Questions covered in Basic

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The value of $\lim_{x \to 3} (x+3)$ is
2. The derivative of $\sin x$ with respect to $x$ is
3. $\lim_{x \to 0} \frac{\sin 3x}{x}$ is equal to
4. The derivative of $5x^3$ is
5. Evaluate $\lim_{x \to 2} \frac{x^2-4}{x-2}$.
6. Evaluate $\lim_{x \to 1} \frac{x^{15}-1}{x^{10}-1}$.
7. Find the derivative of $f(x) = 2x^2 + 3x - 5$ at $x = -1$.
8. Find the derivative of $f(x) = \sin x + \cos x$.
9. Evaluate $\lim_{x \to 0} \frac{\sqrt{1+x} - 1}{x}$.
10. Find the derivative of $f(x) = x \sin x$.
11. Find the derivative of $f(x) = x^3$ from first principles.
12. Case Study: The displacement $s$ (in meters) of a particle moving in a straight line is given by $s(t) = t^2 + 2t$, where $t$ is in seconds.
    (i) Find the velocity at $t=2$ seconds.
    (ii) Find the acceleration of the particle.
    (iii) Find the initial velocity (at $t=0$).