Question 1: Given the function xₙ₊₁ = 0.5xₙ + 4, calculate the next three terms starting with x₀ = 8.

Answer: x₁=8, x₂=8, x₃=8

Question 2: For the iteration xₙ₊₁ = 2xₙ - 3, find x₁ if x₀ = 5.

Answer: 7

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

Answer: Student plots points (-3,-9), (-2,-6), (-1,-3), (0,0), (1,3), (2,6), (3,9).

Question 4: Construct a triangle on the grid with vertices at (0,0), (4,0), and (2,3).

Answer: Student draws the triangle accordingly.

Question 5: Calculate x₁ and x₂ given the recurrence xₙ₊₁ = xₙ + 3, starting with x₀ = 2.

Answer: x₁=5, x₂=8

Question 6: A population of bacteria doubles every hour, starting with 50 bacteria. Write the iteration formula and find the population after 4 hours.

Answer: xₙ₊₁=2xₙ, x₀=50; after 4 hours: 50×2⁴=800

Question 7: Identify the mistake in calculating x₁ = 0.5×8 + 4 = 2 + 4 = 6, then find the correct x₁ for x₀=8.

Answer: The calculation is correct; x₁=6.

Question 8: Using xₙ₊₁ = 1.5xₙ + 2, find the value of xₙ after 5 iterations starting from x₀=4.

Answer: x₁=8, x₂=13, x₃=22.5, x₄=36.75, x₅=58.625

Question 9: A toy robot moves forward 5 units each step. Write the iteration formula and calculate its position after 7 steps starting from position 0.

Answer: xₙ₊₁= xₙ + 5; after 7 steps: position = 5×7=35

Question 10: A bank account increases by $100 monthly, starting with $500. Write the recursive formula and find the amount after 12 months.

Answer: xₙ₊₁= xₙ + 100, x₀=500; after 12 months: 500+100×12=1700

Question 11: Explain a common mistake when calculating x₁ = 2×x₀ - 5 if x₀=4, and correct it.

Answer: Mistake: Using addition instead of multiplication. Correct: x₁=2×4-5=3.