The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point ( -4, 6);
i)The equation of the curve
ii)The value of x at which the curve cuts the x – axis
b) Determine the area enclosed by the curve and the x – axis
The equation of a curve is given by y = 5x − 1/2 x2
(a) On the grid provided, draw the curve of y = 5x − 1/2 x2 for 0 ≤ x ≤ 6
(b) By integration, find the area bounded by the curve, the line x =6 and the x-axis.
(c) (i) On the same grid as in,(a).draw the line y = 2x.
(ii) Determine the area bounded by the curve and the line y = 2 x.
The acceleration of a body moving along a straight line is (4 - t) m/s2 and its velocity is v m/s after t seconds.
(a) (i) If the initial velocity of the body is 3 m/s, express the velocity v in terms of t.
(ii) Find the velocity of the body after 2 seconds.
(b) Calculate: (i) the time taken to attain maximum velocity;
(ii) the distance covered by the body to attain the maximum velocity.
The equation of a curve is y = 2x3 + 3x2.
(i) the x - intercept of the curve;
(ii) the y - intercept of the curve.
(b) (i) Determine the stationery points of the curve.
(ii) For each point in (b) (i) above, determine whether it is a maximum or a minimum.
(c) Sketch the curve.
(a) Using the trapezium rule with seven ordinates, estimate the area of the region bounded by the curve y = -x2 +,6x+ 1, the lines x = 0, y = 0 and x = 6.
(b) Calculate: (i) the area of the region in (a) above by integration;
(iii) the percentage error of the estimated area to the actual area of the region,correct to two decimal places.
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