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November 2010 Paper 4 1)a) 5 x 8 ÷ 2 = 20cm2 2) Colour Red Probability 0.58 P (Pink) = 0.12 Blue 0.30 Pink 3)a) There are 20 beads in box A. In box B there are twice as many beads as in box A. Box B = 40 In box C there are ¾ of the number of beads as in box A. Box C = 15 In box D there are 10% more beads than in box A. Box D = 22 Total = 20 + 40 + 15 + 22 = 97 4)a) 3 x 100 = 300g 4)b) 4 x 6 = 24 people 5)a) 5)b) 6)a) 7x + 2y – x + y = 6x + 3y b) 2x + 3 = 10 2x = 7 x = 3.5 c)i) c x c = c c)ii) e12 ÷ e4 = e8 7) 8 x 100 = 40% 20 8) 19 31 a) Modal class is 10-19 b) Median is 30th person so lies in the class 20-29 8) 9) 2.42927(0474) 10)a) −2, −1, 0, 1, 2 b) 2x < 10 3 2x < 30 x < 15 11) A B C D and and and and 3 2 4 1 12) T = 7x + 5y 13) Speed = Speed distance time = 7120 8 = 890 km/h 14)a) 14)b) 15)a) She only asks the best students or The sample is too small or The sample is biased 15)b) All the choices are positive There is no box for someone who doesn’t like maths 15)c) How many hours do you spend on your maths homework in a day? 0 hours 1-2 hours 3+ hours 1 mark for question with time frame 1 mark for three non-overlapping response boxes (no marks for inequalities) 16) a) (0, 3, 2) b) (5, 3, 0) 16) a) b) 3(x + 5) + 2(5x – 6) = 3x + 15 + 10x – 12 = 13x + 3 2x + 4 = x + 2 2 c) 5x + 10 = 5(x + 2) d) x2y + xy2 = xy(x + y) 17) a) b) 8.25 x 107 1.456 x 10-15 18) 19.5 litres = 19500 millilitres (1 mark) 19500 ÷ 210 = 92.85714 (1 mark) Therefore a maximum of 92 full cups can be poured (1 mark) 19)a) Age (A years) 20 < A < 30 20 < A < 40 20 < A < 50 20 < A < 60 20 < A < 70 Cumulative Frequency 26 61 82 94 100 19)b) 19)c) 2 marks for 36-38 or for correct reading from your graph if reading lines are drawn on 19)d) 2 marks for 9-11 or for correct reading from your graph if reading lines are drawn on 20)a) 56 28 4 2 2 7 2 56 = 2 x 2 x 2 x 7 = 23 x 7 20)b) 14 21) hyp adj cos 37 = AB 8 (1 mark) AB = cos 37 x 8 (1 mark) AB = 6.389 (1 mark) 22)a) x -2 -1 0 1 2 3 y -15 -8 -7 -6 1 20 22)b) 23) 256° 52° 1 mark for 256° or 52 seen in working or on diagram 1 mark for x = 104° 22) b) OB2 = OA2 + AB2 OB2 = 82 + 62 OB2 = 100 OB = 10 BC = OB – 6 = 4cm 23) (x − 3)(x + 5) x2 – 3x + 5x – 15 x2 + 2x – 15 b) x2 + 8x − 9 = 0 (x + 9)(x – 1) = 0 either x + 9 = 0 or x – 1 = 0 x = -9 x=1 24) 35.5 x 26.5 = 940.75 1 mark for 35.5 or 26.5 1 mark for 35.5 x 26.5 1 mark for 940.75 25)a) (2x + 4y)(4x – 5y) 8x2 + 16xy – 10xy – 20y2 = 8x2 + 6xy – 20y2 25)b) = (x + 10)5 (x + 10)4 x + 10 25)c) x2 – 25 x2 + 7x + 10 = (x – 5)(x + 5) (x +2)(x + 5) = x–5 x+2 25)d) = x2 + 6x − 2 = (x + p)2 + q (x + 3)2 – 11 (x + 3)2 = x2 + 6x + 9 26) 6/ 10 7/ 11 4/ 11 W B W 4/ 10 B 7/ 10 W 3/ 10 B White then black = 7/11 x 4/10 = 28/110 Black then white = 4/11 x 7/10 = 28/110 One of each = 56/110 (or equivalent) 26)b) P = 40 V P = 40 2 P = 20 27)a) 27)b) 28)a) Area = ½ x 10.5 x 8.3 x sin 62 = 38.474... cm2 28)b) QR2 = 10.52 + 8.32 – 2x10.5x8.3xcos62 QR2 = 97.311111 QR = 9.8646... cm