1. Rearrange the equation 2p + 1 = 11 to make p the subject. what has happened to p? inverse 2 p + 1 = - 1 11 2

2. Rearrange the equation uv + f = t to make v the subject. what has happened to v? inverse u v + f = - f t u

y - 4x = + 4x 11 Wrong answers Gradient 3. Line L1 has equation y – 4x = 9, by rearranging the equation write down the gradient of the line L1 Wrong answers There is a temptation to say that the gradient is -4 (as this is what is multiplying x) or -4x y - 4x = + 4x 11 Gradient We have rearranged the equation of the line from y – 4x = 9 to y = 9 + 4x , the gradient is therefore + 4 (as this is what is multiplying x)

y - 6x = + 6x 12 Wrong answers Gradient 4. Line L2 has equation y – 6x = 12, by rearranging the equation write down the gradient of the line L2 Wrong answers There is a temptation to say that the gradient is -6 (as this is what is multiplying x) or -6x y - 6x = + 6x 12 Gradient We have rearranged the equation of the line from y – 6x = 12 to y = 12 + 6x , the gradient is therefore + 6 (as this is what is multiplying x)

2 y - 6x = + 6x 12 2 y = 6 + 3x Wrong answers Gradient 5 (b) By rearranging the equation 2y – 6x = 12 to make y the subject write down the gradient of the line 2y – 6x = 12 There is a temptation to say that the gradient is -6 (as this is what is multiplying x), -6x or + 6 (taking -6x across the equals). Wrong answers 2 y - 6x = + 6x 12 2 Gradient If we divide the top of the fraction by two we get: y = 6 + 3x The gradient of the line is 3, as this is multiplying x.

y = 6 + 3x y = m x + c 6 rearranged equation general equation gradient 5 (c) A student looks at the equation 2y – 6x = 12 and writes down the y-intercept as equal to 12. Explain whether the student is correct or not. rearranged equation y = 6 + 3x general equation y = m x + c gradient y-intercept = 6

1 x 2 x 2 x2 1 x 5 5 x 5 2 x 10 x 25 Collect like terms 6. Multiply out the brackets and collect like terms 1 x 2 x 2 x2 1 x 5 5 x 5 2 x 10 x Collect like terms 25 Will have to press more than once

+ + + + + Collect like terms 6. Multiply out the brackets and collect like terms + + + Collect like terms + + Will have to press more than once

2 x 3 x 6 x2 2 x 4 8 x 3 3 x 9 x 12 Collect like terms 6. Multiply out the brackets and collect like terms 2 x 3 x 6 x2 2 x 4 8 x 3 3 x 9 x Collect like terms 12 Will have to press more than once

+ + + + + Collect like terms 6. Multiply out the brackets and collect like terms + + + Collect like terms + + Will have to press more than once

3 x 2 x 6 x2 3 x -1 -3 x 1 2 x 2 x -1 Collect like terms 6. Multiply out the brackets and collect like terms 3 x 2 x 6 x2 3 x -1 -3 x 1 2 x 2 x Collect like terms -1 Will have to press more than once

+ + + + + Collect like terms 6. Multiply out the brackets and collect like terms + + + Collect like terms + + Will have to press more than once

1 x 1 x 1 x2 1 x -1 -1 x 2 1 x 2 x -2 Collect like terms 6. Multiply out the brackets and collect like terms 1 x 1 x 1 x2 1 x -1 -1 x 2 1 x 2 x Collect like terms -2 Will have to press more than once

Collect like terms + + + + + 6. Multiply out the brackets and collect like terms + + + Collect like terms + + Will have to press more than once

1 x 1 x 1 x2 1 x y 1 xy y 1 x 1 xy y2 Collect like terms 6. Multiply out the brackets and collect like terms 1 x 1 x 1 x2 1 x y 1 xy y 1 x 1 xy Collect like terms y2 Will have to press more than once

+ + + + + Collect like terms 6. Multiply out the brackets and collect like terms + + + Collect like terms + + Will have to press more than once