Cambridge IGCSE Mathematics 0580 — 2014 Oct/Nov Paper 3 · Variant 1

1 A carton of fruit juice contains apple, orange, pineapple and tropical juices. (a) They are mixed in the ratio apple : orange : pineapple : tropical = 9 : 7 : 4 : 5. The carton contains 540 millilitres of apple juice. (i) Show that the total amount of fruit juice in the carton is 1.5 litres. Answer(a)(i) [3] (ii) Calculate the amount of tropical juice in the carton. Give your answer in millilitres. Answer(a)(ii) ........................................... ml [2] (iii) 70% of the tropical juice is mango. Calculate the amount of mango juice in the carton. Answer(a)(iii) ........................................... ml [2] (b) A shopkeeper pays $36 for 16 cartons. (i) How much does he pay for one carton? Answer(b)(i) $ ................................................. [1] 7 (ii) He sells of the 16 cartons for $3.40 each and the rest for $2.50 each. 8 Calculate the total amount he receives from selling the cartons. Answer(b)(ii) $ ................................................. [2] (iii) Calculate his percentage profi t. Answer(b)(iii) .............................................% [3] __________________________________________________________________________________________

Mark scheme: Qu. Answers Mark Part Marks Alternative method 1 (a) (i) 540 ÷ 9 M1 M1 540 ÷ 1000 their 60 × (9 + 7 + 4 + 5) M1FT M1FT their 0.54 ÷ 9 A1 A1 0.06 × (9 + 7 + 4 + 5) 1500 ÷ 1000 If 0 scored SC1 for 0.54 + 0.42 + 0.24 + 0.3 (ii) 2 M1 for 5 ÷ (9 + 7 + 4 + 5) × 1500 300 or (540/9) × 5 or 60 × 5 (iii) 2FT M1 for 70 ÷ 100 × their (a)(ii) oe 210 (b) (i) 1 2.25 (ii) 52.6[0] 2 B1 for 14 or (7/8) × 16 × 3.4[0] (iii) 46.1 3FT M2 for (their (b)(ii) – 36) ÷ 36 × 100 or M1 for their (b)(ii) – 36 M2 for their (b)(ii) ÷ 36 × 100 – 100 M1 for their (b)(ii) ÷ 36 [× 100]

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2 y 9 8 7 6 5 4 3 P 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 H –6 G –7 –8 –9 Two congruent quadrilaterals, G and H, and a point P are shown on this 1 cm2 grid. (a) (i) Write down the mathematical name of the shaded quadrilateral. Answer(a)(i) ................................................ [1] (ii) Calculate the area of the shaded quadrilateral. Give the units of your answer. Answer(a)(ii) .................................. ........... [3] (b) Describe fully the single transformation that maps quadrilateral G onto quadrilateral H. Answer(b) ........................................................................................................................................... ............................................................................................................................................................. [3] (c) On the grid, draw the images of quadrilateral G after the following transformations. (i) Refl ection in the line y = 0. [2] -5 (ii) Translation by the vector [2] e 7 o. (iii) Enlargement by scale factor 0.5 with centre P. [2] (d) On quadrilateral H mark, with an arc, an obtuse angle. [1] __________________________________________________________________________________________

Mark scheme: 2 (a) (i) Trapezium 1 (ii) 16 2 M1 for ½(2 + 6) × 4 oe cm2 1 (b) Rotation B1 Independent marks 90°[anti-clockwise] oe B1 [centre] (–2, –8) B1 (c) (i) Correct reflection in y = 0 2 SC1 for correct reflection in x = 0 (ii) Translation 5 left and 7 up 2 SC1 for one of 5 left or 7 up (iii) Correct Enlargement 2 SC1 for enlargement, SF ½, but incorrectly placed. (d) Obtuse angle marked 1

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3 12 athletes took part in the 100 metres race. 11 of these athletes also took part in the long jump. The times and distances, each measured correct to 3 signifi cant fi gures, for these athletes are shown in the table. Athlete A B C D E F G H I J K L 100 m time (seconds) 12.1 10.3 12.8 10.7 12.6 11.2 12.0 12.4 10.6 12.7 11.8 11.1 Long jump (metres) 7.60 5.15 7.25 6.72 6.30 5.60 6.20 6.90 5.70 6.85 6.70 × (a) The scatter diagram shows the times and distances for athletes B to H. (i) Plot the times and distances for athletes I, J, K and L. 8.0 7.5 7.0 Long jump (metres) 6.5 6.0 5.5 5.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0 100 m time (seconds) [2] (ii) On the scatter diagram, draw a line of best fi t. [1] (iii) Athlete A did not take part in the long jump. Use your line of best fi t to estimate a long jump distance for athlete A. Answer(a)(iii) ............................................ m [1] (iv) What type of correlation is shown on the scatter diagram? Answer(a)(iv) ................................................ [1] (v) Describe in words the relationship between the time for 100 metres and the distance in the long jump. Answer(a)(v) ............................................................................................................................... ..................................................................................................................................................... [1] (b) Use the table of times and distances to work out (i) the mean of the 100 metres times, Answer(b)(i) .............................................. s [2] (ii) the percentage of athletes who ran 100 metres in less than 11.5 seconds, Answer(b)(ii) ............................................ % [2] (iii) the range of the distances jumped by the 11 athletes, B to L. Answer(b)(iii) ............................................ m [1] __________________________________________________________________________________________

Mark scheme: 3 (a) (i) 4 points correctly plotted. 2 B1 for 1 correct (ii) Correct continuous ruled line of best fit. 1 Dependent on at least 8 points on graph (iii) Distance on their line of best fit. 1FT FT their single straight line in part (ii). (iv) Negative 1 (v) Faster the time, the longer the distance oe 1 ÷ 12 (b) (i) 11.7 or 11.69... NFWW 2 M1 for Attempt at ∑f 5 (ii) 41.7 or 41.66 to 41.67 2 B1 for seen 12 (iii) 2.45 1

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4 180 cm NOT TO SCALE x cm 50 cm x cm 30 cm 20 cm 480 cm The diagram shows the cross section of a medal presentation platform. (a) Show that x = 150. Answer(a) [2] (b) Work out the perimeter of the cross section. Answer(b) .......................................... cm [2] (c) (i) Calculate the area of the cross section. Answer(c)(i) ......................................... cm2 [2] (ii) The platform is a prism, 170 cm deep. Find the volume of the platform. Answer(c)(ii) ......................................... cm3 [1] (iii) The prism is completely fi lled with a light material. 1 cubic metre of this material has mass 16 kg. Calculate the mass of the material used. Answer(c)(iii) ........................................... kg [2] __________________________________________________________________________________________

Mark scheme: 4 (a) x + x + 180 = 480 M1 M1 2x = 300 (b) 2 M1 for 2 × 480 + 2 × (20 + 30) oe 1060 [cm] (c) (i) 2 M1 for 30 × 150 + 50 × 180 + 20 × 16 500 150 oe (ii) 1FT FT their (c)(i) × 170 2 805 000 (iii) 44.9 or 44-88 2FT FT their (c)(ii) ÷ 100³ × 16 M1 for their (c)(ii) × 16

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5 (a) Write in fi gures six million three thousand and seventy six. Answer(a) ................................................ [1] (b) (i) Work out the value of p when p = –0.6 ÷ 1.6 . Answer(b)(i) p = ................................................ [1] (ii) Work out the value of q when q = –0.6 – 1.6 . Answer(b)(ii) q = ................................................ [1] (iii) Use one of the symbols >, <, [, Y, = to complete this statement. p ........................ q [1] (c) Mount Robson in Canada has a height of 3950 metres, correct to the nearest 10 metres. Complete the following statement about the height, h m, of Mount Robson. Answer(c) .................... Y h < .................... [2] 1 1 . (d) Calculate 2 ÷ 1 12 4 Give your answer as a decimal, correct to 4 signifi cant fi gures. Answer(d) ................................................ [2] (e) (i) Write down the value of 80. Answer(e)(i) ................................................ [1] (ii) Work out 5–3. Write your answer as a fraction. Answer(e)(ii) ................................................ [1] (iii) Simplify the expression. 8x5 × 3x4 Answer(e)(iii) ................................................ [2] __________________________________________________________________________________________

Mark scheme: 5 (a) 6 003 076 1 (b) (i) –0.375 1 (ii) –2.2 1 (iii) > 1FT FT their answers to (i) and (ii) (c) 3945, 3955 1, 1 SC1 for both correct but reversed 2 (d) 1.667 cao 2 B1 for 1 3 or better (e) (i) 1 1 1 (ii) 1 125 (iii) 24x9 2 B1 for 24xk or kx9

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6 (a) (i) Complete the table of values for y = 8 – x2. x –3 –2 –1 0 1 2 3 y –1 8 7 –1 [2] (ii) On the grid, draw the graph of y = 8 – x2 for –3 Y x Y 3 . y 12 11 10 9 8 7 6 5 4 3 2 1 x –3 –2 –1 0 1 2 3 –1 –2 –3 –4 [4] (iii) Write down the equation of the line of symmetry of the graph. Answer(a)(iii) ................................................ [1] (iv) Use your graph to solve the equation 8 – x2 = 0. Answer(a)(iv) x = .......................... or x = .......................... [2] (b) (i) On the grid, plot the points (–2, 8) and (2.5, –1). Draw a straight line through these points. [2] (ii) Find the equation of your line in the form y = mx + c. Answer(b)(ii) y = ................................................ [3] (iii) Write down the co-ordinates of the point of intersection of your line with y = 8 – x2. Answer(b)(iii) (..................... , .....................) [1] __________________________________________________________________________________________

Mark scheme: 6 (a) (i) 4, 7, 4 2 B1 for 2 correct (ii) 7 points correctly plotted 3FT B2 for 5 or 6 correct B1 for 3 or 4 correct Correct curve through the points 1 (iii) x = 0 1 (iv) 2.7 to 2.9, –2.7 to –2.9 1, 1 (b) (i) Points correctly plotted and a ruled line 2 B1 for 1 correct plot. (even if line is through points and beyond them. not drawn) (ii) [y =] –2x + 4 3 B2 for –2x + j or B1 for kx + 4 k ≠ 0 or [gradient =] riserun correct values (iii) 1 ( –1.2 to –1.4, 6.4 to 6.6)

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7 The scale drawing represents the positions of 3 towns, A, B and C. The scale is 1 centimetre represents 4 kilometres. North A B C Scale: 1 cm to 4 km (a) Measure the bearing of B from A. Answer(a) ................................................ [1] (b) A transmitter is placed near to the 3 towns. (i) The transmitter is equidistant from A and B. Using a straight edge and compasses only, construct the locus of points equidistant from A and B. [2] (ii) The transmitter is also on the bisector of angle ABC. Using a straight edge and compasses only, construct the bisector of angle ABC. [2] (iii) Mark the position, T, of the transmitter on the scale drawing. [1] (c) Work out the actual distance, in kilometres, of town A from T. Answer(c) .......................................... km [2] (d) The signal from the transmitter has a range of 30 kilometres in all directions. On the scale drawing, construct the locus of points 30 kilometres from T. [2] (e) Would the signal from the transmitter reach town C ? Give a reason for your answer. Answer(e) .................... because ......................................................................................................... ............................................................................................................................................................. [1] __________________________________________________________________________________________

Mark scheme: 7 (a) 106 to 110 1 (b) (i) Correct bisector of AB constructed with 2 2 B1 for correct bisector pairs of arcs. (ii) Correct bisector of angle ABC with arcs 2 B1 for correct bisector without arcs (iii) T marked at intersection of their bisectors 1FT (c) 24.4[km] to 26.0[km] 2FT FT their AT B1 for their AT correctly measured. (d) Circle, radius 7.5(±0.2)cm centre T. 2FT FT their intersection SC1 for circle centre T, incorrect radius. (e) No It is outside the circle. oe 1FT FT their circle.

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8 (a) One day a survey is taken of the ages of 120 children at a fairground. The results are shown in the frequency table. Age in completed years Number of children 1 to 3 12 4 to 6 19 7 to 9 32 10 to 12 41 13 to 15 9 16 to 18 7 (i) On the grid, draw a bar chart for this data. Complete the scale on the frequency axis. Frequency 1 to 3 4 to 6 7 to 9 10 to 12 13 to 15 16 to 18 Age in completed years [3] (ii) What is the modal age group? Answer(a)(ii) ................................................ [1] (iii) One of the 120 children is chosen at random. Write down the probability that the child is aged 4 to 6. Answer(a)(iii) ................................................ [1] (b) Lalia says the probability of taking a yellow bead from a bag containing yellow beads and black 7 beads is . 5 7 Explain why cannot be a correct probability. 5 Answer(b) ........................................................................................................................................... [1] (c) Another bag contains 9 green marbles and 11 red marbles. A marble is taken at random. Write down the probability that the marble is (i) green, Answer(c)(i) ................................................ [1] (ii) blue. Answer(c)(ii) ................................................ [1] __________________________________________________________________________________________ Question 9 is printed on the next page.

Mark scheme: 8 (a) (i) Correct diagram with scale 3 B1 scale correct. B1 for all widths the same B1 for all 6 heights correct (ii) 10 to 12 cao 1 19 (iii) or 0.158[3....] or 15.8[3......]% 1 120 (b) Probability must be between 0 and 1 oe 1 9 (c) (i) or 0.45 or 45% 1 20 (ii) 0 oe 1

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9 Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagrams 1 to 4 show a sequence of shapes made up of lines and dots at the intersections of lines. (a) (i) Complete the table showing the number of dots in each diagram. Diagram 1 2 3 4 5 6 Dots 3 8 13 [3] (ii) Write down the rule for continuing the sequence of dots. Answer(a)(ii) ............................................................................................................................... [1] (iii) Write down an expression, in terms of n, for the number of dots in Diagram n. Answer(a)(iii) ................................................ [2] (iv) Find the number of dots in Diagram 15. Answer(a)(iv) ................................................ [1] (b) The dots are joined by sloping lines and horizontal lines. (i) Diagram 1 has 2 sloping lines and Diagram 2 has 6 sloping lines. Find the number of sloping lines in Diagrams 3 and 4. Answer(b)(i) Diagram 3 ................................................ Diagram 4 ................................................ [2] (ii) Write down an expression, in terms of n, for the number of sloping lines in Diagram n. Answer(b)(ii) ................................................ [2]

Mark scheme: 9 (a) (i) 18 23 28 1, 1, 1 Allow one mark for each addition of 5 to the previous answer (ii) Add 5 oe 1 (iii) 5n – 2 oe 2 B1 for 5n + j or kn – 2 k ≠ 0 (iv) 73 1FT FT their (a)(iii) if linear. (b) (i) 10 14 1, 1 Allow 1 mark for addition of 4 on their value for 3rd diagram. (ii) 4n – 2 oe 2 B1 for 4n + j or kn – 2 k ≠ 0

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