4 Formative Assessments
2 Original Student Tutorials
1 Problem-Solving Task
MFAS Formative Assessments
Original Student Tutorials Mathematics - Grades 9-12
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Assessed: Yes
Test Item Specifications
Assessment Limits :
In items where the student has to complete the square to find the
center and radius of the circle, coefficients of quadratic terms should
equal 1 and all other terms should have integral coefficients.
Calculator :
Clarification :
Students will use the Pythagorean theorem, the coordinates of a
circle's center, and the circle's radius to derive the equation of a
circle.
Students will determine the center and radius of a circle given its
equation in general form.
Stimulus Attributes :
Items may be set in a real-world or mathematical context.
Response Attributes :
Items may require the student to draw a circle that matches an
Sample Test Items (1)
Test Item #: Sample Item 1
Johnny wants to find the equation of a circle with center (3,-4) and a radius of 7. He uses the argument shown.
There are three highlights in the argument to show missing words or phrases. For each highlight, click on the word of phrase that correctly fills the blank.
Difficulty: N/A
Type: ETC: Editing Task Choice
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))
Formative Assessments
Complete the Square for Center-Radius 2:
Students are asked to find the center and radius of a circle given its equation in general form.
Type: Formative Assessment
Derive the Circle – General Points:
Students are given the coordinates of the center, (h, k), and the radius, r, of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.
Derive the Circle – Specific Points:
Students are given the coordinates of the center and the radius of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.
Complete the Square for Center-Radius:
Circle Reasoning:
Students use the Pythagorean Theorem (Distance Formula) to derive the Standard Equation of a Circle; then move between descriptions and equations of a circle.
Equations of Circles 1:
This lesson unit is intended to help you assess how well students are able to use the Pythagorean theorem to derive the equation of a circle and translate between the geometric features of circles and their equations.
This lesson unit is intended to help you assess how well students are able to translate between the equations of circles and their geometric features and sketch a circle from its equation.
Run Fido, Run!:
A guided practice for deriving the equation of a circle and then identifying a location to tether a dog to maximize movement.
Where IS that Cell Tower?:
Find the location and coverage area of cell towers to determine the center and radius of a circle given its equation, using a strategy completing the square in this interactive tutorial.
Circle Up!:
Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions in this interactive tutorial.
Problem-Solving Task
Slopes and Circles:
The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever ?AXB is a right angle
Type: Problem-Solving Task