Home / iGCSE Mathematics (0580) :E4.2 Measure and draw lines and angles.iGCSE Style Questions Paper 2

iGCSE Mathematics (0580) :E4.2 Measure and draw lines and angles.iGCSE Style Questions Paper 2

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IGCSE Mathematics(0580) Practice Questions Paper 2 - All Chapters
Question

Using a ruler and compasses only, construct this triangle. Leave in your construction arcs. The side of length 12cm has been drawn for you.

Triangle construction
▶️ Answer/Explanation
Answer: Correct triangle with construction arcs.
Steps:
1. Use the given 12cm side as the base.
2. With a compass, draw arcs from both ends of the base using the other two given side lengths.
3. The intersection point of the arcs is the third vertex of the triangle.
4. Connect the points to complete the triangle, leaving the construction arcs visible.
Question

AB is the diameter of a circle.
C is a point on AB such that AC = 4 cm.
(a) Using a straight edge and compasses only, construct
(i) the locus of points which are equidistant from A and from B,

▶️ Answer/Explanation
Solution

(a)(i) Ans: Perpendicular bisector of AB

The locus of points equidistant from A and B is the perpendicular bisector of AB. Construct this by drawing arcs from A and B with the same radius (greater than half of AB) and connecting their intersection points.

(a)(ii) Ans: Circle centered at C with radius 4 cm

The locus of points 4 cm from C is a circle centered at C with radius 4 cm. Use a compass to draw this circle.

(b) Ans: Shaded region

The required region is the intersection of:
1. Points nearer to B than to A (below the perpendicular bisector).
2. Points less than 4 cm from C (inside the circle centered at C).

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