availability unverified.
- 2019–2026 (Part IB): Complete worked solutions: availability unverified.
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- 2017–2018 (Part II): Public model-answer/mark-scheme bundle advertised; full worked coverage unverified.
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- MPhil in micro- and nanotechnology enterprise course of the University of Cambridge. Complete worked solutions: availability unverified.
- 2017–2023: Download 2024 50 Dai ZIP.
- Past exam of the MPhil in nuclear energy course of the University of Cambridge. The 2019 and 2021 NE2 papers match Engineering 4I10 papers with public worked cribs: 2019 crib and 2021 crib. The 2020 NE1 cover explicitly crosslists Engineering 4M16; Engineering advertises student access to examination cribs for all years in its library. These three papers are skipped for new solutions. Student-answer availability for the other held papers remains unverified.
- 2019–2021: Download 2022 471 Smith PDF.
- Biology of Cells (NST IA). Complete worked solutions: availability unverified.
- 2021–2023: Download 2024 208 Ye PDF.
- 2013–2019: Download 2024 208 Ye PDF.
- Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge (NST IA). Student Moodle papers and suggested answers for the past ten years; skip new solutions for the advertised answer years, including held 2016–2025 papers. The dated 2025/26 guide places 2016 within the ten preceding completed examination years; this boundary is inferred from the advertisement, not a private file inspection. The held 2013–2015 IA papers are also skipped: the 2023/24 IA handbook advertises suggested answers for papers more than five years old. Existing wiki drafts are retained.
- 2024–2025: Download 2026 862 Stack PDF.
- 2021–2023: Download 2024 208 Ye PDF.
- 2013–2019: Download 2024 208 Ye PDF.
- Evolution and Behaviour (NST IA). Complete worked solutions: availability unverified.
- 2021–2023: Download 2024 208 Ye PDF.
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- 2012: Download 2023 278 Yeung PDF.
- 2010: Download 2023 278 Yeung PDF.
- Undated: Download 2023 278 Yeung PDF. Standalone question sheet; no year assigned.
- Past exam of the materials science course of the University of Cambridge (NST IA). Complete worked solutions: availability unverified.
- 2022: Download 2024 51 Peacock PDF.
- 2015–2019: Download 2025 1239 Hagendoorn PDF.
- Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge (NST IA). Complete worked solutions: availability unverified.
- Mathematical Biology (NST IA). Complete worked solutions: availability unverified.
- 2021–2022: Download 2024 208 Ye PDF.
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- 2010–2012: Download 2023 278 Yeung PDF.
- Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge (NST IA). Complete worked solutions: availability unverified except where specified below.
- 2024: Download 2026 862 Stack PDF.
- 2021–2022: Download 2022 639 Sullivan PDF.
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- 2012–2016: Download 2023 399 Zahid PDF.
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- Physiology of Organisms (NST IA). Complete worked solutions: availability unverified.
- 2021–2022: Download 2024 208 Ye PDF.
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- Undated: Download 2024 208 Ye PDF. Standalone Section C essay sheet; no year assigned.
- Animal Biology (NST IB). Complete worked solutions: availability unverified.
- 2017–2019: Download 2025 233 Vongtanakiat PDF.
- Past exam of the biochemistry and Molecular Biology course of the University of Cambridge (NST IB). Historical supervisor data-handling specimen answers advertised; exact years and complete worked coverage unverified.
- 2023–2025: Download 2026 642 Cui Part1 PDF.
- 2021–2022: Download 2025 233 Vongtanakiat PDF.
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- Past exam of the chemistry A course of the University of Cambridge (NST IB). Student Moodle papers and suggested answers for the past ten years; skip new solutions for the advertised answer years, including held 2017–2025 papers. Private contents and older boundary years remain unverified. Existing wiki drafts are retained.
- Past exam of the chemistry B course of the University of Cambridge (NST IB). Student Moodle papers and suggested answers for the past ten years; skip new solutions for the advertised answer years, including held 2017–2025 papers. Private contents and older boundary years remain unverified. Existing wiki drafts are retained.
- Evolution and Animal Diversity (NST IB). Complete worked solutions: availability unverified.
- 2020–2022: Download 2025 233 Vongtanakiat PDF.
- Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge (NST IB). Complete worked solutions: availability unverified.
- Past exam of the mathematical and Computational Biology course of the University of Cambridge (NST IB). Complete worked solutions: availability unverified.
- Past exam of the physics A course of the University of Cambridge (NST IB). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
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- 2012–2016: Download 2023 399 Zahid PDF.
- 2010–2011: Download 2026 628 Smith PDF.
- Past exam of the physics B course of the University of Cambridge (NST IB). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
- 2018–2019: Download 2022 639 Sullivan PDF.
- 2017: Download 2022 639 Sullivan PDF. Selected final answers are supplied; complete worked coverage remains unverified.
- 2012–2016: Download 2023 399 Zahid PDF.
- 2010–2011: Download 2026 628 Smith PDF.
- Plant and Microbial Sciences (NST IB). Complete worked solutions: availability unverified.
- 2021–2022: Download 2025 233 Vongtanakiat PDF.
- 2017–2018: Download 2025 233 Vongtanakiat PDF.
- Past exam of the astrophysical fluid dynamics course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
- 2017–2019: Download 2022 639 Sullivan PDF.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the advanced quantum physics course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
- 2017–2019: Download 2022 639 Sullivan PDF.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the biochemistry course of the University of Cambridge (NST II). Specimen answers advertised in the departmental library for Part II students; years and complete worked coverage unverified.
- Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge (NST II). Student Moodle papers and suggested answers for the past ten years; skip new solutions for the advertised answer years, including held 2017–2025 papers. Private contents and older boundary years remain unverified. Existing wiki drafts are retained.
- 2022: Download 2022 476 Whittaker PDF.
- 2021: Download 2023 126 James bundle 1 PDF.
- 2018–2019: Download 2023 126 James bundle 1 PDF.
- Past exam of the genetics course of the University of Cambridge (NST II). Complete worked solutions: availability unverified.
- Past exam of the optics and electrodynamics course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
- 2017–2019: Download 2022 639 Sullivan PDF.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the plant Sciences course of the University of Cambridge (NST II). Complete worked solutions: availability unverified.
- Past exam of the particle and nuclear physics course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
- 2017–2019: Download 2022 639 Sullivan PDF.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the quantum condensed matter course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
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- 2012–2016: Download 2023 399 Zahid PDF.
- 2004–2009: Download course-archive papers.
- Past exam of the relativity course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
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- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the soft condensed matter course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2021–2022: Download 2022 639 Sullivan PDF.
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- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the theoretical physics I course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2022: Download 2022 639 Sullivan PDF.
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- Past exam of the theoretical physics II course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2017–2019: Download 2022 639 Sullivan PDF.
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- Past exam of the thermal and statistical physics course of the University of Cambridge (NST II). Complete worked solutions: availability unverified except where specified below.
- 2022: Download 2022 639 Sullivan PDF. Public worked solutions are included in the Sullivan release, pages 448–455; skip for new solutions.
- 2021: Download 2022 639 Sullivan PDF.
- 2017–2019: Download 2022 639 Sullivan PDF.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the zoology course of the University of Cambridge (NST II). Complete worked solutions: availability unverified.
- Past exam of the atomic and Optical Physics course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the atmospheric physics course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2014: Download 2023 399 Zahid PDF.
- Past exam of the advanced Quantum Condensed Matter Physics course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Biological Physics course of the University of Cambridge (NST III, major topic). Complete worked solutions: availability unverified except where specified below.
- 2016: Download 2023 399 Zahid PDF.
- Biological Physics course of the University of Cambridge (NST III, minor topic). Complete worked solutions: availability unverified except where specified below.
- 2012–2015: Download 2023 399 Zahid PDF.
- Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge (NST III). Student Moodle papers and suggested answers for the past ten years; skip new solutions for the advertised answer years, including held 2016–2025 papers. The dated 2025/26 guide places 2016 within the ten preceding completed examination years, inferred from the advertisement rather than a private file inspection. The held 2011 and 2013–2015 Chemistry interdisciplinary papers are also skipped under the 2015 departmental policy releasing suggested answers after five years; applying the Parts III policy to shared IDP1–3 is a scope inference, not an inspected private answer file. Existing wiki drafts are retained.
- Climate Change (NST III). Skip the held 2013 and 2015 shared interdisciplinary papers under the Chemistry policy releasing suggested answers after five years. Applying that departmental policy to shared IDP2 is a scope inference supported by its official shared-course identity; the exact private answer files were not inspected.
- 2015: Download 2023 399 Zahid PDF.
- 2013: Download 2023 399 Zahid PDF.
- Past exam of the exoplanets and Planetary Systems course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2015–2016: Download 2023 399 Zahid PDF.
- Past exam of the frontiers of experimental condensed matter physics course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2013: Download 2023 399 Zahid PDF.
- Past exam of the frontiers of Observational Astrophysics course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the formation of Structure in the Universe course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the gauge field theory course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- IDP3: Materials, Electronics & Renewable Energy course of the University of Cambridge (NST III). The 2025/26 Chemistry guide includes this shared interdisciplinary examination and advertises ten years of student suggested answers. Skip the held 2016 paper under that advertised-answer rule; private completeness was not inspected. The held 2012–2015 interdisciplinary papers are also skipped under the 2015 departmental policy releasing suggested answers after five years; applying the Parts III policy to shared IDP1–3 is a scope inference, not an inspected private answer file.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the medical physics course of the University of Cambridge (NST III). Skip the held 2013–2016 papers under Engineering student library access to cribs for all years. The 2014–2016 covers explicitly crosslist Engineering, while the 2013 Engineering notice identifies shared module 4I8 as Medical Physics. That exact shared identity has not been established for the held 2012 paper in the checked historical material; its answer availability remains unverified. The 2012 wiki draft covers generic physics and mathematics, with biology and clinical applications explicitly deferred. Private crib completeness was not inspected.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the nonlinear Optics and Quantum States of Light course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2014–2016: Download 2023 399 Zahid PDF.
- 2012: Download 2023 399 Zahid PDF.
- Nuclear Power Engineering course of the University of Cambridge (NST III, Engineering module 4M16). Skip the held 2012–2013 shared examinations: Engineering advertises student library access to past papers and cribs for all years. Exact shared-paper identity is recorded in the course catalogue; private completeness was not inspected.
- 2012–2013: Download 2023 399 Zahid PDF.
- Past exam of the particle Astrophysics course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the physics of the Earth as a Planet course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the physics of Nanoelectronic Systems course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
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- Particle Physics course of the University of Cambridge (NST III). Public worked solutions and errata for every held year; skip for new solutions.
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- Past exam of the phase transitions and collective phenomena course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012: Download 2023 399 Zahid PDF.
- Past exam of the quantum Condensed Matter Field Theory course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the quantum information course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the relativistic Astrophysics and Cosmology course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the soft matter and biological physics course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2015: Download 2023 399 Zahid PDF.
- Past exam of the superconductivity and Quantum Coherence course of the University of Cambridge (NST III). Complete worked solutions: availability unverified except where specified below.
- 2012–2016: Download 2023 399 Zahid PDF.
- Past exam of the systems biology course of the University of Cambridge (NST III). Complete worked solutions: availability unverified.
- 2020–2024: Download 2024 1168 Locke PDF.
- Theories of quantum matter (NST III). Public worked solutions accompany every held year; these papers are skipped for new solutions.
A shunt electrical resistance inserted between the conductors of a uniform lossless transmission line of characteristic impedance has voltage reflection coefficient and transmission amplitude . Equally spaced shunts produce coherent reflected waves. The round-trip phase between neighbours is , so interference repeats in frequency with spacing for nondispersive phase speed .
A periodic lossless line can consist of equal-length sections with impedances . Its semi-infinite input is a fixed point of the two-section impedance transformation. The physical solution selects a forward-energy or decaying Bloch wave. At special frequencies where the cell matrix is the identity, the fixed-point equation alone loses uniqueness; limiting absorption or a termination specifies the response.
A length with impedance ratio between identical matched lossless lines has multiple internal reflections. Summing their amplitudes gives the displayed power transmission when the propagation speed is the same in all sections. It is unity at half-wave resonances even though either individual interface reflects. Matched remote terminations remove external echoes but not this frequency dependence.
Coupling models at different spatial or temporal resolutions while making their interfaces, units and conservation requirements explicit.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
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Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. - Infinitely deep tables of contents:
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