Getting your questions ready
Getting your questions ready
Beat the crowd
10 questions No timer
50 free High School Math trivia questions with answers — trivia quiz, new questions added Aug 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 50 questions with answers and explanations. Play the quiz
Q 01How many people in a room make it more likely than not that two share a birthday, the famous birthday paradox?
23
With 23 people the chance is 50.7%, because there are 253 different pairs who might match, not just 23 people compared with you.
Q 02In the Monty Hall problem, what is the chance of winning the car by switching doors after the host reveals a goat?
2/3
Switching wins 2/3 of the time, a result so counter-intuitive that nearly 1,000 PhDs wrote to Parade magazine insisting Marilyn vos Savant had got it wrong.
Q 03Which Greek, whose followers reportedly could not eat beans, gives his name to the right-triangle rule a² + b² = c²?
Pythagoras
Pythagoras's rule has been proved more ways than possibly any other theorem, including a proof published by future US president James Garfield.
Q 04Which constant, celebrated on March 14 (also Einstein's birthday), is a circle's circumference divided by its diameter?
π
NASA's Jet Propulsion Laboratory uses π to just 15 decimal places even for interplanetary navigation, enough to size a circle 40 billion miles across with an error of little more than half an inch.
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 06A price is cut by 20% and then cut by 20% again; what percentage of the original price remains after both reductions?
64%
Two 20% cuts leave 64% because the second cut comes off the already-reduced price: 0.8 × 0.8 = 0.64, not the 0.6 that adding the cuts suggests.
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
0.999… is exactly 1: 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 Persian scholar's Latinised name gave us 'algorithm', and his book Al-Jabr the word 'algebra'?
Al-Khwarizmi
Al-Khwarizmi's Al-Jabr, written around 820, set out the first systematic solution of linear and quadratic equations, with 'al-jabr' meaning restoring or completion.
Q 10Which Pisan merchant's son 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 ten Indian digits, zero included, 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
Nobody knows for certain why m was chosen for the slope; the letter first appears in an 1844 English textbook that wrote the line as y = mx + b.
Q 13What is 2 + 3 × 4 under the usual order of operations, the convention that ranks multiplication above addition?
14
Q 21How many degrees do a flat triangle's three angles add up to, a total that grows larger on a sphere?
180
On a sphere a triangle's angles add up to more than 180° and can reach as much as 540°; the surplus is called the spherical excess.
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
Regular hexagons tile with three meeting at every corner, and a honeycomb uses them because the shape makes the most efficient use of space and wax.
Multiplying first gives 2 + 12 = 14; many simple calculators work strictly left to right and would show 20, which is why the convention matters.
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 La Géométrie, appended to his 1637 Discourse on the Method, united algebra and geometry?
René Descartes
Descartes also coined the word 'imaginary' for square roots of negative numbers, intending it as a put-down of a concept he thought useless.
Q 17Which Scottish laird published the first logarithms in 1614, so astronomers could multiply big numbers by adding?
John Napier
Napier's invention, said Laplace, 'doubled the life of the astronomer' by reducing months of calculation 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's irrationality so unsettled the ancient Greeks that legend has Hippasus drowned at sea for revealing that some lengths cannot be written as fractions.
Q 24Which polygon, the shape of Britain's 50p coin, is the smallest regular one that compass and straightedge cannot draw?
Heptagon
The heptagon became a coin shape in 1969 with the 50p, the world's first seven-sided coin; its curved sides have constant width, so it rolls through vending machines.
Q 25Which side of a right triangle, always the longest, is the denominator of both SOH and CAH in the SOHCAHTOA mnemonic?
Hypotenuse
Hypotenuse comes from the Greek for 'stretching under' the right angle; the word reached English in the 1570s by way of Latin and French.
Q 26How far apart are the points (0, 0) and (6, 8) on a coordinate grid, by the distance formula?
10
The distance is 10 because √(6² + 8²) = √100; the two points and the origin's axes form a 6-8-10 triangle, a scaled-up 3-4-5.
Q 27An arc subtends 40° at a circle's centre; what angle does it subtend at a point on the remaining circumference?
20°
The inscribed angle is always half the central angle on the same arc, so 40° at the centre becomes 20° at the edge, wherever on the arc the point sits.
Q 28How many Platonic solids exist, the shapes Kepler nested inside one another in 1596 to model the Solar System?
5
The five are the tetrahedron, cube, octahedron, dodecahedron and icosahedron; Plato matched four of them to earth, air, fire and water.
Q 29Whose Elements, compiled around 300 BC in Alexandria, contains the classic proof that the prime numbers never run out?
Euclid
Euclid's Elements has appeared in over a thousand editions since its first printing in 1482, a record said to be second only to the Bible.
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 Great Pyramid's height from its shadow, at the moment when his own shadow equalled his height.