By Hugh Neill, Douglas Quadling, Julian Gilbey

Written to compare 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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Extra info for Advanced Level Mathematics: Pure Mathematics 1

Sample text

Jxt =if?. Fractional powers can also be written as x 1l 2 , xm/n and so on . 1 1 . Simplify (a) 92, (a) 9! J9 = 3. (c) Method 1 Method 2 1 3 (b) 32 x 32 3 , (b) (c) 16-4. 3tx3'~=3t+f=3 2 =9. 16-t = (2 4 )-t = r3 = l8. · . t , 3 16 4 (~/16)3 2 ·' r: ,,;. •: - 28 PURE MATHEMATICS l There are often good alternative ways for solving problems involving indices, and you should try experimenting with them. l(c), makes good sense as a first step. 2 Simplify I (a) (2i)-t,

1 Write x 2 + lOx + 32 in completed square form. :,. r! 2 2 2 x + lOx+ 32 = (x + lOx) + 32 = {(x+ 5) -25} + 32 = (x+ 5) 2 + 7. 2 Don't try to memorise the form x +bx+ c = ( x 2 the coefficient of x, and write x +bx= ( x + + ~ b) 2 -;} b t b) -i b 2 2 . 2 + c . Learn that you halve Then add c to both sides. If you need to write ax 2 +bx+ c in completed squ~e form, but the coefficient a of x 2 is not 1, you can rewrite ax 2 + bx + c by taking out the factor a from the first two terms: 2 ax + bx + c = a( x 2 + ~ x) + c .

A) x=3andy=x 2 +4x-7 (c) y = 8 and y = x 2 +2x (b) y=3andy=x 2 -5x+7 (d) y+3 = 0 and y = 2x 2 +Sx-6 2 Find the points of intersection for the following lines and curves. I l -, (a) y=x+landy=x 2 -3x+4 (b) y=2x+3andy=x 2 +3x-9 (c) y=3x+llandy=2x 2 +2x+5 (d) y=4x+l and y=9+4x-2x 2 (e) 3x+y-1=0 and y=6+10x-6x 2 3 In both the following, show that the line and curve meet only once and find the point of intersection. (a) y = 2x + 2 and y = x 2 - 2x + 6 (b) y=-2x-7 and y=x 2 +4x+2 4 Find the points of intersection between the curve y (a) y = x, =x 2 - x and the line (b) y=x-1.