The quest to understand the fundamental nature of light has sparked debate for centuries and ultimately played a pivotal role in the development of quantum physics. Even the earliest recorded speculations about light contained the seeds of concepts that would, centuries later, be woven into our quantum understanding of reality. Some of the earliest recorded ideas about the nature of light appeared in the 6th century BCE. In India, for instance, the Vaisheshika school of philosophy described light as consisting of fire-like particles moving at a high speed. In ancient Greece, the Pythagoreans (6th 5th century BCE) and later Euclid (c. 300 BCE) advocated the emission theory of vision, suggesting that rays of light emanate from the eyes toward objects. In contrast, Epicurus (341 270 BCE) proposed an intromission theory, arguing that light consists of material images or "eidola" emitted by objects that travel to the eyes. Further insights into the nature of light emerged in Egypt, where Ptolemy (c. AD 90 168), working in Alexandria, conducted experiments showing that light reflects off smooth surfaces and bends when passing through transparent materials of different optical densities. Building on these concepts, Arab scholars made significant contributions to the understanding of light by establishing foundational principles governing its behavior in lenses, mirrors, and prisms. The most influential among them was the 11th-century scholar Ibn al-Haytham, who lived in present-day Iraq. Ibn al-Haytham corrected the emission theory, stating thatvision results from light entering the eye rather thanemanating from it. By the 17th century, European scientists were dividedbetween two competing theories about the fundamentalnature of light: whether it behaved as a wave or as aparticle. Dutch physicist Christiaan Huygens argued thatlight propagates as waves according to his wave-frontprinciple, which explains how waves evolve when theyencounter obstacles. In contrast, Isaac Newton proposeda corpuscular theory, suggesting that light consists ofparticles traveling in straight paths, capable of reflectingoff surfaces like mirrors. Newton's prism experiments,which showed white light splitting into colors with distinctrefraction angles, supported his corpuscular theory bysuggesting that light consists of particles of differentsizes, each corresponding to a different color, whichbend by different amounts. Both theories, however, were incomplete. Huygens' wavetheory struggled to fully explain why light travels in astraight path, and Newton's particle theory couldn'taccount for diffraction, the spreading of light as it passesaround edges or through narrow openings. Nevertheless,Newton's theory gained significant influence not onlybecause of his clever prism experiments, but alsobecause he was highly revered in the scientificcommunity, making his ideas difficult to challenge foryears. But science doesn't bow to reputation. As RichardFeynman famously pointed out in his 1964 MessengerLectures at Cornell University, "It doesn't matter howbeautiful your theory is, it doesn't matter how smart youare. If it doesn't agree with the experiment, it's wrong."Indeed, nearly a century after Newton's corpusculartheory of 1704, the scientific consensus gradually shiftedtoward the wave theory of light through decades ofexperiments, modeling, and debates. One of the keycontributors to this shift was Thomas Young, an Englishpolymath. In 1801, Young passed sunlight through anarrow slit to produce a coherent light beam. He thenplaced a thin obstacle, such as a hair or a narrow strip,across the beam, splitting it into two waves that spreadout and overlapped. When these waves recombined on ascreen, they produced a pattern of bright and dark bands.This interference pattern provided clear and compellingevidence that light behaves as a wave rather than as aparticle. A familiar example of this phenomenon is when waves onthe surface of water either combine to form larger peaksor cancel each other out. Later, in 1845, another Englishphysicist Michael Faraday showed that magnetic fieldscould alter the polarization plane of light, revealing aconnection between light and electromagnetism. In the1860s, Scottish physicist James Clerk Maxwell built onthis connection by formulating the theory ofelectromagnetism, describing light as an electromagneticwave composed of oscillating electric and magnetic fields at right angles to each other and to the wave's direction of travel. Heinrich Hertz's experimental confirmation of Maxwell's predictions in the 1880s provided further validation of the electromagnetic wave theory of light. By the 1890s, Maxwell's mathematical description of electromagnetic waves was considered so successful, particularly for its predictive power, that many physicists believed the fundamental nature of light was fully understood. But in the early 20th century, experimental discoveries began to challenge this consensus. The electromagnetic wave theory failed to predict how matter emits and absorbs radiation at thermal equilibrium. To address this question, German physicist Max Planck introduced a revolutionary idea known as energy quantization. He proposed that electromagnetic radiation is emitted or absorbed in discrete amounts, now called quanta, with higher frequency light corresponding to larger quanta. His theory accurately matched experimental results and earned him the Nobel Prize in Physics in 1918. Another major blow to the wave theory of light came from the photoelectric effect, first observed by Heinrich Hertz in 1887, when ultraviolet light caused electric charge to be emitted from a metal surface. By 1900, Philipp Lenard conducted detailed experiments to show that the energy of ejected electrons depended on light frequency, not intensity, an observation that classical wave theory struggled to explain. In 1905, Albert Einstein addressed this by proposing that light is made of discrete energy packets, now called photons, each carrying an energy proportional to its frequency according to Planck's quantization rule. This idea successfully explained the photoelectric effect and was later confirmed by Robert Millikan's experiments in 1915, which verified that the energy of the ejected electrons depends on light frequency and that intensity affects only the number of ejected electrons. Einstein's explanation earned him the 1921 Nobel Prize in Physics. The existence of the photon was further reinforced in 1923 by American physicist Arthur Compton, who showed that X-rays scatter off electrons and emerge with smaller frequencies. The photoelectric effect showed that light interacts with matter through discrete, fundamental processes, behaving as if it were made up of particles known as photons. On the other hand, Young's double-slit experiment provided convincing evidence that light also exhibits wave-like behavior through interference. These seemingly contradictory findings reveal the dual nature of light, a concept known as wave-particle duality. Today, this principle is central to quantum physics, which describes light as a quantum electromagnetic field. This field has discrete energy excitations called photons that can produce particle-like effects, while also exhibiting wave-like behavior depending on how light interacts with its environment. https://quantum2025.org/news-link/the-history-of-light-and-the-birth-of-q uantum-physics/ (adapted)

Read the text below to answer question

“To read these books, in this way, as an exercise in self-knowledge, carries certain risks. Risks that are both personal and political. Risks that every student of Political Philosophy has known. These risks spring from the fact that philosophy teaches us, and unsettles us, by confronting us with what we already know. There is an irony: the difficulty of this course consists in the fact that it teaches what you already know. It works by taking what we know from familiar unquestioned settings, and making it strange. [...] Philosophy estranges us from the familiar, not by supplying new information, but by inviting and provoking a new way of seeing.

    But, and here is the risk, once the familiar turns strange, it is never quite the same again. Self-knowledge is like lost innocence; however unsettling you find it, it can never be 'unthought' or 'unknown'. What makes this enterprise difficult, but also riveting, is that Moral and Political Philosophy is a story, and you don't know where the story would lead, but you do know that the story is about You.”

Text taken from: “Justice: What's the Right Thing to Do?” Introduction Class ― Michael Sandel

The Reasons Why We Dance

1. As a choreographer, I get asked to share my opinion about a myriad of dance-related
2. topics, from the practical, like “How can dance help you get in shape?” to the existential, like “Is
3. my dancing a projection of my self-image?”. But the question I think matters most is: why do
4. people dance? What is about moving our bodies to a song we love that is so joyfully Pavlovian?
5. Why do we watch videos and take lessons on something that could be labeled as trivial? Why do
6. we love it so?
7. There are the obvious answers. We dance for physical fitness, mental clarity, emotional
8. stability, and other such pluses. However, all these benefits could be attained by other means –
9. though I confess I have yet to find a better alternative than a great “cha cha”* to lift both one’s
10. heart rate and spirits. There must be something glorious about dancing that is more than just
11. intangible. We cannot seem to explain it, yet we all know it so well that we do not hesitate to
12. tap our feet to a Gershwin melody or pulse with the percussion of a samba rhythm.
13. Perhaps dance is the way we express ourselves when words are insufficient. The joy we
14. feel over newfound love, the determination we have in the face of great sorrow or adversity, the
15. passionate fire of our youth, and the peacefulness of our softer and more graceful years – maybe
16. they are never expressed more fully than through a waltz, or a tango, or a jive. We all want to
17. be understood, and if we could truly speak the words that describe our feelings, how deep and
18. powerful they would surely be. But alas, those words never seem to come to us just right. Maybe
19. dance is simply a translator for the human heart.
20. Perhaps dance is the medium through which we show the world who we truly are and who
21. we can be. All of us, if we are honest, believe deep down that we are not ordinary. We know
22. ourselves to be wonderfully unique, with many layers of personality and talent woven in such a
23. way that no one on earth could possibly have our same make-up. We know it. We just do not
24. always know how to prove it. Maybe dance gives us the opportunity. And perhaps dance is how
25. we choose to remember, how we hold on to the past. It is how we relive __ fun-filled days of
26. our youth or __ time we looked into their eyes and knew they were the one. It is our tribute to
27. the heroes of yesterday who jitterbugged like carefree boys and girls, when tomorrow they would
28. march as men and women to defend freedom’s cause. It is the chance to be __ princess again,
29. waiting for __ outstretched hand and the call to __ romance that is graceful, true, and not as
30. forgotten as the cynics say. When we dance, we can remember them all a little better, feel the
31. butterflies once again, and if only for a moment, return to the purest part of our lives when time
32. was of no matter…for we were dancing.
33. Why do we dance? Every answer will be different, and that is as it should be. Perhaps the
34. better question is, “Why would we not?”

*Cha Cha: an energetic modern dance.

(Available in: https://dancewithmeusa.com/why-we-dance-the-reasons/ – text especially adapted for this test).

Text 1

Structure of education in Singapore

The complete control and management of Singapore’s education is in the hands of the Ministry of Education (MOE). With continuous endeavour from MOE, today Singapore can be considered to have a strong and well-reputed education system. As per recent study Singapore is ranked fourth in terms of World’s Best Education System.

The preschools are run by the private sector, including religious bodies, community foundations, business groups, etc. However, every preschool need to register itself with the Singapore Ministry of Education before being functional.

After completion of 6 years of primary education, students have to appear for a Primary School Leaving Exam (PSLE). All those students who passed the exam are admitted in a secondary level course, which is usually completed in 4-5 years. It is similar to attending seventh grade through tenth grade in the American education system.

After completion of the secondary education, the students need to appear in Singaporean GCE ‘O’ Level exam. Based on the merit in that exam, students proceed to pre-university education, which is similar to attending eleventh grade and twelfth grade as per the American education system. At this level students can opt for a wide range of subjects from varied academic areas covering Humanities, Arts and Languages, Sciences and Mathematics streams.

www.singaporeeducation.info/Education-System/ Structure-of-Education