Scale drawings — Paper 3 · IGCSE Mathematics 0580

7 For C Examiner's Use R Sea North North Land 14 km A B At midday, a ship is somewhere along the line from A to C. (a) By measuring an angle, write down the three figure bearing of the ship from A. Answer(a) [2] (b) The coastguard at B sees the ship on a bearing of 350o. (i) On the diagram draw accurately the line showing a bearing of 350o from B. [1] (ii) On the diagram mark the position of the ship, S. [1] (c) (i) Measure the length, in centimetres, of the line AB on the diagram. Answer(c)(i) cm [1] (ii) The distance from A to B is 14 kilometres. Calculate the scale of the drawing. Give your answer in the form 1:n. Answer(c)(ii) 1: [2] (d) The ship is sailing straight for the rocks, R. For There is a lighthouse at A. Examiner's The range of the light from the lighthouse is 10 kilometres. Use (i) Using your scale, draw the locus of points that are 10 kilometres from A. [2] (ii) Draw the line SR on the diagram. How far is the ship from the rocks when the light from the lighthouse is first seen on the ship? Answer(d)(ii) km [2] (e) If the ship does not alter course it will hit the rocks at 12 40. A lifeboat sets off from the coastguard station, B, at 12 00 and sails straight towards the rocks. (i) Measure and calculate the distance, in kilometres, from the coastguard station, B, to the rocks, R. Answer(e)(i) km [2] (ii) Calculate the speed, in kilometres per hour, at which the lifeboat must sail to reach the rocks by 12 40. Answer(e)(ii) km/h [3] (iii) A knot is 1 nautical mile per hour. One nautical mile is equal to 1.85 kilometres. Calculate the speed found in part (e)(ii) in knots. Answer(e)(iii) knots [2]

18 marks

Mark scheme: 7 (a) 050 ( ± 2) 2 M1 for correct angle but not 3 figures i.e. 50 ( ± 2 ) (b) (i) correct line drawn 1 length at least 3 cms long ( ± 2) (ii) correct position 1 f.t. f.t is from line drawn in (b)(i) marked ( ± 2 mm) but must be on the line AC (c) (i) 7 ( ± 2 mm) 1 (ii) 200000 2 c.a.o. 1 for figs 2 or SC1 for figs 1.94 to 2.06 IGCSE – JUNE 2005 0580/0581 3 (d) (i) correct locus drawn 2 f.t. f.t. is for their scale (normally 5 cm) at least over sea allow dotted/dashed locus SC1 for any other circle with centre A drawn SC1 for ¼ correct circle over sea (ii) correct line SR 1 f.t. f.t. is for their S allow dotted/dashed line drawn 5 to 6 incl. 1 no f.t. on this part (e) (i) 18.6 to 19.4 incl. 2 SC1 for 9.3 to 9.7 incl. seen (ii) 27.9 to 29.1 incl. 3 M1 for conversion of minutes to hours (min of 0.66, 0.67 if dec.) M1 (indep) f.t. for their distance (e)(i)/their time taken (iii) 15.4 2 f.t. f.t. is (e)(ii)/1.85 M1 for (e)(ii)/1.85 seen 18

This question in 0580/31 May/June 2005

5 For North Examiner's Use A 110o 6 km 5 km NOT TO C SCALE B In triangle ABC, AB = 5 km, AC = 6 km and angle BAC = 110º. The bearing of C from A is 100°. (a) Make a scale drawing of the triangle ABC. Use a scale of 1 centimetre to represent 1 kilometre. Start at the point A marked below, where a North line has been drawn. North A [4] (b) Measure and write down For Examiner's (i) angle ABC, Use Answer(b)(i) Angle ABC = [1] (ii) the bearing of B from C. Answer(b)(ii) [1] (c) Find the distance in kilometres between B and C. Answer(c) km [1] (d) A well is 4 kilometres from A and 5 kilometres from C. (i) Use your compasses to find two possible positions for the well. Label the two positions P and Q. [3] (ii) The well is less than 6 kilometres from B. Use a measurement from your drawing to complete the following statement. Answer(d)(ii) The well is at position and is kilometres from B.[2]

12 marks

Mark scheme: 5 (a) bearing 99 to 101° B1 drawn angle BAC 109 to 111° B1 drawn AB 4.9 to 5.1 cm B1 AC 5.9 to 6.1 cm B1 (b) (i) 37 to 40 1√ (ii) 247 to 250 1√ ft from (b)(i) (c) 8.9 to 9.1 1√ (d) (i) Two positions found, 3 2 for two positions without arcs with appropriate arcs and labelled 1 for one position found and labelled (ii) P or Q 1 4.0 to 4.4 √1 ft for correct measurement of their closest position to B [12] IGCSE – NOVEMBER 2005 0580/0581 3

This question in 0580/31 Oct/Nov 2005

9 The sketch shows the positions of three islands A, B and C. For B is 150 kilometres due West of A. Examiner's C is 110 kilometres due North of A. Use C North NOT TO 110 km SCALE B A 150 km (a) Using a scale of 1 centimetre to represent 20 kilometres draw accurately the triangle ABC. A is marked for you. A [3] (b) A boat sets out from B to sail directly to C. (i) Use your protractor to find the three-figure bearing of B from C. Answer(b) (i) [2] (ii) Measure BC on your diagram and hence find the distance in kilometres of B from C. For Examiner's Use Answer(b) (ii) km [2] (iii) The boat sails at 20 knots. [1 knot is 1.85 kilometres per hour.] How long will the boat take for the first 100 kilometres of the journey? Give your answer in hours and minutes, to the nearest minute. Answer(b) (iii) hours min [4] (iv) The boat takes 45 minutes for the next 18 kilometres. Calculate this speed in kilometres per hour. Answer(b) (iv) km/h [2] (v) A radio beacon at A has a range of 100 kilometres. On your diagram in part (a) draw accurately the locus of points that are 100 kilometres from A. [2] (vi) For how many kilometres is the boat within range of the beacon? Answer(b) (vi) km [2]

17 marks

Mark scheme: 9 (a) Correct accurate drawing. 3 M1 for angle = 90° = BAC. (lengths ± 0.2 cm, angles ± 1°) M1 for AB = 7.5cm and AC = 5.5 cm. A1 for completed triangle. (Dependent on at least one M) (b) (i) 233° to 235° 2ft From their diagram. M1 for their angle BCA measured correctly (± 1°) (ii) 182 to 190 2ft Their BC × 20. M1 for their BC (correct is 9.1 cm to 9.5 cm) (iii) 2 (hours) 42 (mins) 4 SC3 for 2.7(0….) M1 for 20 × 1.85 M1 for 100 ÷ their 37 SC2 for 2 hr 7 mins with no method. B1 for their time correctly changed to hours and minutes. (iv) 24 2 M1 for 18 ÷ 0.75 oe (v) Correct circle drawn 2 M1 for partial circle (crossing AB and AC) (vi) 84 to 100 2ft M1 for 4.2 to 5.0 Follow through their diagram, dependent on intersections seen on BC 17 Total marks 104

This question in 0580/31 Oct/Nov 2006

9 In this question, all construction arcs must be shown clearly. For Examiner's Jalal buys an area of land on which to build a school. Use The land, ABCDE, is in the shape of a polygon with 5 sides. (a) Write down the mathematical name of this polygon. Answer(a) [1] (b) Jalal starts to make an accurate plan of the land, as shown below. He uses a scale of 1 centimetre to represent 10 metres. D A m 45 m B C 70 m (i) The actual lengths of AB and BC are written on the plan. Write the actual length of CD on the plan. [1] (ii) Use compasses to find the point E such that AE = 64 m and DE = 58 m. Draw the lines AE and DE. [2] (c) The land is to be divided into distinct regions. For Examiner's Construct, using a straight edge and compasses only, Use (i) the perpendicular bisector of BC, [2] (ii) the bisector of angle ABC. [2] (d) The music department building will be nearer to B than to C and nearer to BC than to BA. Write a letter M on the plan where the music department could be. [1] (e) The school gate, PQ, will be 8 metres wide. It will lie along AB so that AP = QB. Mark P and Q accurately on the plan. [2]

11 marks

Mark scheme: 9 (a) Pentagon B1 (b) (i) 61 to 63 B1 (ii) AE = 6.3 to 6.5 cm and DE = 5.7 to 5.9 cm B1 correct arcs seen B1 accept concave polygon SC1 if lengths reversed and with arcs (c) (i) perpen.bisector of BC B1 +/- 1mm and +/- 1 degree accuracy correct arcs seen B1 (ii) bisector of angle ABC B1 +/- 1 degree accuracy correct arcs seen B1 (d) "M" correctly marked B1 dep. on at least first B1 in each part of (c) (e) 2 marks 0.8 (+/-0.1) apart B1 1.85 (+/-0.1) from A and B B1 [11]

This question in 0580/31 May/June 2008

3 Here is a scale drawing of a shop floor, EFGH. For The scale is 1 centimetre represents 2 metres. Examiner's Use F G H Scale: 1 cm to 2 m E (a) What is the mathematical name of the shape EFGH? Answer(a) [1] (b) What type of angle is angle EFG? Answer(b) [1] (c) Find the actual length, in metres, of the side EH. Answer(c) m [2] (d) Measure angle FEH. Answer(d) Angle FEH = [1] (e) Complete this part using ruler and compasses only. All construction arcs must be clearly shown. A table is placed • nearer to E than to H and • less than 14 m from H. By constructing two loci on the scale drawing, find and label the region R, where the table is placed. [5] (f) The shop sells shoes which are packed in boxes. Each box is a cuboid 33.2 cm long, 16.8 cm wide and 11 cm high. Calculate the volume of one of these shoe boxes. Answer(f) cm3 [2]

12 marks

Mark scheme: 3 (a) quadrilateral 1 (b) obtuse 1 (c) 23.6–24.4 2 M1 for 11.8 – 12.2 (d) 31–35 1 (e) construction of perpendicular 5 B1 for two pairs of arcs, same radius, centres E bisector of EH and H part circle centre H radius 7 cm B1 for bisector within 2mm of correct one, ± 2° of indication of region correct angle B1 for part circle centre H B1 for radius 7 cm B1ft for an indication of the region, ft dependent on at least B2 from above (f) 6135.36 or 6135.4 or 6135 or 6140 2 M1 for 33.2 × 16.8 × 11

This question in 0580/33 May/June 2012

5 For B 20 m C Examiner's Use NOT TO SCALE 15 m A 32 m D The diagram shows a plot of land, ABCD, in the shape of a trapezium. (a) Show that CD = 19.2 m, correct to 1 decimal place. Answer(a) [2] (b) A fence is built around the perimeter of the plot of land. The cost of the fence is $35 for each metre. Calculate the total cost of the fence. Answer(b) $ [2] (c) Calculate the area of the plot of land. Give your answer in square metres. Answer(c) m2 [2] (d) A house is built on the plot of land. For The area of the plot is divided in the ratio house : grounds = 3 : 7 . Examiner's Use Calculate the area of the grounds. Answer(d) m2 [2] (e) (i) In the space below, make a scale drawing of the plot of land. Use a scale of 1 centimetre to represent 4 metres. The side AB has been drawn for you. B A [2] (ii) Measure angle ADC. Answer(e)(ii) Angle ADC = [1] (iii) Use your diagram to find the actual length BD in metres. Answer(e)(iii) BD = m [1]

12 marks

Mark scheme: 5 (a) (CD2 =) (32 – 20)2 + 152 oe M1 (CD =) 369 = 19.20 to 19.21 A1 A0 for 19.2 alone. 2 M1 for 20 + 15 + 32 + 19.2(1) [implied by (b) 3017 86.2(1)] Or M1 for (20 × 35) + (15 × 35) + (32 × 35) + (19.2(1) × 35) 2 M1 for (20 + 32) × 15 ÷ 2 oe (c) 390 2ft M1 for ‘their (c)’ × 7 ÷ 10 (d) 273 2 B1 for C or D correctly positioned (e) (i) trapezium constructed BC = 5 cm, AD = 8 cm Both 90o to AB 1ft (ii) 49 – 53° 1ft (iii) 34.4 – 36.4 m

This question in 0580/31 Oct/Nov 2012

7 The diagram shows the plan of a field QRST. For The scale is 1 centimetre represents 10 metres. Examiner's Use S T Q R Scale: 1 cm = 10 m (a) Nothing is grown within 35 metres of T. Construct the boundary, inside QRST, of the region where nothing is grown. [2] (b) Use a straight edge and compasses only for the constructions in parts (b)(i) and (b)(ii). For Leave in all your construction arcs. Examiner's Use (i) Construct the bisector of angle RQT. Draw your line to meet the side ST. [2] (ii) Construct the locus of points equidistant from Q and from R. Draw your line to meet the side ST. [2] (c) Flowers are grown in the region • nearer to QR than to QT and • nearer to Q than to R. (i) Label this region F. [1] (ii) Calculate the actual area in which flowers are grown. Give your answer in square metres. Answer(c)(ii) m2 [4]

11 marks

Mark scheme: 7 (a) Arc of circle 3.5 cm from T. 2 M1 for any arc, centre T. (b) (i) Correct construction with 4 2 B1 for correct but without 4 arcs correct arcs (ii) Bisector of QR with 2 pairs of 2 B1 for correct but without 2 pairs of arcs arcs. (c) (i) F in correct region 1dep Dependent on at least B1 and B1 in (b) IGCSE – October/November 2012 0580 32 (ii) 1200 to 1700 (m2) 4dep Dependent on at least B1 and B1 in (b) If at least B1 and B1 in (b) then B1 for base 33 Y b Y 37(m) or 3.3 Y b Y 3.7(cm) B1 for height 70 Y h Y 96(m) or 7.0 Y h Y 9.6(cm) M1 for ½ × their base × their height If B0 in either (b)(i) or (b)(ii) but F marked in any triangle SC1 for their base ± 2(m) or ± 0.2(cm) SC1 for their perpendicular height ± 2(m) or ± 0.2(cm) SC1 for ½ × their base × their height

This question in 0580/32 Oct/Nov 2012

10 (a) The diagram shows the positions of three towns A, B and C. For The scale is 1 cm represents 2 km. Examiner's Use North North C A North B Scale: 1 cm = 2 km (i) Find the distance in kilometres from A to B. Answer(a)(i) km [2] (ii) Town D is 9 km from A on a bearing of 135°. Mark the position of town D on the diagram. [2] (iii) Measure the bearing of A from C. Answer(a)(iii) [1] (b) The population of town C is 324 100. (i) Write this number in standard form. Answer(b)(i) [1] (ii) The population of town D is 7.64 × 104. Which town, C or D, has the larger population and by how much? Give your answer in standard form. Answer(b)(ii) Town by [3]

9 marks

Mark scheme: 10 (a) (i) 14.8 to 15.2 2 M1 7.4 to 7.6 (ii) D correctly marked 133 –137° and 2 B1 for correct bearing or distance. 4.3 −4.7 cm from A (iii) 260 to 264° 1 (b) (i) 3.24 (1) × 105 1 (ii) C by 2.477 × 105 3 SC2 for C by figs 2477 or figs 248 or 2.48 × 105 M1 324100 – 76400 or their (b) − 7.64 × 104 evaluated

This question in 0580/33 Oct/Nov 2012

4 The diagram is part of a map showing the position of two towns Anderro, A, and Bratena, B. For Examiner′s The scale is 1 centimetre represents 10 kilometres. Use North B North A Scale: 1 cm to 10 km (a) Work out the distance, in kilometres, from Anderro to Bratena. Answer(a) … km [2] (b) Measure the bearing of Bratena from Anderro. Answer (b) … [1] (c) Carribon is 80 km from Anderro. The bearing of Carribon from Anderro is 304°. Mark the position of Carribon on the diagram. Label it C. [2] _____________________________________________________________________________________

5 marks

Mark scheme: 4 (a) 56 to 60 2 B1 for 5.6 to 6.0 (b) [0]35 to [0]39 1 (c) Correct length and bearing 2 B1 for correct length 7.8 to 8.2 B1 for correct bearing 302º to 306º IGCSE – May/June 2013 0580 32

This question in 0580/32 May/June 2013

5 (a) For Examiner′s North Use C B D North A Scale: 1 cm to 12 km The diagram shows four towns, A, B, C and D, joined by straight roads AB, BC and BD. The scale is 1 centimetre represents 12 kilometres. (i) Measure the bearing of B from A. Answer(a)(i) … [1] (ii) Work out the distance in kilometres from A to B. Answer(a)(ii) … km [2] (iii) Saraswati takes 1 hour 30 minutes to drive from A to B. Calculate her average speed, in kilometres per hour, for this journey. Answer(a)(iii) … km/h [1] (b) At B, Saraswati follows another straight road which is equidistant from BC and BD. For Examiner′s Use Using a straight edge and compasses only and leaving in all your construction lines, construct the line of this road on the diagram. [2] (c) Another motorist, Leah, leaves C and drives on a bearing of 165° to meet Saraswati at town E. Town E is on the road in part (b). Show Leah’s journey on the diagram and mark the town E. [1] (d) Saraswati travelled from B to E at an average speed of 55 km/h. Calculate the time, in hours and minutes, that she took. Answer(d) … h … min [4] (e) There is a speed limit of 50 km/h on all roads within 30 km of town D. On the diagram, show the boundary of the region where this speed limit applies. [2] _____________________________________________________________________________________

13 marks

Mark scheme: 5 (a) (i) (0)35 to (0)39 1 (ii) 117.6 to 122.4 [km] 2 B1 for (10 ± 0.2) cm seen (iii) 80 or 78.4 to 81.6 1ft ft their (a)(ii) ÷ 1.5 (b) Bisector of angle CBD with 2 2 B1 correct line (±2°), some or all arcs absent correct pairs of arcs. (c) Ruled line from C to BD on a 1 bearing of 165° (d) 1 [h] 18 [min] to 1 [h] 26 [min] 4 B1ft measure BE www M1 change to kilometres. M1 for their distance ÷ 55 (e) Circle, centre D, with radius 2 M1 for 2.5 ± 0.2 soi. 2.5 ± 0.2 cm SC1 for circle, centre D, incorrect radius or freehand ‘correct’ circle IGCSE – May/June 2013 0580 33

This question in 0580/33 May/June 2013

3 (a) The diagram shows the position of town A and town B, on a map. For Examiner′s Use North A B (i) Measure the length, in millimetres, of the line AB. Answer(a)(i) … mm [1] (ii) Measure the bearing of town B from town A. Answer(a)(ii) … [1] (b) A triangular fi eld has sides of length 550 m, 300 m and 400 m. (i) Construct the triangle, using a ruler and compasses only. Use a scale of 1 cm to represent 50 m. The side of length 550 m has been drawn for you. 550 m [3] (ii) By making a suitable measurement on your diagram, calculate the area of the fi eld. Give your answer in square metres. Answer(b)(ii) … m2 [3] _____________________________________________________________________________________

8 marks

Mark scheme: 3 (a) (i) 44 – 46 1 (ii) 231 – 235 1 (b) (i) Fully correct drawing with arcs 3 B2 for correct triangle without arcs B1 for 1 correct length side Or arc of 6cm or 8cm 1 52250 to 60500 nfww 3FT M2 for × 550 × 2 (their correct height × 50) 1 Or × 11 × their correct height in cm 2 or B1 for their correct height in cm or their correct height × 50 seen 1 If 0 scored then SC1 for × 550 × 2 (50 × k)

This question in 0580/31 Oct/Nov 2013

4 (a) For Examiner′s Use North Sea B North A The scale drawing shows the position of two airfi elds, A and B. The scale is 1 cm represents 50 km. (i) Find the actual distance between A and B. Give your answer in kilometres. Answer(a)(i) … km [2] (ii) Measure the bearing of B from A. Answer(a)(ii) … [1] (iii) A third airfi eld, C, is 525 km from airfi eld A and 350 km from airfi eld B. On the scale drawing, construct the position of airfi eld C. [2] (iv) Measure the bearing of B from C. Answer(a)(iv) … [1] (b) A plane is at airfi eld C at 10 40. For Examiner′s It fl ies 525 km to airfi eld A at a speed of 700 km/h. Use Work out the time when the plane reaches airfi eld A. Answer(b) … [3] (c) This plane has a maximum take-off weight of 4173 kg. Write 4173 kg correct to the nearest hundred kilograms. Answer(c) … kg [1] (d) The plane can fl y at a maximum height of 13 107 m. Write 13 107 m in kilometres, correct to 3 signifi cant fi gures. Answer(d) … km [2] (e) In one week, the plane fl ies a total distance of 8520 km, correct to the nearest ten kilometres. Write down the lower bound of this distance. Answer(e) … km [1] _____________________________________________________________________________________

13 marks

Mark scheme: 4 (a) (i) 370 to 380 2 B1 for 7.4 to 7.6 seen (ii) [0]36 to [0]40 1 (iii) Intersecting arcs: 2 Arc centre A radius 10.5 cm B1 for one correct arc Arc centre B radius 7 cm or C correct with no arcs (iv) 300 to 310 1FT (b) 11 25 3 M2 for 525 ÷ 700 × 60 or better soi Or M1 for 525 ÷ 700 soi by 0.75 (c) 4200 1 (d) 13.1 2 B1 for 13 100 or 13.107 or 13.100 Or B1FT their conversion to 4 or more sig figs seen and then correctly rounded to 3 sig figs (e) 8515 1

This question in 0580/32 Oct/Nov 2013

3 The Wong family spend the day at the zoo. (a) The Wong family has 2 adults and 3 children aged 2, 5 and 11 years old. Admission Adults $8.50 Children 11-16 years $6.00 Children 3-10 years $4.50 Children under 3 years FREE Mr Wong pays for his family to go into the zoo using a $50 note. Work out the change he receives. Answer(a) $ … [3] (b) The dolphin show fi nishes at 11 05. It lasts for 1 hour and 20 minutes. Write down the time the dolphin show starts. Answer(b) … [1] (c) Torty the tortoise was born on 27 December 1898. Work out how many years old she was on 3 January 2003. Answer(c) … years [1] (d) Last year, the ratio snakes : lizards = 3 : 5 . There were 45 lizards. (i) Work out how many snakes there were last year. Answer(d)(i) … [2] (ii) This year, there are 3 more snakes and the same number of lizards. Write down the new ratio snakes : lizards. Give your answer in its simplest form. Answer(d)(ii) … : … [2] (e) Mr Wong hires a vehicle to drive around the zoo. The cost is $25 for the fi rst hour and $7.50 for every extra half hour. He pays $85 altogether. For how long does he hire the vehicle? Answer(e) … hours [3] (f) Mrs Wong wants to buy some food for the giraffes. Small Bag Medium Bag Large Bag 225g 250g 325g 60 cents 70 cents 90 cents Work out which bag is the best value for money. Show how you decide. Answer(f) … [3] (g) The diagram shows a map of the zoo. The scale is 1 centimetre represents 50 metres. North Entrance Scale: 1 cm to 50 m Flamingos North Exit (i) Measure the bearing of the fl amingos from the entrance. Answer(g)(i) … [1] (ii) Xanthe looks after all the animals within 200 m of the exit. Draw accurately the locus of points inside the zoo which are 200 m from the exit. [2] (iii) A shop, S, is on a bearing of 212° from the entrance and a bearing of 293° from the exit. Mark the point S on the map. [3] __________________________________________________________________________________________

21 marks

Mark scheme: 3 (a) 22.5[0] 3 M1 for (2 × 8.5 + 6 + 4.50) M1 for 50 – their total (b) [0]9 45 1 (c) 104 1 45 (d) (i) 27 2 M1 for × 3 5 (ii) 2 : 3 cao 2 M1 for (their 27 + 3) : 45 or better If zero SC1 for 3 : 2 85− 25 (e) 5 3 M1 for soi by 8 7.50 their 8 M1 for + 1 2 (f) 3.75, 3.57... 3.61... [g / c] 3 M1 for 1 correct division, not evaluated small [bag] M1 for 2 further consistent correct divisions, not evaluated (g) (i) 105 1 (ii) correct locus drawn 2 M1 for any arc centre exit (iii) S marked correctly 3 B1 for indication of bearing of 212° B1 for indication of bearing of 293°

This question in 0580/33 May/June 2014

8 North Q North 48 km P (a) The scale drawing shows a ship’s voyage from port P to port Q. The straight line distance from P to Q is 48 km. (i) Measure the bearing of Q from P. Answer(a)(i) … [1] (ii) Complete the following statement. The scale of the drawing is 1 centimetre represents … kilometres. [2] (b) From port Q, the ship sails on a bearing of 125° for 76 km to port R. Show this part of the voyage on the scale drawing. [3] (c) L North NOT TO 8.5 km SCALE P W 297° Another ship leaves port P and sails on a bearing of 297° to a lighthouse, L. PL = 8.5 km. (i) Show that angle LPW = 27°. Answer(c)(i) [1] (ii) Using trigonometry, calculate PW. Give your answer correct to 2 signifi cant fi gures. Answer(c)(ii) PW = … km [3] (d) The diagram shows the positions of two beacons, A and B. A ship sails on a course that is the perpendicular bisector of the line AB. Using a straight edge and compasses only, construct the ship’s course. B A [2] __________________________________________________________________________________________

12 marks

Mark scheme: 8 (a) (i) [0]63 to [0]67 1 (ii) 8 2 B1 for 6 ± 0.2 [cm] seen in working (b) QR on bearing 123o to 127o 1 B1 for bearing of 123o to 127o 9.3 cm to 9.7 cm continuous ruled line 2FT M1FT for 76 ÷ their (a)(ii) soi by calculation or distance on diagram (c) (i) 297 – 270 1 or 90 – (360 – 297) PW PW (ii) 7.6 cao nfww 3 M1 for cos27° = or sin63° = or 5.8 5.8 better A1 for 7.57(...) B1ind for correctly rounding their 7.57(...) to 2 sig figs if their 7.57(…) is to 3 sig figs or more (d) Correct continuous perpendicular 2 B1 for correct continuous bisector without arc bisector of AB with two pairs of correct or with incorrect arcs arcs

This question in 0580/32 Oct/Nov 2014

4 The diagram shows the positions of two villages Dormouth, D, and Greenton, G. The scale is 1 centimetre represents 20 kilometres. North G North Scale: 1 cm to 20 km D (a) Find the distance, in kilometres, from Dormouth to Greenton. Answer(a) … km [1] (b) Measure the bearing of Dormouth from Greenton. Answer(b) … [1] (c) Foxhill is 84 km from Dormouth. The bearing of Foxhill from Dormouth is 105°. Mark the position of Foxhill on the diagram. Label it F. [2] (d) A straight road joins Dormouth to Foxhill. A car drives from Dormouth to Foxhill at a constant speed of 54 km/h. Calculate the time it takes to complete the 84 km journey. Give your answer to the nearest minute. Answer(d) … h … min [3] (e) Change 54 km/h to m/s . Answer(e) … m/s [2] __________________________________________________________________________________________

9 marks

Mark scheme: 4 (a) 126 1 Accept 122 to 130 (b) 240 1 (c) Correct position on diagram 2 B1 for angle 103° to 107° B1 for distance 4.0 cm to 4.4 cm (d) 1 hour and 33 min 3 84 M2 for × 60 oe 54 84 30 or M1 for or × 60 54 54 54 × 1000 (e) 15 2 M1 for or better 60 × 60

This question in 0580/32 Feb/March 2015

4 The Patel family flies from their home town, H, to Kiruna, K, in Lapland. (a) The scale drawing shows their journey. The scale is 1 centimetre represents 40 kilometres. North K North Scale: 1 cm to 40 km H (i) Measure the bearing of K from H. Answer(a)(i) … [1] (ii) Work out the distance in kilometres from H to K. Answer(a)(ii) … km [2] (iii) The average speed of the plane is 450 km/h. Find the average speed in m/s. Answer(a)(iii) … m/s [2] (b) The probability that the plane arrives on time is 0.15 . (i) Write down the probability that the plane does not arrive on time. Answer(b)(i) … [1] (ii) Every year there are 240 flights from H to K. Calculate the expected number of flights that arrive on time. Answer(b)(ii) … [1] (c) The Patel family has six suitcases. The number of items in each suitcase is shown below. 15 16 16 18 19 21 (i) Find the range. Answer(c)(i) … [1] (ii) Write down the mode. Answer(c)(ii) … [1] (iii) Work out the median. Answer(c)(iii) … [1] (iv) Calculate the mean. Answer(c)(iv) … [2] (v) Find the probability that a suitcase chosen at random has more than 18 items. Answer(c)(v) … [1] (d) Mr Patel buys a bag of sweets. The bag of sweets costs $3.25 . (i) Calculate the cost of the sweets in euros (€) when the exchange rate is €1 = $1.24 . Answer(d)(i) € … [2] (ii) The weight, w grams, of the bag of sweets is 250 g correct to the nearest 10 g. Complete this statement about the value of w. Answer(d)(ii) …  w < … [2] __________________________________________________________________________________________

17 marks

Mark scheme: 4 (a) (i) 292 1 (ii) 380 2 B1 for ( 9.5 ± 0.2 ) If zero scored, SC1 for figs ‘372 to 388’ 450 × 1000 (iii) 125 2 M1 for or better 60 × 60 (b) (i) 0.85 1 (ii) 36 1 (c) (i) 6 1 (ii) 16 1 (iii) 17 1 (iv) 17.5 2 M1 for (15+16+16+18+19+21) ÷ 6

This question in 0580/31 May/June 2015

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.

11 marks

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

This question in 0580/32 May/June 2015

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] __________________________________________________________________________________________

13 marks

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

This question in 0580/31 Oct/Nov 2015

7 Burton City is a football team. (a) Burton City has 1732 supporters who want to travel to the next game. The football club hires some buses. Each bus seats 52 supporters. (i) Work out the number of buses needed to take these supporters to the game. … [2] (ii) The cost of the buses will be shared equally amongst these supporters. Each bus costs $198 to hire. Work out the amount that each supporter must pay. Give your answer correct to the nearest 10 cents. $ … [3] (b) Adam and Mabel are two supporters. The scale drawing shows the positions of Adam’s home, A, and Mabel’s home, M. The scale is 1 centimetre represents 500 metres. North A North Scale: 1 cm to 500 m M (i) Work out the distance in kilometres from A to M. … km [2] (ii) Burton City’s football ground is on a bearing of 105° from A and on a bearing of 068° from M. Mark the position of the football ground on the scale drawing. [3] (c) Teams are given points for winning or drawing games. A win is given w points and a draw is given d points. No points are given when the team loses. (i) Burton City has 24 points after winning 2 games and drawing 5 games. Complete the equation. 2w + 5d = … [1] (ii) Sowton Rovers is another football team. Sowton Rovers has 29 points after winning 3 games and drawing 4 games. Write this information as an equation. … = … [2] (iii) Solve your two equations to find the number of points for a win and the number of points for a draw. You must show all your working. w = … d = … [4] (iv) Another team, Cranbrook United, has played 12 games. It has won 4 games, drawn 5 games and lost 3 games. Work out the number of points Cranbrook United has after 12 games. … [1]

18 marks

Mark scheme: 1732 7 (a) (i) 34 2 M1 for 52 198 ×their 34 (ii) 3.90 3FT M1FT for 1732 A1FT 3.88 to 3.89 A1FT their answer rounded to nearest 10c (b) (i) 3.9 2 M1 for 7.8 If zero scored SC1 for figs 38 to 40 (ii) football ground indicated in 3 B1 for bearing of 105° from A correct position B1 for bearing of 068° from M B1FT for indication of the football ground’s position, dpt on at least one B1

This question in 0580/32 Feb/March 2016

5 (a) The scale drawing shows port A and port B. The scale is 1 centimetre represents 15 kilometres. North North B A Scale: 1 cm to 15 km A ship sails from port A to port B. (i) Measure the bearing of port B from port A. … [1] (ii) Find the actual distance from port A to port B. … km [2] (iii) The ship then sails from port B to port C. Port C is 90 km from port B on a bearing of 146°. On the scale drawing mark the position of port C. [2] (b) Another ship sails from port P to port Q. It then sails from port Q to port R before returning to port P. North NOT TO Q North SCALE 84° North 67° R 43° P (i) Find angle RPQ. Angle RPQ = … [1] (ii) Find the bearing of port P from port R. … [2] (c) North T NOT TO 356 km SCALE S 267 km Port T is 267 km east and 356 km north of port S. Calculate the distance ST. ST = … km [2]

10 marks

Mark scheme: 5 (a) (i) [0]67 1 (ii) 135 2 B1 for 9 (cm) (iii) Correct diagram 2 B1 for correct bearing B1 for correct length

This question in 0580/31 May/June 2016

10 The scale drawing shows the positions of two towns, X and Y. The scale is 1 centimetre represents 5 kilometres. North X North Y Scale: 1 cm to 5 km (a) Work out the actual distance from town X to town Y. … km [2] (b) Measure the bearing of town X from town Y. … [1] (c) An airport, A, is 22.5 km from town Y on a bearing of 050°. Mark and label the position of A on the scale drawing. [2]

5 marks

Mark scheme: 10 (a) 35 2 B1 for 7 (b) 305 1 (c) Point marked in correct 2 B1 for point at 4.5 cm or 050 ° from Y position

This question in 0580/31 Oct/Nov 2016

5 (a) The scale drawing shows the positions of three villages, A, B and C. The scale is 1 centimetre represents 5 kilometres. North North A B C Scale: 1 cm to 5 km (i) Find the actual distance between village A and village B. … km [2] (ii) Measure the bearing of B from A. … [1] (iii) Another village, D, is 30 km from village B on a bearing of 215°. On the scale drawing, mark the position of village D. [2] (iv) A power station, P, is 25 km from village C. It is equidistant from village A and village B. Using a ruler and compasses only, construct and mark a position of the power station, P. [3] (b) A bus takes workers from village C to the power station. Each journey takes 35 minutes. (i) Complete the timetable for the bus. Village C 05 45 Power station 06 50 08 05 [3] (ii) The bus travels 25 km from village C to the power station. Calculate the average speed of the bus in kilometres per hour. … km/h [2]

13 marks

Mark scheme: 5 (a) (i) 40 to 42 2 M1 for 8.0 to 8.4 or 80 to 84 seen (ii) 104 to 108 1 (iii) D marked correctly 2 B1 for bearing 215° B1 for distance 6 cm (iv) P marked correctly with 3 B1 for arc centre C radius 5 cm arcs B1 for two correct pairs of intersecting arcs (for perpendicular bisector of AB) B1 P marked in correct position (b) (i) 05 45 [0]6 15 [0]7 30 3 B1 for each [0]6 20 06 50 08 05 25 25 25 (ii) 42.9 or 42.85 to 42.86 2 M1 for or or × 60 oe 35 0.583... 35 2 2

This question in 0580/32 Oct/Nov 2016

4 (a) The diagram shows the positions of three towns, A, B and C. B is 24 km due North of A. C is 18 km from A and 15 km from B. North B NOT TO SCALE 15 km 24 km C 18 km A (i) Using a ruler and compasses only, construct a scale drawing to show the positions of B and C. Town A has been marked for you. Use a scale of 1 centimetre to represent 3 kilometres. North A Scale: 1 cm to 3 km [3] (ii) Using your scale drawing, measure the bearing of C from A. … [1] (iii) Town D is on a bearing of 023° from town A. Work out the bearing of town A from town D. … [2] (b) The scale drawing shows the positions of three ports P, T and W. A ship, S, is • the same distance from P and T • 300 km from W. Using a ruler and compasses only, construct and mark the two possible positions of the ship. Use a scale of 1 centimetre to represent 50 kilometres. T P W Scale: 1 cm to 50 km [5]

11 marks

Mark scheme: 4 (a) (i) B correct 1 C correct with arcs 2FT B1 for C correct without arcs or correct pair of arcs or correct lengths reversed with arcs If zero scored, SC1 for AB=8 or AC=6 or BC=5 (ii) [0]37 to [0]41 1 Correct or FT (iii) 203 2 M1 for 180 + 23 (b) Correct perpendicular bisector 2 B1 for correct perpendicular bisector of PT with of PT with arcs no / incorrect arcs or two correct pairs of intersecting arcs arc centre W radius 6 cm 2 B1 for any arc centred on W both points marked on 1dep dep on an attempt at bisector and attempt at the intersection of line and arc arc

This question in 0580/33 Oct/Nov 2016

4 (a) Complete this statement. To be obtuse, an angle must be between … degrees and … degrees. [1] (b) parallelogram square rectangle kite trapezium rhombus Choose one word from the box to complete each statement. A … has no lines of symmetry but has rotational symmetry of order 2. A … has two lines of symmetry but no right angles. A … has one line of symmetry but no rotational symmetry. [3] (c) a° NOT TO SCALE 56° 73° b° c° The diagram shows four straight lines. Write down the values of a, b and c. Give a geometrical reason for each answer. a = … because … b = … because … c = … because … [6] (d) The scale drawing shows the positions of two towns F and G. The scale is 1 cm represents 1.5 km. North North F G Scale: 1 cm to 1.5 km (i) Measure the bearing of G from F. … [1] (ii) Find the distance, in kilometres, between town F and town G. … km [1] (iii) Another town, H, is 10.5 km from town G. The bearing of H from G is 174°. On the scale drawing, mark the position of town H. [2]

14 marks

Mark scheme: 4 (a) 90, 180 1 (b) parallelogram 1 rhombus 1 kite 1 (c) 56 vertically opposite [to 56°] 1,1 56 corresponding [to 56°] 1,1 73 alternate [to 73°] 1,1 (d) (i) 113 1 (ii) 7.5 km 1 (iii) H correct 2 B1 for correct angle or correct distance

This question in 0580/32 Feb/March 2017

8 The scale drawing shows the positions of Bogota (B) and Quito (Q). The scale is 1 centimetre represents 150 kilometres. North B North Scale: 1 cm to 150 km Q (a) (i) Measure the length of the line BQ. … cm [1] (ii) Work out the actual distance from Bogota to Quito. … km [1] (iii) Measure the bearing of Quito from Bogota. … [1] (b) A plane leaves Quito and flies straight to Manaus. Manaus is 2100 km on a bearing of 100° from Quito. On the scale drawing, mark the position of Manaus (M). [3] (c) The plane flies the 2100 km from Quito to Manaus at an average speed of 550 km/h. Calculate the time taken for this flight (i) in hours, correct to 3 significant figures, … h [2] (ii) in hours and minutes, correct to the nearest minute. … h … min [1] Question 9 is printed on the next page.

9 marks

Mark scheme: 8(a)(i) 4.4 1 8(a)(ii) 660 1FT their (a)(i) × 150 8(a)(iii) 220 1 8(b) 14 [cm] from Q 2 M1 for 2100 ÷ 150 soi 100° from Q 1 8(c)(i) 3.82 cao 2 M1 for 2100 ÷ 550 8(c)(ii) 3[h] 49[min] 1FT their time correctly converted

This question in 0580/31 May/June 2017

4 (a) Measure the reflex angle at A. A … [1] (b) b° NOT TO SCALE 68° Find the value of b. Give a reason for your answer. b = … because … [2] (c) e° NOT TO 36° SCALE d° c° Find the values of c, d and e. c = … d = … e = … [3] (d) A regular polygon has 24 sides. Work out the size of one of the interior angles of the polygon. … [3] (e) Town Y is 6.7 km from town X. The bearing of town Y from town X is 113°. On the scale drawing, draw a line from X and mark the position of Y. The scale is 1 centimetre represents 1 kilometre. North Scale: 1 cm to 1 km X [2] (f) Give the correct mathematical name for each of the shapes described below. (i) I am a quadrilateral. I have two pairs of parallel sides but no right angles. I have two lines of symmetry. … [1] (ii) I am a quadrilateral. I have one pair of opposite angles that are equal. I have one line of symmetry. … [1]

13 marks

Mark scheme: 4(a) 328 1 4(b) 68 1 corresponding 1 4(c) 72 1 108 1FT FT is 180 – their c 72 1FT FT is their c 4(d) 165 3 360 M2 for 180 – or (180 × ( 24 − 2 ) ÷ 24 ) or better 24 360 or M1 for or 180 × (24 – 2) or better 24 4(e) Correct distance XY 1 Correct bearing 1 4(e)(ii) Rhombus 1 4(e)(ii) Kite 1

This question in 0580/33 May/June 2017

8 The quadrilateral ABCD is a scale drawing of a farmer’s field. Side AD and side BC are parallel. Angle DAB and angle ABC are right angles. A D B C (a) Write down the mathematical name of the quadrilateral. … [1] (b) The side of the field, AB, is 28 m. (i) Complete this statement. The scale of the diagram is 1 centimetre represents … metres. [2] (ii) Work out the actual area of the field in m2. … m2 [3] (c) The field has two fences. Each fence extends across the field until it meets another side. • Fence 1 is the perpendicular bisector of CD. • Fence 2 is the bisector of angle ABC. Using a straight edge and compasses only, construct the two fences on the diagram. Show all your construction arcs. [4] (d) The region of the field that is 16 m or less from A is planted with wheat. (i) Using a ruler and compasses only, construct and shade the region planted with wheat. [3] (ii) Work out the actual area of the region that is planted with wheat. … m2 [2] Question 9 is printed on the next page.

15 marks

Mark scheme: 8(a) trapezium 1 8(b)(i) 4 2 B1 for 7 cm seen 8(b)(ii) 1120 nfww 3 B1 for 8 [cm] and 12 [cm] seen or 8 × their (b)(i) [m] or 12 × their (b)(i) [m] evaluated ( their 8 + their12 ) M1 for × their 7 or 2 ( their 32 + their 48 ) × 28 oe 2 8(c) correct perpendicular bisector 2 B1 for correct bisector drawn without arcs or wrong arcs drawn with 2 pairs of arcs and or correct short line with arcs extending across field to side or for two pairs of correct arcs BC correct angle bisector drawn 2 B1 for correct bisector drawn without arcs or wrong arcs with 2 pairs of arcs and or correct short line with arcs extending across field to side or for two pairs of correct arcs AD 8(d)(i) Accurately drawn and correct 3 B1 for 4 cm length seen or implied region shaded B1 one arc drawn centre A and touching AB and AD B1 correct shading Maximum B2 8(d)(ii) 201 nfww or 201.06 to 201.09 2 M1 for π × 162 or π × their radius 2 or better

This question in 0580/33 May/June 2017

5 The scale drawing shows the positions of three towns A, B and C. The scale is 1 centimetre represents 12 kilometres. North North B North C A Scale: 1 cm to 12 km (a) Find the actual distance between town A and town B. … km [2] (b) Measure the bearing of town B from town A. … [1] (c) Measure the bearing of town B from town C. … [1] (d) Town D is 84 km from town A and 42 km from town C. (i) In this part, use a ruler and compasses only and show your construction arcs. On the diagram, construct a possible position for town D. [3] (ii) A plane takes 10 minutes to fly the 84 km from town A to town D. Work out the average speed of the plane in kilometres per hour. … km/h [2] (e) The bearing of town E from town A is 118°. Work out the bearing of town A from town E. … [2]

11 marks

Mark scheme: 5(a) 51.6 2 B1 for 4.3[cm] 5(b) [0]47 1 5(c) 292 1 5(d)(i) Arc centre A radius 7 cm 1 Arc centre C radius 3.5 cm 1 One point marked at intersection 1 If zero scored, SC1 for any arc centred on A or C, of correct arcs or correct point marked with no arcs 5(d)(ii) 504 2 M1 for 84 ÷ their time or 84 × 6 5(e) 298 2 M1 for 118 + 180 oe

This question in 0580/31 Oct/Nov 2017

6 The diagram shows the positions of two towns, A and B. The scale is 1 centimetre represents 10 kilometres. North A B Scale: 1 cm to 10 km (a) (i) Find the actual distance from A to B. … km [2] (ii) Measure the bearing of B from A. … [1] (b) (i) Another town, C, is 78 km from A on a bearing of 103°. Mark and label the position of town C on the diagram. [2] (ii) Chailai takes 45 minutes to drive the 78 km from town A to town C. Calculate her average speed in kilometres per hour. … km/h [2] (c) In this part, use a ruler and compasses only and show your construction arcs. Mr Lei is moving house. He wants to live • nearer to town B than town A and • less than 70 km from town A. Construct and shade the region on the diagram in which he wants to live. [5]

12 marks

Mark scheme: 6(a)(i) 95 2 B1 for 9.5 6(a)(ii) 135 1 6(b)(i) Correct length and bearing 2 B1 for 7.8 cm from A B1 for 103° from A 6(b)(ii) 104 2 78 M1 for × 60 oe 45 78 or for time 6(c) Correct region shaded with correct 5 B2 for correct bisector with correct arcs arcs or B1 for short bisector with correct/incorrect/no arcs or for correct arcs but no line B2 for arc 7 cm centre A or B1 for short arc 7 cm from centre A

This question in 0580/32 Oct/Nov 2017

5 (a) The scale drawing shows the positions of a lighthouse L and a ship S. The scale is 1 centimetre represents 5 kilometres. North L North S Scale: 1 cm to 5 km (i) Work out the actual distance, in kilometres, from S to L. … km [2] (ii) Measure the bearing of S from L. … [1] (iii) Another ship, T, is 22 km from L on a bearing of 210°. Mark and label the position of T on the scale drawing. [2] (b) In this part, use a ruler and compasses only and show your construction arcs clearly. The scale drawing shows the positions of two yachts, P and Q. The scale is 1 centimetre represents 100 metres. Q P Scale: 1 cm to 100 m (i) Construct the locus of points equidistant from P and Q. [2] (ii) Another yacht, Y, is • closer to P than to Q and • less than 700 m from Q. On the scale drawing, construct and shade the region where yacht Y is. [3]

10 marks

Mark scheme: 5(a)(i) 37 2 B1 for 7.4 5(a)(ii) 133 1 5(a)(iii) T plotted correctly 2 B1 for T 4.4 cm from L B1 for bearing 210° 5(b)(i) Correct perpendicular bisector of 2 B1 for correct bisector with wrong/no arcs PQ or for no line and two pairs of correct arcs or for short bisector with correct/incorrect/no arcs 5(b)(ii) Arc centre Q, radius 7 cm 2 B1 for short arc centre Q , radius 7 cm Correct region shaded 1

This question in 0580/31 Oct/Nov 2018

3 The scale drawing shows the positions of three towns A, B and C on a map. The scale is 1 centimetre represents 10 kilometres. North A C North B Scale : 1 cm to 10 km (a) Work out the actual distance between town A and town B. … km [2] (b) (i) Measure the bearing of town C from town A. … [1] (ii) Show how to use your answer to part (b)(i) to find the bearing of town A from town C. … [1] (c) Town D is 96 km from town C on a bearing of 100°. (i) Mark the position of town D on the map. [2] 1 (ii) Jez drives from town C to town D in 1 hours. 2 Work out his average speed. … km/h [2] (iii) Change 96 km into miles. Assume that 8 km equals 5 miles. … miles [2]

10 marks

Mark scheme: 3(a) 60 2 B1 for 6 [cm] 3(b)(i) 255 1 3(b)(ii) Subtract 180 from their (b)(i) 1 FT their (b)(i) if greater than 180 3(c)(i) D in correct position 2 B1 for D 9.6 cm from C B1 for D 100° from C 3(c)(ii) 64 2 M1 for 96 ÷ 1.5 oe 3(c)(iii) 60 2 M1 for 96 ÷ 8 × 5 oe

This question in 0580/33 Oct/Nov 2018

7 The scale drawing shows the positions of an airport (A) and a train station (T) on a map. The scale is 1 centimetre represents 2 kilometres. North A North T Scale: 1 cm to 2 km (a) Work out the actual distance, in kilometres, of the train station from the airport. … km [2] (b) Measure the bearing of the airport from the train station. … [1] (c) There is a straight road that is equidistant from T and A. Using a straight edge and compasses only, construct the position of the road on the map. Show all your construction arcs. [2] (d) Krishna’s house is • on a bearing of 203° from the airport and • 8.8 km from the train station. On the map, mark the two possible positions of Krishna’s house. Label each of these points K. [4] (e) The bus station is not shown on the map. The bearing of the bus station from the train station is 318°. Work out the bearing of the train station from the bus station. … [2]

11 marks

Mark scheme: 7(a) 19.2 2 B1 for 9.6 cm seen 7(b) [0]45 1 7(c) Correct ruled perpendicular bisector 2 B1 for correct bisector drawn without arcs with 2 pairs of arcs or for two pairs of correct arcs 7(d) K marked correctly twice 4 B1 for line indicating correct bearing of 203° measured B2 for an arc radius 4.4 cm, centre T, the arc length being fit for purpose or B1 for an arc of any radius, centre T or M1 for 8.8 ÷ 2 soi by 4.4 K marked correctly once implies 3 marks 7(e) 138 2 M1 for 318 − 180 or a correct diagram seen

This question in 0580/32 Feb/March 2019

4 The scale drawing shows town A, town B and town C on a map. There is a straight road between town A and town B. The scale of the map is 1 centimetre represents 8 kilometres. North A North C North B Scale: 1 cm to 8 km (a) Measure the bearing of town A from town B. … [1] (b) Work out the actual distance, in kilometres, between town A and town B. … km [2] (c) Write the scale of the map in the form 1 : n. 1 : … [1] (d) A straight road from town C is on a bearing of 246°. It meets the road from town A to town B at point X. On the map, draw the road from town C to point X. Label the position of X. [1] (e) (i) Josie is at point X at 10 50. She arrives at town B 37 minutes later. Work out the time that she arrives at town B. … [1] (ii) Sammy leaves town A and travels to town B at a constant speed of 75 km/h. (a) Work out the time for this journey. Give your answer in hours and minutes, correct to the nearest minute. … h … min [3] (b) Sammy wants to arrive at town B at the same time as Josie. Work out the time that Sammy must leave town A. … [1]

10 marks

Mark scheme: 4(a) 322 1 4(b) 96 2 B1 for [AB =] 12 cm 4(c) 800 000 1 4(d) Ruled line CX drawn on map 1 4(e)(i) 11 27 1 4(e)(ii)(a) 1[h] 17 [min] 3 FT their(b) their (b) M2 for × 60 oe 75 their(b) or M1 for 75 4(e)(ii)(b) 10 10 1 FT their (e)(i) and their (e)(ii)(a)

This question in 0580/32 May/June 2019

8 (a) The scale drawing shows the positions of two buoys, A and B, in the sea. The scale is 1 centimetre represents 20 kilometres. North North B Land A Sea Scale : 1 cm to 20 km Land (i) Work out the actual distance between buoy A and buoy B. … km [2] (ii) Measure the bearing of buoy B from buoy A. … [1] (iii) Buoy C is 120 km from buoy B on a bearing of 300°. On the scale drawing, mark the position of buoy C. [2] (iv) Marco sails his boat so that he is always equidistant from buoy A and buoy B. On the scale drawing, use a straight edge and compasses only to construct the path of the boat. Show all your construction arcs. [2] (b) The amount of fuel, t litres, in the boat’s fuel tank is 135 litres, correct to the nearest litre. Complete the statement about the value of t. … G t 1 … [2] (c) Marco has ropes of four different colours. He takes a rope at random. Colour Brown White Red Green Probability 0.35 0.04 0.2 Complete the table. [2] (d) When Marco arrives at a port the temperature is 5 °C. At midnight the temperature has fallen by 7 °C. Find the temperature at midnight. … °C [1] (e) Last year the cost to keep a boat at the port was $14 per night. This year the cost has increased by 12%. Calculate the cost this year. $ … [2] (f) Marco watched 25 boats enter the port, of which 9 had a mast. There are a total of 200 boats in the port. Calculate an estimate of the number of boats in the port that have a mast. … [2] Question 9 is printed on the next page.

16 marks

Mark scheme: 8(a)(i) 220 2 M1 for 11 8(a)(ii) [0]80° 1 8(a)(iii) C in correct position 2 B1 for correct distance of 6 cm or bearing of 300° from B 8(a)(iv) Correct line drawn with 2 pairs of 2 B1 for correct line with no or incorrect arcs correct arcs or correct arcs but no line 8(b) 134.5, 135.5 2 B1 for one correct or both correct but reversed 8(c) 0.41 2 M1 for 1 – (0.35 + 0.04 + 0.2) 8(d) –2 1 8(e) 15.68 cao 2 12 M1 for (1+ ) ×14 oe 100 8(f) 72 2 9 M1 for × 200 oe 25

This question in 0580/31 Oct/Nov 2019

6 (a) The scale drawing shows the positions of town A and town B. The scale is 1 centimetre represents 12 kilometres. North A North B Scale : 1 cm to 12 km (i) Measure the bearing of town B from town A. … [1] (ii) Find the actual distance from town A to town B. … km [2] (iii) Town C is on a bearing of 064° from town A and 028° from town B. On the scale drawing, mark the position of town C. [2] (b) The bearing of town D from town E is 245°. Work out the bearing of town E from town D. … [2] (c) The diagram shows three towns, P, Q and R. North Q P NOT TO SCALE R The bearing of town Q from town P is 090°. (i) Complete the statement. Town … is due west of town … . [1] (ii) PQ and QR are two sides of a regular decagon. Work out angle PQR. Angle PQR = … [3]

11 marks

Mark scheme: 6(a)(i) 115 1 6(a)(ii) 63.6 2 B1 for 5.3 [cm] 6(a)(iii) Correct position of town C 2 B1 for indication on diagram of either a bearing of 064° from A or a bearing of 028° from B 6(b) [0]65 2 M1 for 245 – 180 oe or for a complete diagram with North lines at D and E and 245° marked correctly at E and 65° marked correctly at D 6(c)(i) P Q 1 6(c)(ii) 144 3 M2 for 180 – (360 ÷ 10) oe 180 × (10 − 2 ) or 10 M1 for 360 ÷ 10 or 180 × (10 – 2) oe

This question in 0580/33 Oct/Nov 2019

7 (a) The scale drawing shows the positions of a rock, R, and a statue, S, on a map. The scale is 1 centimetre represents 6 metres. North R North S Scale: 1 cm to 6 m (i) Work out the actual distance between R and S. … m [2] (ii) A flagpole, F, is on a bearing of 164° from S. Work out the bearing of S from F. … [2] (iii) Ishaan uses the map to find some treasure, T. T is on a bearing of 076° from R and on a bearing of 337° from S. Mark the position of T on the map. [2] (b) The treasure is a bag of coins. The coins are made from three different metals. Pie chart Metal Percentage sector angle Copper 70% Zinc 20% Tin 10% (i) Complete the table. [2] (ii) Complete the pie chart. [2]

10 marks

Mark scheme: 7(a)(i) 54 2 B1 for 9 seen 7(a)(ii) 344 2 M1 for 164 + 180 or 360 – 16 7(a)(iii) T marked correctly 2 B1 for correct bearing of 076 or 337 7(b)(i) 252, 72, 36 2 B1 for one or two correct 7(b)(ii) Correct pie chart drawn 2 FT provided their angles sum to 360° B1 for one correctly drawn sector

This question in 0580/32 Feb/March 2020

10 Point B is 36 km from point A on a bearing of 140°. (a) Using a scale of 1 centimetre to represent 4 kilometres, mark the position of B. North A Scale: 1 cm to 4 km [2] (b) (i) Point C is 28 km from A and 20 km from B. The bearing of C from A is less than 140°. Using a ruler and compasses only, construct triangle ABC. Show all your construction arcs. [3] (ii) Measure angle ACB. Angle ACB = … [1]

6 marks

Mark scheme: 10(a) Correct position of town B 2 B1 for correct bearing B1 for correct distance 10(b)(i) Correct triangle drawn 3 B2 for correct triangle with no or wrong arcs or correct position of C with arcs (no triangle) or B1 for one line correct length drawn or 7 and 5 seen 10(b)(ii) 38 to 42 1 FT their measured angle at C

This question in 0580/31 May/June 2020

4 The scale drawing shows the positions of Kendra’s house, K, and Latika’s house, L, on a map. North L North K (a) Jesminder’s house, J, is on a bearing of 036° from K and on a bearing of 284° from L. Mark the position of J on the map. [2] (b) The actual distance between K and L is 9600 metres. (i) Complete the scale of the map. 1 cm represents … metres [2] (ii) Kendra walks from K to L at a constant speed of 4.5 km/h. She leaves K at 10 15. Work out the time she arrives at L. … [3] (c) (i) Kendra and Latika leave Latika’s house at 15 00 to go to the cinema. (a) They walk for 20 minutes at a constant speed of 4.5 km/h. Work out the distance they walk. … km [1] (b) After walking for 20 minutes, they then run a distance of 6 km at a constant speed for 40 minutes. Draw their journey to the cinema on the travel graph. 10 9 8 7 6 Distance (km) 5 4 3 2 1 Latika’s house 015 00 16 00 17 00 18 00 19 00 Time [2] (ii) Kendra and Latika leave the cinema at 18 05. They travel back to Latika’s house in a taxi at a constant speed of 30 km/h. Complete the travel graph. [2]

12 marks

Mark scheme: 4(a) J marked in correct position 2 M1 for bearing 036 from K or bearing 284 drawn from L 4(b)(i) 800 2 9600 M1 for 11.8 ⩽ k ⩽ 12.2 soi k 4(b)(ii) 12 23 3 9.6 M1 for oe 4.5 or B1 for figs 213 or 2133.. A1 for 2h 8min If A0 scored, SC1 for 10 15 + their time correctly evaluated 4(c)(i)(a) 1.5 1 4(c)(i)(b) Ruled lines 2 B1FT for (15 00,0) to (15 20, their 1.5) (15 00,0) to (15 20,1.5) B1FT (15 20, their1.5) to (15 20,1.5) to (16 00,7.5) (16 00, their1.5+6) 4(c)(ii) Ruled lines 2 FT (their16 00, their7.5) (16 00,7.5) to (18 05,7.5) B1FT (their16 00, their7.5) to (18 05,7.5) to (18 20,0) (18 05, their7.5) B1FT line back to distance = 0 with correct gradient

This question in 0580/32 Feb/March 2021

3 The scale drawing shows the position of town R on a map. The scale is 1 centimetre represents 5 kilometres. North R Scale : 1 cm to 5 km (a) Town M is 36 km from R on a bearing of 163°. Mark the position of M on the map. [2] (b) A railway track, 36 km long, is to be built in a straight line from R to M. (i) The track costs $1070 per metre to build. Work out the cost of building the track. $ … [2] (ii) 15 people can build 60 metres of track per day. Work out how many days it will take 45 people to build the whole track. … days [3] (c) Trains will travel the 36 km at an average speed of 75 km/h. Work out the journey time. Give your answer in minutes. … min [2] (d) Town K is on a bearing of 312° from R. Work out the bearing of R from K. … [2]

11 marks

Mark scheme: 3(a) M marked correctly 2 B1 for correct bearing B1 for correct distance 3(b)(i) 38 520 000 2 M1 for [1070 ×] 36 × 1000 or 1070 × 36 or figs 3852 oe 3(b)(ii) 200 3 36 × 1000 × 15 M2 for oe 60 × 45 or figs 2 nfww 36 × 1000 60 × 45 M1 for oe or oe 60 15 3(c) 28.8 2 36 M1 for [× 60 ] 75 3(d) 132 2 M1 for 312 −180 or 180 − 48

This question in 0580/31 May/June 2021

6 (a) The scale drawing shows the positions of house A and house B. The scale is 1 centimetre represents 12 metres. North B North A Scale: 1 cm to 12 m (i) Work out the actual distance, in metres, from house A to house B. … m [2] (ii) Measure the bearing of house A from house B. … [1] (iii) Another house, C, is 102 metres from house B on a bearing of 157°. On the scale drawing, mark the position of house C. [3] (b) P 98 m Q NOT TO SCALE 67 m R S The diagram shows a field PQRS. PQ = 98 m, QR = 67 m and angle PQR = 90°. There is a straight path from P to R. Calculate the length of this path. … m [2]

8 marks

Mark scheme: 6(a)(i) 87.6 2 B1 for 7.1 to 7.5 6(a)(ii) 247 1 6(a)(iii) Point C correctly plotted 3 B2 for line from B 8.3 cm to 8.7 cm long or M1 for 102 ÷ 12 and B1 for bearing 155° to 159° 6(b) 119 or 118.7... 2 M1 for 982 + 672 or better

This question in 0580/32 May/June 2021

5 Rebecca records the flight distance and the ticket price for each of her last 12 plane journeys. Flight distance 95 230 70 500 200 450 600 350 100 275 380 540 (km) Ticket price 220 210 60 380 130 270 340 250 120 170 310 305 ($) 400 300 Ticket 200 price ($) 100 0 0 100 200 300 400 500 600 Flight distance (km) (a) Complete the scatter diagram. The first eight points have been plotted for you. [2] (b) What type of correlation is shown in the scatter diagram? … [1] (c) On the scatter diagram, put a ring around the point for the journey that has the highest price per kilometre travelled. [1] (d) On the scatter diagram, draw a line of best fit. [1] (e) The scale drawing shows two airports, K and L. The scale is 1 centimetre represents 50 kilometres. L K Scale: 1 cm to 50 km A plane flies in a straight line from K to L. Use the scale drawing and your line of best fit to find an estimate for the ticket price of the journey from K to L. $ … [3]

8 marks

Mark scheme: 5(a) Four points correctly plotted 2 B1 for 2 or 3 points correctly plotted 5(b) Positive 1 5(c) Point at (95, 220) indicated 1 5(d) Ruled line of best fit drawn 1 5(e) Correct estimate supported 3 B2 for 310 to 330 (km) by their line of best fit and a or B1 for 6.2 to 6.6 seen distance of 310 to 330 or M1 for their KL×50

This question in 0580/32 May/June 2022

2 (a) a (i) Measure the size of angle a. … [1] (ii) Write down the mathematical name of this type of angle. … [1] (b) The scale drawing shows the positions of town B and town C. The scale is 1 cm represents 8 km. North B Scale: 1 cm to 8 km C (i) Work out the actual distance between town B and town C. … km [2] (ii) Measure the bearing of town C from town B. … [1] (c) 47° x° NOT TO SCALE y° The diagram shows two parallel lines and a straight line crossing them. Find the value of x and the value of y. x = … y = … [2] (d) A triangle has angles 119°, 31° and d °. Explain why this triangle is scalene. You must show your working. … … [2] (e) Find the size of one interior angle of a regular 15-sided polygon. … [2] (f) One of the angles in a parallelogram is 64°. Find the other three angles in this parallelogram. … , … , … [3]

14 marks

Mark scheme: 2(a)(i) 76 1 2(a)(ii) Acute 1 2(b)(i) 45.6 2 B1 for 5.7 cm or M1 for their 5.7  8 2(b)(ii) 124 1 2(c) 133 2 B1 for each 47 2(d) 30 and 2 M1 for 180 – 119 – 31 oe all three angles different oe 2(e) 156 2 360 (15 −2 )  180 M1 for 180 − oe or oe 15 15 2(f) 64, 116, 116 3 B1 for 64 as an answer B1 for 116 seen or M1 for (360 – 2 × 64) ÷ 2 oe

This question in 0580/32 Oct/Nov 2022

7 The scale drawing shows the positions of three towns, R, S and T, on a map. RS and ST are straight roads between the towns. The scale is 1 centimetre represents 8 kilometres. North North T R North S Scale: 1 cm to 8 km (a) Work out the actual distance between R and S. … km [2] (b) Another town, V, is on a bearing of 163° from R and on a bearing of 215° from T. Mark the position of V on the map. [2] (c) A man cycles at a constant speed of 24 km/h along the straight road from S to T. After 1 hour and 50 minutes he stops at a café, C. Mark the position of C on the map. You must show all your working. [3] (d) A hotel, H, is on a bearing of 321° from R. Work out the bearing of R from H. … [2] (e) Write the scale 1 cm to 8 km in the form 1 : n. 1 : … [1]

10 marks

Mark scheme: 7(a) 48 2 B1 for 6 cm or M1 for their 6  8 7(b) The position of V correctly marked on the 2 B1 for V on bearing 163° from R diagram B1 for V on bearing 215° from T 7(c) The position of C correctly marked on the 3 B2 for 5.5 seen diagram with correct working seen 24 their time or M2 for oe 8 or M1 for 24 their time oe If 0 scored, SC1 for C correctly marked on diagram with no working 7(d) 141 2 M1 for 321 −180 or a clear diagram with both 321 marked and the reverse bearing to be found shown 7(e) 800 000 1

This question in 0580/32 Feb/March 2023

2 (a) The diagram shows a circle. NOT TO SCALE (i) The diameter of this circle is 168 mm. Write down the radius of this circle. … mm [1] (ii) On the diagram, draw a chord of this circle. [1] (b) The scale drawing shows the position of ship A and the position of ship B. The scale is 1 cm represents 6 km. North B North A Scale : 1 cm to 6 km Another ship, C, is 45 km from ship B on a bearing of 124°. (i) On the scale drawing, mark the position of ship C. [2] (ii) Find the actual distance of ship C from ship A. … km [2] (c) (i) Show that the interior angle of a regular octagon is 135°. [1] (ii) NOT TO SCALE Show that two regular octagons and a square meet at a point without any gaps. [1] (d) E F NOT TO 49° SCALE D The diagram shows points D, E and F on the circumference of a circle. DF is a diameter of the circle. Find angle EDF. Angle EDF = … [2]

10 marks

Mark scheme: 2(a)(i) 84 1 2(a)(ii) Any chord 1 2(b)(i) Accurate position marked 2 B1 for accurate distance or accurate angle 2(b)(ii) 57 2 FT their diagram for 1 and 2 marks B1 for 9.2 to 9.6 seen or M1 for their length  6 2(c)(i) 360 ( 8 − 2 )  180 M1 180 – or 8 8 2(c)(ii) 135 + 135 + 90 = 360 M1 2(d) 41 2 M1 for 180 – 90 – 49 oe or angle DEF identified as 90°

This question in 0580/31 Oct/Nov 2023

2 (a) Bayside, Millwater and Westbridge are towns beside a lake. The scale drawing shows the positions of Bayside (B) and Millwater (M). The scale is 1 centimetre represents 2 kilometres. North B M Scale: 1 cm to 2 km (i) Find the actual distance between Bayside and Millwater. … km [2] (ii) Westbridge (W) is 17 km from Bayside on a bearing of 155°. On the scale drawing, mark the position of Westbridge. [2] (b) (i) A boat travels from Bayside to Westbridge. The table gives some information about its journey. Bayside departs 10 50 arrives 11 36 Millwater departs 11 45 Westbridge arrives 13 07 Work out how long the boat takes to travel from Millwater to Westbridge. Give your answer in hours and minutes. … h … min [1] (ii) The boat returns directly to Bayside. It takes 1 hour 20 minutes to travel the 17 km. Work out the average speed of this journey. … km/h [2] (c) Here are the ticket prices for a boat trip from Bayside to Westbridge. 1 person Group of 6 people Group of 15 people $9.80 $57.30 $138.75 (i) Calculate the cost per person for a group of 15 people. $ … [1] (ii) A group of 24 people buy tickets for the boat trip from Bayside to Westbridge. Calculate the least amount of money the group needs to pay. $ … [2]

10 marks

Mark scheme: 2(a)(i) 9 2 B1 for 4.5 or M1 for their 4.5 × 2 2(a)(ii) W correctly placed 2 B1 for correct bearing of 155 from B or for correct distance of 8.5 cm from B 2(b)(i) 1 hour 22 mins 1 2(b)(ii) 12.75 2 M1 for 17 ÷ their time 2(c)(i) 9.25 1 2(c)(ii) 225.45 cao 2 M1 for 3 × 9.8[0] + 57.3 + 138.75 oe or B1 for 9.55

This question in 0580/33 Oct/Nov 2023

6 (a) Town S is 44 km from town R on a bearing of 117°. (i) Using a scale of 1 cm represents 8 km, mark the position of town S. North R Scale: 1 cm to 8 km [2] (ii) Anvi cycles the 44 km from R to S. She leaves R at 13 15 and cycles at a speed of 12 km/h. Work out the time she arrives at S. … [3] (b) A tower has a height of 16 metres. When Jai makes a scale drawing of the tower it has a height of 20 cm. Work out the scale Jai uses, giving your answer in the form 1 : n. 1 : … [2] (c) X, Y and Z are three towns. Z North NOT TO 9.7 km SCALE X 6 km Y X is on a bearing of 288° from Y. Z is on a bearing of 018° from Y. (i) Show that angle XYZ is 90°. [2] (ii) XY = 6 km and YZ = 9.7 km . Calculate XZ. XZ = … km [2]

11 marks

Mark scheme: 6(a)(i) The position of S correctly marked on the 2 B1 for S on bearing 117° from R diagram B1 for S 5.5 cm from R 6(a)(ii) 16 55 3 B2 for 3 [h] 40 [min] 44 or M1 for 12 6(b) [1:]80 2 M1 for 20:1600 or 0.2:16 or better 1600 16 or or 20 0.2 or B1 for answer figs 8 6(c)(i) 360 − 288 + 18 oe M2 M1 for 360 − 288 or 288 − 18 If 0 scored SC1 for 72 and 18 correctly marked on the diagram 6(c)(ii) 11.4 or 11.40 to 11.41 2 M1 for 6 2 + 9.7 2 or better

This question in 0580/32 Feb/March 2024

7 (a) The scale drawing shows the position of a castle, C. The scale is 1 centimetre represents 2 kilometres. North C Scale: 1 cm to 2 km Micah walks at 4.8 km/h for 3 hours on a bearing of 236° from C, to his house, H. Mark the position of H on the scale drawing. [3] (b) A restaurant, R, is on a bearing of 083° from C. (i) Work out the bearing of C from R. … [2] (ii) The distance, d km, from R to C is 5 km, correct to the nearest kilometre. Complete this statement about the value of d. … G d 1 … [2] (c) A model of the castle is made. On the model, the length of one of the castle walls is 5 centimetres. The actual length of the wall is 90 metres. Find the scale of the model in the form 1| n . 1| … [2] (d) The castle has two kitchens with rectangular floors. F G B C NOT TO SCALE 5.6 m 9.2 m A 8.4 m D E x m H Rectangle ABCD is mathematically similar to rectangle EFGH. Calculate the value of x. x = … [2] (e) The castle has a cylindrical tower. The tower has a radius of 2.4 m and a height of 25 m. Calculate the curved surface area of the tower. Give the units of your answer. … … [3] Question 8 is printed on the next page.

14 marks

Mark scheme: 7(a) H correctly marked 3 B2 for H 7.2 cm from C 7.2 cm from C on bearing 236° or M1 for 4.8×3 B1 for H on bearing 236 from C 7(b)(i) 263 2 M1 for 83  180 oe or indicates correct angle on diagram 7(b)(ii) 4.5 5.5 2 B1 for each If 0 scored SC1 for both correct but reversed 7(c) [1 : ] 1800 2 M1 for 5 : 9000 or 0.05:90 9000 90 or or 5 0.05 or B1 for answer figs 18 7(d) 13.8 2 9.2 5.6 M1 for  oe or better x 8.4 7(e) 377 or 376.9 to 377.04 2 M1 for 2 2.4  25 m2 1

This question in 0580/31 May/June 2024

3 (a) The grid shows a trapezium. On the grid, draw an enlargement of the trapezium with scale factor 3. [2] (b) The diagram shows four triangles, A, B, C and T, and a point P on a grid. y 5 4 P 3 2 A T 1 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 C – 2 – 3 B – 4 – 5 (i) Write down the coordinates of point P. ( … , … ) [1] (ii) Describe fully the single transformation that maps (a) triangle T onto triangle A … … [2] (b) triangle T onto triangle B … … [2] (c) triangle T onto triangle C. … … [3]

10 marks

Mark scheme: 3(a) Correct enlargement 2 B1 for 2 sides correct length 3(b)(i) 4,3 1 3(b)(ii)(a) Reflection 2 B1 for each x = −1 oe 3(b)(ii)(b) Translation 2 B1 for each  3      5  3(b)(ii)(c) Rotation 3 B1 for each (0,0) 180°

This question in 0580/33 May/June 2024

11 The scale drawing shows the positions of two lighthouses, P and Q. The scale is 1 centimetre represents 0.8 kilometres. North North P Q Scale: 1 cm to 0.8 km (a) (i) Find the actual distance between P and Q. … km [2] (ii) Measure the bearing of Q from P. … [1] (b) A boat, B, is on a bearing of 127° from P. Calculate the bearing of P from B. … [2]

5 marks

Mark scheme: 11(a)(i) 7.6 2 B1 for 9.5 [cm] or M1 for 0.8×k , 9 k 10 11(a)(ii) 102 1 11(b) 307 2 M1 for 180 + 127 or 360 − (180 − 127 ) or the correct angle is indicated on a sketch

This question in 0580/32 Feb/March 2025

13 The scale drawing shows the position of ship A. The scale is 1 centimetre represents 50 kilometres. North A Scale: 1 cm to 50 km Ship B is 300 km from ship A on a bearing of 105°. On the scale drawing mark the position of ship B. [2]

2 marks

Mark scheme: 13 Correct point marked 2 B1 for bearing of B from A 105° B1 for AB drawn length 6 cm

This question in 0580/31 May/June 2025

11 The scale drawing shows the position of a hospital, H. The scale is 1 centimetre represents 6 kilometres. North H Scale: 1 cm to 6 km A school, S, is 33 km from H on a bearing of 155°. Mark the position of S on the scale drawing. [2]

2 marks

Mark scheme: 11 S marked correctly 2 B1 for HS drawn length 5.5cm B1 for bearing of S from H 155˚

This question in 0580/32 May/June 2025

16 The scale drawing shows a path from S to P. The scale is 1 cm represents 2.5 km. North P North S Scale: 1 cm to 2.5 km (a) Work out the actual distance between S and P. … km [2] (b) Measure the bearing of S from P. … [1] (c) E is 20 km from P on a bearing of 070°. On the scale drawing, mark the position of E. [2]

5 marks

Mark scheme: 16(a) 16.25 2 B1 for 6.5 or M1 for their 6.5 × 2.5 16(b) 142 1 16(c) E correctly placed 2 B1 for E on a bearing of 070 from P or for E 8 cm from P If 0 scored, SC1 for fully correct but from S not P

This question in 0580/33 May/June 2025

15 The scale drawing shows the position of ship A. The scale is 1 centimetre represents 40 kilometres. North A Scale : 1 cm to 40 km Ship B is 220 km from ship A on a bearing of 140°. On the scale drawing, mark the position of ship B. [2]

2 marks

Mark scheme: 15 Correct point marked 2 B1 for B on bearing 140° from A or B1 for B 5.5cm from A

This question in 0580/32 Oct/Nov 2025