I have a slightly embarrassing confession about a maths quiz I put together once: I was the one who got the most wrong. I'm decent at mental arithmetic but the moment you move into geometry, sequences, or anything involving a formula I haven't used since A-level, I am genuinely struggling. What I found, though, was that the same was true for almost everyone else at the table — and the people who did best were often the ones who'd been quiet all evening. Maths is the great leveller.
There's something specifically satisfying about maths quiz questions, because the answer is either right or it isn't. No arguments about interpretation, no debates about which version of events is correct. The number is the number. That certainty makes the maths round one of the most dramatic in any quiz — people argue before the answers are revealed, and then the reveal is final in a way that no other subject quite manages.
Fifty questions across five rounds: basic arithmetic (which is more interesting than it sounds once you add the time pressure), geometry (shapes, angles, formulas), famous numbers and constants (pi, Fibonacci, and their less famous cousins), number puzzles (lateral thinking applied to numbers), and mathematical history (the people and stories behind the theorems). The history round tends to be the biggest surprise — mathematicians lived unexpectedly dramatic lives.
Don't worry if maths isn't your strongest subject — these questions are designed to be engaging rather than genuinely difficult, and the number puzzles round in particular is more about thinking than calculation. You don't need to be a mathematician to enjoy a maths quiz.
Test your maths knowledge live
Play an interactive maths quiz — 10 questions, live countdown timer, instant scoring.
Play Maths Quiz →
Play an interactive maths quiz — 10 questions, live countdown timer, instant scoring.
Play Maths Quiz →
Round 1: Basic Arithmetic (Questions 1–10)
1. What is 17 × 13?
✓ 221
💡 Multiplying two numbers that straddle a multiple of 10 can be made easier using the identity (a+b)(a−b) = a²−b²; here, 15×13 + 2×13 = 195 + 26 = 221. Practising mental multiplication tricks like this is a core element of vedic mathematics, a system of calculation derived from ancient Indian texts.
2. What is the square root of 144?
✓ 12
💡 144 is the twelfth Fibonacci number as well as a perfect square, making it notable in two important number sequences simultaneously. Fibonacci numbers are found throughout nature in the spiral patterns of shells, sunflower seeds, and pine cones.
3. What is 15% of 200?
✓ 30
💡 To calculate 15% mentally, a quick method is to find 10% first (20) and then add half of that (10), giving 30. Percentage calculations are among the most practically useful arithmetic skills, forming the basis of tax, interest, discounts, and statistical analysis.
4. What is 2 to the power of 10 (2¹⁰)?
✓ 1,024
💡 The fact that 2¹⁰ ≈ 10³ is foundational in computing — it is why 1 kilobyte is 1,024 bytes rather than exactly 1,000. This approximation is the reason binary and decimal units appear close but are not identical, leading to the separate standards of kibibytes (KiB) and kilobytes (KB).
5. What is the highest common factor (HCF) of 48 and 36?
✓ 12
💡 The HCF of two numbers can be found efficiently using Euclid's algorithm, one of the oldest known algorithms, described around 300 BC. Euclid's algorithm works by repeatedly replacing the larger number with the remainder of dividing the larger by the smaller, until the remainder is zero.
6. What is 7! (7 factorial)?
✓ 5,040
💡 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040, which is the number of ways seven distinct objects can be arranged in a line. Plato notably suggested in his work Laws that a city of 5,040 citizens was ideal because the number is divisible by every integer from 1 to 12 except 11.
7. If a train travels at 80 km/h for 2 hours and 30 minutes, how far does it travel?
✓ 200 km
💡 2 hours 30 minutes = 2.5 hours; distance = speed × time = 80 × 2.5 = 200 km. The formula Distance = Speed × Time is one of the most widely tested arithmetic applications in school mathematics and forms the basis of all navigation and logistics calculations.
8. What is 0.125 expressed as a fraction in its simplest form?
✓ 1/8
💡 0.125 = 125/1000, which simplifies by dividing numerator and denominator by 125 to give 1/8. Powers of two are particularly clean as fractions: 0.5 = 1/2, 0.25 = 1/4, 0.125 = 1/8, 0.0625 = 1/16 — a pattern exploited in binary computing.
9. What is the sum of the interior angles of a triangle?
✓ 180 degrees
💡 The fact that a triangle's angles sum to 180° holds in Euclidean (flat) geometry but not in spherical or hyperbolic geometry. On the surface of a sphere, a triangle can have three right angles and an angle sum of 270°, which is why the geometry of the Earth's surface requires non-Euclidean mathematics.
10. What is the result of 999 × 999?
✓ 998,001
💡 A fast way to compute 999² is to use (1000 − 1)² = 1,000,000 − 2,000 + 1 = 998,001. This difference-of-squares technique, often attributed to Persian mathematician al-Khwarizmi's algebraic methods, significantly reduces the complexity of large multiplications.
Round 2: Geometry (Questions 11–20)
11. What is the formula for the area of a circle?
✓ A = πr² (pi times radius squared)
💡 Archimedes derived a close approximation of this formula around 250 BC by inscribing and circumscribing polygons around a circle with increasing numbers of sides. His method was the precursor to integral calculus, which provides the rigorous proof used today.
12. A right-angled triangle has legs of length 3 cm and 4 cm. What is the length of the hypotenuse?
✓ 5 cm
💡 The 3–4–5 triangle is the smallest Pythagorean triple — a set of three integers satisfying a² + b² = c². It was known to ancient Egyptian builders, who used knotted ropes divided in a 3:4:5 ratio to construct right angles when laying foundations.
13. How many faces does a cube have?
✓ 6
💡 A cube is one of the five Platonic solids — regular polyhedra in which every face is an identical regular polygon and the same number of faces meet at each vertex. The five Platonic solids are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
14. What is the volume of a cylinder with radius 3 cm and height 10 cm? (Give your answer in terms of π)
✓ 90π cm³ (approximately 282.7 cm³)
💡 Volume of a cylinder = πr²h = π × 9 × 10 = 90π. The formula follows directly from the area of the circular cross-section multiplied by the height, and was one of the key results established by Archimedes in his work On the Sphere and Cylinder.
15. What is the sum of the interior angles of a regular hexagon?
✓ 720 degrees
💡 The formula for the sum of interior angles of any polygon with n sides is (n − 2) × 180°; for a hexagon, n = 6, giving 4 × 180° = 720°. Each interior angle of a regular hexagon is therefore 120°, which is why hexagonal tiling perfectly covers a flat surface with no gaps.
16. What is the name of the theorem stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides?
✓ Pythagoras' Theorem (the Pythagorean Theorem)
💡 Although named after Pythagoras (c. 570–495 BC), the relationship was known to Babylonian mathematicians over 1,000 years earlier, with clay tablets surviving that list Pythagorean triples. Pythagoras or his school is credited with the first formal proof, though none of his original writings survive.
17. If the circumference of a circle is 31.4 cm, what is its diameter? (Use π ≈ 3.14)
✓ 10 cm
💡 Circumference = πd, so d = circumference / π = 31.4 / 3.14 = 10 cm. The ratio of circumference to diameter being the constant π is one of the most fundamental relationships in mathematics and appears in fields as diverse as probability theory, quantum mechanics, and signal processing.
18. How many degrees are there in a full rotation (one complete turn)?
✓ 360 degrees
💡 The division of a circle into 360 degrees is believed to derive from the ancient Babylonian base-60 (sexagesimal) number system and their observation that the Earth travels approximately 1 degree along its orbit per day. The same Babylonian system gives us 60 minutes in an hour and 60 seconds in a minute.
19. What is the area of a trapezium with parallel sides of 5 cm and 9 cm, and a height of 4 cm?
✓ 28 cm²
💡 Area of a trapezium = ½ × (a + b) × h = ½ × 14 × 4 = 28 cm². The trapezium formula can be derived by treating the shape as the average of two rectangles, a neat geometric intuition that makes the formula easy to remember.
20. How many edges does a regular tetrahedron have?
✓ 6
💡 A tetrahedron has 4 vertices, 6 edges, and 4 faces — values that satisfy Euler's formula for polyhedra: V − E + F = 2 (4 − 6 + 4 = 2). Euler's formula holds for all convex polyhedra and is one of the most elegant results in topology.
Round 3: Famous Numbers & Constants (Questions 21–30)
21. To five decimal places, what is the value of π (pi)?
✓ 3.14159
💡 Pi has been calculated to over 100 trillion decimal places and shows no repeating pattern, confirming it is irrational and almost certainly normal (containing each digit with equal frequency). The record for memorising pi's digits stands at over 70,000 decimal places, recited by Rajveer Meena of India in 2015.
22. What is Euler's number, e, approximately equal to?
✓ Approximately 2.71828
💡 Euler's number e is the base of the natural logarithm and arises naturally in problems involving continuous growth or decay — from compound interest to radioactive decay. It appears so frequently that mathematician Benjamin Peirce called it "the most important constant in mathematics."
23. What is the Golden Ratio, φ (phi), approximately equal to?
✓ Approximately 1.618 (more precisely (1 + √5) / 2)
💡 The golden ratio appears when a line is divided such that the ratio of the whole to the larger part equals the ratio of the larger to the smaller part. It appears in the proportions of the Parthenon, many Renaissance paintings, and the spiral of nautilus shells, though some of its claimed appearances in nature have been overstated by popular accounts.
24. What is the square root of −1 in mathematics?
✓ i (the imaginary unit)
💡 The imaginary unit i was introduced to allow the square roots of negative numbers, leading to complex numbers of the form a + bi. Despite the name "imaginary," complex numbers have profoundly real applications in electrical engineering, quantum mechanics, and signal processing.
25. What is the value of 0! (zero factorial)?
✓ 1
💡 0! = 1 is defined this way because it represents the number of ways to arrange zero items, and there is exactly one way to do nothing. It also ensures that the recursive formula n! = n × (n−1)! holds consistently when n = 1: 1! = 1 × 0! = 1 × 1 = 1.
26. Which famous constant connects e, i, π, 1, and 0 in a single equation?
✓ Euler's Identity: e^(iπ) + 1 = 0
💡 Euler's identity is frequently voted the most beautiful equation in mathematics because it unites the five most fundamental constants — e, i, π, 1, and 0 — in a single, simple expression. The physicist Richard Feynman called it "the most remarkable formula in mathematics."
27. In binary (base 2), what is the decimal number 10 written as?
✓ 1010
💡 Binary works by expressing numbers as sums of powers of 2: 10 = 8 + 2 = 2³ + 2¹, so in binary it is written as 1010. The binary system underpins all modern digital computing, since electronic circuits naturally represent the two states of a transistor (on/off) as 1 and 0.
28. What is a prime number? Give an example.
✓ A number greater than 1 that has no positive divisors other than 1 and itself (e.g., 2, 3, 5, 7, 11, 13…)
💡 As of 2026 the largest known prime number has over 41 million digits and is a Mersenne prime of the form 2^p − 1. Prime numbers are the building blocks of all whole numbers and their properties form the backbone of modern cryptography and internet security.
29. What is the value of sin(90°)?
✓ 1
💡 The sine of 90° equals 1 because at a right angle, the opposite side equals the hypotenuse in the unit circle definition. Trigonometric functions like sine and cosine were first systematically tabulated by the Indian mathematician Aryabhata around 500 AD, predating the European development of trigonometry by over 1,000 years.
30. What does the number 1,000,000,000 represent in words (in the short scale system used in the US and modern UK)?
✓ One billion
💡 Britain officially adopted the US short scale (where 1 billion = 10⁹) for official government use in 1974; before that, the UK used the long scale where a billion meant one million million (10¹²). The confusion between the two scales has caused numerous translation errors in international finance and scientific literature.
Round 4: Number Puzzles (Questions 31–40)
31. What is the next number in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, ___?
✓ 55
💡 In the Fibonacci sequence each number is the sum of the two preceding it; 34 + 21 = 55. The sequence is named after Leonardo of Pisa (nicknamed Fibonacci), who described it in his 1202 work Liber Abaci, though Indian mathematicians had studied it centuries earlier.
32. I am thinking of a two-digit number. When you reverse its digits and add the result to the original, you get 121. The digits sum to 11. What is the number?
✓ 65 (or 56; both work: 65 + 56 = 121, and 6 + 5 = 11)
💡 Any two-digit number and its reverse always sum to a multiple of 11, a neat property arising from the fact that a two-digit number ab = 10a + b, and its reverse = 10b + a; their sum = 11(a + b). This makes 11 and digit reversal unusually elegant partners in number puzzles.
33. A snail climbs 3 metres up a 10-metre wall each day, but slides back 2 metres each night. On which day does it reach the top?
✓ Day 8
💡 The snail gains 1 net metre per day/night cycle, reaching 7 metres after 7 cycles. On day 8 it climbs 3 metres from 7, reaching exactly 10 metres and escaping before sliding back. This classic puzzle tests whether solvers account for the snail's final day correctly rather than blindly dividing 10 by 1.
34. What four-digit number is both a perfect square and a palindrome (reads the same forwards and backwards)?
✓ There are several — a well-known example is 7921 (= 89²); also accept 1001 is not a perfect square; the cleanest answer is 7921
💡 Palindromic perfect squares are rare — below 10,000 the only four-digit palindromic perfect squares are 7921 (89²). The word palindrome comes from the Greek palindromos meaning "running back again," and the concept applies equally to numbers, words, and phrases.
35. If you fold a piece of paper in half 10 times, how many layers thick is it?
✓ 1,024 layers (2¹⁰)
💡 Each fold doubles the number of layers, so n folds gives 2ⁿ layers; after 10 folds that is 1,024. If you could fold it 42 times, the stack would be taller than the distance from the Earth to the Moon — an illustration of how exponential growth quickly outpaces intuition.
36. What is the missing number? 2, 6, 12, 20, 30, 42, ___
✓ 56
💡 The sequence is n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7, 7×8 = 56. These are called pronic (or oblong) numbers, and each is exactly twice a triangular number — a beautiful connection between rectangular and triangular arrangements of dots.
37. In a room of 23 people, what is the approximate probability that at least two share a birthday?
✓ About 50% (approximately 50.7%)
💡 This famous result is called the Birthday Problem and surprises most people because intuition suggests 23 out of 365 days is a small fraction. The reason it works is that we are counting pairs, and 23 people form 253 possible pairs — enough to make a shared birthday more likely than not.
38. What is the sum of all integers from 1 to 100?
✓ 5,050
💡 The formula n(n+1)/2 gives the sum of integers from 1 to n; for n = 100, that is 100 × 101 / 2 = 5,050. The young Carl Friedrich Gauss is said to have computed this instantly as a schoolboy, impressing his teacher — though historians note the story may be apocryphal.
39. How many zeros are at the end of 100! (100 factorial)?
✓ 24
💡 Trailing zeros in n! are produced by factors of 10 = 2 × 5; since factors of 2 are more plentiful, we count factors of 5: ⌊100/5⌋ + ⌊100/25⌋ = 20 + 4 = 24. This technique is a standard exercise in combinatorics and number theory courses worldwide.
40. Three friends split a restaurant bill. The bill is £25 and they each pay £10, receiving £5 change. They each keep £1 and give £2 to the waiter. So each paid £9, making £27 total, plus £2 tip = £29. Where is the missing £1?
✓ There is no missing pound — the puzzle contains a logical error; the £27 the friends paid already includes the £2 tip
💡 This is a classic misdirection puzzle: the £27 paid breaks down as £25 to the restaurant + £2 to the waiter — there is no separate £2 to add. The puzzle works by tricking you into adding instead of subtracting, exploiting our tendency to trust arithmetic that sounds plausible.
Round 5: Mathematical History (Questions 41–50)
41. Which ancient Greek mathematician wrote Elements, the foundational textbook of geometry?
✓ Euclid
💡 Euclid's Elements, written around 300 BC, is the second most reprinted book in Western history after the Bible, with over 1,000 editions published since the invention of the printing press. It established the axiomatic method — starting from a small set of self-evident truths and deriving all other results by pure logic.
42. Who is credited with inventing calculus, independently and simultaneously in the 17th century?
✓ Isaac Newton and Gottfried Wilhelm Leibniz
💡 The priority dispute between Newton and Leibniz became one of the most bitter controversies in the history of science, dividing British and Continental European mathematicians for decades. Today both are credited: Newton developed his "method of fluxions" around 1666, while Leibniz independently arrived at his version around 1675 and published first in 1684.
43. What name is given to the unproven conjecture that every even integer greater than 2 is the sum of two prime numbers?
✓ Goldbach's Conjecture
💡 Goldbach's Conjecture was proposed by Christian Goldbach in a 1742 letter to Euler and has been verified computationally for all even numbers up to 4 × 10¹⁸ as of 2014, yet remains unproven for all numbers. It is one of the oldest and most famous unsolved problems in mathematics.
44. What nationality was the mathematician Srinivasa Ramanujan, known for his extraordinary intuitive work on number theory?
✓ Indian
💡 Ramanujan (1887–1920) was largely self-taught and sent unsolicited letters containing groundbreaking mathematical results to British mathematician G. H. Hardy in 1913. Hardy recognised his genius and arranged for Ramanujan to come to Cambridge, where the two collaborated until Ramanujan's early death at age 32.
45. Which mathematician proved Fermat's Last Theorem in 1994, ending a 358-year search?
✓ Andrew Wiles
💡 Fermat's Last Theorem states that there are no positive integer solutions to aⁿ + bⁿ = cⁿ for n > 2. Andrew Wiles worked on the proof in secret for seven years, and his initial 1993 announcement contained an error that took a further year to fix — making the moment of final proof in 1995 all the more dramatic.
46. What was the name of the first mechanical calculator, invented by Blaise Pascal in 1642?
✓ The Pascaline
💡 Pascal built the Pascaline to help his father, a tax commissioner, with tedious arithmetic calculations — making it arguably the first machine built to automate intellectual labour. It could perform addition and subtraction directly, and multiplication and division by repeated operations.
47. Which famous problem, solved in 2003 by Grigori Perelman, is the only one of the Millennium Prize Problems to have been solved so far?
✓ The Poincaré Conjecture
💡 Grigori Perelman declined both the Millennium Prize of $1 million and the Fields Medal for his proof, reportedly saying the prize was unjust because his work was no more important than that of his predecessors. He subsequently retired from mathematics and withdrew from public life.
48. In which century was the symbol = (equals sign) first introduced, and by which mathematician?
✓ 16th century (1557), by Robert Recorde
💡 Welsh mathematician Robert Recorde introduced the equals sign in his 1557 work The Whetstone of Witte, writing that he chose two parallel lines "because no two things can be more equal." Before this, mathematicians wrote words like "is equal to" in full to express equality.
49. What is the name of the branch of mathematics that studies shapes that are "broken" or self-similar at different scales?
✓ Fractal geometry
💡 Fractal geometry was formalised by Benoît Mandelbrot in his 1982 book The Fractal Geometry of Nature, though the underlying mathematical objects had been studied since the 19th century. Fractals appear throughout nature in coastlines, snowflakes, mountain ranges, and the branching of blood vessels and trees.
50. Who developed the theory of relativity and also contributed a famous thought experiment involving a cat both alive and dead?
✓ Albert Einstein developed relativity; the cat thought experiment was Erwin Schrödinger's
💡 Schrödinger's Cat (1935) was a thought experiment designed to expose what Schrödinger saw as the absurdity of the Copenhagen interpretation of quantum mechanics — not to support it. Einstein and Schrödinger were allies in their scepticism of quantum indeterminacy, famously expressed in Einstein's remark that "God does not play dice."
Ready to test your maths knowledge?
Play our interactive maths quiz — 10 questions, live countdown, instant scoring. Free, no signup.
Play Maths Quiz Now →
Play our interactive maths quiz — 10 questions, live countdown, instant scoring. Free, no signup.
Play Maths Quiz Now →
The best thing about a maths quiz round is what happens in the ten seconds between the question and the answer — you can see people's faces as they work through it, and that process is genuinely fascinating to watch. There's nowhere to hide with a maths question, and that honesty is quite refreshing.
If you spot any errors (which in a maths post would be especially embarrassing), or have a number-related topic you'd like covered, drop a message to hello@simplyquizzes.com. More quiz content — including less numerical topics — on the blog.