Question 1: Rearrange the formula to make x the subject: y = 3x + 5.

Answer: x = (y - 5)/3

Question 2: Solve for x: 2x - 7 = 3x + 4.

Answer: x = -11

Question 3: If z = 2x + y, rearrange to make x the subject: z = 2x + y.

Answer: x = (z - y)/2

Question 4: Rearrange the formula to make x the subject: a = b / x.

Answer: x = b / a

Question 5: Plot the graph of y=2x, where x is on the response grid.

Answer: Students draw the line y=2x

Question 1: Rearrange the formula: w = m * n to make n the subject.

Answer: n = w / m

Question 2: Solve for x: 5x + 2 = 3x + 8.

Answer: x = 3

Question 3: Make x the subject: c = d / (x + 1).

Answer: x = (d / c) - 1

Question 1: A formula for the area of a rectangle is A = l * w, where l is length and w is width. Rearrange to make w the subject, then find w when A=24 and l=6.

Answer: w = A / l; w = 24 / 6 = 4

Question 2: A scientist uses the formula p = k / t, where p is pressure. Rearrange to find t in terms of p and k. If p=5 and k=25, what is t?

Answer: t = k / p; t = 25 / 5 = 5

Question 1: The formula for the speed of a car is s = d / t, where d is distance and t is time. Rearrange to find t. If d=150 km and s=50 km/h, what is the time taken?

Answer: t = d / s; t = 150 / 50 = 3 hours

Question 1: Given the formula E = mc^2, rearrange to make c the subject. If E=50 and m=5, find c.

Answer: c = sqrt(E / m); c = sqrt(50 / 5) = sqrt(10) ≈ 3.16

Question 2: Solve for x: 4x^2 + 5x - 3 = 0, then make x the subject (solve the quadratic).

Answer: x = [-5 ± sqrt(25 - 4*4*(-3))]/(2*4); x = [-5 ± sqrt(25 + 48)]/8; x = [-5 ± sqrt(73)]/8

Question 1: Rearrange to make x the subject: y = (a + bx) / c.

Answer: x = (cy - a)/b

Question 2: If y=10, a=4, b=2, c=3, find x using the rearranged formula.

Answer: x = (3*10 - 4)/2 = (30 - 4)/2 = 13

Question 1: A student rearranged y = 2x + 5 to x = y + 5 / 2. Find the mistake and write the correct formula.

Answer: Mistake: incorrect order of operations. Correct formula: x = (y - 5)/2