Unit 01 Honors / Extended Practice

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Honors / Extended pathway

Calculus I Bridge & Integration Fluency

Deeper proof, synthesis, parameter analysis, and unfamiliar applications.

1. Find F if F′(x)=6x²−4 and F(1)=5.

2. Which statement best describes the central reasoning in Antiderivative Families, Constants & Initial Conditions?

3. Evaluate ∫₀²(3x²+1)dx.

4. Which statement best describes the central reasoning in The Fundamental Theorem as an Evaluation and Accumulation Principle?

5. A velocity is v(t)=3t−6 on 0≤t≤4. Find displacement.

6. Which statement best describes the central reasoning in Net Change, Total Change & Units?

7. Evaluate ∫2x(x²+5)^4 dx.

8. Which statement best describes the central reasoning in Substitution with Algebraic Structure?

9. Evaluate ∫6x e^{3x²}dx.

10. Which statement best describes the central reasoning in Substitution with Exponential, Logarithmic & Trigonometric Forms?

11. Choose a first step for ∫(x²+2x)/x dx.

12. Which statement best describes the central reasoning in Integration Strategy Triage?

13. A student claims ∫2x/(x²+1)dx=2ln(x²+1)+C. Diagnose the error.

14. Which statement best describes the central reasoning in Readiness Synthesis, Error Analysis & Technology Verification?

β Beta Program