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6 NOT TO SCALE B A North The bearing of A from B is 227°. Find the bearing of B from A. ................................................. [2]
IGCSE Mathematics 0580 · Topic practice
Use right-angled trigonometry, Pythagoras, bearings and the sine and cosine rules. Label the sides relative to the angle before choosing a ratio or rule.
Appears inPaper 1 33Paper 2 139Paper 3 33Paper 4 140
You’re practising 2016–2018 papers. The 2019–2026 papers, including 2026, need a plan.
Unlock from $6/mo6 NOT TO SCALE B A North The bearing of A from B is 227°. Find the bearing of B from A. ................................................. [2]
7 A B C 2.5 cm 4.1 cm NOT TO SCALE Calculate the length of AC. AC = ........................................ cm [2]
7 A and B are two towns on a map. The bearing of A from B is 140°. Work out the bearing of B from A. ................................................. [2]
12 x° is an obtuse angle and sin x° = 0.43 . Find the value of x. x = ............................................... [2]
14 84.6° 17.8 cm 5.9 cm C A B NOT TO SCALE Use the sine rule to find angle ABC. Angle ABC = .............................................. [3]
16 NOT TO SCALE M B O A The diagram shows a circle, centre O. AB is a chord of length 12 cm. M is the mid-point of AB and OM = 4.5 cm. Calculate the radius of the circle. .......................................... cm [3]
16 1.6 m 2.8 m A B C NOT TO SCALE (a) Find the area of triangle ABC. ............................................. m2 [2] (b) Calculate AC. AC = .................................... m [2]
19 N L M 19 cm 14 cm 16 cm NOT TO SCALE Calculate angle LMN. Angle LMN = ............................................... [4]
22 A B 8 cm NOT TO SCALE 5.5 cm 16.2 cm The diagram shows a cuboid with dimensions 5.5 cm, 8 cm and 16.2 cm. Calculate the angle between the line AB and the horizontal base of the cuboid. ................................................ [4]
23 x° 5 cm 11 cm 13 cm NOT TO SCALE Calculate the value of x. x = ................................................ [4]
23 NOT TO SCALE 4 cm 6 cm C P Q B D A 12 cm The diagram shows a triangular prism. AB = 12 cm, BC = 6 cm, PC = 4 cm, angle BCP = 90° and angle QDC = 90°. Calculate the angle between AP and the rectangular base ABCD. ................................................. [4]
2 D NOT TO SCALE C A B The vertices of a square ABCD lie on the circumference of a circle, radius 8 cm. (a) Calculate the area of the square. ......................................... cm2 [2] (b) (i) Calculate the area of the shaded segment. ......................................... cm2 [3] (ii) Calculate the perimeter of the shaded segment. .......................................... cm [4]
4 The diagram shows a right-angled triangle ABC. 4(x – 1) cm (2x + 5) cm A B C NOT TO SCALE The area of this triangle is 30 cm2. (a) Show that 2x2 + 3x – 20 = 0. [3] (b) Use factorisation to solve the equation 2x2 + 3x – 20 = 0. x = ...................... or x = ...................... [3] (c) Calculate BC. BC = .......................................... cm [3]
5 NOT TO SCALE O B A C 8 cm 7 cm 78° The diagram shows a design made from a triangle AOC joined to a sector OCB. AC = 8 cm, OB = OC = 7 cm and angle ACO = 78°. (a) Use the cosine rule to show that OA = 9.47 cm, correct to 2 decimal places. [4] (b) Calculate angle OAC. Angle OAC = ................................................ [3] 9 (c) The perimeter of the design is 29.5 cm. Show that angle COB = 41.2°, correct to 1 decimal place. [5] (d) Calculate the total area of the design. ......................................... cm2 [4]
5 6 cm 18 cm h cm x° NOT TO SCALE The diagram shows a prism with length 18 cm and volume 253.8 cm3. The cross-section of the prism is a right-angled triangle with base 6 cm and height h cm. (a) (i) Show that the value of h is 4.7 . [3] (ii) Calculate the value of x. x = ............................................... [2] (b) Calculate the total surface area of the prism. ........................................ cm2 [6]
6 (a) A D C B E 6 cm 6 cm 12 cm NOT TO SCALE In the pentagon ABCDE, angle ACB = angle AED = 90°. Triangle ACD is equilateral with side length 12 cm. DE = BC = 6 cm. (i) Calculate angle BAE. Angle BAE = ............................................... [4] (ii) Calculate AB. AB = ......................................... cm [2] (iii) Calculate AE. AE = ......................................... cm [3] 13 (iv) Calculate the area of the pentagon. ......................................... cm2 [4] (b) P A B C D S R Q 5 cm 8 cm 4 cm NOT TO SCALE The diagram shows a cuboid. AB = 8 cm, BC = 4 cm and CR = 5 cm. (i) Write down the number of planes of symmetry of this cuboid. ................................................ [1] (ii) Calculate the angle between the diagonal AR and the plane BCRQ. ................................................ [4]
6 B C D A NOT TO SCALE 80° 13 cm 11 cm 4 cm 8 cm (a) Calculate angle ACB. Angle ACB = ................................................. [4] (b) Calculate angle ACD. Angle ACD = .................................................. [4] 13 (c) Calculate the area of the quadrilateral ABCD. ........................................... cm2 [3]
7 In this question, all measurements are in metres. 2x – 3 x 6 NOT TO SCALE The diagram shows a right-angled triangle. (a) Show that 5x2 - 12x - 27 = 0. [3] (b) Solve 5x2 - 12x - 27 = 0. Show all your working and give your answers correct to 2 decimal places. x = ......................... or x = ......................... [4] (c) Calculate the perimeter of the triangle. ............................................ m [2] (d) Calculate the smallest angle of the triangle. ................................................. [2]
7 (a) 130.6° 8.9 cm 12.5 cm Q P R NOT TO SCALE Calculate the area of triangle PQR. ........................................ cm2 [2] (b) 123.5° 21.3 cm 11.6 cm 18 cm A D B C NOT TO SCALE In the diagram, AB = 18 cm, BC = 21.3 cm and BD = 11.6 cm. Angle BDC = 123.5° and angle ABC is a right angle. (i) Calculate angle BCD. Angle BCD = ............................................... [3] 11 (ii) Calculate AD. AD = ......................................... cm [5]
8 248 km North NOT TO SCALE 42° P L M The diagram shows two ports, L and P, and a buoy, M. The bearing of L from P is 201° and LP = 248 km. The bearing of M from P is 127°. Angle PML = 42°. (a) Use the sine rule to calculate LM. LM = ......................................... km [4] (b) A ship sails directly from L to P. (i) Calculate the shortest distance from M to LP. .......................................... km [3] (ii) The ship leaves L at 20 45 and travels at a speed of 40 km/h. Calculate the time the next day that the ship arrives at P. ................................................. [3]