Pure Mathematics 1: Cambridge International As & a Level by Sophie Goldie

By Sophie Goldie

This fresh sequence has been written for the college of Cambridge foreign Examinations direction for AS and a degree arithmetic (9709). This identify covers the necessities of P1. The authors are skilled examiners and academics who've written generally at this point, so have ensured all mathematical ideas are defined utilizing language and terminology that's acceptable for college students internationally. scholars are provded with transparent and designated labored examples and questions from Cambridge overseas earlier papers, in order that they be able for lots of crucial examination perform. every one e-book encompasses a unfastened CD-ROM which positive factors the original 'Personal educate' and 'Test your self' electronic assets that would support scholars revise and make stronger options clear of the study room: With own educate every one scholar has entry to audio-visual, step by step aid via exam-style questions The try out your self interactive a number of selection questions determine weaknesses and element scholars within the correct course

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5 1 f--- r--- 2 - --· t- -r -- 3 [\ - 5 6 - - r-- \ I 4 ±'--- 7 8 9 10 h Non-linear simultaneous equations P1 The simultaneous equations in the examples so far have all been linear, that is their graphs have been straight lines. A linear equation in, say, x and y contains only terms in x and y and a constant term. So 7x + 2y = 11 is linear but 7x 2 + 2y= 11 is not linear, since it contains a term in x 2 • You can solve a pair of simultaneous equations, one of which is linear and the other not, using the substitution method.

35 Solve 3x+ 5y= 12 2x- 6y= -20 SOLUTION CD x6 @x5 Adding Giving Substituting x = -1 in equation CD Adding 3 to each side Dividing by 5 Therefore x= -1, y= 3. => => => 18x+ 30y 10x- 30y 72 -100 -28 -1 28x X => => = = -3 + 5y 5y = 12 = 15 y= 3 Note In this example, both equations were multiplied, the first by 6 to give +30y and the second by 5 to give -30y. Because one of these terms was positive and the other negative, it was necessary to add rather than subtract in order to eliminate y. Ill 3" Returning now to the pair of equations giving the prices of hens and ducks, I» :I CD CD 6h+ d = 40 4h+3d = 36 c ;:; 0 c Cll @ CD J:l .

Such equations are called simultaneous equations. If you need to find values of two variables, you will need to solve two simultaneous equations; if three variables, then three equations, and so on. The work here is confined to solving two equations to fmd the values of two variables, but most of the methods can be extended to more variables if required. 34 At a poultry farm, six hens and one duck cost $40, while four hens and three ducks cost $36. What is the cost of each type of bird? SOLUTION Let the cost of one hen be $hand the cost of one duck be $d.

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