Question 1: List all prime numbers between 1 and 20.

Answer: 2, 3, 5, 7, 11, 13, 17, 19

Question 2: Identify whether 21 is prime or composite. Show your reasoning.

Answer: Composite because it is divisible by 3 and 7.

Question 3: Calculate whether 29 is a prime number. Provide your working process.

Answer: 29 is only divisible by 1 and itself; no other divisors found up to √29 (~5.39). Therefore, 29 is prime.

Question 4: Construct a list of prime numbers less than 50. Explain your method.

Answer: Prime numbers less than 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Found by testing divisibility up to √n for each number.

Question 5: A student claims that 39 is prime. Identify the mistake and correct it.

Answer: The student incorrectly identified 39 as prime. 39 is divisible by 3 and 13, so it's composite.

Question 6: Determine whether 51 is prime. Show your reasoning.

Answer: 51 is divisible by 3 (since 5 + 1 = 6, divisible by 3), so it is composite.

Question 7: Explain why 2 is the only even prime number.

Answer: Because all other even numbers are divisible by 2 and at least one other number, they are composite. 2 is only divisible by 1 and itself, making it prime.

Question 8: Identify the errors in the following statement: 'All numbers greater than 1 that are only divisible by 1 and themselves are prime, except for 1.'

Answer: The mistake is including 1 as a prime number. 1 is not prime because it has only one divisor.

Question 9: Find the next prime number after 37.

Answer: 41

Question 10: Verify whether 49 is prime. Show your working.

Answer: 49 is divisible by 7 (7 × 7 = 49), so it is composite.

Question 11: Identify the prime numbers in the set: {15, 23, 27, 31, 45, 47}.

Answer: 23, 31, 47

Question 12: A student attempts to determine if 91 is prime by checking divisibility by 7. Is this sufficient? Why or why not?

Answer: No, because 91 is divisible by 7 (7 × 13 = 91). Checking only 7 is not enough; students should check all possible prime factors up to √91 (~9.54).