Singapore GCE O-Level · Additional Mathematics

Integration and Kinematics

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

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All 52 questions

Evaluate the definite integral: $\int_{0}^{2} (3 x^{2} - 4 x + 1) d x$ .
Find the exact area of the region bounded by the curve $y = e^{2 x}$ , the $x$ -axis, and the lines $x = 0$ and $x = 1$ .
A particle moves in a straight line so that its velocity $v m/s$ at time $t$ seconds is given by $v = 6 t - 2 t^{2}$ . Find the total distance travelled by the particle from $t = 0$ to $t = 4$ .
Evaluate $\int sin (4 x - \frac{π}{3}) d x$ .
Given that $\frac{d}{d x} [x ln x] = 1 + ln x$ , evaluate $\int_{1}^{e} ln x d x$ .
Find the area of the finite region enclosed between the curve $y = 6 - x^{2}$ and the line $y = x$ .
Find $\int 6 x^{2} d x$ .
Find $\int 4 x^{3} d x$ .
Find $\int 10 x^{4} d x$ .
Find $\int 9 x^{2} d x$ .
Find $\int 8 x^{3} d x$ .
Find $\int 12 x^{5} d x$ .
Evaluate $\int_{0}^{2} (2 x^{2} + 3 x + 1) d x$ .
Evaluate $\int_{0}^{3} (4 x^{2} + 1 x + 5) d x$ .
Evaluate $\int_{0}^{1} (6 x^{2} + 2 x + 1) d x$ .
Evaluate $\int_{0}^{2} (3 x^{2} + 3 x + 3) d x$ .
Evaluate $\int_{0}^{4} (2 x^{2} + 5 x + 0) d x$ .
Evaluate $\int_{0}^{2} (6 x^{2} + 4 x + 2) d x$ .
Evaluate $\int_{0}^{2} (3 x^{2} + 6 x + 1) d x$ .
Evaluate $\int_{0}^{1} (4 x^{2} + 2 x + 3) d x$ .
Find the area of the region bounded by the curve $y = 2 x^{2}$ , the $x$ -axis and the lines $x = 1$ and $x = 3$ .
Find the area of the region bounded by the curve $y = 1 x^{2}$ , the $x$ -axis and the lines $x = 2$ and $x = 4$ .
Find the area of the region bounded by the curve $y = 6 x^{2}$ , the $x$ -axis and the lines $x = 2$ and $x = 3$ .
Find the area of the region bounded by the curve $y = 6 x^{2}$ , the $x$ -axis and the lines $x = 1$ and $x = 2$ .
Find the area of the region bounded by the curve $y = 3 x^{2}$ , the $x$ -axis and the lines $x = 1$ and $x = 4$ .
Evaluate $\int_{0}^{1} e^{2 x} d x$ , giving your answer in terms of $e$ .
Evaluate $\int_{0}^{1} e^{3 x} d x$ , giving your answer in terms of $e$ .
Evaluate $\int_{0}^{2} e^{2 x} d x$ , giving your answer in terms of $e$ .
Evaluate $\int_{0}^{1} e^{4 x} d x$ , giving your answer in terms of $e$ .
Find $\int cos 2 x d x$ .
Find $\int cos 3 x d x$ .
Find $\int cos 4 x d x$ .
Find $\int cos 5 x d x$ .
Find $\int \frac{1}{1 x + 3} d x$ .
Find $\int \frac{1}{2 x + 1} d x$ .
Find $\int \frac{1}{1 x + 5} d x$ .
Find $\int \frac{1}{3 x + 2} d x$ .
A particle starts with velocity $2$ m/s and moves with a constant acceleration of $6$ m/s $^{2}$ . Find its velocity after $3$ s.
A particle starts with velocity $3$ m/s and moves with a constant acceleration of $4$ m/s $^{2}$ . Find its velocity after $3$ s.
A particle starts with velocity $5$ m/s and moves with a constant acceleration of $2$ m/s $^{2}$ . Find its velocity after $3$ s.
A particle starts with velocity $1$ m/s and moves with a constant acceleration of $8$ m/s $^{2}$ . Find its velocity after $3$ s.
A particle starts with velocity $4$ m/s and moves with a constant acceleration of $10$ m/s $^{2}$ . Find its velocity after $3$ s.
The velocity of a particle is $v = 6 t^{2} - 12 t$ m/s. Find its displacement from $t = 0$ to $t = 2$ .
The velocity of a particle is $v = 3 t^{2} - 6 t$ m/s. Find its displacement from $t = 0$ to $t = 2$ .
The velocity of a particle is $v = 6 t^{2} - 18 t$ m/s. Find its displacement from $t = 0$ to $t = 2$ .
The velocity of a particle is $v = 3 t^{2} - 9 t$ m/s. Find its displacement from $t = 0$ to $t = 2$ .
The velocity of a particle is $v = 6 t^{2} - 24 t$ m/s. Find its displacement from $t = 0$ to $t = 2$ .
A curve has gradient $\frac{d y}{d x} = 6 x$ and passes through the point $(1, 5)$ . Find the $y$ -intercept of the curve.
A curve has gradient $\frac{d y}{d x} = 4 x$ and passes through the point $(2, 9)$ . Find the $y$ -intercept of the curve.
A curve has gradient $\frac{d y}{d x} = 3 x$ and passes through the point $(1, 2)$ . Find the $y$ -intercept of the curve.
A curve has gradient $\frac{d y}{d x} = 6 x$ and passes through the point $(2, 11)$ . Find the $y$ -intercept of the curve.
A curve has gradient $\frac{d y}{d x} = 2 x$ and passes through the point $(3, 10)$ . Find the $y$ -intercept of the curve.

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Integration and Kinematics

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