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The toughest math quiz questions online — 20 tough questions spanning probability, statistics and number theory.
1. Is 1 considered a prime number?
💡 By modern mathematical definition, 1 is not considered a prime number since it has only one positive divisor.
2. What does standard deviation measure?
💡 Standard deviation measures how spread out data points are from the mean.
3. What is the sum of the interior angles of a polygon with n sides?
💡 The sum of interior angles of any polygon is given by the formula (n-2) x 180 degrees.
4. What is the probability of drawing an ace from a standard deck of 52 cards?
💡 There are 4 aces in a 52-card deck, giving a probability of 4/52, which simplifies to 1/13.
5. What is a composite number?
💡 A composite number has more than two positive divisors, unlike a prime number.
6. What is the number of permutations of 3 items from a set of 5 (5P3)?
💡 Using the permutation formula, 5P3 equals 5 x 4 x 3 = 60.
7. What is a perfect square?
💡 A perfect square, like 4, 9, or 16, results from multiplying a whole number by itself.
8. What is the probability of not rolling a 6 on a die?
💡 Since there are 5 outcomes other than rolling a 6, out of 6 total, the probability is 5/6.
9. What is a twin prime?
💡 Twin primes are pairs of prime numbers that differ by exactly 2, such as 11 and 13.
10. What is a prime number?
💡 A prime number has exactly two distinct positive divisors: 1 and itself.
11. What is 6! (6 factorial)?
💡 6! means 6 x 5 x 4 x 3 x 2 x 1, which equals 720.
12. What is 0.1 as a fraction?
💡 0.1 equals 1/10 as a fraction.
13. What is the number of ways to arrange 4 different books on a shelf?
💡 This is 4 factorial (4!), which equals 4 x 3 x 2 x 1 = 24.
14. What is the probability of flipping a coin and getting heads?
💡 A fair coin has two equally likely outcomes, so the probability of heads is 1/2.
15. What is the number of combinations of choosing 2 items from a set of 5 (5C2)?
💡 Using the combination formula, 5C2 equals 10.
16. What is the probability of rolling a sum of 7 with two dice?
💡 There are 6 combinations that sum to 7 out of 36 total outcomes, giving a probability of 1/6.
17. What is Goldbach's Conjecture about?
💡 Goldbach's Conjecture, still unproven, states that every even integer greater than 2 can be written as the sum of two prime numbers.
18. What is the probability of drawing a red card from a standard 52-card deck?
💡 Half of a standard deck's 52 cards are red, giving a probability of 1/2.
19. What is the probability of getting at least one head in two coin flips?
💡 Out of four equally likely outcomes (HH, HT, TH, TT), three include at least one head, giving 3/4.
20. In statistics, what does 'variance' measure?
💡 Variance quantifies how much the data points in a set differ from the mean.