MEI AS Pure Mathematics (3rd Edition) by Roger Porkess, Val Hanrahan, Peter Secker

By Roger Porkess, Val Hanrahan, Peter Secker

The highly-acclaimed MEI sequence of textual content books, helping OCR's MEI based arithmetic specification, totally fit the necessities of the requisites, and are reknowned for his or her pupil pleasant process.

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MEI AS Pure Mathematics (3rd Edition)

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2a ⇒ x= b 2 - 4ac 2a -b ! b 2 - 4ac 2a Solving quadratic equations Factorise the left-hand side and tidy up the right-hand side: C1 1 This important result, known as the quadratic formula, has significance beyond the solution of awkward quadratic equations, as you will see later. The next two examples, however, demonstrate its use as a tool for solving equations. 31 Use the quadratic formula to solve 3x 2 – 6x + 2 = 0. SOLUTION Comparing this to the form ax 2 + bx + c = 0 gives a = 3, b = –6 and c = 2.

I) (a + 2)(a + 3) (ii) (b + 5)(b + 7) (iii) (c – 4)(c – 2) (iv) (d – 5)(d – 4) (v) (e + 6)(e – 1) (vi) (g – 3)(g + 3) (viii) (2i – 3)2 (x) (x + y)(x – y) (vii) (h (ix) 3 + Factorise the following quadratic expressions. (i) x 2 + 6x + 8 (ii) x 2 – 6x + 8 (iii) y 2 + 9y + 20 (iv) r 2 + 2r – 15 (v) r 2 – 2r – 15 (vi) s 2 – 4s + 4 (viii) x 2 + 2x + 1 (x) (x + 3)2 – 9 (ix) – 5x – 6 a2 – 9 Factorise the following expressions. (i) 2x 2 + 5x + 2 (ii) 2x 2 – 5x + 2 (iii) 5x 2 + 11x + 2 (iv) 5x 2 – 11x + 2 (v) 2x 2 + 14x + 24 (vi) 4x 2 – 49 (viii) 9x 2 – 6x + 1 (x) 2x 2 – 11xy + 5y 2 (vii) 6x 2 (ix) t12 5 5)2 (a + b)(c + d) (vii) x 2 4 – 5z + 5z – 25 C1 1 Exercise 1D (i) – 5x – 6 – t22 Simplify the following expressions.

The cost of a pear is 5p greater than that of an apple. 64. (i) (ii) Write this information as a pair of simultaneous equations. Solve your equations to find the cost of each type of fruit. 31 C1 1 4 A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110 kmh–1, the rest on country roads at an average speed of 70 kmh–1. (i) Basic algebra (ii) 5 Solve the following pairs of simultaneous equations. (i) (iv) (vii) 6 Write this information as a pair of simultaneous equations.

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