x² + y² = r²: Challenge & Extension
Mathematics
Grade 6
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A challenging worksheet exploring the equation x² + y² = r² for Grade 6 students, including practice, problem solving, real-world applications, and extensions.
Topics covered:
Worksheet Preview
Full preview • 15 questions
x² + y² = r²: Challenge & Extension
Subject: MathematicsGrade: Grade 6
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade Grade 6
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Given the circle equation x² + y² = 16, what is the radius of the circle?
[2 marks]2.
Plot the circle described by x² + y² = 25 on the grid.
[3 marks]3.
If a circle has equation x² + y² = 36, what are the coordinates of points on the circle at the top and bottom?
[2 marks]4.
Construct a circle with radius 3 centered at (2, -1). Write its equation.
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working where applicable.
1.
A circle passes through the points (0, 5), (0, -5), and (3, 0). Find the equation of the circle.
[4 marks]2.
Explain why the equation x² + y² = 9 represents a circle with radius 3 centered at the origin.
[3 marks]3.
A circle has a radius of 7 units. Write its equation assuming it is centered at the origin.
[2 marks]4.
Determine whether the point (4, 3) lies on the circle x² + y² = 25.
[2 marks]C
Real-world Applications
Answer all questions with detailed reasoning.
1.
A circular fountain has a radius of 4 meters. If the fountain is centered at point (10, 8), write its equation.
[3 marks]2.
A drone flies around a circular path described by x² + y² = 36. If the drone starts at point (6, 0), what is its initial distance from the center?
[2 marks]D
Challenge & Extension
Answer the most challenging questions. Show detailed solutions.
1.
Find the equation of a circle that passes through points (1, 4), (4, 1), and (5, 5).
[4 marks]2.
A circle has an equation x² + y² + 6x - 8y + 9 = 0. Find its center and radius.
[4 marks]E
Mixed Review & Error Analysis
Answer all questions carefully. Review common mistakes in your answers.
1.
Identify and correct the mistake in this circle equation: x² + y² = -25.
[2 marks]2.
The equation x² + y² = 0 represents a circle. Is this true? Explain.
[3 marks]3.
What is the mistake in assuming that x² + y² = 9 has solutions only when x and y are integers?
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet