Combining Loci: Fluency & Practice
Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet covering Combining Loci - Regions for GCSE Foundation students to develop procedural mastery and problem-solving skills.
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Combining Loci: Fluency & Practice
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Read the key concept before attempting the questions.
1.
When combining loci, the resulting region is found by overlapping the individual loci. The key formula involves understanding the intersection of these loci to identify common regions.
[2 marks]B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Construct the locus of points equidistant from two fixed points A and B. Describe the region formed when this locus is combined with the locus of points equidistant from point C and the line through A and B.
[3 marks]2.
Plot the graph of y = 2x and draw the locus of points 3 units away from this line. Then, shade the region where the two loci overlap.
[3 marks]3.
A point P is on the locus of points equidistant from points A and B. If A is at (2, 3) and B at (6, 7), find the equation of the locus of P.
[3 marks]4.
Explain how the region changes when the two loci are moved closer together. What does this imply about the combined region?
[2 marks]5.
Construct the locus of points that are 4 units from a given circle with radius 3. Identify the resulting region when combined with the locus of points 2 units from a line tangent to the circle.
[3 marks]6.
A school wants to find a region accessible to students living within 2 km of the school and also within 3 km of the sports centre. The school is at (4, 5) and the sports centre at (10, 8). Find the combined region using loci.
[4 marks]7.
Given two circles with centers at (0,0) and (6,0) and radii 4 and 3 respectively, find the region formed by the intersection of the loci of points within 4 units of the first circle and within 3 units of the second circle.
[3 marks]8.
Describe a real-world scenario where combining loci could be used to determine a safe zone or optimal location.
[2 marks]9.
Using the given loci, find the common region when the loci are defined by: (a) points 2 units from line AB, and (b) points 3 units from circle centered at (4,4) with radius 2.
[4 marks]10.
Identify and correct the mistake in the following reasoning: 'The locus of points equidistant from two points is a circle, so when combining two such loci, the resulting region is always a circle.'
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet