Study Guide — Conic sections

Pre-calculus

Study guide for Conic sections at standard high school depth.

What this standard means

• Write and graph equations of circles and parabolas
• Identify foci and vertices of ellipses and hyperbolas
• Complete the square to put conics in standard form
• Solve systems involving conics and lines

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Plot points and verify distances 2. Use slope for parallel and perpendicular lines 3. Complete the square for circle equations

_See printable PDF for diagram._

Common mistakes

• Slope sign errors
• Wrong center or radius in circle equation

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Conic sections.

• [ ] Uses distance and midpoint formulas
• [ ] Writes equations of lines and circles
• [ ] Completes coordinate proofs

Materials for this standard

• Practice Problems — 20 printable sets
• Review — 10 difficulty levels
• Practice Test — 10 difficulty levels
• Answer key — for parents and tutors