Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.7

ALG2.240 Intersections of Conics and Lines Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.240 Intersections of Conics and Lines. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.240 Intersections of Conics and Lines - Select the correct solution(s) to systems involving a line and a circle or parabola and select the correct interpretation of the number and meaning of intersection points. (CCSS A-REI.7; A-REI.11; CA CCSSM A-REI.7; A-REI.11; MA 2017 A-REI.7; A-REI.11; NY NGLS A-REI.7; A-REI.11; TX TEKS Algebra II: §111.40)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.240 Intersections of Conics and Lines skill assessments:

Problem 1Difficulty: Mastery
Which statement correctly connects the discriminant from substitution to the intersections of a line and a circle or parabola?
AD > 0 means two intersections, D = 0 means one tangent intersection, and D < 0 means no real intersections.
BD > 0 means no intersections, D = 0 means two intersections, and D < 0 means one intersection.
CThe discriminant tells the shape of the conic but not the number of intersections.
DEvery line-conic system has exactly two intersections because substitution creates a quadratic.
Solution & Explanation:After substitution, the real roots of the resulting equation give intersection x-values. A positive discriminant gives two real roots, zero gives one repeated root, and a negative discriminant gives no real roots.
Problem 2Difficulty: Mastery
The table shows values for f(x) = x2 - 2x and g(x) = 8: x = -2, -1, 1, 4; f(x) = 8, 3, -1, 8; g(x) = 8, 8, 8, 8. Which points are intersections?
A(-2, 8) and (4, 8)
B(-1, 3) and (1, -1)
C(-2, -2) and (4, 4)
D(0, 8) only
Solution & Explanation:The functions are equal where the table shows the same y-value. At x = -2 and x = 4, both functions equal 8, so the intersection points are (-2, 8) and (4, 8).
Problem 3Difficulty: Mastery
For which values of h is the vertical line x = h tangent to the circle (x - 2)2 + (y + 1)2 = 16?
Ah = -2 and h = 6
Bh = 2 only
Ch = -1 and h = 1
Dall real values of h
Solution & Explanation:The circle has center (2, -1) and radius 4. Vertical tangent lines are 4 units left and right of the center, so h = 2 - 4 = -2 and h = 2 + 4 = 6.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard A-REI.7 (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.7. Skill statement in this prompt cell: Select the correct solution(s) to systems involving a line and a circle or parabola and select the correct interpretation of the number and meaning of intersection points. Associated standards listed with this skill in the curriculum source: CCSS A-REI.7; A-REI.11; CA CCSSM A-REI.7; A-REI.11; MA 2017 A-REI.7; A-REI.11; NY NGLS A-REI.7; A-REI.11; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).

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