Cambridge IGCSE Mathematics 0580 — 2011 Oct/Nov Paper 4 · Variant 2

9 (a) Emile lost 2 blue buttons from his shirt. For Examiner's A bag of spare buttons contains 6 white buttons and 2 blue buttons. Use Emile takes 3 buttons out of the bag at random without replacement. Calculate the probability that (i) all 3 buttons are white, Answer(a)(i) [3] (ii) exactly one of the 3 buttons is blue. Answer(a)(ii) [3] (b) There are 25 buttons in another bag. For Examiner's This bag contains x blue buttons. Use Two buttons are taken at random without replacement. 7 The probability that they are both blue is . 100 (i) Show that x2 O x O 42 = 0. Answer (b)(i) [4] (ii) Factorise x2 O x O 42. Answer(b)(ii) [2] (iii) Solve the equation x2 O x O 42 = 0. Answer(b)(iii) x = or x = [1] (iv) Write down the number of buttons in the bag which are not blue. Answer(b)(iv) [1]

Mark scheme: 120 5 9 (a) (i) oe 0.357(1…) 3 Accept fraction, %, dec equivalents (3sf or better) 336 14 throughout but not ratio or words isw incorrect cancelling/conversion to other forms Pen –1 once for 2sf answers 6 5 4 M2 for × × 8 7 6 5 or M1 for seen 7 180 15 2 6 5 6 2 5 6 5 2 (ii) oe 0.536 or 0.5357… 3 M2 for × × + × × + × × 336 28 8 7 6 8 7 6 8 7 6 2 × 5 × 6 Accept 3 × 6 × 7 × 8 2 × 5 × 6 60 5 or M1 for oe seen ( oe ) 6 × 7 × 8 336 28 x x − 1 7 x x − 1 (b) (i) × = M2 M1 for or seen 25 24 100 25 24 x 2 −x 7 = 600 100 7 or x(x – 1) = × 25 × 24 M1 Or better, min requirement is x² – x = 7 × 6 100 x² – x – 42 = 0 E1 With no errors or omissions (ii) (x + 6) ( x – 7) B2 SC1 any other (x + a)(x + b) where a × b = –42 or a + b = –1 (iii) –6, 7 B1ft Correct or follow through dep on at least SC1 in (b)(ii) (iv) 18 B1ft Correct or ft 25 – their positive integer solution Dep on pos and neg answer to (b)(iii) Answer must be positive integer

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