Cambridge IGCSE Mathematics 0580 — 2015 Oct/Nov Paper 3 · Variant 1

1 (a) 120 children take part in an athletics competition. (i) Complete the table to show the number of children in each group. Girls Boys Total Age 15 65 Age 16 44 Total 70 120 [2] (ii) One child is selected at random. Find the probability that it is a girl aged 16. Give your answer as a fraction in its lowest terms. Answer(a)(ii) ................................................ [2] (iii) Write down the ratio number of girls aged 15 : number of boys aged 15. Give your answer in its simplest form. Answer(a)(iii) ....................... : ....................... [2] (b) Here are the distances, in metres, recorded in the boys’ shot putt. 9.23 6.21 9.86 8.64 7.15 7.72 9.01 7.34 6.53 6.89 (i) Find the median. Answer(b)(i) ............................................ m [2] (ii) Find the range. Answer(b)(ii) ............................................ m [1] (iii) Another boy was a late entry to the competition. After his attempt, the range increased by 20 cm. Work out the two possible distances of his attempt. Answer(b)(iii) .............................. m or .............................. m [2] __________________________________________________________________________________________

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 2 B1 for 3 or 4 correct 26 39 65 44 11 55 70 50 120 (ii) 11 cao 2 B1 for 44 or 22 30 120 60 (iii) 2 : 3 cao 2 B1FT for 2k : 3k where k is an integer or their 26 : their 39 or better with integer values (b) (i) 7.53 2 M1 for attempt at ordered list, or 7.34 and 7.72 identified (ii) 3.65 1 (iii) 10.06 6.01 2 B1 for 1 correct

More questions on Classifying statistical data

2 (a) Write down a number between 20 and 30 that is (i) a multiple of 6, Answer(a)(i) ................................................ [1] (ii) a square number, Answer(a)(ii) ................................................ [1] (iii) a cube number, Answer(a)(iii) ................................................ [1] (iv) a prime number. Answer(a)(iv) ................................................ [1] (b) Find (i) 3 4913 , Answer(b)(i) ................................................ [1] (ii) 35, Answer(b)(ii) ................................................ [1] (iii) 60, Answer(b)(iii) ................................................ [1] (iv) 2–4. Answer(b)(iv) ................................................ [1] (c) (i) Write 84 as a product of its prime factors. Answer(c)(i) ................................................ [2] (ii) Find the highest common factor (HCF) of 84 and 126. Answer(c)(ii) ................................................ [2] __________________________________________________________________________________________

Mark scheme: 2 (a) (i) 24 or 30 1 (ii) 25 1 (iii) 27 1 (iv) 23 or 29 1 (b) (i) 17 1 (ii) 243 1 (iii) 1 1

More questions on Types of number

3 (a) Luis buys a season ticket to watch his local football team. The season ticket costs $595. (i) Luis buys the season ticket online and gets a 5% discount on the $595. Work out how much Luis pays for the season ticket online. Answer(a)(i) $ ................................................. [2] (ii) A ticket to watch one match costs $38. Luis watches 16 matches. How much did Luis save by buying a season ticket online instead of 16 tickets at $38 each? Answer(a)(ii) $ ................................................. [2] (b) The football stadium has 26 272 seats. The number of people who attend one match is 23 854. Calculate the percentage of the 26 272 seats that are empty. Answer(b) ............................................ % [2] (c) The total number of people attending matches at the stadium last season was 506 762. Write 506 762 in standard form, correct to 3 significant figures. Answer(c) ................................................ [2] (d) Last season the team played a total of 45 matches. The table shows the results of these matches. Result Number of matches Pie chart sector angle Won 20 160° Drawn 15 Lost 10 (i) Complete the table. [3] (ii) Complete the pie chart. Won [1] (e) The table shows the total attendance figures for all the teams in the league for two seasons. Season Total attendance A 9.76 × 106 B 1.36 × 107 Work out how much greater the attendance was in season B than in season A. Give your answer in standard form. Answer(e) ................................................ [2] __________________________________________________________________________________________

Mark scheme: 3 (a) (i) 565.25 2 M1 for − 1 5  × 595 oe  100  (ii) 42.75 2FT 2FT if positive difference (ie (a)(i) < 608) M1 for 38 × 16 (or 608) – their (a)(i) (b) 9.2[0…] 2 M1 for  26272 − 23854  × 100 oe or  26272  − 1 23854  × 100 oe or  26272  23854 100 − × 100 oe 26272 (c) 5.07 × 105 cao 2 B1 for figs 507 or for a × 105 (a ≠ 0) (d) (i) 120° 3 B2 for one correct 80° 15 10 160 or M1 for × 360 or × 360 or × 15 45 45 20 160 or × 10 or better 20 (ii) Pie chart correct 1FT FT if their angles add to 200° (e) 3.84 × 106 2 B1 for answer figs 384

More questions on Percentages

4 Three friends are going on holiday. They travel by plane. (a) Ahmed’s suitcase has mass m kilograms. (i) The mass of Sonia’s suitcase is 5 kg more than the mass of Ahmed’s suitcase. Write down an expression, in terms of m, for the mass of Sonia’s suitcase. Answer(a)(i) ............................................ kg [1] (ii) The mass of Hala’s suitcase is twice the mass of Ahmed’s suitcase. Write down an expression, in terms of m, for the mass of Hala’s suitcase. Answer(a)(ii) ............................................ kg [1] (iii) The total mass of the three suitcases is 47 kg. Write down an equation in terms of m. Answer(a)(iii) ............................................................ [1] (iv) Solve your equation and find the mass of each suitcase. Answer(a)(iv) Ahmed’s suitcase ........................................... kg Sonia’s suitcase ........................................... kg Hala’s suitcase ........................................... kg [3] (b) Each friend carries one bag of hand luggage onto the plane. (i) The rule for the maximum size of each bag of hand luggage is length + width + height  115 cm. The measurements of Ahmed’s bag are shown in the table. Length Width Height 550 mm 395 mm 200 mm Can Ahmed carry this bag onto the plane? Explain your answer. Answer(b)(i) ......................... because ........................................................................................ ..................................................................................................................................................... [2] (ii) The mass of Ahmed’s bag is 5 kg, correct to the nearest kilogram. Write down the upper bound of the mass of his bag. Answer(b)(ii) ........................................... kg [1] (c) The friends change money from dollars into euros (€) to spend on holiday. The exchange rate is $1 = €0.68 . (i) Sonia changes $150 into euros. Work out how many euros she receives. Answer(c)(i) € ................................................. [1] (ii) Hala pays €25.50 for a meal. Work out how much this is in dollars. Answer(c)(ii) $ ................................................. [2] __________________________________________________________________________________________

Mark scheme: 4 (a) (i) m + 5 1 (ii) 2m 1 (iii) m + m + 5 + 2m = 47 isw 1FT FT m + their (a)(i) + their (a)(ii) = 47 isw or 4m + 5 = 47 isw (iv) 10.5 3 M1FT for correct first step to solve their (a)(iii) 15.5 A1FT for m = 10.5 21 (b) (i) Yes, [total = ] 114.5 [cm] 2 M1 for 55 + 39.5 + 20 oe or for 1145 mm (ii) 5.5 1 (c) (i) 102 1 (ii) 37.5[0] 2 M1 for 25.5[0] ÷ 0.68

More questions on Introduction to algebra

5 The scale drawing shows two villages, A and B, joined by a straight road. The scale is 2 centimetres represents 1 kilometre. North A North B Scale: 2 cm to 1 km (a) (i) Work out the distance, in kilometres, from A to B. Answer(a)(i) .......................................... km [2] (ii) Measure the bearing of B from A. Answer(a)(ii) ................................................ [1] (b) Another village, C, is 3.2 km from A on a bearing of 310°. Mark and label the position of C on the diagram. [2] (c) In this part use a straight edge and compasses only and show your construction arcs clearly. Construct the perpendicular bisector of AB. [2] (d) A school is • closer to village A than to village B and • less than 3 kilometres from village B. On the diagram, shade the region in which the school must be. [3] (e) Nelson cycles from village B to the nearest town. He cycles a total distance of 12 km at an average speed of 15 km/h. He leaves village B at 10 15. Work out the time he arrives at the nearest town. Answer(e) ................................................ [3] __________________________________________________________________________________________

Mark scheme: 5 (a) (i) 4.8 2 B1 for 9.6 seen (ii) 137 1 (b) Correct length and bearing 2 B1 for AC = 6.4 cm B1 for correct bearing 310° (c) Perpendicular bisector with 2 sets 2 B1 for correct line with some or no or incorrect of correct arcs arcs or B1 for 2 sets of correct arcs (d) Correct area shaded 3 B2 for arc centre B radius 6 cm touching their bisector twice or B1 for arc centre B, with radius 6 cm but incorrect length or for arc centre B, with incorrect radius (e) 11 03 3 M2 for 12 ÷ 15 × 60 or M1 for 12 ÷ 15 soi If zero scored, SC1 for their time added to 10 15 correctly

More questions on Scale drawings

6 Irina has some solid building blocks. (a) Write down the mathematical name of this solid. Answer(a) ................................................ [1] (b) Irina describes the shape of a different block. She says: It has 12 edges and 8 vertices. All the faces are the same shape. Write down the mathematical name of this solid. Answer(b) ................................................ [1] (c) The diagram shows the end face of another block. A NOT TO 6 cm SCALE 3 cm B C (i) Show that BC = 5.2 cm, correct to 1 decimal place. Answer(c)(i) [3] (ii) Find the area of triangle ABC. Answer(c)(ii) ......................................... cm2 [2] (iii) This block is a triangular prism with length 8 cm. Calculate the volume of the block. Answer(c)(iii) ......................................... cm3 [1] (d) The diagram shows another building block. NOT TO SCALE 6 cm 4 cm x cm 8 cm (i) Calculate the area of the end face of this block. Answer(d)(i) .........................................cm2 [2] (ii) The volume of this block is 336 cm3. Find the value of x. Answer(d)(ii) x = ................................................ [1] __________________________________________________________________________________________

Mark scheme: 6 (a) Cylinder 1 (b) Cube or cuboid 1 (c) (i) 6 2 − 3 2 M2 M1 for 62 = 32 + BC2 or (BC2 = ) 62 – 32 5.19… A1 (ii) 7.79 to 7.8 2 M1 for 0.5 × 5.2 × 3 (iii) 62.4 1FT FT 8 × their (c)(ii) (d) (i) 28 2 M1 for 0.5 × (6 + 8) × 4 oe (ii) 12 1FT FT 336 ÷ their (d)(i)

More questions on Pythagoras’ theorem

67 (a) The table shows some values of y = . x x –5 –4 –3 –2 –1 1 2 3 4 5 y –1.2 –1.5 6 2 1.5 1.2 (i) Complete the table. [2] 6 (ii) On the grid, draw the graph of y = for –5  x  –1 and 1  x  5. x y 6 5 4 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 –4 –5 –6 [4] (iii) On the same grid, draw the line y = 4. [1] 6 (iv) Find the co-ordinates of the point where the line y = 4 crosses the graph of y = . x Answer(a)(iv) (.................. , ..................) [1] (b) y 5 4 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 –4 –5 (i) On this grid, plot the point A (–1, –3). [1] (ii) Draw a line with gradient 2 through point A. [1] (iii) Write down the equation of your line in the form y = mx + c. Answer(b)(iii) y = ................................................ [2] __________________________________________________________________________________________

Mark scheme: 7 (a) (i) –2, –3, –6, 3 2 B1 for 2 or 3 correct (ii) Correct curves 4 B3FT for 9 or 10 correctly plotted points or B2FT for 7 or 8 correctly plotted points or B1FT for 5 or 6 correctly plotted points (iii) Ruled line y = 4 1 (iv) (1.4 to 1.6, 4) 1 SC1 for (4, 1.4 to 1.6) from line x = 4 drawn (b) (i) (–1, –3) plotted 1 (ii) Correct ruled line 1FT FT line with gradient 2 through their A (iii) 2x – 1 2FT FT 2x + their y-intercept for 2 marks B1 for 2x + k or mx – 1 (m ≠ 0) or mx + their y-intercept (m ≠ 0)

More questions on Fractions, decimals and percentages

8 (a) (i) Write down the order of rotational symmetry of this shape. Answer(a)(i) ................................................ [1] (ii) Draw the lines of symmetry on the shape. [2] (b) y 7 6 P 5 4 3 A 2 1 x –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 B –5 –6 –7 (i) On the grid, reflect triangle A in the line x = –1. [2] (ii) On the grid, enlarge triangle A with centre P and scale factor 3. [2] (iii) Describe fully the single transformation that maps triangle A onto triangle B. Answer(b)(iii) .............................................................................................................................. ..................................................................................................................................................... [3] __________________________________________________________________________________________

Mark scheme: 8 (a) (i) 2 1 (ii) Two correct lines of symmetry 2 B1 for one correct line drawn (b) (i) Correct reflection 2 B1 for reflection in x = k or y = –1 (ii) Correct enlargement 2 B1 for correct shape, incorrect position or enlargement correct centre, incorrect scale factor (iii) Rotation B1 90° clockwise oe B1 [Centre] (0, 0) oe B1

More questions on Symmetry

9 (a) Expand and simplify. 2(3x + 2) – 4(x + 1) Answer(a) ................................................ [2] (b) Factorise completely. 3y2 – 6y Answer(b) ................................................ [2] (c) Make b the subject of the formula. b a = – 5 4 Answer(c) b = ................................................. [2] (d) Solve the simultaneous equations. You must show all your working. 3x + 2y = 11 6x – y = 32 Answer(d) x = ................................................ y = ................................................ [3] __________________________________________________________________________________________

Mark scheme: 9 (a) 2x final answer 2 M1 for 6x + 4 or –4x – 4 (b) 3y(y – 2) final answer 2 B1 for 3(y2 – 2y) or y(3y – 6) (c) 4a + 20 or 4(a + 5) 2 M1 for a + 5 = b or 4a = b – 20 4 (d) Correct working and 3 M1 for correctly eliminating one variable [x =] 5, [y =] –2 A1 for x = 5 A1 for y = –2 If zero scored, SC1 for 2 values satisfying one of the original equations SC1 if no working shown, but 2 correct answers given

More questions on Equations