1.
A line with equation y = 4x + 2 intersects a curve with the equation y = x² + 2 at the points M and N. Evaluate the area enclosed between the curve and the line
4.
The table below shows the velocity V m/s of a particle in a relation to time t s within a period of t seconds
t 0 1 2 3 4 5 6
V 10 12 15 16 11 5 3
Use trapezoid rule:
1/2 h(y1 +2y2 + 2y3 + ... + yn)
Find the approximate distance traveled
5.
A line with equation y = 4x + 2 intersects a curve with the equation y = x² + 2 at the points M and N. Determine the coordinates of M and N
6.
The velocity v m/s of a body moving at any time t, is given by v = 2t² - 1/3t³ + 10, determine the values of t at which the acceleration of the particle is zero.
7.
A body is projected from a point O in a straight line with an initial velocity of 10 m/s. If the acceleration is 5t² + 3t, find the velocity after 3 seconds.
8.
Find the area bounded by the curve y = -5 + 6x - x² and the x-axis
11.
The gradient of a curve which passes through the point (1, 2) is 3+2x.
Find its equation.
12.
The gradient of a curve that passes through the point (-2, 6) is given by x. Determine the equation of the curve.
13.
A body starting from the origin O moves in a straight line, and its velocity, v m/s, after t s is given by v = 12 + 20t - 3t². Calculate the distance moved by the particle in 2 s.
14.
Given that dy/dx = 6x² + 5x, find the function which passes through the point (2, 30).
16.
A curve y has gradient
dy/dx = 3x² - 6x + 2.
If the curve passes through the origin,
find its equation.
17.
Find the area bounded by the curve y = x(2 - x), the x-axis, x=0 and x= 2.
19.
The gradient of a curve at any point (x, y) is given by dy/dx = 2(x - 3) and the point(3, -12) lies on the curve. Find the equation of the curve.
20.
An object travels in a straight line with velocity, v m/s at time t s is given by v = 3t² + 7. What is the distance travelled by the object from t = 2 s to t = 5 s?
22.
The acceleration of a moving particle at the end of t seconds is given by (5 - t) m/s². If the particle starts from rest, find its velocity at the end of 4 s?
23.
Find the area of the region lying below the x-axis and bounded by the parabola
y = x(x - 2) and the x-axis.
25.
The gradient of a curve is given by
x² - 4x + 3
If the curve passes through the point (3, 1).
Find the maximum point on the curve
