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Maths Quiz — 50 Questions with Answers

5 rounds · 50 questions

Round 1 of 5 · Question 1 of 50

Mental Maths Warm-Up

What is 7 × 8?

Show all 50 questions with answers and explanations

Every question, answer and explanation

Mental Maths Warm-Up

  1. What is 7 × 8?

    Answer 56

    The one square of the times table that people hesitate on longest. There is a mnemonic that fits it exactly: 5, 6, 7, 8 — because 56 = 7 × 8.

  2. What is 144 ÷ 12?

    Answer 12

    144 is 12 × 12, so dividing it by 12 gives 12 back. Recognising the square is faster than dividing: the twelve times table ends at the number you are dividing by.

  3. What is 9 squared (9²)?

    Answer 81

    Squaring means multiplying a number by itself, so 9² is 9 × 9. If 81 does not come instantly, 9 × 9 is 10 × 9 minus one 9 — that is 90 − 9.

  4. What is 25 × 4?

    Answer 100

    Four quarters make a whole, and 25 is a quarter of 100. That is also the shortcut for multiplying anything by 25: multiply by 100 and divide by 4.

  5. What is 15% of 200?

    Answer 30

    Split the percentage instead of computing it in one go. Ten percent of 200 is 20, half of that is 10, and 20 + 10 is 30.

  6. What is 1000 − 478?

    Answer 522

    Subtracting from a round number is easier one step down. Take 478 from 999 first — no borrowing at all, giving 521 — then add back the 1 you set aside.

  7. What is the square root of 169?

    Answer 13

    The square root asks which number times itself gives 169. It sits between 12 × 12 = 144 and 14 × 14 = 196, and the answer has to end in 3 or 7 because those are the digits whose squares end in 9.

  8. What is 13 × 7?

    Answer 91

    Break the 13 apart: 10 × 7 is 70 and 3 × 7 is 21, and 70 + 21 is 91. Splitting one factor into tens and units works for any two-digit multiplication.

  9. What is 0.5 as a fraction?

    Answer 1/2

    The digit after the decimal point is the tenths place, so 0.5 is five tenths. Five tenths reduces to one half because both numbers divide by 5.

  10. What is 38 + 47?

    Answer 85

    Round up to make it easy, then pay the rounding back. 40 + 47 is 87, and since you added 2 to the 38, take 2 off again.

Shapes

  1. The angles inside a triangle add up to...?

    Answer 180 degrees

    Always 180, no matter how stretched or squashed the triangle is. You can see why by tearing off the three corners and laying them side by side — they form a straight line.

  2. A full circle is how many degrees?

    Answer 360

    The number is a leftover from Babylonian counting, not from geometry itself. It survived because 360 divides evenly by so many numbers, which makes halves, thirds, quarters and sixths all whole.

  3. How many faces does a cube have?

    Answer Six

    Top, bottom and four sides. The three counts that describe a cube are worth holding together: 6 faces, 12 edges, 8 corners.

  4. How many sides does a pentagon have?

    Answer Five

    The prefix carries the count — penta is five in Greek, the same root as in pentathlon. Hexagon, heptagon and octagon follow the same rule.

  5. Pi (π) is approximately...?

    Answer 3.14

    Pi is the distance around a circle divided by the distance across it, and the ratio is the same for every circle. It never settles into a repeating pattern, so 3.14 is where we cut it off, not where it ends.

  6. A right angle measures...?

    Answer 90 degrees

    A quarter of the full turn of 360. The small square drawn in the corner is the standard mark for it, used instead of writing the number.

  7. The area of a triangle is...?

    Answer Base × height ÷ 2

    Any triangle is exactly half of a rectangle drawn around its base and height. That is where the divide-by-two comes from, and it holds for slanted triangles too.

  8. How many edges does a cube have?

    Answer Twelve

    Four edges around the top, four around the bottom, and four uprights joining them. Together with 6 faces and 8 corners, that is the whole cube counted.

  9. The diameter of a circle is how many times the radius?

    Answer Twice

    The radius runs from the centre to the edge; the diameter runs all the way across, so it covers that distance twice. This is why the area formula uses r and not d.

  10. At exactly 3 o'clock, the angle between the clock hands is...?

    Answer 90 degrees

    At three o'clock the minute hand points at 12 and the hour hand at 3, which is a quarter of the way around. Each hour mark is 30 degrees, so three of them make 90.

The World of Numbers

  1. What is the smallest prime number?

    Answer 2

    A prime has exactly two divisors, itself and 1, which rules out 1 straight away — it has only one. That leaves 2, and it is the only even prime, since every other even number divides by 2.

  2. Which of these is NOT a prime number?

    Answer 9

    Nine is 3 × 3, so it has a third divisor and cannot be prime. It is the odd number people misfile most often, because being odd feels like being prime.

  3. Is zero even or odd?

    Answer Even

    Even means divisible by 2 with nothing left over, and 0 ÷ 2 is 0 exactly. It also sits between two odd numbers, −1 and 1, which is where even numbers belong.

  4. The Roman numeral X equals...?

    Answer 10

    Roman numerals build from I, V, X, L, C, D and M. The X for ten is the one that survives everywhere else — in the word decade and in the ten-mark on old clock faces.

  5. The Roman numeral L equals...?

    Answer 50

    L is fifty and C is a hundred, which is the pair people most often swap. C is the easier of the two to anchor, because it matches centum, the Latin for hundred.

  6. In the Fibonacci sequence 1, 1, 2, 3, 5, 8 — what comes next?

    Answer 13

    Each number is the sum of the two before it, so 5 + 8 gives 13. The rule is the whole sequence — nothing else needs to be remembered.

  7. What is the least common multiple of 4 and 6?

    Answer 12

    Count up in fours and in sixes and find where the lists first meet: 4, 8, 12 and 6, 12. Twelve is the first number both reach.

  8. An even number plus an odd number is always...?

    Answer Odd

    An even number is a pile that splits into pairs; the odd one has a leftover. Adding them keeps that leftover, so the total is odd every time.

  9. One million is 10 to which power?

    Answer The 6th

    One million is a 1 with six zeros, and the exponent counts the zeros. That is the whole rule: 10³ is a thousand, 10⁶ is a million, 10⁹ is a billion.

  10. How many divisors does 12 have?

    Answer Six

    List them in pairs that multiply to 12: 1 and 12, 2 and 6, 3 and 4. Pairing this way is also how you check quickly that you have not missed one.

Puzzles

  1. A number times 3, plus 4, equals 25. What is the number?

    Answer 7

    Undo the steps in reverse order. The last thing done was adding 4, so take it off: 25 − 4 is 21, and 21 ÷ 3 is 7.

  2. Chickens and rabbits total 10 heads and 28 legs. How many rabbits?

    Answer Four

    If all ten animals were chickens there would be 20 legs, but there are 28 — eight extra. Each rabbit adds two legs over a chicken, so eight extra legs means four rabbits.

  3. What is the sum of all numbers from 1 to 100?

    Answer 5050

    Pair the ends inward: 1 + 100, 2 + 99, 3 + 98, each pair making 101. There are 50 such pairs, and 50 × 101 is 5050.

  4. Three consecutive numbers add up to 33. What is the middle one?

    Answer 11

    Consecutive numbers are spread evenly around the middle one, so the middle is simply the average. That makes it 33 ÷ 3, and the three numbers are 10, 11 and 12.

  5. A square has a perimeter of 36cm. How long is one side?

    Answer 9cm

    A square has four equal sides, so the perimeter is one side four times over. Dividing 36 by 4 gives 9.

  6. A £100 item is halved, then raised 50%. What is the price now?

    Answer £75

    Percentages apply to whatever the price is at that moment, which is why the halving and the raise do not cancel. Half of £100 is £50, and 50% of £50 is £25, so the price lands at £75.

  7. What is the largest two-digit prime number?

    Answer 97

    Work down from 99 and test each odd number. 99 divides by 3, and 97 does not divide by 2, 3, 5 or 7 — and testing up to 10 is enough, because 10 × 10 already passes 97.

  8. A brother is 4 years older than his sister; together they are 20. How old is the sister?

    Answer 8

    Set the gap aside first. Take the 4-year difference out of the 20 and you have 16 to split evenly, so the sister is 8 and the brother is 12.

  9. Five people all shake hands with each other once. How many handshakes?

    Answer 10

    Each of the five people shakes four hands, which counts 20 — but every handshake got counted twice, once from each side. Halving gives 10.

  10. Half of half of a number is 5. What is the number?

    Answer 20

    Half of a half is a quarter, so a quarter of the number is 5. Multiplying back by 4 gives 20.

Hard Mode

  1. What is 6 factorial (6!)?

    Answer 720

    A factorial multiplies every whole number down to 1, so 6! is 6 × 5 × 4 × 3 × 2 × 1. It also counts orderings — 720 is the number of ways to arrange six things in a row.

  2. What is 2 to the 10th power (2¹⁰)?

    Answer 1024

    Doubling ten times: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. This is why a kilobyte is 1024 bytes rather than 1000 — computers count in doublings.

  3. What is 5 to the power of 0 (5⁰)?

    Answer 1

    Anything to the power of 0 is 1, and the reason is division. 5³ ÷ 5³ is 1, and subtracting the exponents gives 5⁰ — so the two answers have to match.

  4. The square root of 2 is...?

    Answer An irrational number

    It cannot be written as one whole number over another, so its decimals never end and never repeat. The proof was known to the ancient Greeks and is one of the oldest in mathematics.

  5. How many seconds are in an hour?

    Answer 3600

    60 seconds in a minute and 60 minutes in an hour, so 60 × 60. The same 60 shows up in both places because the split of the hour was inherited from Babylonian base-60 counting.

  6. The area of a circle is...?

    Answer πr²

    Radius squared, then multiplied by pi. Doubling the radius therefore multiplies the area by four, not by two — the r is squared and the doubling is squared with it.

  7. What is 111 × 111?

    Answer 12321

    Repunits multiply into palindromes: 11 × 11 is 121, 111 × 111 is 12321, and 1111 × 1111 is 1234321. The digits count up to the number of ones and back down.

  8. How many prime numbers are there up to 100?

    Answer 25

    Four of them are below 10 — 2, 3, 5 and 7 — and 21 more lie between 10 and 100. Primes thin out as numbers grow: there are 25 below 100 but only 168 below 1000.

  9. Of the numbers 0 and 1, which equal their own square?

    Answer Both 0 and 1

    0 × 0 is 0 and 1 × 1 is 1, so both come back to themselves. No other number does — squaring makes anything larger than 1 grow and anything between 0 and 1 shrink.

  10. After a 15% discount an item costs £85. What was the original price?

    Answer £100

    The £85 is not the discount, it is what is left: 85% of the original. Dividing 85 by 0.85 gives 100 — and the common slip is to add 15% to £85, which lands at £97.75 instead.

About the Maths Quiz

Most of the maths an adult uses in a week is estimation, done at speed and never checked: whether that is roughly a third off, whether the bill has been split about right, whether there is time to get across town. It is done well by people who would tell you they were hopeless at maths, and it has almost nothing to do with the thing they were hopeless at — which was, usually, being asked to be fast in front of the class.

This maths quiz runs fifty questions in five rounds of ten: a mental maths warm-up, shapes, the world of numbers, puzzles, and a hard round. Four options each, with the answer revealed as you pick. No calculator is needed at any point. The numbers are deliberately small, and the questions that look like heavy lifting are the ones with a trick in them — the sum of every number to a hundred is a famous case, and it takes about four seconds once you have seen how.

The rounds are arranged so that the arithmetic is over early. What follows is closer to what mathematics feels like when nobody is marking it: shapes and their properties, the odd behaviour of primes and zero, and a round of the puzzles that were being set to schoolchildren long before anybody taught them algebra.

How it works
  1. Pick one of four answers. There is no clock and no scoring penalty for taking your time over one.
  2. The verdict shows straight away, with the correct answer marked, and stays a moment longer when you have got it wrong. Tap anywhere to carry on.
  3. A card announces each round, and the difficulty steps up between them rather than within them — the last question of a round is rarely the hardest one in it.
  4. The back arrow lets you look at an earlier question again, though answered ones are locked and cannot be changed.
  5. At the end you get fifty points broken into five round scores, and the whole set with answers is listed below the quiz.

Frequently asked questions

Is this based on a school syllabus?

No. It is roughly the maths that survives into adult life — the parts most people met at school and then either kept or quietly lost. There is no coverage requirement behind the fifty, nothing is here because a curriculum says it should be, and a child part-way through school will find some of it easy and some of it years ahead.

There is nowhere to write anything down.

There is not, and that is not meant as a restriction — paper is perfectly allowed and for two or three of the puzzles it is the sensible approach. What we avoided was building a working-out box, because the moment a maths quiz gives you one it starts to feel like an examination, and the numbers here are small precisely so that most people will not need it.

Are the puzzle questions trick questions?

Not in the sense of hiding something in the wording. Each one has a straightforward route and a quicker one, and the quicker route is a pattern rather than a piece of cleverness. The classic with the animals and the legs is the clearest example: you can find it by trying a few numbers, or you can see the structure and write it down in one step, and both count as having solved it.

I am slow at mental arithmetic. Does that matter?

Not here, since nothing is timed, and not much elsewhere either. Speed at mental arithmetic is a practised skill with a very ordinary training curve — it goes when it is not used and comes back when it is. It is worth separating from number sense, which is the ability to tell when an answer is roughly wrong, and which is by far the more useful of the two in everyday maths.

Where should a decent score land?

Around thirty-five is a decent maths score. The warm-up round should be nearly free if your times tables are intact, so the interesting variation sits in shapes and the world of numbers. A high arithmetic score beside a low shapes score is the most common pattern we would expect, and it says something about how geometry is taught rather than about you.

Is it free, and is it timed?

Free — no account, no email, and there is no clock anywhere in it. That is deliberate: a timer turns arithmetic into a stress response, and what is worth measuring here is whether you can get there at all, not how fast you panic. Nothing you answer is sent anywhere, and nothing is kept once the tab closes.

How long does it take?

About twelve minutes for the fifty — longer than a trivia set, because a few of the puzzles genuinely need a moment. If one is taking longer than that, guessing and moving on costs you nothing: there is no penalty for a wrong answer.