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Calculus (Year 12 Maths Advanced) quiz

12questions. Pick an answer and you'll see why right away.

  1. The derivative of f(x) = x^3 - 4x is:

  2. The derivative of e^(2x) is:

  3. The integral of 1/x with respect to x is:

  4. A function f has f'(x) = 0 at x = 2 and f''(2) < 0. At x = 2, f has:

  5. Integration by substitution u = x^2 + 1 applied to the integral of 2x/(x^2 + 1) dx gives:

  6. The area between y = x^2 and y = 4 from x = -2 to x = 2 equals:

  7. The function y = sin(x) has derivative y' = cos(x). At x = pi/2, y' equals:

  8. The volume of revolution of y = x from x = 0 to x = 2 about the x-axis is:

  9. A particle's velocity is v(t) = 3t^2 - 6t. Its displacement from t = 0 to t = 3 is:

  10. If f(x) = ln(x), then f'(x) is:

  11. The maximum value of f(x) = -x^2 + 4x - 3 over the real line is:

  12. Which is the strongest opening for an HSC Maths Advanced extended question on optimisation?