Compound shapes and parts of shapes — Paper 4 · IGCSE Mathematics - International 0607

9 E 50° NOT TO SCALE 13 cm D 70° A B C 15 cm In the diagram, ABC is a straight line, AE = BE = 13 cm and BC = 15 cm. Angle EAB = 70°, angle EBD = 90° and angle BED = 50°. Calculate (a) the length of the perpendicular line from E to AB, … cm [2] (b) the length BD, BD = … cm [2] (c) the length CD, CD = … cm [4] (d) the area of the quadrilateral ACDE. … cm2 [3]

11 marks

Mark scheme: 9(a) 12.2 or 12.21 to 12.22 2 [ ] M1 for sin70 = oe 13 9(b) 15.5 or 15.49… 2 BD M1 for tan50 = oe 13 9(c) 5.32 or 5.316 to 5.319… 4 B1 for [angle DBC = ] 20 M1 for (theirBD)2 + 152 – 2 × their BD × 15cos(their DBC) A1 for 28.26 to 28.30… 9(d) art 195 3 M2 two of 5.0 × 13 × 13 × sin 40 oe 0.5 × 13 × their BD oe 0.5 × 15 × their BD × sin(their 20) or M1 for one of above

This question in 0607/41 May/June 2018

5 16 m A P D NOT TO SCALE 30 m S Q 18 m 12 m B R C 24 m 40 m In the diagram, ABCD is a rectangle. (a) Find PS. PS = … m [2] (b) Find angle BRS. Angle BRS = … [2] (c) Find the perimeter of PQRS. … m [3] (d) Find the shaded area. … m2 [3] (e) Explain why triangle ASP is similar to triangle BSR. … … [2]

12 marks

Mark scheme: 5(a) 20 2 2 2 M1 for 16 + ( 30 − 18 ) 5(b) 36.9 or 36.86 to 36.87 2 18 M1 for tan[ ] = oe 24 5(c) 100 3 2 2 M2 for 2 × (their (a) + 18 + 24 ) oe or M1 for 182 + 24 2 or RS = 30 or PQ = 30 seen 5(d) 576 3 M2 for (40 × 30) − 2 × (0.5 × 18 × 24) − 2 × (0.5 × 16 × 12) oe or M1 for any correct and relevant area 5(e) Correct explanation 2 B1 for partial explanation e.g. ratio of two sides the same, with names or numbers given.

This question in 0607/42 May/June 2018

8 A 13 cm NOT TO B SCALE 9 cm 6 cm D 11 cm C ABCD is a quadrilateral. (a) Show that BD = 9.22 cm, correct to 3 significant figures. [3] (b) Calculate angle ABD. Angle ABD = … [3] (c) Calculate the total area of the quadrilateral ABCD. … cm2 [3] (d) Calculate the length of the diagonal AC. AC = … cm [3]

12 marks

Mark scheme: 8(a) Correct Pythagoras statement M2 or M1 for [BD]2 + 62 = 112 oe leading to 112 – 62 or 121 – 36 or 85 9.219… A1 9.219… implies M1 A1 8(b) 43.8 or 43.80... nfww 3 9.22 2 + 132 − 9 2 M2 for cos[ABD] = 2 × 9.22 × 13 or better or M1 for 92 = 9.222 + 132 – 2 × 9.22 × 13 cos [ABD] oe 8(c) 69.1 or 69.13 to 69.14... nfww 3 M1 for 0.5 × 9.22 × 6 oe M1 for 0.5 × 9.22 × 13 × sin (their 43.8) oe 8(d) 17.7 or 17.69... 3 M1 for 62 + 132 – 2 × 6 × 13 cos (90 + their 43.8) A1 for 313 or 312.9 to 313.0

This question in 0607/41 May/June 2019

7 The diagram shows a radio in the shape of a prism. This diagram shows the base of the radio. E F A D G B C H I ABC is an equilateral triangle. The circles have their centres at A, B and C and each has a radius of 5 cm. DE, FG and HI are tangents to the circles. (a) Show that AB = 8.66 cm, correct to 3 significant figures. [3] (b) Calculate the area of the base of the radio. … cm2 [4] (c) The height of the radio is 12 cm. Calculate the volume of the radio. … cm3 [1]

8 marks

Mark scheme: 7(a) 2 × 5 × cos 30 M2 x or M1 for = cos 30 oe 5 8.660... A1 7(b) 241 or 240.9... to 241.2... 4 M1 for 3 × 8.66 × 5 120 M1 for 3 × × π × 52 360 M1 for × 8.662 × sin 60 7(c) 2890 to 2895 1 FT 12 × their (b)

This question in 0607/43 May/June 2020

9 F NOT TO SCALE B A E 20 cm D C 12 cm The diagram shows rectangle ABCD and two right-angled isosceles triangles, ABF and BCE. (a) Find the perimeter of the quadrilateral CDFE. … cm [3] (b) (i) Find the area of the quadrilateral CDFE. … cm2 [3] (ii) Quadrilateral Q is similar to quadrilateral CDFE. The area of quadrilateral Q is 158 cm2. Find the length of the shortest side of quadrilateral Q. … cm [2] (c) Calculate angle AFE. Angle AFE = … [2]

10 marks

Mark scheme: 9(a) 106 or 106.4 to 106.5 3 2 2 2 2 M2 for 32 + 12 and 20 + 20 oe or M1 for 322 + 122 or 202 + 202 oe 9(b)(i) 632 3 M2 for 0.5 × 20 × 20 and 0.5 × 32 × 12 and 20 × 12 oe or M1 for 0.5 × 20 × 20 or 0.5 × 32 × 12 or 0.5 × 12 × 12 or 0.5 × 12 × 12 9(b)(ii) 6 2 their 632 158 M1 for or 158 their 632 9(c) 69.4 or 69.42 to 69.45 2 32 M1 for tan [ x ] = oe 12

This question in 0607/41 May/June 2021

10 (a) A NOT TO E SCALE 54° O F D 62° B C G A, B, C, D and E are points on the circle centre O. FBG is a tangent to the circle at B. Angle ABF = 62° and angle BED = 54° . Find (i) angle AEB, Angle AEB = … [1] (ii) angle BAD, Angle BAD = … [1] (iii) angle EAD, Angle EAD = … [1] (iv) angle BCD, Angle BCD = … [1] (v) angle FBD. Angle FBD = … [1] (b) A NOT TO 6 cm SCALE O 120° P B PA and PB are tangents to the circle centre O. The radius of the circle is 6 cm and angle AOB = 120° . The shaded area = ( a 3 - b r) cm 2 . Find the value of a and the value of b. a = … b = … [5]

10 marks

Mark scheme: 10(a)(i) 62 1 10(a)(ii) 54 1 10(a)(iii) 36 1 FT 90 – their BAD 10(a)(iv) 126 1 10(a)(v) 126 1 10(b) [a =] 36 5 B3 for 36 3 [b =] 12 or M1 for [AP =] 6tan 60 oe (6 3 ) (10.392...) 1 M1 for 2 × × 6 × their 6 3 oe (62.35...) 2 B2 for 12π 120 2 or M1 for  π  6 (37.699...) 360

This question in 0607/43 May/June 2022

8 A E 8 cm NOT TO 16 cm 60° SCALE B 17 cm 32° 18 cm 55° D C The diagram shows a pentagon ABCDE and diagonals BD and BE. (a) (i) Calculate angle BCD. Angle BCD = … [1] (ii) Calculate BC. BC = … cm [3] (b) Calculate angle EBD. Angle EBD = … [3] (c) Calculate the area of the pentagon ABCDE. … cm2 [4] (d) Calculate the shortest distance from C to AE. … cm [4]

15 marks

Mark scheme: 8(a)(i) 93 1 8(a)(ii) 14.8 or 14.76… 3 18sin55 M2 for sin ( their ( i ) ) sin ( their ( i ) ) sin55 or M1 for = oe 18 BC 8(b) 59.7 or 59.65… 3 16 2 + 182 − 17 2 M2 for 2  16  18 or M1 for 172 = 162 + 182 – 2  16  18cos(…) 8(c) 250 or 249.7 to 250.3… 4 1 M1 for 8 16  sin60 oe 2 1 M1 for  16  18  sin theirEBD oe 2 1 M1 for  18  theirBC  sin32 oe 2 8(d) 21[.0] or 21.1 or 20.95 to 21.07 4 Triangle BXC where X is on AB extended and angle BXC = 90° M3 for 8 + their BCcos(180 – 60 – 32 – their(a)) or M2 for their BCcos(180 – 60 – 32 – their(a)) or M1 for angle XBC = 180 – 60 – 32 – their(a) If 0 scored, SC1 for recognition of correct shortest distance, e.g. AX OR M1 for [AC2 =] 82 + (theirBC)2 – 2  8  (theirBC) cos(60 + theirEBD + 32) oe M1 for theirAC theirBC = sin ( 60 + theirEBD + 32 ) sin BAC oe M1 for perp = sin ( 90 − theirBAC ) oe theirAC If 0 scored, SC1 for recognition of correct shortest distance

This question in 0607/43 Oct/Nov 2022

8 North B NOT TO 55 km SCALE A C 37 km 64 km 28° D The diagram shows four points A, B, C and D on level ground. B is due north of A and C is due east of A. (a) Calculate AB. AB = … km [3] (b) Calculate the obtuse angle ACD. Angle ACD = … [3] (c) Find the bearing of (i) D from A … [2] (ii) A from D. … [1] (d) Calculate the area of the quadrilateral ABCD. … km2 [3]

12 marks

Mark scheme: 8(a) 40.7 or 40.69… 3 M2 for 552 – 372 oe soi by 1656 or M1 for 552 = AB2 + 372 oe 8(b) 125.7 or 126 or 125.7… 3 64  sin28 M2 for [sin ACD =] 37 64 37 or M1 for = oe sin ACD sin28 8(c)(i) 116 or 116.2 to 116.3 2 M1 for 180 – 28 – their(b) soi by 26.29 or 26.3 8(c)(ii) 296 or 296.2 to 296.3 1 FT 180 + their (c)(i) 8(d) 1280 or 1277 to 1278 3 M1 for 0.5 × their(a) × 37 M1 for 0.5 × 64 × 37 × sin(180 – 28 – their(b))

This question in 0607/42 Feb/March 2023

5 (a) Calculate the area of an equilateral triangle with side length 12 cm. … cm2 [2] (b) Calculate the area of a circle with circumference 60 cm. … cm2 [3] (c) 6 cm NOT TO SCALE O The diagram shows part of a regular 10-sided polygon with centre O and side length 6 cm. Calculate the area of the polygon. … cm2 [4]

9 marks

Mark scheme: 5(a) 62.4 or 62.35... 2 1 M1 for  12  12  sin60 oe 2 5(b) 286 or 286.4 to 286.5 3 M2 for π × (their radius)2 or M1 for 2πr = 60 or better 5(c) 277 or 276.9 to 277.0 4 1 M3 for [10 ×] their6 height oe 2 1  3  2 or [10]     sin36 2  sin18  3 or M2 for 3 tan72 or oe sin18 or M1 for angles 72 or 36 or 18 or 144 seen

This question in 0607/42 May/June 2024

7 NOT TO SCALE A B 12 cm 12 cm C The diagram shows a logo made from an isosceles triangle and two semicircles. The perimeter of the logo is 37 cm. (a) Show that the diameter of each semicircle is 4.14 cm, correct to 3 significant figures. [2] (b) Calculate angle ACB. Angle ACB = … [3] (c) Calculate the area of the logo. … cm2 [3] (d) A mathematically similar logo has an area of 35 cm2. Calculate the perimeter of this logo. … cm [3]

11 marks

Mark scheme: 7(a) πd = 37 – 12 – 12 oe M1 4.137 to 4.138... A1 7(b) 40.3 or 40.4 3 4.14 M2 for 2 × sin-1 oe or 40.33 to 40.36… 12 12 2  12 2   2  4.14  2 or cos ACB  2  12  12 4.14 or M1 for sin(...) = 12 2  12 2  2  12  12  cos ACB or  2  4.14  2  12 7(c) 60[.0] or 60.1 3 1 M1 for  12  12  sin( their b ) oe or 60.01 to 60.13 2 1  4.14  2 M1 for 2    oe 2  2  7(d) 28.2 or 28.3 3 35 or 28.23 to 28.26 M2 for 37  oe their c 35 their c or M1 for or their c 35 35  p  2 or   their c  37 

This question in 0607/43 May/June 2024

1 This shape is made using 2 rectangles. 4 NOT TO 2x SCALE 3x 7 (a) Find the perimeter of the shape. Give your answer, in terms of x, in its simplest form. … [2] (b) Find the area of the shape. Give your answer, in terms of x, in its simplest form. … [2]

4 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6x + 14 or 2(3x + 7) Final answer 2 M1 for 3x + 4 + 3x + (7 – 4) + 7 oe or B1 for 6x + k (k ≠ 22) or kx + 14 (k ≠ 8) or correct answer spoilt 1(b) 15x 2 M1 for area of one correct rectangle e.g. 21x, 12x, 7x

This question in 0607/42 Feb/March 2025

7 A 23 cm B NOT TO SCALE D C The diagram shows a trapezium, ABCD. AD = DC = CB and AB = 23 cm. The perimeter of the trapezium is 62 cm. (a) Calculate the area of the trapezium. … cm2 [5] (b) Calculate angle BAD. Angle BAD = … [2]

7 marks

Mark scheme: 7(a) 216 5 B1 for 13 23 −their13 M1 for 2 M1 for (their13)2 = (their5)2 + h2 1 M1 for (23 + their13)(theirh ) oe h < 13 2 7(b) 67.4 or 67.38… 2 their 5 M1 for cos = oe, h < 13 if used in their13 trig

This question in 0607/41 Oct/Nov 2025