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Form 4 Maths area and approximation: Mid-Ordinate Rule questions and answers

In this online learning session, we are going to solve Form 4 Mathematics questions are and approximation using mid-ordinate rule.

Lessons (9)

• 1.    The figure below shows the shape of a piece of land OABC. Using the mid-ordinate rule with 11 ordinates, estimate the area of the land.
  4m 45s

• 2.    The shaded region below represents a forest. The region has been drawn to scale where 1cm represents 5km. use the mid-ordinate rule with six strips to estimate the area of the forest in hectares.
  0m 0s

• 3.    The table below shows some values of the function #y=x^2 + 2x-3# (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 curve #y=x^2 + 2x – 3# and the lines y=0, x=-6 and x=-3. (c) (i) By integration, find the actual area of the region in (b) above.
  9m 1s

• 4.    The diagram below is a sketch of the curve #y=x^2 + 5#. (a) (i) Use the mid-ordinate rule, with six strips to estimate the area enclosed by the curve, the x-axis, the y-axis and line x=3. (ii) Calculate the same area using integration method. (b) Assuming the area calculated in (a) (ii) is exact, calculate the percentage error made when the mid-ordinate rule is used.
  4m 27s

• 5.    The table below shows some values of the function #y=x^2 + 3#. (a) Complete the table. (b) Use the mid-ordinate rule with six ordinates to estimate the area bounded by #y=x^2 + 3#, the y-axis, the x-axis and the line x=6.
  4m 3s

• 6.    The figure below is a sketch of a curve whose equation is #y=x^2 + x + 5#. It cuts the line y=11 at points P and Q. (a) Find the area bounded by the curve #y=x^2 + 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.
  6m 48s

• 7.    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.
  2m 33s

• 8.    Use the mid-ordinate rule with six strips to find the area bounded by the curve #y=x^2 + 1#, the lines x=-4, x=8 and the x-axis.
  2m 33s

• 9.    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
  0m 0s