Calculus
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50 free Calculus trivia questions with answers — science & nature quiz, new questions added Oct 2026.
Calculus is the mathematics of change, and its story is far livelier than the average textbook lets on. It was invented twice, by two brilliant men whose supporters then spent years trading accusations of theft, and it went on to explain everything from the motion of the planets to the thrill of a roller coaster. This quiz is a game of fun calculus facts and gentle problems. You will meet the people behind the ideas, the odd origins of the symbols students scribble every day, curves with impossible-sounding properties, and the places calculus turns up outside the classroom, from the cinema to the dentist's chair. A handful of questions ask you to differentiate a function or add up a series, but nothing needs more than a first course. It suits students who want a break from problem sets, teachers looking for a warm-up game, and anyone curious about how the subject came to be. Every question comes with its answer and a short explanation, so a wrong guess still teaches something.
30 of 50 questions with answers and explanations. Play the quiz
Q 01The word calculus comes from the Latin for which small object, once moved around Roman counting boards?
Pebble
Pebble is the literal meaning: Romans did their sums by sliding little stones along a board. Doctors still use the same word for a kidney stone.
Q 02The fourth, fifth and sixth derivatives of position are jokingly named after the mascots of which breakfast cereal?
Rice Krispies
Rice Krispies supplied the names, borrowed from the trio of cartoon characters on the box. The joke is said to have been started by a NASA engineer working on the Apollo programme.
Q 03Zeno's paradox, later untangled by the calculus of infinite series, has swift Achilles forever chasing which animal?
Tortoise
Tortoise is the answer: given a head start, Zeno argued, it can never be caught, because Achilles must first reach where it was. Endless shrinking steps can still add up to a finite distance.
Q 04Isaac Newton developed much of his calculus at home in 1665–66 while which disaster kept Cambridge University closed?
The Great Plague
The Great Plague shut the university just after Newton took his degree. In two years at the family farm in Woolsthorpe he also built his theories of optics and gravitation.
Q 05Dentists use the word calculus for which tooth problem, scraped away during a professional cleaning?
Tartar
Tartar is plaque that has hardened with minerals from saliva. Once it has formed it is too firmly attached for a toothbrush to shift, which is why a hygienist uses a scaler.
Q 06Which 1988 film stars Edward James Olmos as a teacher coaching East Los Angeles students through AP Calculus?
Stand and Deliver
Stand and Deliver tells the true story of Jaime Escalante, whose 18 students at Garfield High passed the exam in 1982. Olmos earned a Best Actor Oscar nomination for the part.
Q 07Gottfried Leibniz, co-inventor of calculus, also championed which number system that now runs every digital computer?
Binary
Binary, which writes every number using only two digits, was a system Leibniz kept returning to throughout his career. The English astronomer Thomas Harriot had devised it decades earlier.
Q 08Germany's Bahlsen company has sold which snack, named after calculus pioneer Gottfried Leibniz, since 1891?
A butter biscuit
A butter biscuit with 52 'teeth' around its edge carries his name. The only link is that Leibniz was one of the more famous residents of Hanover, where Bahlsen is based.
Q 09Professor Calculus is the hard-of-hearing inventor who builds a Moon rocket in which Belgian comic series?
Tintin
Tintin is the series: the absent-minded professor first appeared in Red Rackham's Treasure in 1943. In Hergé's original French he is Professeur Tournesol, which means sunflower.
Q 10The squeeze theorem for limits in calculus is also nicknamed after which lunchtime food?
Sandwich
Sandwich theorem is the other name, because a function trapped between two others must share their limit. It is also known as the two policemen and a drunk theorem.
Q 11The derivative of a function at a point equals the slope of which line drawn to its curve there?
Tangent
Tangent is the line: it grazes the curve at a single point and shares its direction there. Its name comes from the Latin word for touching.
Q 12A basic Riemann sum in calculus estimates the area under a curve by adding up thin strips of which shape?
Rectangles
Rectangles do the job, which is why the technique is also called the rectangle rule. The thinner the strips, the smaller the error, and an integral is what the total settles on.
Q 13In calculus, the second derivative of an object's position with respect to time gives which physical quantity?
Acceleration
Q 21Isaac Newton never called his invention calculus; English schools long knew it as the science of what?
Fluxions
Fluxions was Newton's word for rates of change, and the name lasted in English schools into the 19th century. His treatise on the method, finished in 1671, was not published until 1736.
Q 22Gottfried Leibniz drew his integral sign ∫ as a stretched letter S, standing for which Latin word?
Summa
Summa was the word he had in mind, because he pictured an integral as endlessly many tiny pieces added together. The shape is the old-fashioned long s once used in print.
Q 23Which ancient Greek from Syracuse found the area under a parabola many centuries before calculus was invented?
Archimedes
Acceleration is how quickly velocity changes, and velocity is itself how quickly position changes. Differentiating twice is the reason its unit carries a 'squared'.
Q 14The third derivative of position over time, which engineers minimise on roller coasters, has which abrupt name?
Jerk
Jerk measures how suddenly a push comes on or eases off. Railway curves and roller-coaster loops are laid out as gradual spirals to keep it low, and lift designers work hard to tame it.
Q 15Calculus students famously lose marks for forgetting which letter, added to the end of every indefinite integral?
C
C stands for the constant of integration. Differentiating wipes out any fixed number added to a function, so working backwards you can never tell which number was there.
Q 16Using the power rule of calculus, what is the derivative of x squared, the function whose graph is a parabola?
2x
2x is the result: the power rule brings the exponent down in front and lowers it by one. So the parabola's slope is 6 where x is 3, and it is flat at the very bottom.
Q 17In calculus, taking the derivative of the sine function gives which other trigonometric function?
cos x
cos x is the derivative of the sine, because a sine wave climbs fastest exactly where the cosine is at its peak. Differentiate four times and you are back where you started.
Q 18In calculus, a function whose derivative is zero everywhere has a graph of which simple shape?
Horizontal line
Horizontal line is right: a derivative measures steepness, and a flat graph has none. That is why differentiating a constant such as 7 leaves nothing behind.
Q 19Which technique in calculus differentiates a function nested inside another, working from the outside in?
Chain rule
Chain rule is the name: differentiate the outer function, then multiply by the derivative of the inner one. In Leibniz's notation the dy and dx terms look as if they cancel like fractions.
Q 20Which function is famous in calculus for being its own derivative, with a slope always equal to its height?
e^x
e^x is the one: apart from constant multiples of it, no other function equals its own derivative. That makes it the model for anything that grows in proportion to its size.
Archimedes cut the region into endlessly many triangles whose areas shrink in a fixed ratio, then added them all up. His method of exhaustion is integration in all but name.
Q 24Which London body ruled for Isaac Newton in the calculus priority dispute, in a report Newton wrote himself?
Royal Society
The Royal Society was hardly neutral ground: Newton was its president at the time, and the committee it set up never asked Leibniz for his version of events.
Q 25Which Irish bishop mocked the vanishing quantities of early calculus as ghosts in his 1734 attack The Analyst?
George Berkeley
George Berkeley addressed his pamphlet to an 'infidel mathematician', and the critique went on to influence how mathematics developed. The Californian city and its university are named after him.
Q 26Which Swiss mathematician began using the letter e for the constant 2.718… that runs all through calculus?
Leonhard Euler
Leonhard Euler first wrote it in the late 1720s, in an unpublished paper on explosive forces in cannons. Nobody knows why he chose that particular letter.
Q 27Isaac Newton's 1687 book, which used calculus-like methods to explain planetary orbits, goes by which short Latin title?
Principia
Principia keeps its calculus out of sight: Newton set out his arguments as geometric propositions about vanishingly small shapes instead of using the new methods openly.
Q 28Isaac Newton's notation for a derivative, still common in physics, places which small mark above a letter?
A dot
A dot goes over the changing quantity, and a second one means differentiate again. The style has been rudely nicknamed flyspeck notation.
Q 29The Kerala school found key infinite series two centuries before European calculus in which present-day country?
India
India is where Madhava of Sangamagrama founded the school in the 14th century. Its results were set down in Sanskrit verse, with the proofs supplied later in a work written in Malayalam.
Q 30A mistranslation of Maria Agnesi's 1748 calculus textbook gave one of her curves which spooky English name?
Witch
Witch of Agnesi is what the curve is still called. Her book used the Italian name versiera, a word about turning, but translator John Colson read it as avversiera, a woman who is against God.