By Hugh Neill, Douglas Quadling, Julian Gilbey

Written to check the contents of the Cambridge syllabus. natural arithmetic 1 corresponds to unit P1. It covers quadratics, capabilities, coordinate geometry, round degree, trigonometry, vectors, sequence, differentiation and integration.

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Example text

01? 11 You are given that y = ~. x Ix I< 1000? x if Iy I> 1000 ? (a) What can you say about y if (b) What can you say about 12 The number, N, of people at a football match was reported as '37 000 to the nearest thousand'. ill inequality using the modulus sign. 13 The mathematics marks, m and n, of two twins never differ by more than 5. Write this · statement as an inequality using the modulus sign. 14 A line has length x cm. You are given that in words? 005. 5 Graphs of the form y = ax 2 +bx+ c ....

If x > 2 or x < -2, the value of 4 - x 2 is negative, and a negative number does not have a square root. 2 x 0 Fig. J4 = 2. So the graph of f(x) = ~ 4 - x 2 , shown in Fig. 2, lies between -2 and 2 inclusive in the x-direction, and between 0 and 2 inclusive in the y-direction. Even when you use a function which has a meaning for all real numbers x, you may be interested in it only when x is restricted in some way. For example, the formula for the volume of a cube is V = x 3 . Although you can calculate x 3 for any real number x, you would only use this formula for x > 0.

2 Draw the complete graph of f(x) = ~ 4 - x 2 . ~ ~-~4-x 2 You can only calculate the values of the function f(x) = ~4 - x 2 if x is between -2 and 2 inclusive. ··:;. If x > 2 or x < -2, the value of 4 - x 2 is negative, and a negative number does not have a square root. 2 x 0 Fig. J4 = 2. So the graph of f(x) = ~ 4 - x 2 , shown in Fig. 2, lies between -2 and 2 inclusive in the x-direction, and between 0 and 2 inclusive in the y-direction. Even when you use a function which has a meaning for all real numbers x, you may be interested in it only when x is restricted in some way.