High School Math Trivia
0Loading crowd target
0Loading crowd target
7correct to beat the crowd
100 free High School Math trivia questions with answers — trivia quiz, new questions added Oct 2026.
High school math is where the famous results live: the rule about right triangles, the formula that solves any quadratic, the constant that turns up in every circle, and the counter-intuitive truths of probability that still fool professionals. These fifty questions mix algebra, geometry, trigonometry, probability and statistics and number theory with the people behind the theorems, from ancient Greece to a 1990s proof that closed a puzzle more than three centuries old. A handful are quick mental-arithmetic problems you can check in your head, and every answer comes with an explanation that adds the detail worth remembering. It suits a classroom starter, a quiz-night round or anyone curious how much of grade 9 to 12 maths actually stuck.
30 of 100 questions with answers and explanations. Play the quiz
Q 01In the famous birthday paradox, what is the smallest group size with a better-than-even chance of a shared birthday?
23
23 people are enough for a 50.7% chance, because they form 253 different pairs who might match, far more than the 22 comparisons any one of them makes.
Q 02In the Monty Hall problem, which move wins the car two times in three?
Switching to the other door
Switching to the other door wins two times in three. When Marilyn vos Savant said so in Parade magazine, thousands of readers, many signing as PhDs, wrote in to tell her she was wrong.
Q 03Which Greek, whose followers were reportedly forbidden to eat beans, gives his name to the right-triangle rule a² + b² = c²?
Pythagoras
Pythagoras's theorem even has a proof by a US president: James Garfield published one in 1876, while he was still a congressman, built around a trapezoid.
Q 04NASA's Jet Propulsion Laboratory steers spacecraft between planets using just 15 decimal places of which constant?
π
π to 15 decimal places is all the laboratory needs for its most exact work, because that pins the edge of a circle billions of miles across to within the length of a little finger.
Q 05After twenty heads in a row, what is the probability that a fair coin lands heads on the next flip?
50%
The chance stays 50% because a coin has no memory; believing a tail is 'due' is the gambler's fallacy, also called the Monte Carlo fallacy after a 1913 roulette run of 26 blacks.
Q 06Which saves a shopper more: one 40% price cut, or a 20% cut followed by 20% off the reduced price?
The single cut
The single cut. The second 20% comes off an already-reduced price, so the double cut leaves 64% of the original (0.8 × 0.8) and saves only 36%.
Q 07What is the repeating decimal 0.999…, the limit of the sequence 0.9, 0.99, 0.999 and so on, in ordinary arithmetic?
Exactly 1
Exactly 1, not a whisker less: tripling 1/3 = 0.333… gives 0.999… on one side and 1 on the other, so the two decimals are simply two names for one number.
Q 08What do the numbers 1 to 100 add up to, famously found fast by pairing 1 with 100, 2 with 99?
5,050
The total is 5,050 because the fifty pairs 1 + 100, 2 + 99 … 50 + 51 each make 101, and 50 × 101 = 5,050.
Q 09Which 9th-century Baghdad scholar's Latinised name gave us 'algorithm', and his book Al-Jabr the word 'algebra'?
Al-Khwarizmi
Al-Khwarizmi wrote Al-Jabr as a practical handbook for what people need in inheritance, lawsuits and trade, and much of the book works through the rules of Islamic inheritance.
Q 10Which mathematician from Pisa brought the sequence 1, 1, 2, 3, 5, 8 to Europe in 1202 via a puzzle about rabbits?
Fibonacci
Fibonacci did not invent the sequence: Indian scholars had described it centuries earlier, and his 1202 Liber Abaci mattered more for spreading the Hindu-Arabic numerals across Europe.
Q 11What is b² − 4ac called, the expression under the quadratic formula's square root, whose sign counts the real roots?
Discriminant
A negative discriminant means the quadratic's graph never touches the x-axis, so its two roots are complex conjugates rather than real numbers.
Q 12In the line equation y = mx + b, what is m, a quantity that is undefined for a vertical line?
The slope
The slope's m is a mystery: nobody knows why the letter was chosen, and the suggestion that it stands for the French monter, 'to climb', has no evidence behind it.
Q 13Which acronym do American schools teach for the order of operations, the rule that makes 2 + 3 × 4 equal 14?
PEMDAS
Q 21How many degrees do a flat triangle's three angles add up to, a total that grows larger on a sphere?
180
180 is the total only on a flat surface: on a sphere the three angles add up to more, anywhere up to 540°, and the bigger the triangle's area, the bigger the surplus.
Q 22What is the sum of the interior angles of an octagon, the shape of the familiar red stop sign?
1,080°
An octagon's angles total 1,080° because it splits into six triangles from one corner; each corner of a regular octagon measures 135°.
Q 23Besides the equilateral triangle and square, which regular polygon is the only one that tiles a floor by itself?
Hexagon
Hexagon floors put three tiles at every corner, and the honeycomb is no accident: Thomas Hales proved in 1999 that no way of dividing a surface into equal cells uses less wall.
PEMDAS puts multiplication ahead of addition, so 2 + 3 × 4 is 2 + 12 = 14 and not the 20 that working left to right gives; British pupils learn the same rule as BODMAS and Canadians as BEDMAS.
Q 14A colony doubles every hour; by what factor has it grown after ten hours, a number every computer scientist knows?
1,024
Ten doublings give 2¹⁰ = 1,024, which is why a kilobyte traditionally meant 1,024 bytes rather than a round 1,000.
Q 15Which curve, the graph of every quadratic function, did Galileo show is also the path of a thrown projectile?
Parabola
A parabola reflects every ray arriving parallel to its axis through one focus, which is why satellite dishes and car headlight reflectors use the shape.
Q 16Which French philosopher's 1637 treatise La Géométrie united algebra and geometry?
René Descartes
René Descartes published it as an appendix to his Discourse on the Method, and in it named 'imaginary' numbers: roots one could imagine, he wrote, though no real quantity matched them.
Q 17Which Scottish laird published the first logarithms in 1614, so astronomers could multiply big numbers by adding?
John Napier
John Napier's logarithms, said Laplace, 'doubled the life of the astronomer' by cutting the labour of many months to a few days.
Q 18Which number, about 1.618 and written with the Greek letter phi, is the positive solution of x² = x + 1?
Golden ratio
The golden ratio is the hardest number to approximate with fractions: its continued fraction is all 1s, so approximations such as 13/8 converge as slowly as possible.
Q 19Which constant, about 2.718, is the base of natural logarithms and the limit of (1 + 1/n)ⁿ as n grows without bound?
e
The constant e was found by Jacob Bernoulli in 1683 while studying compound interest: compounding a 100% yearly rate ever more often tops out at a factor of 2.718.
Q 20Which number, the length of a 1 × 1 square's diagonal, was probably the first ever proved to be irrational?
√2
√2 carries a grim legend: Hippasus, the Greek said to have shown it cannot be written as a fraction, was supposedly drowned at sea for it, though the ancient accounts differ on his crime.
Q 24Which polygon, the shape of Britain's 50p coin, is the smallest regular one that compass and straightedge cannot draw?
Heptagon
Heptagon coins arrived in 1969 with Britain's 50p, whose sides are curved so that it is the same width whichever way it is measured and rolls through vending machines like a round coin.
Q 25Which side of a right triangle is the denominator of both SOH and CAH in the SOHCAHTOA mnemonic?
Hypotenuse
Hypotenuse, the name of the longest side, comes from the Greek for 'stretching under', because the side stretches across beneath the right angle it faces.
Q 26How far apart are the points (0, 0) and (6, 8) on a coordinate grid, by the distance formula?
10
10, because √(6² + 8²) = √100: the line joining the points is the long side of a 6-8-10 right triangle, the famous 3-4-5 with every side doubled.
Q 27An arc subtends 40° at a circle's centre; what angle does it subtend at a point on the remaining circumference?
20°
20°: the angle at the circumference is always half the angle at the centre on the same arc, wherever the point sits, which is why any angle drawn in a semicircle is a right angle.
Q 28Which astronomer nested the five Platonic solids inside one another in 1596 to model the Solar System?
Johannes Kepler
Johannes Kepler thought the five solids explained why there were just six planets: nested with a sphere around each, they marked out six shells, one for every planet then known.
Q 29Whose Elements, compiled around 300 BC in Alexandria, contains the classic proof that the prime numbers never run out?
Euclid
Euclid's argument is short: multiply any list of primes together and add 1, and the result must have a prime factor that the list left out.
Q 30Which Greek, reputed to have predicted a 585 BC eclipse, is credited with proving every angle in a semicircle is 90°?
Thales
Thales is said to have measured the height of Egypt's pyramids from their shadows, at the moment when his own shadow was as long as he was tall.