Cambridge IGCSE Mathematics 0580 — 2011 Oct/Nov Paper 3 · Variant 3

1 Caroline goes to a shop. For Examiner's The shopping bill shows the items she buys. Use Item Cost ($) 1 packet of cereal 1.20 3 bottles of water at $0.45 each 1.35 2 cartons of milk at $0.82 each 4 kg of rice at $0.90 per kg 0.7 kg of apples at $2.40 per kg (a) Complete the shopping bill. [3] (b) (i) Calculate the total amount of money Caroline spends at the shop. Answer(b)(i) $ [1] (ii) Caroline pays with a $10 note. Calculate how much change she receives. Answer(b)(ii) $ [1] (c) Caroline arrived at the shop at 09 48. For She was in the shop for 18 minutes. Examiner's She then took 5 minutes to walk to a café. Use She was in the café for 20 minutes. (i) At what time did Caroline leave the café? Answer(c)(i) [2] (ii) Caroline then went to the library. She was in the library for 45 minutes. Work out the ratio time in the shop : time in the library. Give your answer in its simplest form. Answer(c)(ii) : [2] (d) When Caroline left home she had $36.50. She returned home with $12.74. Calculate $12.74 as a percentage of $36.50. Answer(d) % [1]

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 1.64 B1 3.6(0) B1 1.68 B1 (b) (i) 9.47 ft 1ft ft their table (ii) 0.53 ft 1ft ft their (i) (c) (i) 10 31 2 B1 for 43 seen (ii) 2 : 5 cao 2 B1 for 18 : 45 oe (d) 34.9 1

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2 James takes 12 science tests during one school term. For These are his marks. Examiner's Use 18 11 20 15 15 12 15 9 11 15 14 13 (a) Find (i) the range, Answer(a)(i) [1] (ii) the mode, Answer(a)(ii) [1] (iii) the median, Answer(a)(iii) [2] (iv) the mean. Answer(a)(iv) [2] (b) James sorts his marks into three levels. For The levels are Satisfactory (less than 12), Good (12 to 16) and Excellent (more than 16). Examiner's Use (i) Complete the frequency table to show this information. Level Satisfactory Good Excellent Frequency 7 [1] (ii) Complete the pie chart accurately and label each sector. Good [2] (c) What fraction of the marks were Satisfactory or Good? Give your answer in its lowest terms. Answer(c) [2]

Mark scheme: 2 (a) (i) 11 1 (ii) 15 1 (iii) 14.5 2 M1 for ordering list or substantial part of list or 14 & 15 (iv) 14 2 M1 for (9 + 11 + 11 + 12 + 13 + 14 + 15 + 15 + 15 + 15 + 18 + 20) (b) (i) 3, …, 2 1 (ii) Angles of 90° and 60° 1ft ft only if total equals 12 Correct labels 1 (Dependent) 5 10 their 3 + 7 (c) cao 2 M1 for or from table 6 12 their 12

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3 For Park 600 Examiner's Use 550 500 450 400 350 Distance from Bruce’s home 300 (metres) 250 200 Jason’s home 150 100 50 Bruce’s home 0 09 00 09 10 09 20 09 30 09 40 09 50 10 00 10 10 Time One morning, Bruce walked from his home to Jason’s home and the two boys walked to the park. The distance-time graph shows Bruce’s journey. (a) How many minutes was Bruce at Jason’s home? Answer(a) min [1] (b) How far from the park were Bruce and Jason at 09 20? Answer(b) m [2] (c) Work out the speed at which Bruce and Jason walked to the park. Give your answer in km/h. Answer(c) km/h [3] (d) Bruce stayed at the park for 35 minutes. He then walked home at a speed of 60 metres per minute. Complete the graph to show Bruce’s time at the park and his journey home. [3]

Mark scheme: 3 (a) 5 1 (b) 150 2 B1 for 450 seen or implied .045 (c) 1.8 3 M2 for oe .025 (M1 for correct distance ÷ correct time) (d) Straight line (09 25, 600) to 1 (10 00, 600) Straight line (10 00, 600 to 10 10, 0) ft 2ft M1 for 600 ÷ 60 oe ft their graph 10 mins to time axis IGCSE – October/November 2011 0580 33

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4 (a) For Examiner's Use W C l On the grid, (i) draw the reflection of W in the line l, [2] (ii) rotate W anticlockwise through 90°, about the point C. [2] (b) y 3 2 1 P R x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 Q –1 –2 –3 –4 (i) Describe fully the single transformation that maps P onto Q. Answer(b)(i) [2] (ii) Describe fully the single transformation that maps P onto R. Answer(b)(ii) [3]

Mark scheme: 4 (a) (i) Correct reflection 2 B1 if reflected in other vertical line (ii) Correct rotation 2 B1 if rotated about C but clockwise through 90° or correct rotation about their reflected C  − 9  (b) (i) Translation,   2 B1 for translation  − 1  B1 for column vector (ii) Enlargement , (centre) (0, 0), 3 B1 B1 B1 1 (sf) 2

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5 (a) For C Examiner's D 92° NOT TO Use 140° SCALE 52° A B X In the quadrilateral ABCD, angle BAD = 52°, angle ADC = 140° and angle DCB = 92°. AB is extended to X. (i) Calculate angle CBX. Answer(a)(i) Angle CBX = [2] (ii) The line BY bisects angle CBX. Complete the statement. The lines BY and AD are because [2] (b) T NOT TO O 4x° x° P SCALE U The diagram shows a circle, centre O. PT and PU are tangents to the circle at T and U. Angle TPU = x° and angle TOU = 4x°. Calculate the value of x. Answer(b) x = [3] (c) The exterior angle of a regular polygon is 20°. Calculate the number of sides of the polygon. Answer(c) [2]

Mark scheme: 5 (a) (i) 104 2 M1 for 360 – (52 + 140 + 92) implied by 76 (ii) Parallel 1 Dependent on (i) correct Angle YBX = 52° oe 1 Dependent on word parallel already given (b) 36 3 M2 for 360 = 90 + 90 + x + 4x oe (B1 if angle T or U = 90° soi) (c) 18 2 M1 if angle sum = 360 soi or long method

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6 (a) Complete the table for y = 4 + 2x O x2. For Examiner's Use x –2 –1 0 1 2 3 4 y 1 5 1 [2] (b) On the grid, draw the graph of y = 4 + 2x O x2 for –2 Y x Y 4 . y 6 5 4 3 2 1 x –2 –1 0 1 2 3 4 –1 –2 –3 –4 [4] (c) (i) Draw the line of symmetry of the graph. [1] (ii) Write down the equation of this line of symmetry. Answer(c)(ii) [1] (d) Use your graph to solve the equation 4 + 2x O x2 = 0. Answer(d) x = or x = [2]

Mark scheme: 6 (a) –4, …, 4, …, 4, …, –4 2 B1 for both –4s B1 for both 4s (b) 7 points plotted ft 3ft P2 for 5 or 6 points plotted ft P1 for 3 or 4 Reasonable curve through at least 6 1ft Only ft if shape parabola points (c) (i) The line x = 1 drawn 1ft (ii) x = 1 1ft (d) –1.4 to –1.1, 3.1 to 3.4 2ft B1 B1ft if not in these ranges

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7 For 8 Examiner's Use 7 6 5 Frequency 4 3 2 1 0 3 3 12 4 4 12 5 5 12 6 6 12 Shoe size The bar chart shows the frequencies of the shoe sizes for a group of students. (a) Use the information in the bar chart to complete the frequency table. 1 1 1 1 Shoe size 3 3 4 4 2 5 5 2 6 6 2 2 Frequency 4 1 [2] (b) How many students are in the group? Answer(b) [1] (c) Calculate the mean shoe size. Answer(c) [3]

Mark scheme: 7 (a) …, 5, 8, 7, 6, 4, 5, … 2 B1 for 4 or 5 correct (b) 40 1ft (c) 4.5375 or 4.537 or 4.538 or 4.54 3 M1 for 4 × 3 + 5 × 3.5 + 8 × 4 + 7 × 4.5 + 6 × 5 www3 + 4 × 5.5 + 5 × 6 + 1 × 6.5 Allow 4.5 but only with working M1 dependent for dividing their 181.5 by their 40 (M1 + M1 implied by 175(.1625)) IGCSE – October/November 2011 0580 33

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8 For Examiner's Use A B (a) Construct triangle ABC accurately, with AC = 10 cm and BC = 8 cm. The line AB has been drawn for you. [2] (b) (i) Using a straight edge and compasses only, construct the bisector of angle A. [2] (ii) The bisector of angle A meets BC at X. Measure the length of BX. Answer(b)(ii) BX = cm [1] (c) (i) Using a straight edge and compasses only, construct the perpendicular bisector of AB. [2] (ii) The perpendicular bisector of AB meets AC at Y and AX at Z. Measure angle CYZ. Answer(c)(ii) Angle CYZ = [1] (d) Shade the region inside triangle ABC which is • nearer to AB than to AC and • nearer to B than to A. [1]

Mark scheme: 8 (a) Correct construction with arcs 2 B1 for two correct lines without arcs or B1 for accurate arcs seen or B1 for 1 correct line with 2 arcs seen SC1 for AC = 8 and BC = 10 correct with arcs (b) (i) Correct construction with arcs 2ft ft their (a) B1ft for accurate line drawn without arcs or B1ft for accurate arcs seen or B1ft for accurate line with arcs bisecting another angle (ii) 4.2 to 4.5 1ft Strict ft their b(i) with intersection on opposite side of triangle (c) (i) Correct construction with arcs 2ft ft their (a) B1ft for accurate line drawn without arcs or B1ft for two pairs of accurate arcs seen or B1ft for accurate line with arcs, bisecting AB or AC (ii) 129° to 133° 1ft Strict ft from their C on triangle, their Y on one side of triangle and their Z on their intersection of b(i) and c(i) (d) Correct quadrilateral shaded 1 From their triangle

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9 For P Examiner's Use 5 cm NOT TO SCALE Q 12 cm R 25 cm The diagram shows a solid triangular prism of length 25 cm. The cross-section of the prism is triangle PQR. PQ = 5 cm, QR = 12 cm and angle PQR = 90°. (a) (i) Calculate the volume of the prism. Answer(a)(i) cm3 [3] (ii) The prism is made from wood. The mass of 1 cm3 of the wood is 0.96 g. Calculate the mass of the prism. Give your answer in kilograms. Answer(a)(ii) kg [2] (b) (i) Show that PR = 13 cm. For Examiner's Answer(b)(i) Use [2] (ii) The prism is completely covered with plastic at a cost of $0.08 per square centimetre. By finding the total area of the two triangles and the three rectangles, calculate the total cost of the plastic used. Answer(b)(ii) $ [4]

Mark scheme: 9 (a) (i) 750 3 M2 for 0.5 × 12 × 5 × 25 seen or implied (M1 for 0.5 × 12 × 5 or M1 for their area of cross-section × 25) (ii) 0.72 2ft ft their (i) × 0.00096 SC1 for 720 (or ft their (i) × 0.96) (b) (i) 52 + 122 M1 169 M1 1 (ii) 64.8(0) www4 4 M2 for 2 × × 12 × 5 + 25 × 13 + 25 × 12 + 25 × 5 2 (M1 for any three correct) M1 for their area × 0.08

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10 (a) Tatiana goes for a walk. For Examiner's (i) She walks for 15 minutes at a speed of 80 metres per minute. Use Calculate the distance she walks. Answer(a)(i) m [1] (ii) She then walks for a further p minutes at w metres per minute. Write down an expression, in terms of p and w, for the total distance Tatiana walks. Answer(a)(ii) m [1] (iii) Write down an expression, in terms of p and w, for Tatiana’s average speed, in metres per minute. Answer(a)(iii) m/min [2] (b) The volume, V, of a solid is given by the following formula. For Examiner's Use V = 3b(t + 12 m) (i) Find V when b = 4, t = 5 and m = 6 . Answer(b)(i) V = [2] (ii) Find b when t =3, m = 2 and V = 84. Answer(b)(ii) b = [3] Question 11 is printed on the next page.

Mark scheme: 10 (a) (i) 1200 1 (ii) 1200 + pw 1ft ft their (i) + pw 1200 + pw (iii) 2ft ft their (ii)/(15 + p) 15 + p M1 for ÷ (15 + p) 1 (b) (i) 96 2 M1 for 3 (4)(5 + ×6) or better 2 1 (ii) 7 3 M1 for 84 = 3b(3 + ×2) or better 2 A1 for equation 12b = 84 oe correct kb = l IGCSE – October/November 2011 0580 33

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11 (a) Write down the next term in each of the following sequences. For Examiner's Use (i) 8, 15, 22, 29, [1] (ii) 3, 6, 12, 24, [1] (iii) 1, 4, 9, 16, [1] (iv) 0, 3, 8, 15, [1] (b) Write down an expression, in terms of n, for the nth term of (i) the sequence in part(a)(iii), Answer(b)(i) [1] (ii) the sequence in part(a)(iv). Answer(b)(ii) [1] (c) The nth term of a sequence is 7n –3 . (i) Write down the value of the 4th term. Answer(c)(i) [1] (ii) Which term has a value of 592? Answer(c)(ii) [2] (d) 1, 2, 2, 4, 8, 32, 256, …… Work out the next two terms of this sequence. Answer(d) , [2]

Mark scheme: 11 (a) 36, 48, 25, 24 ft 4 B1 each ft their 25 – 1 (b) (i) n2 oe 1 (ii) n2 – 1 oe 1ft ft their (i) – 1, if expression in n (c) (i) 25 1 (ii) 85 2 M1 for 7n – 3 = 592 or better (d) 8192, 2 097 152 2 B1 each SC1ft 256 × their 8192

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