Question 1: Solve for x and y: \( x + y = 5 \) and \( x^2 - y = 0 \).

Answer: x=2.5, y=2.5

Question 2: Given \( y = 3x + 1 \) and \( y = x^2 - 4 \), find the values of x and y.

Answer: x= -1, y= -2

Question 3: Construct the quadratic equation with roots at 2 and -3, and a linear equation passing through (0,1) and (2,5).

Answer: Quadratic: y = (x - 2)(x + 3) = x^2 + x - 6; Linear: y = 2x + 1

Question 4: Solve for x and y: \( 2x - y = 4 \) and \( y = x^2 + 2 \).

Answer: x=1, y=3

Question 5: A shop sells apples and oranges. The total cost is represented by \( 3a + 2o = 20 \), and the total weight by \( a^2 + o^2 = 25 \). Find the number of apples (a) and oranges (o).

Answer: a=3, o=4

Question 6: Plot the graph of \( y = 2x \) and \( y = x^2 - 1 \).

Answer: Students plot the two curves on the grid.

Question 7: Construct a triangle with vertices at points (1,2), (4,2), and (3,5) on the grid.

Answer: Students draw the triangle accurately on the grid.

Question 8: Solve for x and y: \( y = 4x + 3 \) and \( y = x^2 - 5x + 6 \).

Answer: x=1, y=7

Question 9: Find the solutions to the simultaneous equations: \( x^2 + y = 10 \) and \( y = 2x - 1 \).

Answer: x=3, y=5

Question 10: A quadratic function is defined as \( y = -x^2 + 4x + 1 \). Find the x-values where y=0.

Answer: x= -0.267, 4.267

Question 11: Identify and correct the mistake: Solve \( x + y = 3 \) and \( x^2 + y^2 = 9 \). The solution is x=3, y=0.

Answer: Incorrect solution; the correct solutions are x= (1.5 ± 1.5√3), y=3 - x.