Question 1: Determine whether the number 37 is prime or composite. Show your reasoning.

Answer: Prime

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

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

Question 3: Calculate the total number of prime numbers less than 50.

Answer: 15

Question 4: Explain why the number 49 is not prime, providing the factors involved.

Answer: 49 is not prime because it has factors other than 1 and itself, specifically 7 and 7 (7×7).

Question 5: Construct a list of all composite numbers between 20 and 30. Use the grid to shade or mark the numbers.

Answer: 21, 22, 24, 25, 26, 27, 28, 30

Question 6: Identify the mistake: A student claims that 51 is a prime number because it is only divisible by 1 and 51. Correct and explain the mistake.

Answer: The mistake is that 51 is divisible by 3 (since 5+1=6, which is divisible by 3), so it is not prime. The correct factors are 3 and 17.

Question 7: Using the grid, construct a Venn diagram showing the classification of numbers 1 to 20 as prime or composite.

Answer: Primes: 2, 3, 5, 7, 11, 13, 17, 19; Composites: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20;

Question 8: Plot the graph of y=2x for x values from 1 to 10. Shade the points where y is prime.

Answer: Points at x=1 (y=2), x=2 (y=4), x=3 (y=6), x=4 (y=8), x=5 (y=10), x=6 (y=12), x=7 (y=14), x=8 (y=16), x=9 (y=18), x=10 (y=20). Prime y-values among these are only y=2 (x=1).

Question 9: Determine whether the following numbers are prime or composite: 81, 97, 121, 131. Provide your reasoning.

Answer: 81 is composite (9×9), 97 is prime, 121 is composite (11×11), 131 is prime.

Question 10: Challenge: Find a number between 100 and 120 that is both prime and has a digit sum divisible by 3. Show your work.

Answer: The number is 113: 1+1+3=5, which is not divisible by 3, so no. The only prime in that range with digit sum divisible by 3 is 111, but 111 is not prime. Therefore, no such number exists.