Form 4 Mathematics
The shaded region on the graph below shows a piece of land ABCD earmarked for building a sub-county hospital.
(a) Write down the ordinates of curves AB and DC for x = 0, 200, 400, 600, 800, 1000 and 1200.
(b) Use trapezium rule, with 6 strips to estimate the area of the piece of land ABCD, in hectares. (c) Use mid-ordinate rule with 3 strips to estimate the area of the piece of land, in hectares.
answers
Form 4 Mathematics
(a) On the grid provided, draw the graph of y = 4 -1/4x2 for -4 ≤ x ≤ 4
(b) Using trapezium rule, with 8 strips, estimate the area bounded by the curve and the x-axis. (c) Find the area estimated in part (b) above by integration. (d) Calculate the percentage error in estimating the area using trapezium rule.
answers
Form 4 Mathematics
(a)On the grid provided, draw a graph of the function y = 1/2 x2 - x + 3 for 0 ≤ x ≤ 6.
b) Calculate the mid ordinates for five strips between x = 1 and x = 6, and hence use the mid- ordinate rule to approximate the area under the curve between x = 1, x = 6 and the x = axis c) Assuming that the area determined by integration to be the actual area, calculate the percentage error in using the mid ordinate rule
answers
Form 4 Mathematics
The figure below represents the curve of an equation
Use the mid-ordinate rule with 4 ordinates to estimate the area bounded by the curve, lines y — 0, x = — 3 and x = 5.
answer
Form 4 Mathematics
(a) Complete the table below for the function y = x2 – 3x + 6 in range -2 ≤ x ≤ 8
(b) Use the trapezium rule with strips to estimate the area bounded by the curve,y = x2 – 3x + 6, the lines x = -2, x = 8, and x - axis
(c) Use the mid-ordinate rule with 5 strips to estimate the area bounded by the curve,y = x2 – 3x + 6, the lines x = -2, x = 8, and x –axis (d) By integration, determine the actual area bounded by the curve y = x2 – 3x + 6, the lines x = -2, x = 8, and x –axis
answers
Form 4 Mathematics
The table below shows the values of x and corresponding values of y for a given curve.
a) Use the trapezium rule with seven ordinates and the values in the table only to estimate the area enclosed by the curve, x – axis and the line x = П/2 to four decimal places. (Take П = 3.142) b) The exact value of the area enclosed by the curve is known to be 0.8940.Find the percentage error made when the trapezium rule is used. Give the answer correct to two decimal places.
Answer
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
The figure below is a sketch of the curve whose equation is y=x2+x+5.
It cuts the line y=11 at points P and Q. 
a) Find the area bounded by the curve = x2+x+5 and the line y=11 using the trapezium rule with 5 strips.
b) Calculate the difference in the area if the mid-ordinate rule with 5 ordinates was used instead of the trapezium rule.
answers
Form 4 Mathematics
The diagram on the grid below represents as extract of a survey map showing two adjacent plots belonging to Kazungu and Ndoe.
The two dispute the common boundary with each claiming boundary along different smooth curves coordinates ( x, y) and (x, y2) in the table below, represents points on the boundaries as claimed by Kazungu Ndoe respectively.
(a) On the grid provided above draw and label the boundaries as claimed by Kazungu and Ndoe
answers
 Use the trapezoidal rule with intervals of 1 cm to estimate the area of the shaded region below. KNEC MARKING SCHEME
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