Right-angled triangles — Paper 1 · IGCSE Mathematics 0580

10 12 m NOT TO h m SCALE 16o A ramp from a car park to a shopping centre slopes upward at an angle of 16° to the horizontal. The length of the ramp is 12 metres. Calculate the difference in height, h metres, between the car park and the shopping centre. Answer m [2]

2 marks

Mark scheme: 10 3.31 or 3.308 or 3.307(….) 2 M1 for 12sin16 (implied by 12 × 0.28 or better) 17 Grads 2.98…. implies M1. 3.3ww no marks

This question in 0580/11 May/June 2005

23 D C NOT TO SCALE O 25o A B E In the diagram, DE is a diameter of the circle, centre O. AEB is the tangent at the point E. The line DCB cuts the circle at C. Angle DEC = 25°. (a) Write down the size of angle DCE. Answer (a) Angle DCE = [1] (b) Calculate the size of angle CDE. Answer (b) Angle CDE = [2] (c) Calculate the size of angle DBE. Answer (c) Angle DBE = [2]

5 marks

Mark scheme: 23 (a) 90 1 (b) 65 2ft M1 for 180 – 25 – their (a) [155 – their (a)] (c) 25 2ft ft. 90 – their (b) B1 for angle DEB = 90° used or 10 B1 for angle CEB = 65° seen

This question in 0580/11 May/June 2005

12 Examiner's T Use NOT TO 1.2 km SCALE S 21o The diagram shows a path, ST, up a hill. The path is 1.2 kilometres long and slopes at an angle of 21° to the horizontal. Calculate the height of the hill, showing all your working. Give your answer in metres. Answer m [3]

3 marks

Mark scheme: 12 ° height M1 (alt. method) 1200 seen B1 sin 21 = oe or better 1 . 2 C’s 1200 sin 21o M1 430 (.0...) A1 f.t. 0.43(0……) A1 430(.0….) B1ft

This question in 0580/11 Oct/Nov 2005

6 NOT TO SCALE 25 m pº 30 m The height of a tree is 25 metres. The shadow of the tree has a length of 30 metres. Calculate the size of the angle marked p° in the diagram. Answer p = [2]

2 marks

Mark scheme: 6 art39.8 2 M1 for tan p = 2530 oe

This question in 0580/11 Oct/Nov 2007

11 North NOT TO SCALE 140º A 50 km B A ship travels 50 kilometres from A to B on a bearing of 140°, as shown in the diagram. Calculate how far south B is from A. Answer km [3]

3 marks

Mark scheme: 11 art38.3 3 M1 for 50d = cos (180 – 140) oe soi M1dep. for ( d =) 50 cos (180 – 140) oe SC1 for 32.1 (distance east) 11

This question in 0580/11 Oct/Nov 2007

21 Examiner's B Use C 16 cm 9 cm NOT TO SCALE 24° A D The diagram shows a quadrilateral ABCD. AB = 16 cm, BD = 9 cm and angle BDC = 24°. Angle ADB = 90° = angle BCD. Calculate the length of (a) AD, Answer(a) AD = cm [3] (b) CD. Answer(b) CD = cm [2]

5 marks

Mark scheme: 21 (a) 13.2 3 M2 for √(162 – 92) or √175 or 13.22 to 13.23 or M1 for 162 = x2 + 92 or better CD (b) 8.22 to 8.23 2 M1 for cos 24 = or better 9

This question in 0580/13 May/June 2010

9 F NOT TO SCALE 53° H 6.3 m G Calculate the length FG. Answer m [2]

2 marks

Mark scheme: h 3.6 9 8.36(0) 2 M1 for = tan 53° or = tan 37° 3.6 h or better

This question in 0580/11 Oct/Nov 2010

16 B NOT TO SCALE O T A C U In the diagram, TAU is a tangent to the circle at A. AB is a diameter of the circle and AC = BC. Find (a) angle BCA, Answer(a) Angle BCA = [1] (b) angle ABC, Answer(b) Angle ABC = [1] (c) angle CAU. Answer(c) Angle CAU = [1]

3 marks

Mark scheme: 16 (a) 90 1 1 (b) 45 1ft ft (180 − their (a)) 2 (c) 45 1ft ft 90 − their (b)

This question in 0580/13 Oct/Nov 2010

18 For C Examiner's Use NOT TO SCALE O B 24° T A A, B and C are points on a circle, centre O. TA is a tangent to the circle at A and OBT is a straight line. AC is a diameter and angle OTA = 24°. Calculate (a) angle AOT, Answer(a) Angle AOT = [2] (b) angle BOC, Answer(b) Angle BOC = [1] (c) angle OCB. Answer(c) Angle OCB = [1]

4 marks

Mark scheme: 18 (a) 66° 2 M1 for 90° clearly identified as A (b) 114° 1ft 180 − their (a) 180 − their (b) their (a) (c) 33° 1ft or 2 2

This question in 0580/11 May/June 2011

16 D NOT TO SCALE 28.5 m 38° A B C 47.1 m A flagpole, BD, is attached to level horizontal ground by ropes, AD and CD. AD = 28.5 m, BC = 47.1 m and angle DAB = 38°. Calculate (a) BD, the height of the flagpole, Answer(a) BD = m [2] (b) angle BCD. Answer(b) Angle BCD = [2]

4 marks

Mark scheme: x 16 (a) 17.5(………) 2 M1 for sin38 = or better 285. (b) 20.38 to 20.44 2ft M1 for tan (BCD =) their (a) ÷ 47.1

This question in 0580/12 May/June 2011

10 For C Examiner's A 27° Use NOT TO 12 cm SCALE B In triangle ABC, AB = 12 cm, angle C = 90° and angle A = 27°. Calculate the length of AC. Answer AC = cm [2]

2 marks

Mark scheme: AC 10 10.7 or 10.69(..….) www 2 M1 for = cos 27 or better 12 2 2

This question in 0580/13 May/June 2011

17 For Examiner's Use NOT TO SCALE 8 m y° 3 m The diagram shows a ladder, of length 8 m, leaning against a vertical wall. The bottom of the ladder stands on horizontal ground, 3 m from the wall. (a) Find the height of the top of the ladder above the ground. Answer(a) m [3] (b) Use trigonometry to calculate the value of y. Answer(b) y = [2]

5 marks

Mark scheme: 17 (a) 7.42 or 7.416... cao 3 M2 for (8 2 − 3 2 ) or complete alternate method or M1 for x2 + 32 = 82 or better 3 (b) 67.97 to 68(.0) cao 2 M1 for cos (y) = oe 8 500 × 5 × 3

This question in 0580/11 Oct/Nov 2011

21 For D Examiner's Use C NOT TO SCALE 58° 40° A B In the quadrilateral ABCD, AB = AD and CB = CD. Angle BAD = 40° and angle CBD = 58°. (a) Calculate (i) angle ABD, Answer(a)(i) Angle ABD = [1] (ii) angle BCD. Answer(a)(ii) Angle BCD = [1] (b) Write down the mathematical name for the quadrilateral ABCD. Answer(b) [1]

3 marks

Mark scheme: 21 (a) (i) 70 1 (ii) 64 1 (b) Kite 1

This question in 0580/13 Oct/Nov 2011

10 For Examiner's NOT TO Use 29 cm SCALE x cm 53.2° Calculate the value of x. Answer x = [2]

2 marks

Mark scheme: x 10 23.2 2 M1 for sin 53.2 = implicit form or better 29

This question in 0580/11 May/June 2012

19 For North Examiner's Use North B 26 km NOT TO SCALE 74 km A 28° C (a) Work out the bearing of A from C. Answer(a) [2] (b) Calculate the distance AB. Answer(b) km [2]

4 marks

Mark scheme: 19 (a) 332 2 M1 for BCA = 28. Or 360 – 28 or 152 marked correctly at C or 180 + 152 (b) 78.4 2 M1 for AB2 = 742 + 262 or better

This question in 0580/13 May/June 2012

19 The diagram shows a ladder of length 8 m leaning against a vertical wall. For Examiner′s Use NOT TO SCALE 8 m h 56° Use trigonometry to calculate h. Give your answer correct to 2 signifi cant fi gures. Answer h = … m [3] _____________________________________________________________________________________

3 marks

Mark scheme: h 19 6.6 cao 3 M1 for sin 56 = oe or better 8 A1 for 6.63 … A1 FT Dependent on M1 scored for their answer correctly rounded to 2sf IGCSE – October/November 2013 0580 11 16 

This question in 0580/11 Oct/Nov 2013

16 For Examiner′s Use 628 m NOT TO h SCALE 15° Calculate the length h. Give your answer correct to 2 signifi cant fi gures. Answer h = … m [3] _____________________________________________________________________________________

3 marks

Mark scheme: 16 160 3 M1 for sin 15 = 628[ ] oe or better A1 for 162.5[3…] or 163 or 162.54 B1 FT correct rounding

This question in 0580/13 Oct/Nov 2013

10 C 8 cm NOT TO SCALE 28° B A Calculate the length of AB. Answer AB = … cm [2] __________________________________________________________________________________________

2 marks

Mark scheme: [ ] 10 7.06 or 7.063 to 7.064 2 M1 for = cos28 or better 8

This question in 0580/12 May/June 2014

22 16 km P North NOT TO SCALE 9 km Q The diagram shows the route of a ship that leaves a port, P. It travels due west for 16 km and then changes course to due south for 9 km. (a) Calculate the straight line distance PQ. Answer(a) PQ = … km [2] (b) Use trigonometry to calculate the bearing of P from Q. Answer(b) … [2]

4 marks

Mark scheme: 22 (a) 18.4 2 M1 for [PQ2 =] 162 + 9 2 or better 16 (b) [0]60.4 to [0]60.73 2 M1 for tan [... = ] or better 9 16 or sin [... = ] or better their (a) 9 or cos[... = ] or better their (a) If zero scored, SC1 for answer [0]29.3 to [0]29.4

This question in 0580/11 Oct/Nov 2014

11 A NOT TO SCALE 11.2 cm 37° B C Calculate AB. Answer AB = … cm [2] __________________________________________________________________________________________

2 marks

Mark scheme: AB 11 6.74[0…] 2 M1 for = sin 37 or better 112.

This question in 0580/11 May/June 2015

7 NOT TO SCALE 5 cm x° 2 cm Calculate the value of x. Answer x = … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 2 7 66.4[2 … ] 2 M1 for cos [….=] oe 5

This question in 0580/13 May/June 2015

16 P 11 cm NOT TO SCALE 37° A O In the diagram, AP is a tangent to the circle at P. O is the centre of the circle, angle PAO = 37° and AP = 11 cm. (a) Write down the size of angle OPA. Answer(a) Angle OPA = … [1] (b) Work out the radius of the circle. Answer(b) … cm [2] __________________________________________________________________________________________

3 marks

Mark scheme: 16 (a) 90 1 OP (b) 8.29 or 8.289 to 8.29 2 M1 for = tan 37° oe 11

This question in 0580/11 Oct/Nov 2015

10 C NOT TO 19.3 m SCALE B A 14.5 m Use trigonometry to calculate angle ACB. Answer Angle ACB = … [2]

2 marks

Mark scheme: 14 5. 10 48.7 or 48.70…. 2 M1 for sin[= ] oe 19 3.

This question in 0580/12 Oct/Nov 2015

11 NOT TO 5 cm SCALE 2 cm x° Calculate the value of x. Answer x = … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 2 11 23.6 or 23.57 to 23.58 2 M1 for sin [ =] oe 5

This question in 0580/13 Oct/Nov 2015

15 C NOT TO SCALE 3.5 m B A 0.9 m Calculate angle BAC. Angle BAC = … [2]

2 marks

Mark scheme: 0.9 15 75.1 or 75.09 to 75.10 2 M1 for cos [...=] 3.5 [ ]

This question in 0580/12 Feb/March 2016

12 B 23 m NOT TO SCALE 16° A C A ramp, AB, with length 23 m, slopes up at an angle of 16° to the horizontal, AC. Use trigonometry to calculate AC. AC = … m [2]

2 marks

Mark scheme: AC 12 22.1 2 M1 for cos 16 = soi 23

This question in 0580/13 May/June 2016

20 y 6 5 A 4 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 B –3 –4 –5 –6 (a) Write down the co-ordinates of point A. ( … , … ) [1] (b) Plot the point (5, –2). Label this point C. [1] (c) Write down the mathematical name of triangle ABC. … [1] (d) Write AB as a column vector. AB = [1] f p - 2 (e) BD = c 5m Write down the co-ordinates of point D. ( … , … ) [1]

5 marks

Mark scheme: 20 (a) (1, 4) 1 (b) Point plotted at ( 5, −2) 1 (c) Isosceles 1FT Strict FT of their (b)  −4  (d)   1  −6  (e) (−5, 3) 1

This question in 0580/11 Oct/Nov 2016

13 NOT TO 14 cm SCALE x cm 32° Use trigonometry to calculate the value of x. x = … [2]

2 marks

Mark scheme: x 13 7.42 or 7.418 to 7.419 2 M1 for sin [32= ]14 or better

This question in 0580/12 Oct/Nov 2016

13 A NOT TO SCALE 6.2 m x° B C 13.8 m Calculate the value of x. x = … [2]

2 marks

Mark scheme: 6.2 13 24.2 or 24.19….. 2 M1 for tan [=] 13.8

This question in 0580/12 Feb/March 2017

16 7 cm NOT TO 4 cm SCALE x° Calculate the value of x. x = … [2]

2 marks

Mark scheme: 16 34.8 or 34.84 to 34.85 2 4 M1 for sin [=] 7

This question in 0580/12 May/June 2017

20 (a) A NOT TO 6.3 m 6.3 m SCALE B C Calculate the length BC. BC = … m [2] (b) D NOT TO 223 cm SCALE 52 cm F E Calculate angle DFE. Angle DFE = … [2]

4 marks

Mark scheme: 20(a) 8.91 2 M1 for [ BC2 =] 6.32 + 6.32 or 6.3 ÷ sin 45 or 6.3 ÷ cos 45 20(b) 13.5 or 13.48… 2 52 M1 for sin [=] 223

This question in 0580/13 May/June 2017

15 8.1 cm NOT TO 6.4 cm SCALE x° Calculate the value of x. x = … [2]

2 marks

Mark scheme: 15 52.2 or 52.19 to 52.20 2 6.4 M1 for sin […=] oe 8.1

This question in 0580/12 Oct/Nov 2017

17 B NOT TO SCALE 8.6 cm 52° C A ABC is a right-angled triangle. Use trigonometry to calculate BC. BC = … cm [3]

3 marks

Mark scheme: 17 10.9 or 10.91 … 3 8.6 M2 for [BC = ] sin52 8.6 or M1 for sin52 = oe BC

This question in 0580/13 Oct/Nov 2017

16 NOT TO SCALE 8 cm x° 5 cm Use trigonometry to calculate the value of x. x = … [2]

2 marks

Mark scheme: 16 51.3 or 51.31 to 51.32 2 5 M1 for cos [x =] 8

This question in 0580/12 May/June 2018

16 NOT TO 16 cm x cm SCALE 35° The diagram shows a right-angled triangle. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 16 9.18 or 9.177… 2 x M1 for sin 35 = or better 16

This question in 0580/13 May/June 2018

7 The diagram shows a right-angled triangle. NOT TO 16 cm SCALE 52° x cm Use trigonometry to calculate the value of x. x = … [2]

2 marks

Mark scheme: 7 9.85 or 9.850 to 9.851 2 x M1 for cos 52 = oe or better 16

This question in 0580/12 Oct/Nov 2018

26 C y cm D 8.2 cm NOT TO 5.3 cm SCALE 4.4 cm x° A B Triangles ABC and BCD are both right-angled triangles. (a) Calculate the value of y. y = … [3] (b) Calculate the value of x. x = … [2]

5 marks

Mark scheme: 26(a) 2.95 or 2.954 to 2.955 3 2 2 M2 for 5.3 − 4.4 or better or M1 for 5.32 = 4.4 2 + y 2 or better 26(b) 40.3 or 40.26 to 40.27… 2 M1 for sin [ x = ]5.3 8.2

This question in 0580/12 Feb/March 2019

12 NOT TO SCALE 12 cm x cm 35° The diagram shows a right-angled triangle. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 12 6.88 or 6.882 to 6.883 2 x M1 for sin 35 [ = ] oe or better 12

This question in 0580/11 May/June 2019

13 x° NOT TO 23 m SCALE 6.2 m The diagram shows a right-angled triangle. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 13 74.4 or 74.36… 2 6.2 M1 for cos[x =] oe 23

This question in 0580/12 May/June 2019

24 D NOT TO SCALE 15 m 38° A B 10.7 m C A vertical flagpole, BD, stands on horizontal ground and is held by two ropes, AD and CD. AD = 15m , BC = 10.7m and angle DAB = 38 ° . (a) Using trigonometry, calculate BD. BD = … m [2] (b) Calculate CD. CD = … m [2]

4 marks

Mark scheme: 24(a) 9.23 or 9.234 to 9.235 2 BD M1 for sin38 = or better 15 24(b) 14.1 or 14.13 … 2 FT their (a) M1 ( their (a))2 + 10.72

This question in 0580/13 May/June 2019

21 NOT TO SCALE x cm 43° 12 cm Use trigonometry to calculate the value of x. x = … [3]

3 marks

Mark scheme: 21 16.4 or 16.40 to 16.41 3 12 12 M2 for [ x =] or [ x =] cos 43 sin 47 12 or M1 for cos [43][=] or x 12 sin 47 [=] x

This question in 0580/11 Oct/Nov 2019

17 A NOT TO SCALE 4.6 m 37° B C The diagram shows a right-angled triangle ABC. Calculate AB. AB = … m [2]

2 marks

Mark scheme: 17 2.77 or 2.768… 2 h M1 for sin[37 = ] or better 4.6

This question in 0580/12 Feb/March 2020

5 A NOT TO 38° SCALE B C D In the triangle ABC, AB = AC and angle BAC = 38°. BCD is a straight line. Work out angle ACD. Angle ACD = … [3]

3 marks

Mark scheme: 5 109 3 M1 for (180 – 38) ÷ 2 oe M1 for 180 – their ACB

This question in 0580/11 May/June 2020

11 A NOT TO SCALE 32° B C Triangle ABC is isosceles. Angle ABC = 32° and AB = AC. Find angle BAC. Angle BAC = … [2]

2 marks

Mark scheme: 11 116 2 M1 for angle ACB = 32 soi

This question in 0580/13 May/June 2020

21 (a) NOT TO SCALE 10 cm x° 18 cm Calculate the value of x. x = … [2] (b) NOT TO k cm SCALE 8 cm 15 cm Calculate the value of k. k = … [2]

4 marks

Mark scheme: 21(a) 29.1 or 29.05… 2 10 M1 for tan [x =] 18 21(b) 17 2 M1 for 82 + 152

This question in 0580/11 Oct/Nov 2020

22 NOT TO SCALE x cm 36° 22 cm Show that the value of x is 27.2, correct to 3 significant figures. [3]

3 marks

Mark scheme: 22 22 M2 22 [x =] oe M1 for cos36 = or better oe cos36 x 27.19[3 … ] A1

This question in 0580/12 Oct/Nov 2020

24 NOT TO 30 cm SCALE 18 cm x° The diagram shows a right-angled triangle. Show that the value of x is 36.9, correct to 1 decimal place. [2]

2 marks

Mark scheme: 24 sin [x =] 18 ÷ 30 oe or better M1 36.87 or 36.86… A1

This question in 0580/13 May/June 2021

15 C NOT TO SCALE 15 cm 38° A B The diagram shows a right-angled triangle, ABC. AC = 15 cm and angle BAC = 38°. Calculate BC. BC = … cm [2]

2 marks

Mark scheme: 15 9.23 or 9.234 to 9.235 2 M1 for sin[38 BC] or better 15

This question in 0580/11 May/June 2022

24 B NOT TO SCALE 53° A D C 5 m 14 m The diagram shows two right-angled triangles, ABD and BCD. AD = 5m , DC = 14m and angle BAD = 53° . Calculate BC. BC = … m [4]

4 marks

Mark scheme: 24 15.5 or 15.49… 4 2 2 M3 for  5  tan53   14 OR M2 for 5  tan53 x or M1 for tan[53=] 5 and M1 for 14 2 theirBD( ) 2

This question in 0580/12 May/June 2022

17 Q C NOT TO SCALE 9.2 cm 9.2 cm 7.3 cm A 7.3 cm B R P The diagram shows two right-angled triangles, ABC and PQR. (a) Complete this statement with a geometrical term. Triangle ABC is … to triangle PQR. [1] (b) Calculate angle ABC. Angle ABC = … [2]

3 marks

Mark scheme: 17(a) Congruent 1 17(b) 37.5 or 37.48 to 37.49 2 7.3 M1 for cos[ABC =] 9.2

This question in 0580/13 May/June 2022

22 NOT TO x cm SCALE 17.5 cm 48° The diagram shows a right-angled triangle. Show that the value of x is 15.8, correct to 3 significant figures. [3]

3 marks

Mark scheme: 22 17.5 M2 17.5 [x =] M1 for tan 48 = tan48 x or [ x =] tan 42×17.5 x or tan (90 – 48) = 17.5 15.75.. or 15.76 A1

This question in 0580/11 Oct/Nov 2022

21 A NOT TO 18 cm SCALE 42° B C ABC is a right-angled triangle. Calculate BC. BC = … cm [2]

2 marks

Mark scheme: 21 13.4 or 13.37 to 13.38 2 BC M1 for cos[42 =] or better or 18 BC sin[48 =] or better 18

This question in 0580/12 Oct/Nov 2022

21 56° NOT TO 21.8 cm SCALE x cm The diagram shows a right-angled triangle. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 21 18.1 or 18.07… 2 x M1 for sin [56 =] or 21.8 x cos [ 34 =] or better 21.8

This question in 0580/13 Oct/Nov 2022

24 NOT TO 46 cm SCALE y 74 cm The diagram shows a right-angled triangle. Show that angle y is 31.9°, correct to 1 decimal place. [2]

2 marks

Mark scheme: 24 46 M1 tan [y =] 74 31.86 to 31.87 A1

This question in 0580/12 Feb/March 2023

22 NOT TO 7.5 cm SCALE y° 12.8 cm The diagram shows a right-angled triangle. Calculate the value of y. y = … [2]

2 marks

Mark scheme: 22 30.4 or 30.36 to 30.37 2 7.5 M1 for tan [y =] or better 12.8

This question in 0580/11 May/June 2023

22 (a) A 8.6 cm NOT TO SCALE 42° B C The diagram shows a right-angled triangle ABC. Calculate AB. AB = … cm [2] (b) P NOT TO SCALE 23.8 cm Q R 11.2 cm S 20 cm The diagram shows right-angled triangles PQS and PRS. PQ = 23. 8 cm , QS = 11.2 cm and SR = 20 cm . Calculate PR. PR = … cm [4] Question 23 is printed on the next page.

6 marks

Mark scheme: 22(a) 5.75 or 5.754 to 5.755 2 AB M1 for sin 42 = or better 8.6 22(b) 29 4 M2 for 23.82 – 11.22 or M1 for […]2 + 11.22 = 23.82 and M1dep for (their 21)2 + 202

This question in 0580/12 May/June 2023

21 ABC is a right-angled triangle. A NOT TO SCALE 34° B 18 cm C Calculate AC. AC = … cm [3]

3 marks

Mark scheme: 21 21.7 or 21.71… 3 18 M2 for [AC = ] oe cos34 18 or M1 for cos 34 = AC

This question in 0580/12 Oct/Nov 2023

18 NOT TO SCALE 14 cm x° 8.5 cm The diagram shows a right-angled triangle. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 18 52.6 or 52.61 to 52.62 2 8.5 M1 for cos[...  ] oe 14

This question in 0580/12 May/June 2024

25 D NOT TO SCALE 21.2 m 48° A B C 16.5 m The diagram shows a flagpole, BD, held by two ropes, AD and CD. ABC is a straight line and angle ABD = 90°. AD = 21.2 m, AB = 16.5 m and angle BCD = 48°. (a) Show that the height of the flagpole BD is 13.3 m, correct to 1 decimal place. [3] (b) Calculate the length of the rope CD. CD = … m [3]

6 marks

Mark scheme: 25(a) 2 2 M2 M1 for BD2 + 16.52 = 21.22 or better [BD =] 21.2  16.5 13.31….. A1 25(b) 17.9 or 17.89 to 17.91….. 3 13.3 M2 for [CD =] or [CD =] sin 48 13.3 cos42 13.3 or M1 for sin 48 [=] or better CD 13.3 or for cos 42 [=] or better CD

This question in 0580/12 May/June 2024

17 C NOT TO SCALE 8 cm 37° A B The diagram shows a right-angled triangle. Calculate AB. AB = … cm [2]

2 marks

Mark scheme: 17 6.39 or 6.389... 2 M1 for cos37 AB oe 8

This question in 0580/13 May/June 2024

23 NOT TO SCALE 9.7 cm x cm 42° The diagram shows a right-angled triangle. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 23 6.49 or 6.490 to 6.491 2 x M1 for sin 42 = or better 9.7

This question in 0580/13 Oct/Nov 2024

14 The diagram shows a smaller triangle DEF which has vertices on the sides of a larger triangle ABC. NOT TO A SCALE 100° E x° 25° D 50° 45° 35° 30° B C F Find the value of x. x = … [3]

3 marks

Mark scheme: 14 10 3 B2 for any two correct angles identified from BDF = 85, FDE = 70 and DFE = 100 or B1 for any one of them OR B1 for AED = 55 and B1 for CEF = 115

This question in 0580/12 Oct/Nov 2025