Question 1: List the first five prime numbers.

Answer: 2, 3, 5, 7, 11

Question 2: Identify which of the following numbers are prime: 14, 17, 21, 29.

Answer: ["17","29"]

Question 3: Calculate the total number of prime numbers between 10 and 30.

Answer: 6

Question 4: Construct a simple map route that passes through only prime-numbered intersections from 2 to 13. Use the grid to draw the route.

Answer: Route passing through 2, 3, 5, 7, 11, 13

Question 5: Explain why the number 21 is not prime, and identify whether it is composite.

Answer: 21 is not prime because it has divisors other than 1 and itself; it is composite, divisible by 3 and 7.

Question 6: On a map, stations are labeled with numbers. If stations 13, 17, 19, 23, and 29 are all prime, which station numbers are composite between 13 and 30?

Answer: 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30

Question 7: Plot a graph of y=2x for x from 1 to 10. How do the prime numbers relate to the graph?

Answer: Prime numbers occur at y=2x where x is prime; the graph shows y-values doubling the x-values, with primes appearing when 2x is prime, such as at x=2, 3, 5, 7, 11, etc.

Question 8: A travel map shows that routes between cities are numbered. If route numbers are prime, what is the significance of selecting only prime-numbered routes for a direct journey?

Answer: Prime-numbered routes are likely to be unique connections, and selecting only prime routes could help in planning a route that avoids repetitive or overlapping paths, possibly simplifying navigation.

Question 9: Identify a common mistake when classifying numbers like 49 and 51 as prime or composite and correct it.

Answer: Students may mistakenly think 49 and 51 are prime because they are odd. Correct: 49 = 7×7 (composite), 51 = 3×17 (composite).

Question 10: Challenge: Find the largest prime number less than 50 that could be used as a stop number on a route passing only through prime-numbered stops between 2 and 50.

Answer: 47