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Math Quiz — 50 Questions with Answers

5 rounds · 50 questions

Round 1 of 5 · Question 1 of 50

Mental Math Warm-Up

What is 7 × 8?

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Every question, answer and explanation

Mental Math 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. Recognizing 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 center 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 Math Quiz

Math is the only school subject adults will announce they were bad at, cheerfully, at a dinner table, as though describing a harmless allergy. Nobody says it about reading. The belief underneath it — that there are math people and non-math people and you find out which you are at about nine years old — does not survive contact with the evidence. But it is durable, and it is the reason a quiz like this one makes people nervous before they have read a single question.

Here is what is actually in it. Fifty questions in five rounds of ten: a mental math warm-up, shapes, the world of numbers, puzzles, and a hard round. Four options each, and the answer is on screen before your finger leaves the button. Nothing needs a calculator, because none of the arithmetic is large — the numbers are kept small enough to carry in your head, and where a question looks like heavy work there is a shortcut hiding in it.

The puzzle round is the one worth staying for. Those questions are centuries older than the algebra that dispatches them in one line, and they were originally solved by ordinary reasoning: guess, check, adjust, notice the pattern. If you set one up as an equation you will be faster. If you cannot, you can still get there, and the fact that both routes arrive at the same place is most of what mathematics is actually about.

How it works
  1. Four options per question, no timer, no penalty for working it out slowly. Pen and paper are entirely legitimate — there is just no scratch space on the page.
  2. The answer appears as soon as you choose, and a wrong pick keeps the right one up for a moment, which is usually when the arithmetic makes sense. Tap the screen to continue.
  3. Rounds change every ten: arithmetic first, then geometry, then the properties of numbers, then puzzles, then the hard round.
  4. You finish with a mark out of fifty and five round scores. Those five numbers are the useful part — arithmetic speed and number sense are separate skills, and this is where you find out which one you have.
  5. The full fifty and their answers are listed below the quiz in round order. Going back to the round that cost you points is faster there than replaying the whole thing — the arithmetic round in particular is worth rereading rather than redoing.

Frequently asked questions

Can I use a calculator?

Nothing stops you, and it will help less than you hope. The arithmetic in every question is deliberately small; the difficulty lives in setting the problem up, and a calculator has no opinion about that. On the two or three questions where the numbers get large, the intended route is a pattern rather than a computation, and typing it out is the slow way.

Why multiple choice for a math quiz?

Because a typed answer would have to be marked as a string, and a half of something can be written as a fraction, a decimal or a percentage. A quiz that accepts one and rejects the others is testing notation rather than mathematics. Options also let a partial method count: if you can narrow four answers to two by estimating, you have done real work, and the format pays you for it.

Is this an intelligence test?

No. Arithmetic speed is a practiced skill that fades when it is not used and returns within weeks when it is, which is not what an intelligence measure is supposed to do. If you want a test built as an intelligence-style reasoning exercise, that is a different page on this site and it says so plainly. This one is about mathematics you have met before.

What level are the questions?

School mathematics that most adults met and then put down — times tables, the angles in a triangle, primes and factors, powers and factorials. Nothing needs a formula sheet, and nothing goes past the point where a symbol would have to be explained before the question could be asked.

How many out of fifty is good?

Thirty-five. The warm-up round should be close to full marks for anyone who did their times tables, so the score is really decided across the shapes and puzzle rounds. A common and completely normal pattern is a perfect arithmetic round beside a shaky shapes round: geometry is the part of school mathematics with the shortest adult afterlife.

Is the Math Quiz free, and is it timed?

Free, with no account and no email, and there is no clock anywhere in it. That is deliberate: timing turns arithmetic into a stress response, and the thing 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 the Math Quiz take?

Twelve minutes is a comfortable estimate for the fifty — longer than a trivia set because a few of the puzzles genuinely need a moment. If a question is taking more than that, guessing and moving on costs you nothing, since there is no penalty for a wrong answer.