Integrated 2 Chapter 10

Section 1 of the is chapter connects completing the square (from Chapter 5) and the pythagorean theorem to write the equation of a circle. Section 2 explores the angles, chords, arcs, tangent and secants in a circle and how to calculate angles and lengths.

Current Chapter Resources and Practice

Background Knowledge Resources

Checkpoint Review: Students master different skills at different speeds. No two students learn exactly the same way at the same time. At some point you will be expected to perform certain skills accurately. Most of the Checkpoint problems incorporate skills previously developed. Each chapter has a different skill that should be mastered.

Checkpoint 10: Solving Quadratic Equations

You e-book has a checkpoint resource (you must have the e-book open to access the link and click on CP 10

Learning Outcomes for Chapter 10: Open your e-book to access the links to the problems

Past Concepts

Master Checkpoint 10: Solving Quadratic Equations, as in problems 10-20(b) and (d), 10-32(c), 10-58(b) and (d), 10-69(c), 10-98, 10-112, and CL 10-122.
Writing the equation of the inverse of a linear function, as in problems 10-10, 10-42, 10‑70, and CL 10-120.
Complete the square to rewrite the equation of a quadratic function given in standard form in graphing form, as in problems 9-44, 9-57, 9-88, 9-143, and CL 9-148.

Current Chapter Concepts

Graph a circle on a coordinate grid, as in problems 10-7, 10-19, 10-41, 10-54, 10-95, 10-109, and CL 10-117. Graph a circle or determine its radius and center given its equation, and also analyze a graph of a circle to write its equation.
Complete the square to change the equation of a circle from general form to graphing form, as in problems 10-18, 10-41(b), 10-54(d), 10-68(b), and CL 10-116.
Understand and use the relationships between central and inscribed angles and their intercepted arcs to calculate arc and angle measures, including for angles inscribed in a semicircle, as in problems 10-66, 10-80, 10-84(b) and (d), 10-97, 10-110, 10-111(c) and (d), and CL 10-119 Combine knowledge about arcs and angles with their understanding of circumference and circle area to calculate arc length and sector area, as in problem 10-97(c).
Understand chord, radii, and angle relationships in circles and use those relationships to solve problems, including calculating the length of a chord or segments formed by intersecting chords, as in problems 10-84(c), 10-96(b), and 10-108(c).
Understand and use the fact that a line tangent to a circle is perpendicular to the radius of the circle at the point of tangency, as in problems 10-94 and 10-108(a) and (b).
Graph a parabola on focus‑directrix paper, or write the equation of a parabola from a geometric description, as in problems 10-40 and 10-71.