New PDF release: Work Out Mathematics GCSE
By G.D. BUCKWELL
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Extra resources for Work Out Mathematics GCSE
1 Directed Numbers There is always great confusion between the concept of a directed number, and the operations of addition and subtraction. The author will try to make it clearer or in this section by writing all numbers negative or positive like (a) Addition @ @= @ @+@=@ @+@=@ @ @. + Addition of any negative number to any other number always gives a smaller answer. Addition of any positive number to any other number always gives a larger This is only helpful advice; the student still has to get the answer right!
Note that this is negative, because] -b X -3 = +3b. 4(c) we showed that (2x - 1) (3x + 1) = 6x 2 - x - 1; the expression 6x 2 - x - 1 is called a quadratic expression. The process of factorizing a quadratic is not easy and will be considered in stages. (i) x 2 + 5x + 6 = x 2 + 2x + 3x + 6 = x(x + 2) + 3 (x + 2) (ii) x 2 (iii) x 2 +x - 6 - = + 3) (x + 2). (x = x2 + 3x - 2x - 6 =x(x+ 3)- 2(x+ 3) = (x - 2)(x + 3). 7x + 10 = x 2 - 5x - 2x + 10 =x(x- 5)- 2(x- 5) = (x - 2)(x - 5). 45 The process is really trial and error, and practice makes perfect.
1) (a) Solve 3x + 4y =2 (2) 5x + 3y = 1. 15x + 20y = 10 15x+ 9y= 3. Multiply (1) by 5: multiply (2) by 3: (3) (4) Each equation has the same number of x's. The equations can be subtracted: -~ ... e. A. '3x= 2 -n--u, The solution to the equations is x =- 2 11 , y = . 1. 11· tr . (b) A slightly harder example: = 14 = 18. 45x- 36y = 126 5x - 4y 7x + 9y Multiply (1) by 9: multiply (2) by 4: (1) (2) (3) (4) 28x + 36y = 72. This time, y can be eliminated by adding the equations: (3) + (4): 73x = 198, :.
Work Out Mathematics GCSE by G.D. BUCKWELL