By J. Newbury PhD (auth.)

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Line which most nearly fits the points you have plotted. 0 cm. Use the graph to estimate the extension of the spring produced by loads of (i) 20 N (ii) 100 N Are these estimates valid? 2. s;;; 4 From the graph, identify: (i) (ii) (iii) the gradient of the line the point of intersection with the x axis (that is, when y = 0) the point of intersection with the y axis (that is, when x = 0) 3. A slow train starts from London for Carlisle at 10 o'c1ock and travels at a constant speed of 60 km/h.

Exercise 81: Is (3x + 2)4x = 12x 2 + 8x? Exercise 82: Express x(x + 2) in a different form as the sum of two terms. Exercise 83: Likewise express 2x(2 + x) in a different form. 6 Expanding Brackets When we express 5x( 3x + 4) in the fonn 15x 2 + 20x we say that we have 'expanded' 5x(3x + 4), orthat we have 'removed the brackets' (that is, removed the need for the brackets). Exercise 84: Expand x(3x -1) Exercise 85: Expand 3x(1-x) Exercise 86: Draw a rectangle which has a length of (2x + 1) and a width of (x + 2).

That is, we can find a value for x which 'fits' the equation. Can you find (by trial and error) a value of x which fits x 2 + 2x - 3 = O? Can }Tou find another value of x which also fits x 2 + 2x - 3 = O? One of the facts of life about quadratic equations is that often there are two düferent values which x may take, either of which fits the question. We can see how the tedious business of 'putting brackets in' may pay off, by trying the following exercises. Is it true that x 2 + 2x - 3 = (x -1)(x + 3)?