questionUse the trapezium rule to estimate the area under the curve y = x^2 + x – 6 over the interval 0 ≤ x ≤ 8 using 4 trapezia. (3 Marks) answer
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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 MathematicsThe table below gives some of the values of x for the function y = ½ x 2 + 2x + 1 in the interval 0≤ x ≤ 6. 
(a) Use the values in the table to draw the graph of the function ( 2 marks) (b) (i) Using the graph and the mid – ordinate rule with six (6) strips, estimate the area bounded by the curve, the x- axis, the y- axis and the line = 6 (ii) If the exact area of the region described in (b) (i) above is 78cm2, calculate the percentage error made when the mid – ordinate rule is used. Give the answer correct to two decimal places ( 2 marks)
Answer
Form 4 Mathematics
Use the mid ordinate rule with six strips to find the area bounded by the curve y = x2 + 1, the lines x = -4 , x = 8 and the x-axis.
answer
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
The table below shows some values of the function y = x2 +3
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 particle is projected from the origin. Its speed was recorded as shown in the table below
Use the trazezoidal rule to estimate the distance covered by the particle within the 35 seconds
Answer
Free 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1The graph below consists of a non- quadratic part ( 0 ≤ x ≤ 2) and a quadrant part ( 2 ≤ x 8) The quadratic part is y = x2 – 3x + 5, 2 ≤ x ≤ 8 
(a) Complete the table below (1 mark)
ANSWER
The table below shows some values of the function y = x2 + 2x - 3
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