1.Evaluate the limit analytically: lim (x -> 3) [(x² - 9) / (x - 3)]
A0
BUndefined (Division by zero)
C6
D3
Grade 12Algebraic ThinkingOriginal practice
Derivatives Rates and Local Models: Apply and Create Worksheet — Grade 12
Derivatives Rates and Local Models: Apply and Create: Build a difference quotient from position values. Starts with 3 practice tasks. Answer guidance included. Print on Letter/A4 or save as PDF from the print window.
3 distinct sets for the same goals and support level. Each set keeps its material and matching answers together. Choose “Save as PDF” in your browser’s print window to keep a copy.
Page layout
0 practice pages · 0 answer pages. Pages are added automatically when needed. Question content and answer keys stay together.
Continue this learning sequence
Unit goals and teaching guide →Independent activity · About 25 minutes · Pencil · Calculus (optional advanced course)
Practice set 1 of 3. Each set keeps the same learning goal and task structures.
Sheet 6E488112 · questions and answers share this ID
About this practice
Grade 12 · Mathematics · Matching answer key included · US Letter and A4
Choose “Save as PDF” in your browser’s print window to keep a copy.
Teaching guide, sample answers and curriculum references
Before you begin
Understand limits, continuity, polynomial expansion and slope units.
How to use this worksheet
- Begin with: Find s(2), with units.
- Connect the response to: Take the limit as h → 0 to find s′(2). State its unit.
- Ask students to apply the idea: Write a tangent-line equation at t = 2 and interpret the slope.
A common mistake to discuss
A derivative is a rate, not a position; an algebraic zero must lie within the model domain.
What to practice next
Revisit the unit goals. Use the criteria to identify a specific response to improve; this activity alone does not establish mastery.
Invented practice data or scenario; not a report of a real study.
Source reference: Selected high-school course targets.
Published 2026-10-08; updated 2026-10-08. Read our editorial policy.
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Practice preview
Grade 12
Key
Derivatives Rates and Local Models
Practice · Independent · 45 min
Build a difference quotient from position values. Calculate a derivative and compare average rates. Interpret a tangent and apply the model domain. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.
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Practice preview
Grade 12
Key
Derivatives Rates and Local Models: Explore and Explain
Explore · Independent · 12 min
Build a difference quotient from position values. Calculate a derivative and compare average rates. Interpret a tangent and apply the model domain. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.
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Practice preview
Grade 12
Key
Derivatives Rates and Local Models: Practice Independently
Practice · Independent · 20 min
Build a difference quotient from position values. Calculate a derivative and compare average rates. Interpret a tangent and apply the model domain. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.
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Practice preview
Grade 12
HSF.IF.B.4 Key
Calculus: Limits, Continuity & Derivative Rules
Practice · Independent · 35 min
Selected optional calculus practice with evidence, conditions and a written explanation.
Shuffle this practice