Singapore GCE A-Level · H2 Mathematics

Calculus: techniques and applications

36 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 36 questions

Find $\frac{d y}{d x}$ at the point $(3, 4)$ on the curve $x^{2} + y^{2} = 25$ .
Find $\frac{d y}{d x}$ at the point $(5, 12)$ on the curve $x^{2} + y^{2} = 169$ .
Find $\frac{d y}{d x}$ at the point $(6, 8)$ on the curve $x^{2} + y^{2} = 100$ .
Find $\frac{d y}{d x}$ at the point $(7, 24)$ on the curve $x^{2} + y^{2} = 625$ .
Find $\frac{d y}{d x}$ at the point $(4, 3)$ on the curve $x^{2} + y^{2} = 25$ .
A curve has parametric equations $x = 1 t^{2}, y = t^{3}$ . Find the gradient when $t = 3$ .
A curve has parametric equations $x = 2 t^{2}, y = t^{3}$ . Find the gradient when $t = 1$ .
A curve has parametric equations $x = 2 t^{2}, y = t^{3}$ . Find the gradient when $t = 3$ .
A curve has parametric equations $x = 3 t^{2}, y = t^{3}$ . Find the gradient when $t = 4$ .
A curve has parametric equations $x = 1 t^{2}, y = t^{3}$ . Find the gradient when $t = 4$ .
A curve has parametric equations $x = 4 t^{2}, y = t^{3}$ . Find the gradient when $t = 1$ .
Find the exact value of $\int_{0}^{1} x e^{2 x} d x$ .
Find the exact value of $\int_{0}^{1} x e^{3 x} d x$ .
Find the exact value of $\int_{0}^{1} x e^{4 x} d x$ .
Find the exact value of $\int_{0}^{1} x e^{5 x} d x$ .
Use the substitution $u = x^{2} + 1$ to evaluate $\int_{0}^{1} 2 x (x^{2} + 1)^{2} d x$ .
Use the substitution $u = x^{2} + 1$ to evaluate $\int_{0}^{1} 2 x (x^{2} + 1)^{3} d x$ .
Use the substitution $u = x^{2} + 1$ to evaluate $\int_{0}^{1} 2 x (x^{2} + 1)^{4} d x$ .
Use the substitution $u = x^{2} + 1$ to evaluate $\int_{0}^{1} 2 x (x^{2} + 1)^{5} d x$ .
Use the substitution $u = x^{2} + 1$ to evaluate $\int_{0}^{1} 2 x (x^{2} + 1)^{6} d x$ .
The region under the curve $y = x$ from $x = 0$ to $x = 2$ is rotated through $36 0^{\circ}$ about the $x$ -axis. Find the exact volume generated.
The region under the curve $y = x$ from $x = 0$ to $x = 3$ is rotated through $36 0^{\circ}$ about the $x$ -axis. Find the exact volume generated.
The region under the curve $y = x$ from $x = 0$ to $x = 4$ is rotated through $36 0^{\circ}$ about the $x$ -axis. Find the exact volume generated.
The region under the curve $y = x$ from $x = 0$ to $x = 6$ is rotated through $36 0^{\circ}$ about the $x$ -axis. Find the exact volume generated.
The region under the curve $y = x$ from $x = 0$ to $x = 8$ is rotated through $36 0^{\circ}$ about the $x$ -axis. Find the exact volume generated.
Find the exact area enclosed between the curve $y = x^{2}$ and the line $y = 2 x$ .
Find the exact area enclosed between the curve $y = x^{2}$ and the line $y = 3 x$ .
Find the exact area enclosed between the curve $y = x^{2}$ and the line $y = 4 x$ .
Find the exact area enclosed between the curve $y = x^{2}$ and the line $y = 6 x$ .
Find the exact area enclosed between the curve $y = x^{2}$ and the line $y = 8 x$ .
Find the coefficient of $x^{3}$ in the Maclaurin series of $ln (1 + 2 x)$ .
Find the coefficient of $x^{3}$ in the Maclaurin series of $ln (1 + 3 x)$ .
Find the coefficient of $x^{3}$ in the Maclaurin series of $ln (1 + 4 x)$ .
Find the coefficient of $x^{3}$ in the Maclaurin series of $sin 2 x$ .
Find the coefficient of $x^{3}$ in the Maclaurin series of $sin 3 x$ .
Find the coefficient of $x^{3}$ in the Maclaurin series of $sin 4 x$ .

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Calculus: techniques and applications

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