Cambridge IGCSE Mathematics 0580 — 2015 May/June Paper 3 · Variant 2

1 (a) 4 3 0 2 9 5 7 From the list above, write down (i) the factors of 24, Answer(a)(i) ................................................ [1] (ii) a prime factor of 24, Answer(a)(ii) ................................................ [1] (iii) the highest common factor (HCF) of 56 and 91, Answer(a)(iii) ................................................ [1] (iv) the square root of 49, Answer(a)(iv) ................................................ [1] (v) the cube root of 27. Answer(a)(v) ................................................ [1] (b) (i) Using four numbers from the list in part (a), form the largest 4-digit number. Answer(b)(i) ................................................ [1] (ii) Write your answer to part (b)(i) in words. Answer(b)(ii) ............................................................................................................................... ..................................................................................................................................................... [1] (c) Find (i) the common multiple of 5 and 8 between 100 and 150, Answer(c)(i) ................................................ [1] (ii) the square number between 350 and 390. Answer(c)(ii) ................................................ [1] __________________________________________________________________________________________

Mark scheme: Qu Answer Mark Part answers 1 (a) (i) 2, 3, 4 1 (ii) 2 or 3 1 (iii) 7 1 (iv) 7 1 (v) 3 1 (b) (i) 9754 1 (ii) Nine thousand seven hundred [and] 1FT FT their (b)(i) provided it has at least four fifty four figures (c) (i) 120 1 (ii) 361 1

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2 (a) Simplify. 7e – 5f + 4e – f Answer(a) ................................................ [2] (b) Find the value of 8g – 9h when g = 5 and h = –3. Answer(b) ................................................ [2] (c) Solve the equation. 4x – 7 = 29 Answer(c) x = ................................................ [2] (d) Simplify. k 4 ÷ k 11 Answer(d) ................................................ [1] (e) Pens cost p cents and pencils cost w cents. (i) Aisha buys 3 pens and 5 pencils for $2.20 . Complete the equation representing this cost in cents. Answer(e)(i) 3p + 5w = ................................................ [1] (ii) Bishen buys 4 pens and 10 pencils for $3.50 . Write down an equation representing this cost in cents. Answer(e)(ii) .................................................................. [1] (iii) Solve your equations to find the value of p and the value of w. Answer(e)(iii) p = ................................................ w = ................................................ [3] __________________________________________________________________________________________

Mark scheme: 2 (a) 11e – 6f as final answer 2 B1 for either 11e or –6f in their final answer (b) 67 2 B1 for 8 × 5 – 9 × –3 or 40 or +27 (c) 9 2 M1 for algebraic first step correct 4x = 29 + 7 7 29 or x – = or better 4 4 (d) k–7 oe 1 (e) (i) 220 1 (ii) 4p + 10w = 350 1 (iii) [p =] 45, [w =] 17 3 M1FT for correct elimination of one variable from their equations A1 for p = 45 A1 for w = 17 If zero scored, SC1FT for 2 values satisfying one of their original equations

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3 A NOT TO SCALE O C B D E The diagram shows a circle, centre O and diameter AD. B is on the circumference of the circle and the line CDE touches the circle at D. AD = 21 cm and CD = 16 cm. (a) Calculate (i) the circumference of the circle, Answer(a)(i) .......................................... cm [2] (ii) the area of the circle. Answer(a)(ii) ......................................... cm2 [2] (b) (i) Write down the size of angle ABD. Answer(b)(i) Angle ABD = ................................................ [1] (ii) BD = 9 cm. Show that AB = 19.0 cm, correct to 3 significant figures. Answer(b)(ii) [3] (c) (i) Calculate the area of triangle ABD. Answer(c)(i) ......................................... cm2 [2] (ii) Work out the total area of the shaded segments of the circle. Answer(c)(ii) ......................................... cm2 [2] (d) (i) Write down the mathematical name of the line CDE. Answer(d)(i) ................................................ [1] (ii) Write down the mathematical name of the line OD. Answer(d)(ii) ................................................ [1] (iii) Use trigonometry to calculate the size of angle OCD. Answer(d)(iii) Angle OCD = ................................................ [2] __________________________________________________________________________________________

Mark scheme: 3 (a) (i) 66.0 or 65.97 to 65.98 … 2 M1 for π × 21 (ii) 346 or 346.3 to 346.4 … 2 M1 for π × (21 ÷ 2)2 (b) (i) 90 1 (ii) ( 212 − 9 2 ) M2 M1 for 212 = AB2 + 92 or [AB2] = 212 – 92 18.97(……) A1 (c) (i) 85.5 2 M1 for 0.5 × 19 × 9 (ii) 87.5 or 87.65 to 87.823 2FT M1FT for 0.5 × their (a)(ii) (d) (i) Tangent 1 (ii) Radius 1 ( 21 ÷ 2 ) (iii) 33.3 or 33.27(……) 2 M1 for tan[ ] = or better 16

More questions on Circles, arcs and sectors

4 (a) (i) Complete the table of values for y = 8 + 3x – x2. x 0 1 2 3 4 5 y 8 10 8 4 [2] (ii) On the grid, draw the graph of y = 8 + 3x – x2 for 0 G x G 5 . y 12 11 10 9 8 7 6 5 4 3 2 1 0 x 1 2 3 4 5 –1 –2 –3 – 4 [3] (iii) Write down the co-ordinates of the highest point of the graph. Answer(a)(iii) (...................... , ......................) [1] 12 . (b) (i) Complete the table of values for y = x x 1 2 3 4 5 y 12 4 2.4 [2] 12 (ii) On the same grid, draw the graph of y = for 1 G x G 5 . [3] x 12 . (c) Use your graphs to write down the solutions of the equation 8 + 3 x - x 2 = x Answer(c) x = ...................... or x = ...................... [2] __________________________________________________________________________________________

Mark scheme: 4 (a) (i) 10 −2 1, 1 (ii) 6 points correctly plotted 3 B2FT for 5 or 6 points correctly plotted correct smooth curve or B1FT for 3 or 4 points correctly plotted (iii) (1.4 to 1.6, 10.1 to 10.4) 1 (b) (i) 6 3 1, 1 (ii) 5 points correctly plotted 3 B2FT for 4 or 5 points correctly plotted correct curve or B1FT for 2 or 3 correct points (c) 1.1 to 1.3 4.1 to 4.3 1FT, 1FT

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5 y 10 9 8 7 6 5 4 3 C 2 1 x –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 –2 –3 –4 A –5 –6 B –7 –8 –9 –10 (a) For the shaded quadrilateral, write down (i) its mathematical name, Answer(a)(i) ................................................ [1] (ii) the number of lines of symmetry. Answer(a)(ii) ................................................ [1] (b) The quadrilaterals are drawn on a 1 cm2 grid. Work out the area of the shaded quadrilateral. Answer(b) ......................................... cm2 [1] (c) Describe fully the single transformation that maps the shaded quadrilateral onto (i) quadrilateral A, Answer(c)(i) ................................................................................................................................ ..................................................................................................................................................... [2] (ii) quadrilateral B, Answer(c)(ii) ............................................................................................................................... ..................................................................................................................................................... [2] (iii) quadrilateral C. Answer(c)(iii) .............................................................................................................................. ..................................................................................................................................................... [3] (d) On the grid, draw the image of the shaded quadrilateral after a rotation of 90° clockwise about the origin. [2] __________________________________________________________________________________________

Mark scheme: 5 (a) (i) Kite 1 (ii) 1 1 (b) 12 1 (c) (i) Translation 1  7  1    −9  (ii) Reflection 1 y = −1 oe 1 (iii) Enlargement 1 1 1 [Scale Factor] 2 1 [Centre] (−6, 0) (d) Correct rotation 2 B1 for a ‘correct’ rotation of 90° anti- clockwise or correct orientation but wrong position 1 1 6 (a) (i) 3 × 60 [= 195] 4 (ii) 22 45 2 B1 for [Total time =] 6 [hours] 30 [minutes] or 1 6 [hours] or 390 [minutes] 2 or M1 for adding to 16 15 their attempt at 1 1 3 + 2 + 45 4 2 (iii) 13 : 10 : 3 2 B1 for 3 1 : 2 1 : 3 or 195 : 150 : 45 or 4 2 4 better or SC1 for 13,10,3 in the wrong order in a ratio (b) (i) 78 1 (ii) 30 1 (iii) 87 1FT 195 – (their (b)(i) + their (b)(ii)) 22 5. − 20 7. (c) 8 3 M2 for × 100 or better 22 5. or B1 for 22.5 – 20.7

More questions on Area and perimeter

7 A machine produces nails. (a) A random sample of 100 nails is taken from the machine. The lengths are measured and recorded in the table. Length (mm) 62 63 64 65 66 67 68 Number of nails 0 12 30 35 8 0 (i) Complete the table. [1] (ii) Write down the modal length. Answer(a)(ii) ......................................... mm [1] (iii) Write down the range of the lengths. Answer(a)(iii) ......................................... mm [1] (iv) Calculate the mean length. Answer(a)(iv) ......................................... mm [3] (v) Nails that have length 64 mm, 65 mm or 66 mm are accepted. Other nails are rejected. Number of nails accepted 80 Number of nails rejected 20 Complete the pie chart to show the proportion of nails that are accepted and rejected. [3] (b) One nail from the machine measures 65 mm, correct to the nearest millimetre. Complete the statement about the length, n mm, of this nail. Answer(b) ........................ G n 1 ........................ [2] __________________________________________________________________________________________

Mark scheme: 7 (a) (i) 15 1 (ii) 65 1 (iii) 4 1 (iv) 64.77 or 64.8 3 M1FT for 63 × 12 + 64 × 30 + 65 × 35 + 66 × their 15 + 67 × 8 M1FT dep for their total ÷ 100 (v) Line at 72° to the given line 3 M2 for 288° or 72° or 80 20 M1 for × 360 or × 360 100 100 (b) 64.5 65.5 1, 1 If zero scored, SC1 for correct but wrong way round

More questions on Averages and range

8 The scale drawing shows one side, AB, of a 4-sided field. The scale is 1 centimetre represents 20 metres. North B A Scale: 1 cm to 20 m (a) (i) Work out the actual distance AB. Answer(a)(i) AB = ............................................ m [2] (ii) Measure the bearing of B from A. Answer(a)(ii) ................................................ [1] (b) In this part use a ruler and compasses only and show your construction arcs clearly. Point C is 240 m from A and 140 m from B. On the scale drawing, construct the position of point C. [2] (c) Point D is 200 m on a bearing of 135° from A. On the scale drawing, draw accurately the line AD. [3] (d) Work out the actual perimeter of the field ABCD. Answer(d) ............................................ m [3] __________________________________________________________________________________________ Question 9 is printed on the next page.

Mark scheme: 8 (a) (i) 116 2 B1 for 5.8 seen (ii) [0]65 1 (b) Correct construction of point C with 2 B1 for correct position but no arcs or arcs incorrect arcs or B1 for one correct arc (c) Correct point D with AD drawn 3 B1 for [bearing] 135° B1 for [AD =] 10 cm (d) 630 [m] to 646 [m] 3 M2FT for their (a)(i) + 140 + 200 + their CD × 20 M1FT for their CD or their CD × 20

More questions on Scale drawings

9 Nina is going on a holiday to Dubai from her home in Mumbai. (a) At the airport she buys 2 packets of sandwiches and 3 magazines. Complete her shopping bill in Indian rupees. 2 packets of sandwiches at 325 rupees per packet = .......................... rupees 3 magazines at 75 rupees per magazine = .......................... rupees Total = .......................... rupees [3] (b) She changed 10 000 rupees to dirhams when the exchange rate was 18.3 rupees = 1 dirham. How much did she receive? Answer(b) .................................. dirhams [2] (c) The flight from Mumbai to Dubai takes 2 hours 50 minutes. The distance from Mumbai to Dubai is 1937 km. (i) Show that the average speed of the flight is 684 km / h, correct to the nearest whole number. Answer(c)(i) [2] (ii) Nina’s flight leaves Mumbai at 13 15. 1 The local time in Mumbai is 1 2 hours ahead of the local time in Dubai. Find the time of arrival in Dubai. Give your answer in the 24-hour clock. Answer(c)(ii) ................................................ [2]

Mark scheme: 9 (a) 650 1 225 1 875 1FT (b) 546 or 546.4 or 546.44 or 546.45 2 M1 for 10 000 ÷ 18.3 (c) (i) 1937 ÷ 2.83[3…] or M1 1937 ÷ 170 × 60 683.6 to 684.4..... A1 but not 684 (ii) 14 35 2 B1 for 16 05 [time in Mumbai on arrival] or B1 for 11 45 [time in Dubai on departure from Mumbai] or M1 for 2 hours 50 mins – 1 hour 30 mins + 1315 or SC1 for answer 2 35pm

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