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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~Topically Analyzed

Use 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)

8/4/2023

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question

Use 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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COMPLETE THE TABLE BELOW:

2/1/2023

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K.C.S.E Mathematics Q & A - MODEL 2019PP1QN23

23/9/2020

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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.
Picture
(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
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K.C.S.E Mathematics Q & A - MODEL 2018PP1QN22

20/9/2020

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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
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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.20

18/9/2020

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Form 4 Mathematics



The table below gives some of the values of x for the function y = ½ x 2 + 2x + 1 in the interval 0≤ x ≤ 6.

Picture

(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
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K.C.S.E Mathematics Q & A - MODEL 2017PP1QN13

15/9/2020

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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
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K.C.S.E Mathematics Q & A - MODEL 2016PP1QN24

14/9/2020

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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
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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN13

10/9/2020

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Form 4 Mathematics


The figure below represents the curve of an equation
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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
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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.11

10/9/2020

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Form 4 Mathematics



The table below shows some values of the function y = x2 +3
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  • a) Complete the table
  • b) Use the mid – ordinate rule with six ordinates to estimate the area bounded by y = x ÷3, the y – axis, the x – axis and the line x = 6
Answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN21

7/9/2020

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Form 4 Mathematics


(a) Complete the table below for the function y = x2 – 3x + 6 in range -2 ≤ x ≤ 8
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(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
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K.C.S.E Mathematics Q & A - MODEL 2002PP2QN021

30/8/2020

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Form 4 Mathematics



The table below shows the values of x and corresponding values of y for a given curve.
Picture

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
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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN11

21/7/2020

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Form 4 Mathematics



A particle is projected from the origin. Its speed was recorded as shown in the table below
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Use the trazezoidal rule to estimate the distance covered by the particle within the 35 seconds
Answer
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K.C.S.E Mathematics Q & A - MODEL 1999PP1QN24

25/6/2020

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Free 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1


The 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
Picture
(a) Complete the table below   (1 mark)
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  • ​(b) Use the trapezoidal rule with six strips to estimate the area enclosed by the  curve, x = axis and the line x = 2 and x = 8 (3 marks)
  • (c) Find the exact area of the region given in (b) (3 marks)
  • (d) If the trapezoidal rule is used to estimate the area under the curve between x = 0 and x = 2, state whether it would give an under- estimate or an over- estimate. Give  a reason for your answer (1 mark)
ANSWER
K.C.S.E Mathematics Q & A - MODEL 1999PP1QN24
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K.C.S.E Mathematics Q & A-MODEL 1996PP1QN21

14/5/2020

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The table below shows some values of the function y = x2 + 2x - 3

Picture

  • a) Complete the table
  • b) Using the completed table and the mid- ordinate rule with six ordinates, estimate the area of the region bounded by the
    y = x2 + 2 x – 3 and the line y = 0, x = -6 and x = -3 ( 3 marks)
  • (i) By integration find the actual area of the region in (b) above (2 marks)
  • (ii) Calculate the percentage error arising from the estimate in (b) (2 marks)

MARKING SCHEME
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