Question 1: Identify whether 37 is a prime number. Show your working.

Answer: Yes, 37 is prime because it has no divisors other than 1 and 37.

Question 2: List all prime numbers between 10 and 30.

Answer: 11, 13, 17, 19, 23, 29

Question 3: Determine if 49 is a prime number. Explain your reasoning.

Answer: No, 49 is not prime because it is divisible by 7 (7×7=49).

Question 4: Calculate whether 51 is prime by testing divisibility. Show your working.

Answer: 51 is divisible by 3 (5+1=6, which is divisible by 3), so 51 is not prime.

Question 5: Identify the prime factors of 91.

Answer: 7 and 13

Question 6: A map shows two cities numbered 101 and 103. Are these numbers likely prime? Explain your reasoning.

Answer: Yes, both 101 and 103 are prime because they are only divisible by 1 and themselves, with no other divisors.

Question 7: On a route, the bus stops are numbered 89, 90, 91, 92, 93. Which stops are at prime numbers? Show your working.

Answer: 89 and 93 are not prime (93 divisible by 3), 90 and 92 are not prime, only 89 is prime.

Question 8: Construct a route map with stops numbered 97, 98, 99, 100, 101. Mark the prime numbers and justify your choices.

Answer: 97 and 101 are prime due to no divisors other than 1 and themselves.

Question 9: A map scale indicates that the distance between two locations is 113 units. Is 113 a prime? Justify your answer.

Answer: Yes, 113 is prime because it has no divisors other than 1 and 113.

Question 10: Error Analysis: A student claims that 121 is a prime number. Identify and correct the mistake.

Answer: The mistake is that 121 is not prime because it is divisible by 11 (11×11=121).

Question 11: Challenge & Extension: Find the next prime number after 113. Show your working.

Answer: The next prime after 113 is 127, as it is not divisible by 2, 3, 5, 7, 11, or 13.