Form 4 Mathematics
The acceleration, a ms-2, of a particle is given by a =25 – 9t2, where t in seconds after the particle passes fixed point O.If the particle passes O, with velocity of 4 ms-1, find:
(a) An expression of velocity V, in terms of t ( 2 marks)
(b) The velocity of the particle when t = 2 seconds ( 2 marks)
Answer
Form 4 Mathematics
The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point ( -4, 6);
a)Find 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
answers
Form 4 Mathematics
The gradient function of a curve is given
If the curve passes through the point, (0, 2), find its equation.
Answer
Form 4 Mathematics
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.
answers
Form 4 MathematicsThe diagram below is a sketch of the curve y =x2 + 5. 
ANSWER
Form 4 Mathematics
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.
answers
Form 4 Mathematics
The graph below shows the relationship between distance s metres and time t seconds in the interval 0 ≤ t ≤ 6.
(a) the average rate of change of distance between t =3 seconds and t =6 seconds;
(b) the gradient at t = 3 seconds.
answers
Form 4 Mathematics
The equation of a curve is y = 2x3 + 3x2.
(a) Find: (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.
answers
Form 4 Mathematics
(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.
answers
Form 4 Mathematics
A particle moves in a straight line with a velocity V ms-1. Its velocity after t seconds is given by V= 3t2 – 6t-9.
The figure below is a sketch of the velocity-time graph of the particle 
Calculate the distance the particle moves between t = 1 and t = 4
answer
Form 4 Mathematics
The diagram below shows a straight line intersecting the curve y = (x-1)2 + 4
At the points P and Q. The line also cuts x-axis at (7,0) and y axis at (0,7)
Answer
Form 3 Mathematics
The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point ( -4, 6);
(a) Find: (i) The equation of the curve (ii) The vales of x, at which the curve cuts the x- axis (b) Determine the area enclosed by the curve and the x- axis
ANSWERS
Form 4 Mathematics
The diagram below shows a sketch of the line y = 3x and the curve y = 4 – x2 intersecting at points P and Q.
a) Find the coordinates of P and Q
(b) Given that QN is perpendicular to the x- axis at N, calculate (i) The area bounded by the curve y = 4 – x2, the x- axis and the line QN (ii) The area of the shaded region that lies below the x- axis (iii)The area of the region enclosed by the curve y = 4-x2, the line y – 3x and the y axis
answers
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AuthorMaurice A Nyamoti is a Mathematics/ Computer Teacher and has passion to assist students improve grades RSS_FEED
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