Book 3 Mastery Check

A mixed review for Calculus I, Calculus II, and Calculus III bridge topics. Use this check to decide whether to review or continue into advanced applied math.

Final Book 3 Review

This is not a grade. It is a readiness check for calculus bridge understanding.

Book 3 focus: limits, derivatives, integrals, series, parametric and polar forms, differential equations, vectors, partial derivatives, gradients, multiple integrals, and vector calculus operators.

1. A limit describes what a function is:

2. Find the derivative of f(x) = x².

3. What does an integral often represent?

4. The area under y = 4 from x = 0 to x = 3 is:

5. Which method uses the formula ∫u dv = uv - ∫v du?

6. Does the series 1 + 1/2 + 1/4 + 1/8 + ... converge or diverge?

7. Which coordinate system uses radius r and angle θ?

8. A differential equation contains a function and its:

9. Find the magnitude of vector <3, 4>.

10. For f(x, y) = x² + y², what is ∂f/∂x?

11. The gradient points in the direction of:

12. Which vector calculus operator describes rotation or swirling behavior?