IB Math · Topic practice · IB Mathematics AA SL · Unit 5

Calculus

A mixed exercise set, like a textbook: every problem type this unit covers, shuffled together and getting harder as you go. Work on paper, reveal to check — and hit on any problem for the same kind with new numbers (202 in the pool).

Practice set — quiz with instant feedback and retries.Review the lessons for this unit first.

Exercises

12 of 202 shown

Let $f(x) = x^3 + 2x + 1$ . Find $f'(1)$ .

Find the equation of the tangent to the curve $y = x^2 + 2x + 1$ at the point where $x = 1$ .

A particle moves in a straight line with displacement $s(t) = 6t - t^2$ metres after $t$ seconds. Find the time at which the particle is instantaneously at rest.

Evaluate $\displaystyle\int_0^{1} (3x^2 + 1)\,dx$ .

Find the $x$ -coordinate of the stationary point of $f(x) = x^2 + 16x - 5$ .

The curve $y = x(2 - x)$ meets the $x$ -axis at $x = 0$ and $x = 2$ . Find the area of the region enclosed by the curve and the $x$ -axis.

Let $f(x) = x^3 - 3x + 1$ . Find $f'(-2)$ .

Find the equation of the tangent to the curve $y = x^2 - 2x + 1$ at the point where $x = -1$ .

A particle moves in a straight line with displacement $s(t) = 7t - 2t^2$ metres after $t$ seconds. Find the time at which the particle is instantaneously at rest.

10.

Evaluate $\displaystyle\int_0^{3} (3x^2 + 1)\,dx$ .

11.

Find the $x$ -coordinate of the stationary point of $f(x) = x^2 + 10x$ .

12.

The curve $y = 2x(5 - x)$ meets the $x$ -axis at $x = 0$ and $x = 5$ . Find the area of the region enclosed by the curve and the $x$ -axis.