Cambridge IGCSE Mathematics - International 0607 — 2021 Oct/Nov Paper 2 · Variant 1

1 (a) Write 4 347 849 correct to the nearest ten thousand. ................................................. [1] (b) Write 0.004 024 3 correct to 2 significant figures. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1(a) 4 350 000 1 1(b) 0.0040 1

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2 90 91 92 93 94 95 96 97 98 99 From this list, write down (a) a prime number, ................................................. [1] (b) a common multiple of 4 and 6. ................................................. [1]

Mark scheme: 2(a) 97 1 2(b) 96 1

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3 Draw all the lines of symmetry on each of these shapes. [2]

Mark scheme: 3 2 B1 for each diagram

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4 The table shows the percentage of students in each of three classes who study physics, chemistry and biology. Physics (P) Chemistry (C) Biology (B) Class H 34 28 38 Class J 24 18 58 Class K 46 32 22 Complete the compound bar chart to show this information. 100 90 80 B 70 60 Percentage 50 C 40 30 20 P 10 0 Class H Class J Class K [3]

Mark scheme: 4 Correct bar chart 3 B2 for 1 correct column or B1 for bottom bar on each column correct If 0 scored, SC1 for bar sections correct heights but in inconsistent order or unequal widths.

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5 Solve. 2 ( 4x - 1) = 3 ( 2x + 1) x = ................................................ [3]

Mark scheme: 5 1 3 M1 for 8x – 2 = 6x + 3 2 oe M1FT for 8x – 6x = 3 + 2 2

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6 (a) Write 0.000 058 6 in standard form. ................................................. [1] (b) ( 2 # 10 a ) ' ( 8 # 10 b ) = k # 10 n where 1 G k 1 10 . (i) Find the value of k. k = ................................................ [1] (ii) Write an expression for n in terms of a and b. n = . ................................................. [1]

Mark scheme: 6(a) 5.86 × 10–5 cao 1 6(b)(i) 2.5 1 6(b)(ii) a – b – 1 1

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7 Mia carries out a survey in a school to find out what students will do when they leave school. These are her results. University Job Training Travelling Total Frequency 112 43 27 18 200 (a) Find the relative frequency of university. ................................................. [1] (b) There are 1600 students in this school. (i) Explain why the result in part (a) is a reasonable estimate of the probability that a student from this school will go to university. ............................................................................................................................................. [1] (ii) Calculate an estimate for the number of students in this school who will go travelling. ................................................. [2]

Mark scheme: 7(a) 112 1 oe 200 7(b)(i) Large sample 1 7(b)(ii) 144 2 18 M1 for × 1600 oe 200

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8 Solve the simultaneous equations. 3x - 2y = 12 5x + y = 7 x = ................................................ y = ................................................ [3]

Mark scheme: 8 Correctly eliminating one variable M1 x = 2 A2 A1 for each y = –3 If 0 scored, SC1 for correct substitution and evaluation to find other variable.

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9 y varies inversely as the square of ( x + 2 ) . When x = 4, y = 0.5 . Find y in terms of x. y = ................................................ [2]

Mark scheme: 9 18 2 k M1 for oe ( x + 2) 2 ( x + 2) 2

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10 NOT TO 6 cm SCALE 30° The diagram shows a sector of a circle with radius 6 cm and sector angle 30°. The area of the shaded segment is ( a r - b )cm 2 . Find the value of a and the value of b. a = ................................................ b = ................................................ [3]

Mark scheme: 10 [a =] 3 3 30 M1 for × π × 62 oe [b =] 9 360 1 M1 for × 6 × 6 × sin 30 oe 2

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11 In this question all lengths are in centimetres. NOT TO SCALE 5 + 3 2 3 x Find the value of x2. Give your answer in the form a + b 3 where a and b are integers. x2 = ................................................ [4]

Mark scheme: 11 16 + 10 3 4 M1 for (5 + 3 )2 = x2 + (2 3 )2 oe B1 for 52 + 5 3 + 5 3 + ( 3 )2 oe B1 for 12

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12 y A NOT TO B SCALE C D E F O x G 1 The diagram shows the lines y = x + 1, y = 3x and 3x + 4y = 12 . 2 These lines divide the space into 7 regions, A, B, C, D, E, F, and G. Write down the letter of the region which is defined by 1 (a) y G x + 1, y G 3x and 3x + 4y G 12 , 2 Region ................................................ [1] 1 (b) y H x + 1, y H 3x and 3x + 4y G 12 . 2 Region ................................................ [1]

Mark scheme: 12(a) F 1 12(b) C 1

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13 y NOT TO SCALE 0 x – 2 3 – 12 The equation of the curve is y = ax 2 + bx - 12 . Find the value of a and the value of b. a = ................................................ b = ................................................ [3]

Mark scheme: 13 a = 2 B1 for one correct. b = –2 3 M1 for (x + 2)(x – 3) [c = –12] OR M1 for correct substitution of 3 points into y = ax2 + bx + c

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14 Solve. (a) log 3 x = 4 x = ................................................ [1] (b) 2 log x - 3 log 2 = log 50 x = ................................................ [3]

Mark scheme: 14(a) 81 1 14(b) 20 3 M1 for one correct use of alog x = log xa M1 for one correct use of log a + log b = log ab a or log a – log b = log b

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