Question 1: Simplify the expression: 3x^2 + 5x^2.

Answer: 8x^2

Question 2: Rearrange the formula A = πr^2 to solve for r^2.

Answer: r^2 = A/π

Question 3: Calculate the value of x when 4x^2 = 36.

Answer: x = ±3

Question 4: A square garden has an area of 64 square meters. Find the length of each side.

Answer: 8 meters

Question 5: If y = 2x^2 + 3x, find y when x = -2.

Answer: y = 2(4) + 3(-2) = 8 - 6 = 2

Question 6: A ball is dropped from a height h, and the height after t seconds is given by h = 100 - 5t^2. How long does it take for the ball to reach the ground?

Answer: t = √(100/5) = √20 ≈ 4.47 seconds

Question 7: Expand and simplify: (x + 3)^2.

Answer: x^2 + 6x + 9

Question 8: Solve for x: 2x^2 - 8 = 0.

Answer: x^2 = 4, so x = ±2

Question 9: A rectangular swimming pool is 10 meters long and has an area of 150 square meters. What is the width?

Answer: Width = 15 meters

Question 10: Construct a triangle on the grid with sides 3 units, 4 units, and 5 units. Use the grid to draw accurately.

Answer: Students draw the triangle with specified side lengths.

Question 11: Identify and correct the mistake: Simplify x^2 + 2x + 1 as (x + 1)^2, but the student writes it as (x + 2)^2.

Answer: Error: The correct factorization is (x + 1)^2, not (x + 2)^2.