Home / iGCSE Mathematics (0580) :C4.1 Use and interpret the geometrical terms. iGCSE Style Questions Paper 3

iGCSE Mathematics (0580) :C4.1 Use and interpret the geometrical terms. iGCSE Style Questions Paper 3

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IGCSE Mathematics(0580) Practice Questions Paper 3 - All Chapters
Question

(a)

Write down the mathematical name for this solid.

(b) 

(i) Measure the size of angle x.
(ii) Write down the mathematical name for this type of angle.

(c)

Points A, B and C lie on the circle, centre O.
AB = 11 cm and BC = 5 cm.

(i) Give a geometrical reason why angle ACB is 90°.
(ii) Calculate the circumference of the circle.
(iii) Show that AC is 9.8 cm, correct to 2 significant figures.

(d) The surface area of a sphere is 250 cm². Calculate the radius of the sphere.
[The surface area, A, of a sphere with radius r is \( A = 4\Pi r^{2}\)]

▶️ Answer/Explanation
Solution

(a) Ans: Cylinder

(b)(i) Ans: 137° (accept 136-138°)

(b)(ii) Ans: Obtuse angle

(c)(i) Ans: Angle in a semicircle is 90°

(c)(ii) Ans: 34.6 cm (using π = 3.142)

Calculation: Circumference = π × diameter = 3.142 × 11 ≈ 34.6 cm

(c)(iii) Ans: Using Pythagoras: √(11² – 5²) = √96 ≈ 9.8 cm

(d) Ans: 4.46 cm

Calculation: Using A = 4πr² → r = √(250/(4π)) ≈ 4.46 cm

Question

(a) The diagram shows a circle.

(i) The diameter of this circle is 168 mm. Write down the radius of this circle.
(ii) On the diagram, draw a chord of this circle.

(b) The scale drawing shows the position of ship A and the position of ship B.
The scale is 1 cm represents 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.
(ii) Find the actual distance of ship C from ship A.

(c) (i) Show that the interior angle of a regular octagon is 135°.

(ii) 

Show that two regular octagons and a square meet at a point without any gaps.

(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.

▶️ Answer/Explanation
Solution

(a)(i) Ans: 84 mm

Radius = Diameter/2 = 168/2 = 84 mm

(a)(ii) Ans: Any straight line connecting two points on the circumference

A chord is any line segment whose endpoints lie on the circle.

(b)(i) Ans: Position marked 7.5 cm from B at 124°

45 km ÷ 6 km/cm = 7.5 cm. Measure 124° from north line at B.

(b)(ii) Ans: 57 km

Measure distance on diagram (about 9.5 cm) and multiply by 6.

(c)(i) Ans: Proof shown

Interior angle = (n-2)×180°/n = (8-2)×180°/8 = 135°

(c)(ii) Ans: Proof shown

135° (octagon) + 135° (octagon) + 90° (square) = 360° which fits perfectly.

(d) Ans: 41°

Angle in semicircle is 90°, so angle EDF = 180° – 90° – 49° = 41°.

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