159 Fun Facts About High School

Whose theorem says the square of a right triangle's hypotenuse equals the sum of the squares of the other sides?

Babylonian clay tablets show the relationship was known a thousand years before Pythagoras was born; he just got the naming rights.

Pi is the ratio of a circle's circumference to what?

Pi is the ratio of a circle's circumference to its diameter, about 3.14159, so every circumference is just over three times the diameter.

What do the interior angles of any triangle add up to?

The interior angles of any flat triangle sum to 180 degrees, a result proved in Euclid's Elements (Book I, Proposition 32) around 300 BC.

What is the only even prime number?

Every other even number is divisible by 2, so it has a factor besides itself and 1 and cannot be prime.

In the quadratic formula, the expression b² − 4ac is called what?

The discriminant b² − 4ac tells how many real roots a quadratic has: negative means none, zero means one repeated root, positive means two.

The imaginary unit i is defined by which equation?

It lets every polynomial have a full set of roots, and it shows up in real-world electrical engineering as the letter j.

What is the highest possible score on the SAT?

The SAT tops out at 1600: two sections scored 200 to 800 each. It ran to 2400 from 2005 to 2016, when a separate writing section was added.

Which organelle is nicknamed the 'powerhouse of the cell'?

The phrase comes from a 1957 Scientific American article, and mitochondria carry their own separate DNA, inherited only from your mother.

Adenine, cytosine and guanine are three of DNA's four bases; what is the fourth?

The fourth DNA base is thymine, which pairs with adenine through two hydrogen bonds; RNA replaces thymine with uracil.

What shape do the two strands of DNA form?

DNA's two strands twist into a double helix, the structure Watson and Crick published in 1953 using X-ray diffraction images from Rosalind Franklin's lab.

Gregor Mendel worked out the basic laws of heredity by breeding which plants?

He grew tens of thousands of pea plants in a monastery garden between 1856 and 1863, and his results were ignored for decades.

Which type of cell division produces sperm and egg cells?

Meiosis produces sperm and egg cells through two rounds of division, ending with four haploid cells that each carry one copy of every chromosome.

Which pigment do plants use to absorb light for photosynthesis?

Chlorophyll absorbs red and blue light to power photosynthesis and reflects green, which is why leaves look green.

People with which blood type are called universal donors for red blood cell transfusions?

O negative red cells carry no A, B or Rh antigens, so they can be given to patients of any blood type; AB positive is the universal recipient.

Which element has atomic number 1?

Hydrogen, with a single proton, is element 1 and the lightest; it makes up roughly three-quarters of the universe's normal matter by mass.

On the pH scale, what value is neutral?

Below 7 is acidic and above 7 is basic; each step is a tenfold change, so pH 5 is a hundred times more acidic than pH 7.

Helium, neon, argon and krypton belong to which group of elements?

Helium, neon, argon and krypton are noble gases, group 18 of the periodic table; their full outer electron shells make them almost completely unreactive.

Who published the first widely accepted periodic table in 1869?

Dmitri Mendeleev's 1869 table left gaps for undiscovered elements and predicted their properties; gallium (1875) and germanium (1886) later filled two of them.

How many chemical elements are on the modern periodic table?

The modern table holds 118 elements; the seventh row was completed with the 2010 discovery of tennessine (117), and the last four elements were named in 2016.

Avogadro's number, the number of particles in one mole, is about 6.022 times ten to what power?

Avogadro's number is 6.022 × 10^23 particles per mole, so a mole of water, about 18 grams, holds that many molecules.

Newton's third law says that for every action there is what?

Newton's third law: every action has an equal and opposite reaction. A rocket throws exhaust backward and the exhaust pushes the rocket forward with equal force.

Roughly how fast does light travel in a vacuum?

Light travels about 300,000 km per second in a vacuum, exactly 299,792,458 metres per second; since 1983 that value has defined the metre.

The Ring of Fire, home to about 90 percent of the world's earthquakes, surrounds which ocean?

The Ring of Fire is a roughly 40,000 km horseshoe of trenches and volcanic arcs rimming the Pacific Ocean, where oceanic plates sink beneath their neighbours.

What is the capital of Australia?

Canberra was purpose-built as a compromise between rivals Sydney and Melbourne; Parliament moved there from Melbourne in 1927.

Which language has the most native speakers in the world?

Mandarin Chinese has roughly 940 million native speakers, far ahead of Spanish at about 485 million; English leads only once second-language speakers are counted.

In which year did the American Civil War end?

The Civil War ended in 1865, when Robert E. Lee surrendered to Ulysses S. Grant at Appomattox Court House on April 9, 1865.

Which amendment to the US Constitution abolished slavery?

The 13th Amendment, ratified December 6, 1865, abolished slavery except as punishment for a crime; the 14th granted citizenship and the 15th protected voting rights regardless of race.

How many amendments make up the Bill of Rights?

The Bill of Rights is the first 10 amendments, ratified in 1791. Congress sent twelve in 1789; the congressional-pay one was finally ratified in 1992 as the 27th.

The United States bought the Louisiana Territory in 1803 from which country?

Napoleon's France sold the territory for about 15 million dollars in 1803, roughly 18 dollars per square mile, doubling the size of the United States.

How many years is 'four score and seven', the opening of Lincoln's Gettysburg Address?

A score is twenty, so four score and seven is 87 years: in 1863 Lincoln was counting back to the Declaration of Independence of 1776.

In which city did the Constitutional Convention meet in 1787?

The Constitutional Convention met in Philadelphia's Pennsylvania State House, now Independence Hall, from May to September 1787, with windows shut to keep the debates secret.

Which amendment recognized women's right to vote nationwide in 1920?

The 19th Amendment was ratified in August 1920 when Tennessee became the 36th state to approve it, after young legislator Harry Burn switched his vote on his mother's advice.

The Wright brothers' first powered flight in 1903 was near Kitty Hawk, in which state?

Kitty Hawk is on North Carolina's Outer Banks; the Wright brothers, from Dayton, Ohio, chose it for steady winds and soft sand, flying on December 17, 1903.

The Wall Street crash that helped tip the world into the Great Depression happened in which year?

The crash came in October 1929: the Dow fell almost 13 percent on Black Monday, October 28, and nearly 12 percent more on Black Tuesday, October 29.

Which 1954 Supreme Court case ruled that racial segregation in public schools was unconstitutional?

Brown v. Board of Education (1954) unanimously held that segregated public schools are inherently unequal, overturning the 'separate but equal' doctrine of Plessy v. Ferguson (1896).

How many members does the US Senate have?

The Senate has 100 members, two per state, serving staggered six-year terms so roughly a third of the seats are contested every two years.

How many voting members sit in the US House of Representatives?

The House has 435 voting members, a total capped by the Permanent Apportionment Act of 1929; seats are redistributed among the states after each census.

How many justices sit on the US Supreme Court?

The number is set by Congress, not the Constitution, and has been nine since 1869; it was as low as six and as high as ten before that.

How many electoral votes does a candidate need to win the US presidency?

There are 538 electors in total, a number unchanged since 1964, so 270 is the smallest possible majority.

The assassination that triggered World War I killed the heir to which throne?

Franz Ferdinand, heir to the throne of Austria-Hungary, was shot by Gavrilo Princip in Sarajevo on 28 June 1914; Austria-Hungary declared war on Serbia a month later.

World War II in Europe began in September 1939 when Germany invaded which country?

Britain declared war two days later; the Soviet Union invaded Poland from the east on 17 September.

Bastille Day, the national holiday marking the 1789 storming of a Paris prison, falls on which date?

The Bastille fell on 14 July 1789; the crowd found only seven prisoners inside, and 14 July became France's national holiday in 1880.

Which monarch sealed Magna Carta at Runnymede in 1215?

King John sealed Magna Carta on 15 June 1215 under pressure from rebel barons, then had Pope Innocent III annul it by late August, reigniting civil war.

In which year did the Berlin Wall open?

On 9 November 1989 East German spokesman Günter Schabowski bungled a press conference, saying the border was open 'immediately', and crowds forced the checkpoints open that night.

Most chronologies date the fall of the Western Roman Empire to which year?

In 476 the Germanic general Odoacer deposed the teenage emperor Romulus Augustulus, the date most chronologies use for the fall of the Western Roman Empire.

Shakespeare's Romeo and Juliet is set in which Italian city?

Verona now maintains a 'Juliet's balcony' for tourists even though the character never existed.

Shakespeare's Hamlet is a prince of which country?

Hamlet is Prince of Denmark; the play, Shakespeare's longest, is set at Elsinore, the real Kronborg fortress in the Danish town of Helsingør.

Who wrote To Kill a Mockingbird?

Harper Lee published To Kill a Mockingbird in 1960 and won the 1961 Pulitzer Prize for Fiction; she did not publish another book until Go Set a Watchman in 2015.

Who wrote The Great Gatsby?

F. Scott Fitzgerald's The Great Gatsby sold poorly in 1925; it became a classic only after about 155,000 free Armed Services Editions went to troops in World War II.

In what year was George Orwell's Nineteen Eighty-Four published?

Nineteen Eighty-Four was published on 8 June 1949 by Secker & Warburg; Orwell finished the manuscript on the Scottish island of Jura in late 1948.

In Orwell's Animal Farm, the pig Napoleon is an allegory for which leader?

Napoleon represents Joseph Stalin; Snowball, the rival he drives off the farm, stands for Trotsky, and Old Major blends Marx with Lenin.

Who wrote Of Mice and Men?

John Steinbeck wrote Of Mice and Men in 1937 as a 'play-novelette' so it could go straight to the stage; it opened on Broadway that November.

In Lord of the Flies, what object do the boys use as a horn to call meetings?

The conch shell, blown by Ralph to summon the boys, gives its holder the right to speak; its shattering when Piggy is killed marks the end of order.

In Homer's Odyssey, Odysseus is king of which island?

Odysseus rules Ithaca, an island in the Ionian Sea; he takes ten years to get home from Troy while Penelope holds off a houseful of suitors.

Who wrote Frankenstein?

Mary Shelley started it at 18 after Lord Byron challenged his guests to each write a ghost story.

Arthur Miller's play The Crucible dramatizes which historical event?

The Crucible dramatizes the Salem witch trials of 1692–93; Miller wrote it in 1953 as an allegory for McCarthyism and was called before HUAC himself in 1956.

Holden Caulfield narrates which 1951 novel?

Holden Caulfield narrates The Catcher in the Rye; J. D. Salinger published nothing after the 1965 story 'Hapworth 16, 1924' and spent decades avoiding the fame it brought.

The epic poem Beowulf was written in which language?

Beowulf is written in Old English (Anglo-Saxon); its 3,182 alliterative lines survive in a single manuscript scorched in the 1731 Cotton library fire.

What is the chemical symbol for gold?

Au comes from aurum, the Latin word for gold; gold is element 79 on the periodic table.

Which astronomer formulated the three laws of planetary motion?

Johannes Kepler published his first two laws of planetary motion in Astronomia Nova (1609) and the third, linking orbital period to distance, in 1619.

What is the largest organ of the human body?

The skin is the largest organ, about 16 percent of body mass and 1.5 to 2 square metres on an adult; the liver is the largest internal organ.

Who narrates The Great Gatsby?

Nick Carraway, Daisy's cousin and Gatsby's neighbour, narrates the novel, telling of Gatsby's obsession with winning back Daisy on Long Island in the summer of 1922.

In George Orwell's Nineteen Eighty-Four, what is Winston Smith's job at the Ministry of Truth?

He alters old newspapers so the past always matches the Party's current line.

In Nineteen Eighty-Four, what is the name of the Party's dictatorial leader whose face is everywhere?

Big Brother is the Party's all-seeing figurehead on every poster; Goldstein is its official enemy and O'Brien the Inner Party member who betrays Winston.

Who was the principal author of the US Declaration of Independence?

Thomas Jefferson drafted the Declaration in about 17 days in June 1776 for the Committee of Five; Congress adopted it on July 4 in what is now Independence Hall.

How long was Abraham Lincoln's Gettysburg Address, delivered in November 1863?

The Gettysburg Address ran about 270 words and under two minutes; the main speaker, Edward Everett, had talked for two hours before Lincoln rose.

Mount Everest sits on the border between Nepal and which other country?

Everest straddles the Nepal–China border, its summit on the line with Tibet; China and Nepal jointly announced a remeasured height of 8,848.86 metres in 2020.

What is the largest hot desert in the world?

The Sahara covers most of North Africa, some 9.2 million square kilometres.

In which English town was William Shakespeare born in 1564?

Stratford-upon-Avon baptised him on 26 April 1564; his surviving works run to some 39 plays and 154 sonnets, and his company built the Globe in London in 1599.

The Mona Lisa, painted by Leonardo da Vinci, hangs in which museum?

The Louvre, Paris, lost it in 1911 to a museum worker, Vincenzo Peruggia, and got it back two years later from Italy.

Which Beethoven symphony ends with a choral setting of Schiller's 'Ode to Joy'?

Beethoven's Ninth Symphony, premiered in Vienna in 1824, closes with soloists and chorus singing Schiller's 'Ode to Joy', the first choral finale in a major symphony.

About how many bones does an adult human skeleton have?

206 is the adult count; babies are born with around 270, but many fuse together as they grow.

How many bits make up one byte?

A byte is 8 bits, enough for 256 distinct values; Werner Buchholz coined the term at IBM in 1956 while designing the Stretch computer.

The Nile flows north and empties into which sea?

The Nile empties into the Mediterranean through its delta north of Cairo; its two main tributaries, the White Nile and Blue Nile, meet at Khartoum in Sudan.

At a pressure of one atmosphere, water boils at what temperature?

At one atmosphere water boils at 100 °C, which is 212 °F; the Celsius scale was defined using water's freezing and boiling points as 0 and 100.

Which Apollo 11 astronaut stayed in lunar orbit while Armstrong and Aldrin walked on the Moon?

Michael Collins circled alone in the command module Columbia for about 21 hours while Eagle sat in the Sea of Tranquility with Armstrong and Aldrin.

In To Kill a Mockingbird, Atticus Finch is appointed to defend which character?

Tom Robinson is a Black man falsely accused of assaulting Mayella Ewell; Boo Radley is the reclusive neighbour who saves the children.

How does Newton's first law describe a body on which no force acts?

Newton's first law: with no net force, a body stays at rest or keeps moving at constant speed in a straight line; that tendency is inertia.

How deep is the Challenger Deep, the lowest known point in the world's oceans?

Challenger Deep, at the southern end of the Mariana Trench, is about 10,900 metres deep, some 2,000 metres more than Everest is tall.

In which Greek city is Shakespeare's 'A Midsummer Night's Dream' set?

The play is set in Athens and the woods outside it, framed by the wedding of Theseus, Duke of Athens, to Hippolyta.

The title of 'A Raisin in the Sun' comes from a poem by which writer?

The title quotes Langston Hughes's 1951 poem 'Harlem' ('Does it dry up / like a raisin in the sun?'); Lorraine Hansberry's play opened on Broadway in 1959.

Which river is the largest in the world by discharge volume?

The Amazon discharges about 209,000 cubic metres per second, roughly a fifth of all river water reaching the oceans; only its length is disputed with the Nile.

Which document served as the first constitution of the United States?

The Articles of Confederation came into force on March 1, 1781, once Maryland became the last of the 13 states to ratify; the Constitution replaced them in 1789.

Chemical elements are distinguished from each other by the number of which particle?

The number of protons in the nucleus is the atomic number; every atom with six protons is carbon, whatever its neutrons or electrons.

Which bacterium caused the Black Death?

Yersinia pestis, spread mainly by flea bites, caused the Black Death of 1347–51, which killed an estimated third to half of Europe's population.

On what date did the Boston Tea Party take place?

On December 16, 1773, Sons of Liberty members boarded three ships in Boston Harbor and dumped 342 chests of East India Company tea overboard.

Who wrote the 1932 dystopian novel 'Brave New World'?

Aldous Huxley published Brave New World in 1932; its outsider John the Savage challenges the engineered World State and its pacifying drug, soma.

The Byzantine Empire ended with the fall of Constantinople to which power in 1453?

Mehmed II's Ottomans took Constantinople on 29 May 1453; the empire's own citizens had called themselves Romans, and 'Byzantine' was coined a century later.

Which molecule stores the energy released by cellular respiration?

ATP (adenosine triphosphate) stores respiration's energy in its phosphate bonds; one glucose molecule yields roughly 30 to 32 ATP in aerobic respiration.

With whom did Charles Darwin jointly present the theory of natural selection?

Alfred Russel Wallace's 1858 letter from the Malay Archipelago prompted the joint reading of his and Darwin's papers at the Linnean Society on 1 July 1858.

What is the value of 5 factorial, written 5!?

5! = 5 × 4 × 3 × 2 × 1 = 120, the number of ways to arrange five distinct objects in a row.

Which type of chemical bond involves sharing electron pairs between atoms?

A covalent bond shares one or more electron pairs between atoms, as in the two O–H bonds of water; ionic bonds instead rely on attraction between oppositely charged ions.

How many days did the Cuban Missile Crisis of October 1962 last?

The crisis ran 13 days, from October 16, 1962, when Kennedy saw the U-2 photos, to October 28, when Khrushchev announced the missiles' removal.

Who is the protagonist of Arthur Miller's 'Death of a Salesman'?

Willy Loman, an ageing travelling salesman in late-1940s Brooklyn, is the protagonist; Biff is his elder son, and the play won the 1949 Pulitzer Prize for Drama.

Which physicist first described the change in pitch of a passing vehicle's sound in 1842?

Christian Doppler proposed the effect in an 1842 paper on binary-star light; Buys Ballot confirmed it for sound in 1845 using trumpeters on a moving train.

Which band of the electromagnetic spectrum has the highest frequency?

From low to high the bands run radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.

Electrons have roughly how many times less mass than the other two atomic constituents?

An electron has roughly 2,000 times less mass than a proton or neutron: a proton weighs about 1,836 electron masses and a neutron about 1,839.

On what date did Lincoln's final Emancipation Proclamation take effect?

The Emancipation Proclamation took effect on January 1, 1863, declaring free more than 3.5 million enslaved people in Confederate-held territory; the preliminary version came on September 22, 1862.

What are the molecules that enzymes act upon called?

Substrates are the molecules an enzyme binds at its active site and converts into products; the enzyme itself is not consumed in the reaction.

Roughly how long is the equator?

The equator, at 0 degrees latitude, is about 40,075 km around, slightly more than the 40,008 km pole-to-pole circumference because Earth bulges at the middle.

What is the name of the fireman protagonist of 'Fahrenheit 451'?

Guy Montag is the fireman who starts stealing the books he is paid to burn; Ray Bradbury published the novel in 1953.

Under what collective pseudonym were the Federalist Papers written?

Hamilton, Madison and Jay signed all 85 Federalist essays as 'Publius', after Publius Valerius Publicola, a founder of the Roman Republic.

In the Fibonacci sequence, how is each element after the first two produced?

Sum of the two before it: the sequence runs 1, 1, 2, 3, 5, 8, 13.

Which event is conventionally taken to mark the end of the French Revolution?

Napoleon's Coup of 18 Brumaire (9 November 1799) overthrew the Directory and installed the Consulate, the conventional end point of the Revolution begun in 1789.

What is the name of the orphan whose education 'Great Expectations' depicts?

Pip (Philip Pirrip) narrates Great Expectations (1861), Dickens's second novel after David Copperfield to be told entirely in the first person.

What term describes the time for a radioactive quantity to drop to 50% of its starting value?

Half-life is the time for half of a radioactive sample to decay; carbon-14's is about 5,730 years, which underpins radiocarbon dating.

Which four empirical laws combine to form the ideal gas law?

Boyle's, Charles's, Avogadro's and Gay-Lussac's laws combine into PV = nRT, first stated by Émile Clapeyron in 1834; Mendeleev added the universal gas constant in 1874.

In which country did the Industrial Revolution begin around 1760?

The Industrial Revolution began in Great Britain around 1760, driven by coal, textile mills and steam power; it spread to continental Europe and the United States by about 1840.

Under what pen name was 'Jane Eyre' first published in 1847?

Charlotte Brontë published Jane Eyre in October 1847 as Currer Bell; her sisters Emily and Anne wrote as Ellis and Acton Bell, keeping their real initials.

Which two senators lead the conspiracy in Shakespeare's play about Caesar?

Shakespeare drew mainly on Thomas North's 1579 translation of Plutarch.

What is the formula for the kinetic energy of a non-rotating object?

Kinetic energy is ½mv², the work needed to accelerate a mass m from rest to speed v; doubling the speed quadruples the energy.

By what other name is the citric acid pathway of respiration known?

The citric acid cycle is the Krebs cycle, after Hans Krebs, who worked it out in 1937 and shared the 1953 Nobel Prize; it oxidises acetyl-CoA to release energy.

What is the logarithm of 1000 to base 10?

log base 10 of 1000 is 3, because 10 raised to the power 3 is 1000; a logarithm is the exponent the base must be raised to.

Which Shakespeare tragedy, first performed around 1606, is his shortest?

Macbeth is Shakespeare's shortest tragedy, roughly half the length of Hamlet; it was first printed in the 1623 First Folio, possibly from a prompt book.

Which Archbishop of Canterbury mediated between King John and the rebel barons at Runnymede in 1215?

Stephen Langton, Archbishop of Canterbury from 1207, mediated between John and the barons and is the first counsellor named in Magna Carta's preamble.

Which 19th-century belief held that Americans were destined to expand westward?

Manifest destiny, a phrase coined by journalist John O'Sullivan in 1845, held that Americans were destined to expand across the continent; it is often called an early expression of American imperialism.

Which 1803 Supreme Court case established judicial review?

Marbury v. Madison (1803), decided under Chief Justice John Marshall, established that courts can strike down laws that violate the Constitution.

About how much aid did the Marshall Plan transfer to Western Europe?

The Marshall Plan, officially the European Recovery Program, moved about $13.3 billion to Western Europe between 1948 and 1951, starting with Truman's signature on April 3, 1948.

Which stage of interphase, when DNA replicates, precedes mitosis?

DNA replicates during S (synthesis) phase, between G1 and G2 of interphase; G2 then leads into mitosis, which ends with telophase and cytokinesis.

Which SI base unit measures amount of substance?

The mole is the SI base unit for amount of substance; since 2019 one mole contains exactly 6.02214076 × 10^23 elementary entities.

Which US foreign policy opposes foreign interference in the Western Hemisphere?

The Monroe Doctrine, declared by President James Monroe in December 1823, warned European powers against further colonisation or interference in the Western Hemisphere.

What are the electric signals fired by neurons called?

Action potentials are the electrical impulses neurons fire: a brief swing of membrane voltage from about −70 mV to +30 mV that travels down the axon.

Who discovered the neutron in 1932?

James Chadwick identified the neutron at Cambridge's Cavendish Laboratory in 1932 and won the 1935 Nobel Prize in Physics; the discovery opened the way to fission in 1938.

Which president introduced the phrase 'New Deal' when accepting his party's 1932 nomination?

Franklin D. Roosevelt promised 'a new deal for the American people' when accepting the Democratic nomination on July 2, 1932, then beat incumbent Herbert Hoover in a landslide.

Ohm's law states current is directly proportional to what?

Ohm's law says current is proportional to voltage: I = V/R, so doubling the voltage across a fixed resistance doubles the current.

In osmosis, solvent moves through a membrane toward which region?

In osmosis water moves toward the side with higher solute concentration (lower water potential), tending to equalise concentrations across a selectively permeable membrane.

Which anti-war Picasso painting depicts a 1937 bombing during the Spanish Civil War?

Guernica (1937) depicts the bombing of the Basque town of Guernica by German and Italian aircraft on 26 April 1937; the mural hangs in Madrid's Reina Sofía.

In the periodic table, what are the horizontal rows called?

Periods run across; the columns are called groups.

Oxygenic photosynthesis releases oxygen as a byproduct of splitting what?

Photosynthesis releases oxygen by splitting water molecules in the light-dependent reactions, as Ruben and Kamen showed in 1941 with oxygen-18 labelled water.

Which earlier idea does the theory of plate tectonics build on?

Plate tectonics builds on Alfred Wegener's 1912 theory of continental drift, which gained acceptance after seafloor spreading was confirmed in the 1960s.

Who is the protagonist of Jane Austen's 1813 novel Pride and Prejudice?

Elizabeth Bennet's story was drafted when Austen was 20-21, though it was not published until 1813.

A natural number greater than 1 that is not prime is called what?

A composite number has a factor other than 1 and itself: 6 = 2 × 3 is composite, while 5, with no such factor, is prime.

What is the SI unit of electric charge?

The coulomb (C) is the SI unit of charge, equal to one ampere flowing for one second; a single electron carries about 1.602 × 10^−19 coulombs.

Who devised the square diagram used to predict genotypes of a cross in 1905?

Reginald Punnett devised the Punnett square around 1905 while working with William Bateson at Cambridge; it lays out parental gametes in a grid to show offspring genotypes.

The quadratic formula comes from applying which method to a general quadratic equation?

Completing the square on ax² + bx + c = 0, after dividing by a, produces x = (−b ± √(b² − 4ac)) / 2a, which is the quadratic formula.

How many constitutional amendments were added during Reconstruction?

Three Reconstruction amendments, the 13th, 14th and 15th, were ratified between 1865 and 1870; Southern states later evaded them with poll taxes and literacy tests.

Which movement took Greek and Roman antiquity as its model in art and learning?

The Renaissance, beginning in 14th-century Italy, took Greek and Roman antiquity as its model in art and learning; Brunelleschi's Florence cathedral dome (1436) is a landmark.

In what year did the Russian Revolution begin?

The Russian Revolution began in 1917: the February Revolution forced Nicholas II to abdicate in March, and the Bolsheviks seized power in the October Revolution that November.

Roughly how long were the Silk Road's overland routes?

The Silk Road's land routes ran roughly 6,400 km from China to the Mediterranean; the name was coined by geographer Ferdinand von Richthofen in 1877.

Which pope commissioned Michelangelo's Sistine Chapel ceiling?

Pope Julius II commissioned the ceiling, painted 1508–1512; the chapel itself was built for his uncle Sixtus IV, for whom it is named.

In mathematics, slope is the ratio of rise to what?

Slope is rise over run: the vertical change divided by the horizontal change between two points, usually written as m in y = mx + b.

About how fast does sound travel in air at 20 °C?

Sound travels about 343 m/s in air at 20 °C, roughly one mile every 4.7 seconds; the speed rises about 0.6 m/s for each degree Celsius.

Which museum acquired Van Gogh's 'The Starry Night' in 1941?

The Museum of Modern Art in New York acquired The Starry Night in 1941 through the Lillie P. Bliss Bequest; it shows the view from Van Gogh's asylum window at Saint-Rémy.

Huckleberry Finn's story is the direct sequel to which Mark Twain novel?

Huckleberry Finn (1884) picks up directly after The Adventures of Tom Sawyer (1876) and was among the first major American novels written throughout in vernacular English.

Pilgrims in 'The Canterbury Tales' travel to the shrine of which saint?

The pilgrims ride to Canterbury Cathedral's shrine of Thomas Becket, the archbishop murdered there in 1170; Chaucer wrote the 24 tales between about 1387 and 1400.

Which family is at the center of Steinbeck's 'The Grapes of Wrath'?

The Joads, tenant farmers driven off their Oklahoma land in the 1930s Dust Bowl, travel Route 66 to California; the novel won the 1940 Pulitzer Prize.

Into how many books are Homer's Iliad and Odyssey each divided?

Each epic is divided into 24 books, one for each letter of the Greek alphabet, a division made by Alexandrian scholars centuries after Homer.

What is the name of the aging fisherman in 'The Old Man and the Sea'?

Santiago, the old Cuban fisherman, battles a giant marlin for three days; the 1952 novella was Hemingway's last major fiction published in his lifetime and won the 1953 Pulitzer.

Who wears the scarlet letter 'A' in Nathaniel Hawthorne's novel?

Hester Prynne must wear the scarlet 'A' for adultery after bearing Pearl out of wedlock; the novel is set in Puritan Boston between 1642 and 1649.

Which federal law set the Trail of Tears in motion?

The Indian Removal Act, signed by Andrew Jackson in May 1830, authorised moving the southeastern tribes west of the Mississippi; about 60,000 people were forced out, thousands dying en route.

On what date was the Treaty of Versailles signed?

The Treaty of Versailles was signed on 28 June 1919 in the Hall of Mirrors, five years to the day after Franz Ferdinand's assassination at Sarajevo.

Trigonometry takes its name from Greek words meaning what?

Trigonometry comes from Greek trigōnon (triangle) and metron (measure), so it means triangle measure; Hipparchus compiled the first known chord table in the 2nd century BC.

On which day is the Sun directly overhead at the Tropic of Cancer?

The Sun is directly overhead at the Tropic of Cancer (23.4° N) at the June solstice, around June 21, the northernmost point of its annual path.

About how many artworks did Van Gogh create in just over a decade?

Van Gogh produced about 2,100 artworks between 1881 and 1890, including around 860 oil paintings, most of them in the last two years of his life.

In which city was Mozart born?

Mozart was born in Salzburg on 27 January 1756 and composed more than 600 works before dying in Vienna at 35.

Ludwig van Beethoven was baptised in which year?

Beethoven was baptised in Bonn on 17 December 1770; his birth date is unrecorded but was probably the day before.

Which biological principle holds that all cells come from pre-existing cells?

Cell theory, set out by Schleiden and Schwann in 1838–39 and completed by Virchow's 1855 dictum omnis cellula e cellula, holds that all cells arise from pre-existing cells.

Which 16th-century movement marked the beginning of Protestantism?

The Reformation began when Martin Luther published his Ninety-five Theses in Wittenberg in 1517, splitting Western Christianity and giving rise to Protestantism.

The ACT college admissions test was introduced in 1959 by a professor in which US state?

Everett Franklin Lindquist of the University of Iowa launched the ACT in November 1959 as a rival to the SAT; each section is scored from 1 to 36.