Question 1: Rearrange the formula s = ut + 0.5at^2 to make u the subject.

Answer: u = (s - 0.5at^2) / t

Question 2: Make x the subject of the formula y = 3x + 4.

Answer: x = (y - 4) / 3

Question 3: Solve for x in the formula 2x - 5 = y.

Answer: x = (y + 5) / 2

Question 4: In the formula F = ma, make m the subject.

Answer: m = F / a

Question 5: Rearrange the formula P = V / T to make T the subject.

Answer: T = V / P

Question 6: Solve the equation 5x + 3 = 2x + 12 for x.

Answer: x = 3

Question 7: Construct a formula to make y the subject of y = kx + c.

Answer: y = kx + c

Question 8: A car travels at speed v for time t, covering distance d. Write an expression to make v the subject.

Answer: v = d / t

Question 9: If y = (x + 2)^2, how do you make x the subject? Show your working.

Answer: x = ±√y - 2

Question 10: Find x in the formula 4x / (x + 1) = 3.

Answer: x = 3 / 4

Question 11: Identify and correct the mistake in rearranging the formula y = 2x + 5 to make x the subject as: x = y / 2 + 5.

Answer: Incorrect; the correct rearrangement is x = (y - 5) / 2

Question 12: A rectangle's area A = l × w, where length l = 2x + 3 and width w = x - 1. Write an expression for x in terms of A, l, and w.

Answer: x = (A / (l) ) + 1, solving for x may require substitution and solving the quadratic.