Cambridge International AS and A Level Mathematics Pure Mathematics 1

Algebra P1^ 1 EXERCISE 1C 1 Make (i) a (ii) t the subject in v = u + at. 2 Make h the subject in V = l wh. 3 Make r the subject ...

Quadratic equations P1^ 1 This equation, involving terms in x^2 and x as well as a constant term (i.e. a number, in this case 60 ...

Algebra P1^ 1 EXAMPLE 1.22 Factorise x^2 + 7 x + 12. SOLUTION Splitting the middle term, 7x, as 4x + 3 x you have x^2 + 7 x + 12 ...

Quadratic equations 15 P1^ 1 This example raises a number of important points. 1 It makes no difference if you write + 4 x − 6 x ...

Algebra 16 P1^ 1 Note The expression in Example 1.24 was a perfect square. It is helpful to be able to rec- ognise the form of s ...

Solving quadratic equations 17 P1^ 1 Note The method used in the earlier examples is really the same as this. It is just that in ...

Algebra P1^ 1 Let y = x^2 x^4 − 13 x^2 + 36 = 0 ⇒ (x^2 )^2 − 13 x^2 + 36 = 0 ⇒ y^2 − 13 y + 36 = 0 Now you have a quadratic equa ...

Exercise 1D 19 P1^ 1 3 Factorise the following quadratic expressions. (i) x^2 + 6 x + 8 (ii) x^2 − 6 x + 8 (iii) y^2 + 9 y + 20 ...

Algebra P1^ 1 10 Find the real roots of the equation^98421 xx +=. 11 The length of a rectangular field is 30 m greater than its ...

Equations that cannot be factorised P1^ 1 x 0 1 2 3 4 5 6 x^20149162536 −6x 0 −6 −12 −18 −24 −30 −36 +2 +2 +2 +2 +2 +2 +2 +2 y + ...

Algebra 22 P1^ 1 EXAMPLE 1.30 Solve the equation x^2 − 6 x + 2 = 0 by completing the square. SOLUTION Subtract the constant term ...

The graphs of quadratic functions 23 P1^ 1 Rewrite the expression with the constant term moved to the right x^2 − 4 x + 5. Take ...

Algebra P1^ 1 ! For this method, the coefficient of x^2 must be 1. To use it on, say, 2x^2 + 6 x + 5, you must write it as 2(x^2 ...

The quadratic formula P1^ 1 4 The curves below all have equations of the form y = x^2 + bx + c. In each case find the values of ...

Algebra 26 P1^ 1 Take the coefficient of x: (^) +ba Halve it: +b 2 a Square the answer: +b a 2 42 Add it to both sides of the eq ...

The quadratic formula P1^ 1 Substituting these values in x bb ac a =––± (^24) 2 gives^2428 24 2 ± ± – = – 24 8 2 24 2 ± ± – – Tr ...

Algebra P1^ 1 The part of the quadratic formula which determines whether or not there are real roots is the part under the squar ...

Simultaneous equations P1^ 1 EXERCISE 1F 1 Use the quadratic formula to solve the following equations, where possible. (i) x^2 + ...

Algebra 30 P1^ 1 Linear simultaneous equations EXAMPLE 1.34 At a poultry farm, six hens and one duck cost $40, while four hens a ...

Simultaneous equations P1^ 1 Note In this example, both equations were multiplied, the first by 6 to give + 30 y and the second ...