CAMBRIDGE IGCSE MATHS (0580)

Question 1:


The diagram represents a field in the shape of a quadrilateral ABCD.
AB = 32m, BC = 43m and AC = 64m.

(a) (i) Show clearly that angle CAB = 37.0° correct to one decimal place.
Answer(a)(i) ............................................... [4]

(ii) Calculate the area of the triangle ABC.
Answer(a)(ii) ............................................... m² [2]

(b) CD = 70m and angle DAC = 55°.
Calculate the perimeter of the whole field ABCD.
Answer(b) ............................................... m [6]

Question 2:


The area of triangle ABC is 130 cm².
AB = 16 cm and BC = 25 cm.

(a) Show clearly that angle ABC = 40.5°, correct to one decimal place.
Answer(a) ............................................... [3]

(b) Calculate the length of AC.
Answer(b) AC = ............................................... cm [4]

(c) Calculate the shortest distance from A to BC.
Answer(c) ............................................... cm [2]

Question 3:


The diagram shows a school playground ABCD.
ABCD is a trapezium.
AB = 55m, BD = 70m, angle ABD = 40° and angle BCD = 32°.

(a) Calculate AD.
Answer(a) AD = ............................................... m [4]

(b) Calculate BC.
Answer(b) BC = ............................................... m [4]

(c) (i) Calculate the area of the playground ABCD.
Answer(c)(i) ............................................... m² [3]

(ii) An accurate plan of the school playground is to be drawn to a scale of 1:200.
Calculate the area of the school playground on the plan.
Give your answer in cm².
Answer(c)(ii) ............................................... cm² [2]

(d) A fence, BD, divides the playground into two areas.
Calculate the shortest distance from A to BD.
Answer(d) ............................................... m [2]

Question 4:


The diagram shows the cross-section, ABCD, of a ramp.

(a) Calculate angle DBC.
Answer(a) Angle DBC = ............................................... [2]

(b) (i) Show that BD is exactly 3m.
Answer(b)(i) ............................................... [2]

(ii) Use the cosine rule to calculate angle ABD.
Answer(b)(ii) Angle ABD = ............................................... [4]

(c) The ramp is a prism of width 4m.
Calculate the volume of this prism.
Answer(c) ............................................... m³ [3]

Question 5:
A field, ABCD, is in the shape of a quadrilateral. A footpath crosses the field from A to C.

(a) Use the sine rule to calculate the distance AC and show that it rounds to 119.9m, correct to 1 decimal place.
Answer(a) ............................................... [3]

(b) Calculate the length of BC.
Answer(b) BC = ........................................... m [4]

(c) Calculate the area of triangle ACD.
Answer(c) .......................................... m² [2]

(d) The field is for sale at $4.50 per square metre. Calculate the cost of the field.
Answer(d) $ ............................................... [3]

Question 6:
(a) ABCD is a trapezium.

(i) Calculate the length of AD.
Answer(a)(i) AD = .......................................... cm [2]

(ii) Calculate the size of angle BCD.
Answer(a)(ii) Angle BCD = ................................................ [3]

(iii) Calculate the area of the trapezium ABCD.
Answer(a)(iii) ......................................... cm² [2]

(b) A similar trapezium has a perpendicular height of 9.4cm. Calculate the area of this trapezium.
Answer(b) ......................................... cm² [3]

Question 7:


A, B, C, and D are points on a circle, center O. CE is a tangent to the circle at C.

(a) Find the sizes of the following angles and give a reason for each answer.
(i) Angle DAC = ..................... because ..........................................................................................
..................................................................................................................................................... [2]
(ii) Angle DOC = ..................... because .........................................................................................
..................................................................................................................................................... [2]
(iii) Angle BCO = ..................... because ..........................................................................................
..................................................................................................................................................... [2]

(b) CE = 8.9cm and CB = 7cm.
(i) Calculate the length of BE.
Answer(b)(i) BE = .......................................... cm [4]
(ii) Calculate angle BEC.
Answer(b)(ii) Angle BEC = ................................................ [3]

Question 8:


The diagram shows some distances between Mumbai (M), Kathmandu (K), Dhaka (D), and Colombo (C).

(a) Angle CKD = 65°.
Use the cosine rule to calculate the distance CD.
Answer(a) CD = .......................................... km [4]

(b) Angle MKC = 40°.
Use the sine rule to calculate the acute angle KMC.
Answer(b) Angle KMC = ................................................ [3]

(c) The bearing of K from M is 050°.
Find the bearing of M from C.
Answer(c) ................................................ [2]

(d) A plane from Colombo to Mumbai leaves at 21:15, and the journey takes 2 hours 24 minutes.
(i) Find the time the plane arrives at Mumbai.
Answer(d)(i) ................................................ [1]
(ii) Calculate the average speed of the plane.
Answer(d)(ii) ....................................... km/h [2]

Question 9:


The diagram shows a field, ABCD.
AD = 180 m and AC = 240 m.
Angle ABC = 50° and angle ACB = 85°.

(a) Use the sine rule to calculate AB.
Answer(a) AB = ............................................ m [3]

(b) The area of triangle ACD = 12,000 m².
Show that angle CAD = 33.75°, correct to 2 decimal places.
Answer(b) ................................................ [3]

(c) Calculate BD.
Answer(c) BD = ............................................ m [5]

(d) The bearing of D from A is 030°.
Find the bearing of:
(i) B from A
Answer(d)(i) ................................................. [1]
(ii) A from B
Answer(d)(ii) ................................................. [2]

Question 10:


The diagram shows a quadrilateral ABCD.

(a) The length of AC is x cm. Use the cosine rule in triangle ABC to show that:
2x² – 17x – 168 = 0.
Answer(a) ............................................. [4]

(b) Solve the equation 2x² – 17x – 168 = 0.
Show all your working and give your answers correct to 2 decimal places.
x = ............................................. or x = ............................................. [4]

(c) Use the sine rule to calculate the length of CD.
Answer(c) CD = .......................................... cm [3]

(d) Calculate the area of the quadrilateral ABCD.
Answer(d) .......................................... cm² [3]

Question 11:
(a) The diagram shows triangle PQR.
The angle 130.6°, side 8.9 cm, and side 12.5 cm are given.
Calculate the area of triangle PQR.
Answer(a) ........................................ cm² [2]

(b) The diagram shows quadrilateral ABCD.
Given: AB = 18 cm, BC = 21.3 cm, BD = 11.6 cm, and angle BDC = 123.5°.
Angle ABC is a right angle.

(i) Calculate angle BCD.
Answer(b)(i) Angle BCD = ........................................ [3]

(ii) Calculate AD.
Answer(b)(ii) AD = ......................................... cm [5]

Question 12:
(a) Calculate angle ACB.
Answer(a) Angle ACB = ................................................. [4]

(b) Calculate angle ACD.
Answer(b) Angle ACD = .................................................. [4]

(c) Calculate the area of the quadrilateral ABCD.
Answer(c) Area of ABCD = ........................................... cm² [3]