You should spend about 20 minutes on Questions 1–13, which are based on Reading Passage 1 below.
Hardened by Heat: The Invention of Bakelite
Until the second half of the nineteenth century, anything that had to be hard, smooth and durable was made from materials that came out of the ground or off the backs of animals. Combs and buttons were carved from horn, bone or tortoiseshell, knife handles from antler and hardwood, and jewellery from amber and ivory. Elephant ivory, the finest material for billiard balls and piano keys, was growing scarce and increasingly costly. Shellac, a resin secreted by an insect, insulated electrical wiring. None of these materials could be produced in unlimited quantities, and each behaved differently in the workshop.
The first serious attempt to create a substitute used cellulose, the fibrous substance that gives plant cell walls their strength. In 1862 the British chemist Alexander Parkes showed, at the Great International Exhibition in London, a material he called parkesine, made by treating cellulose with nitric acid and then adding a plasticiser, a substance that makes a hard material softer and easier to work. Parkesine could be moulded while warm and carved when cold, and it won a medal at the exhibition. Yet the material proved difficult to manufacture consistently, and the company Parkes founded collapsed within a few years.
The first plastic to reach the market in quantity was celluloid, developed by John Wesley Hyatt, an American printer, and his brother Isaiah. Hyatt was looking for something to replace ivory in billiard balls, a search encouraged by a prize of ten thousand dollars. In 1869 he patented a way of combining cellulose nitrate with camphor, a waxy substance obtained from the camphor tree, which made the mixture easier to shape. Celluloid could be rolled into thin sheets, dyed in vivid colours and pressed into combs, collars, dental plates and the first flexible cinema film. Its weakness was that it was highly flammable.
A different route relied on protein from milk. Casein, obtained by souring milk, could be hardened with formaldehyde into a horn-like solid. The German chemist Adolf Spitteler patented such a material in 1899, and it was sold as galalith for buttons, knitting needles, pen barrels and fancy goods. It was cheap and took dyes well, but it absorbed water, swelled, and could not be moulded with the precision needed for mechanical parts.
The man who solved these problems was Leo Baekeland, a Belgian-born chemist. Born in Ghent in 1863, he studied chemistry at the university there, and in 1889 he emigrated to the United States. He invented Velox, a photographic paper that could be developed under artificial light rather than sunlight, and sold the rights to Eastman Kodak for a sum that made him financially independent. He then turned to the reaction between phenol, a chemical obtained from coal tar, and formaldehyde, a sharp-smelling gas that dissolves readily in water. Chemists already knew that these two substances react together to give a hard, insoluble solid.
The difficulty was controlling the reaction. Heat was needed to start it, but once it began the mixture foamed and set solid, and the resulting material was brittle and full of bubbles. Baekeland's insight was to divide the process into two stages. He first warmed the ingredients gently until they formed a thick, sticky liquid that could still be poured; only then did he place it in a mould and heat it under pressure in a sealed vessel that his assistants nicknamed the Bakelizer. The pressure prevented the material from foaming as it hardened. He applied for a patent in July 1907.
The resulting material had properties that none of its predecessors could match. Celluloid and casein were thermoplastics: they softened when heated and could be reshaped. Bakelite was thermosetting. Once the chemical bonds had formed, it could not be melted, remoulded or dissolved, and it resisted heat, many solvents and, most importantly, electricity. Its first large market was electrical equipment — insulators, switches, sockets and the caps of car ignition systems — followed by telephone handsets and radio cabinets. The one obvious limitation was colour: the resin itself ranged from amber to near-black, and the fillers added to strengthen it, such as wood flour or asbestos, darkened it further.
Baekeland presented his material to the American Chemical Society at a meeting in New York in February 1909, and the press reports were enthusiastic. The company he founded in 1910, General Bakelite, promoted it as a substance with a thousand uses, and although the phrase was advertising rather than arithmetic, the range of applications grew rapidly.
Demand came first from the electrical industry and then from broadcasting. As radio sets became a domestic necessity in the 1920s, cabinets, dials and internal parts were made of moulded phenolic resin. In 1927 a cast version of the resin, produced without fillers, made translucent and brightly coloured pieces possible, and it was soon used for jewellery, clock cases and small radio sets. In the 1930s resins made from urea and from melamine brought pale, washable colours to tableware, while entirely different plastics — polystyrene, polyvinyl chloride, polythene and nylon — appeared in the same decade.
After the Second World War, cheaper thermoplastics that could be shaped by fast injection moulding displaced Bakelite from many household goods. Phenolic resins survived wherever heat and friction were a problem: in brake linings, in electrical laminates, in pan handles and in the heat shields that protect spacecraft during re-entry. Baekeland himself died in 1944, having seen his material spread across the world. Its importance, though, lay less in the objects it made than in the demonstration it gave: that a synthetic material could be designed for a purpose, rather than merely imitating something that nature had already provided.
You should spend about 20 minutes on Questions 14–26, which are based on Reading Passage 2 below.
Bending the Rules: The Rise of Flexible Electronics
Silicon, the material at the heart of almost every electronic device, is supplied as flat polished wafers. It is also brittle: a wafer a fraction of a millimetre thick will crack if it is bent far. For decades this hardly mattered, because computers, televisions and telephones were boxes that stayed still. But engineers increasingly wanted electronics that could be wrapped around a wrist, laminated onto packaging or laid across the surface of the skin. Flexible electronics is the attempt to build circuits and displays on materials that can be bent, rolled or folded without ceasing to work.
The most direct solution is to make the silicon thinner. Bending a layer stretches its outer surface and compresses its inner one, and the amount of stretching depends on the distance from the middle of the layer and on how tightly it is bent. A film only a few micrometres thick, a fraction of the width of a human hair, therefore experiences very little strain even when it is rolled around a pencil. Two techniques make such films possible: etching away most of a wafer from behind, or growing a thin crystalline layer on a sacrificial film and lifting it onto a plastic sheet. In a stack of layers, engineers also try to place the delicate circuit near the neutral plane, the level at which bending produces neither tension nor compression.
An alternative is to abandon silicon altogether and use organic semiconductors, materials built from chains of carbon-based molecules. Because they can be dissolved in solvents, they can be applied as an ink: sprayed, spin-coated or printed with the same kind of equipment that prints newspapers. Printing on long rolls of plastic, a process known as roll-to-roll, promises high output at low cost, and it requires nothing like the temperatures of several hundred degrees needed to grow crystalline silicon. The penalty is performance. Charge carriers in organic materials move far more slowly than in silicon, so organic transistors suit displays and simple sensors but not fast logic. Many organic materials also deteriorate when exposed to air and moisture, which makes them hard to seal.
Displays and touch panels need a layer that conducts electricity and lets light through. The standard choice, indium tin oxide, is transparent and reasonably conductive, but it is a brittle ceramic that develops fine cracks after repeated bending, and the cracks grow into visible failures. Researchers are testing alternatives: films of silver nanowires thin enough to be almost invisible, sheets of graphene, and conducting polymers. Each has drawbacks, whether in cost, conductivity or stability, and none has yet displaced indium tin oxide across the board. In the laboratory the best of them survive bending far better than the oxide, but they are harder to pattern into fine lines.
The most visible application is the flexible display. In a conventional liquid-crystal screen, a backlight shines through a layer of crystals that switch the light on and off. An organic light-emitting diode, or OLED, works differently: each pixel contains a stack of organic layers that emits its own light when a current passes through it. Since no backlight is required, an OLED screen can be extremely thin and can be built on a plastic substrate instead of glass. Foldable phones, curved televisions and rollable screens all rely on this design. The engineering difficulty lies in the folding itself: the layers must survive hundreds of thousands of cycles, and a single particle of dust trapped during manufacture becomes a flaw that grows with use.
Organic materials and many metal contacts are attacked by water vapour and oxygen, and even a tiny amount of moisture can create dark spots in a display. Glass was traditionally used to keep them out. A flexible device instead needs thin-film encapsulation: several alternating layers of an inorganic material such as silicon nitride and a polymer, deposited directly onto the device. Every layer must be almost free of pinholes, since water finds its way through the smallest gap. When the stack is bent, the brittle inorganic layers tend to crack, and each crack becomes a channel for moisture. Designing a barrier that is both impermeable and flexible is one of the field's hardest problems.
Flexible electronics already appear in products that are not marketed as technology. Hospitals use patches that monitor the heartbeat and temperature continuously, and researchers have demonstrated sensors that conform to the skin and measure the oxygen in the blood. In packaging, cheap printed circuits act as labels that record whether a shipment of food has been kept cold. Flexible solar cells, of the kind used on portable chargers, are commercially available, and electronic paper, which holds an image without using power, created the first mass market for flexible displays.
Cost and lifetime remain the obstacles. A flexible display is currently more expensive to produce than a rigid one, partly because manufacturing yields are lower, and nobody yet knows how long a bendable device will survive daily use. Performance is a limit too: flexible transistors cannot match the speed of conventional silicon. The next step is stretchable electronics, which can be pulled in two directions rather than merely bent. Here the wiring is often shaped into wavy lines or spirals, so that a connection unfolds rather than stretching itself, and several groups are experimenting with biodegradable substrates so that medical sensors can be composted after use. Costs are falling as production volumes rise, but the gap with rigid electronics is unlikely to close soon.
You should spend about 20 minutes on Questions 27–40, which are based on Reading Passage 3 below.
The Calculator in the Examination Room
Should a machine that does the arithmetic be allowed to sit the paper?
When the first pocket calculators appeared in the early 1970s, teachers and examiners responded with something close to alarm. Here was a machine that would do a pupil's arithmetic silently, in the middle of an examination, and nobody could tell whether the answer on the page had been worked out or merely copied from a screen. Half a century later the devices are unremarkable, yet the argument has not gone away. My contention is that this argument is not really about calculators at all. It is about what we believe an examination should measure, and about which skills we are prepared to let machinery perform.
The case against the machines rests on a serious claim: that fluency with numbers is not one skill among many but the foundation on which the rest is built. A pupil who has to reach for a calculator to multiply 17 by 6 has no feel for the size of an answer, and children without that feel will accept a result of 100 or 10,000 with equal confidence. Mental arithmetic also teaches the properties of numbers — that multiplication can be done in any order, for instance — which pressing buttons does not.
The other side begins from a different premise: that arithmetic is the least interesting part of mathematics, and that most of what matters — recognising a pattern, choosing a method, interpreting a result — is precisely what calculators leave untouched. Freed from long multiplication, a class can spend its time on problems that use real data. It is often said that pupils who lose their way in arithmetic give up on mathematics altogether, and that a calculator can keep them in the subject long enough to succeed in it.
What does research show? The most frequently cited summary is a meta-analysis published by Aimee Ellington in 2003, which pooled dozens of small studies of calculator use in schools. Its overall finding was modestly positive: pupils who used calculators performed a little better, not worse, on tests of both computation and problem-solving, and the gains were largest when the devices were part of ordinary teaching rather than an occasional treat. Such studies cannot settle every question, but the widespread fear that calculators would damage basic arithmetic received little support. What the evidence does suggest is that the effect depends less on the machine than on the way it is used.
The question that matters, then, is not whether calculators are allowed but what a paper asks candidates to do. A well-designed calculator paper does not reward the ability to press keys; it sets problems in which the arithmetic is tedious but the reasoning is the point, and in which an answer must still be interpreted, checked for plausibility and explained. Examiners who allow calculators therefore take on a harder job than those who forbid them: they must write questions that a calculator cannot answer for the candidate.
This reasoning explains why the age of the candidate matters so much. In the early years of school, arithmetic itself is the subject being taught, so a calculator removes the very thing that is being practised. I would therefore keep the devices out of the hands of young children until they can add, subtract, multiply and divide without one. I accept that routine use of calculators in the later years will mean that some pencil-and-paper skills are practised less, but that seems to me a price worth paying. By the age of sixteen the position is different. In England, the GCSE mathematics qualification is examined through one paper on which calculators are forbidden and two on which they are expected, a split that recognises both needs at once.
Two practical objections remain. The first concerns fairness. Graphing calculators with large screens and programmable memories cost far more than basic models, and a rule that permits any calculator favours the pupil whose parents can buy the best one. Exam boards in England respond by specifying which models may be taken into the examination, and schools generally supply them, but the difficulty is real and any policy must address it. The second concerns what candidates bring into the room: a device that can store text is a device that can store notes.
It is worth remembering that the anxiety is not new. Logarithm tables and slide rules were once standard equipment in examinations, and the same fears were expressed when electronic devices replaced them. Comparisons between countries are sometimes used to support a ban: it is said that pupils in places where calculators are restricted do better at arithmetic. Such comparisons tell us almost nothing, because the countries differ in their curriculums, in the training of their teachers and in a hundred other respects, and no one can isolate the effect of a single rule.
My conclusion is that banning calculators outright is nostalgia dressed up as rigour. The devices are embedded in the work that scientists, engineers and accountants actually do, and an examination that pretends otherwise prepares nobody for anything. What matters is that the assessment is designed deliberately: a paper without calculators to protect fluency in arithmetic, papers with calculators that test judgement and interpretation, and questions that no machine can answer on the candidate's behalf. The calculator is not the enemy of mathematical education. Careless examination design is.
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