Mastering Constructions & Loci
Mathematics
GCSE Higher
11 questions
~22 mins
0 views0 downloads
About This Worksheet
A worksheet covering Constructions & Loci for GCSE Higher students. It includes procedural, reasoning, and real-world questions to develop understanding and application skills.
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Mastering Constructions & Loci
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Construct an equilateral triangle with side length 6 cm. Label the vertices A, B, and C.
[3 marks]2.
Using a compass and ruler, bisect the line segment AB of length 8 cm. Draw the bisector and mark the midpoint M.
[3 marks]3.
Construct a circle with radius 4 cm centered at point P. Mark any point Q on the circle.
[2 marks]4.
Draw a triangle with vertices at (0,0), (4,0), and (2,3). Construct the perpendicular bisector of side AC.
[3 marks]5.
Construct the locus of points equidistant from points P and Q, where P is at (1,2) and Q at (5,2).
[4 marks]6.
Given a triangle ABC, construct the incenter of the triangle.
[3 marks]7.
Construct a locus of points that are exactly 5 cm from a fixed point P outside a given circle.
[4 marks]8.
A circle with center at (3,3) passes through point (6,7). Construct the circle and find its radius.
[3 marks]9.
In triangle PQR, construct the locus of points inside the triangle that are equidistant from side PQ and side PR.
[4 marks]10.
Challenge: A park is designed with a circular pond at the center. Construct the locus of points where children can slide from the edge of the pond to the boundary of the park, assuming the slide is a straight line and the pond has radius 3 meters, the park radius is 10 meters.
[5 marks]11.
Real-world application: A new roundabout is to be constructed with a central circle of radius 5 meters. Roads must be tangent to the circle at four points. Construct these tangents and explain the reasoning.
[5 marks]Quick Actions
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet