Calculate and interpret average rates of change as secant slopes, and estimate instantaneous rates of change numerically and graphically as tangent slopes with appropriate signs and units. Evaluate finite and infinite one-sided and two-sided limits from graphs, tables, and algebraic expressions using substitution, factoring, canceling, or rationalizing, distinguishing limiting behavior from the value at the point. Identify removable, jump, and infinite discontinuities and relate the limit of difference quotients to instantaneous rate of change and the derivative when it exists, without formal - proofs or advanced generalizations.
On this page:
- Master skills like “Identify discontinuities”, “Determine one-sided limits”, and “Evaluate limits from graphs” with unlimited, free practice problems
- Download (or modify) free worksheets on Rates of Change and Limits you can use at home or in class with practice problems across all skills in this group including “Evaluate limits from tables”, “Evaluate limits algebraically”, “Calculate average rate of change”.
- Start working on adaptive units like “Functions - Average Rate of Change - Intro” or “Functions - End and Root Behaviour - Intro” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Rates of Change and Limits: Individual Skills
Master 9 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
Practice 'Calculate average rate of change'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
Hover a skill above to start practicing.
Download/Modify Free Grade 12 'Rates of Change and Limits' Worksheet
Print this free 'Rates of Change and Limits' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Calculate average rate of change
- Determine one-sided limits
- Estimate instantaneous rate of change graphically
- Estimate instantaneous rate of change numerically
- Evaluate limits algebraically
- Evaluate limits from graphs
- Evaluate limits from tables
- Identify discontinuities
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Rates of Change and Limits) through scaffolded problems that grow in difficulty as concepts are understood.