Question 1: Calculate the value of 5^0.

Answer: 1

Question 2: Simplify the expression: 10^0 × 7^0.

Answer: 1

Question 3: A map shows a city where distances between locations are scaled such that 1 cm = 2 km. If a route of 3 cm is taken on the map, what is the real distance? Show your working.

Answer: 6 km

Question 4: Plot the graph of y=2x for x values from -3 to 3 on the grid.

Answer: Student draws the line accordingly

Question 5: Construct a triangle with vertices at (0,0), (4,0), and (0,3). Calculate the length of the hypotenuse.

Answer: 5

Question 6: Explain why any number raised to the zero power equals 1, using a proof based on the laws of exponents.

Answer: Because a^n / a^n = a^{n-n} = a^0, and any non-zero number divided by itself equals 1.

Question 7: A hiker's map scale is 1:50,000. If the hiker walks 4 km in real life, how many centimeters will this be on the map? Show your working.

Answer: 8 cm

Question 8: Identify the common mistake: What is the value of 2^0 + 3^0? A student says it's 0. Why is this incorrect?

Answer: Because 2^0 and 3^0 are each 1, so their sum is 2, not 0.

Question 9: A delivery drone travels in a straight line. Its initial distance from the starting point is described by the formula d = 5^t, where t is time in hours. What is the distance traveled after 0 hours? Explain.

Answer: 0, because 5^0 = 1, but since the formula describes distance relative to start, initial distance is 5^0 = 1 (unit), indicating starting point, or interpret as initial distance 1. Alternatively, clarify the question based on context.

Question 10: What is the value of 1^n for any integer n? Use proof based on properties of exponents.

Answer: 1, because any number to any power is 1.

Question 11: Identify and correct the error: A student claims that 0^0 = 0. Explain the correct value and reason.

Answer: 0^0 is undefined or considered 1 in combinatorics because it represents an empty product.