Full unit practice requiring complete reasoning and representation checks.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u12-l01', 'number': 1, 'title': 'Average Rate of Change Revisited', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Find the average rate of change of x² from 2 to 5.
2. {'id': 'u12-l01', 'number': 1, 'title': 'Average Rate of Change Revisited', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Simplify [(x+h)²−x²]/h.
3. {'id': 'u12-l01', 'number': 1, 'title': 'Average Rate of Change Revisited', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Evaluate lim_{x→3}(2x+1).
4. {'id': 'u12-l01', 'number': 1, 'title': 'Average Rate of Change Revisited', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Evaluate lim_{x→2}(x²−4)/(x−2).
5. {'id': 'u12-l01', 'number': 1, 'title': 'Average Rate of Change Revisited', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Can a two-sided limit exist if one-sided limits differ?
6. {'id': 'u12-l01', 'number': 1, 'title': 'Average Rate of Change Revisited', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Name the discontinuity in (x²−1)/(x−1) at x=1.
7. {'id': 'u12-l02', 'number': 2, 'title': 'Difference Quotients and Secant Lines', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Find the average rate of change of x² from 2 to 5.
8. {'id': 'u12-l02', 'number': 2, 'title': 'Difference Quotients and Secant Lines', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Simplify [(x+h)²−x²]/h.
9. {'id': 'u12-l02', 'number': 2, 'title': 'Difference Quotients and Secant Lines', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Evaluate lim_{x→3}(2x+1).
10. {'id': 'u12-l02', 'number': 2, 'title': 'Difference Quotients and Secant Lines', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Evaluate lim_{x→2}(x²−4)/(x−2).
11. {'id': 'u12-l02', 'number': 2, 'title': 'Difference Quotients and Secant Lines', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Can a two-sided limit exist if one-sided limits differ?
12. {'id': 'u12-l02', 'number': 2, 'title': 'Difference Quotients and Secant Lines', 'family': 'limits', 'week': 33, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Name the discontinuity in (x²−1)/(x−1) at x=1.