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# Form 3 Mathematics Approximations and Errors Questions and Answers

Form 3 Mathematics Approximations and Errors Questions and Answers.

We are going to solve several exam standard questions on approximations and errors. All answers are in video format.

Lessons (**16**) * SHARE*

- 1.
(a) Work out the exact value of: #R= 1/ (0.003146-0.003130)# (b) An approximate value of R may be obtained by first correcting each of the decimals in the denominator to 5 decimal places. Work out
(i) the approximate value (ii) the error introduced by the approximation.

4m 38s - 2.
The figure below represents a hollow cylinder.The internal and external radii are estimated to be 6 cm and 8 cm respectively ,to the nearest whole number.The height of the cylinder is exactly 14 cm
(a) Determine the exact values for internal and external radii which will give maximum volume of the material used.

6m 33s - 3.
The radius of a circle is given as 2.8 cm to 2 significant figures. (a) If C is the circumference of the circle ,determine the limits between which #C/pi# lies . (b) By taking ?? to be 3.142,find ,to 4 significant figures ,the limits between which the circumference lies.

6m 13s - 4.
The length and breadth of a rectangular floor were measured and found to be 4.1 m and 2.2 m respectively.If a possible error of 0.01 m was made in each of the measurements,find the: (a)maximum and minimum possible area of the floor.
(b) maximum possible wastage in a carpet ordered to cover the whole floor.

3m 11s - 5.
The length and breadth of a rectangular paper were measured to the nearest centimeter and found to be 18 cm and 12 cm respectively.Find the percentage error in its perimeter.

3m 41s - 6.
The sides of a triangle were measured and recorded as 8 cm,10 cm and 15 cm.Calculate the percentage error in the perimeter ,correct to 2 decimal places.

4m 47s - 7.
In this question mathematical tables should not be used. The base and perpendicular height of a triangle measured to the nearest centimeter are 6 cm and 4 cm respectively.Find: (a)the absolute error in calculating the area of the triangle
(b)the percentage error in the area,giving the answer to 1 decimal place.

5m 26s - 8.
By correcting each number to one significant figure, approximate the value of 788× 0.006.Hence calculate the percentage error arising from this approximation.

3m 26s - 9.
A rectangular block has a square base whose side is exactly 8 cm.Its height, measured to the nearest millimeter, is 3.1 cm.Find in cubic centimeters, the greatest possible error in calculating its volume.

3m 57s - 10.
The top of a table is a regular hexagon.Each side of the hexagon measures 50.0 cm.Find the maximum percentage error in calculating the perimeter of the top of the table.

4m 12s - 11.
The length and width of a rectangle measured to the nearest millimeter are 7.5 cm and 5.2 cm respectively.Find ,to four significant figures,the percentage error in the area of the rectangle.

5m 23s - 12.
The radius of a spherical ball is measured as 7 cm,correct to the nearest centimeter . Determine,to 2 decimal places,the percentage error in calculating the surface area of the surface area of the ball.

7m 48s - 13.
The base and height of a right angled triangle were measured as 6.4 cm and 3.5 cm respectively. Calculate the maximum absolute error in the area of the triangle.

3m 50s - 14.
The length of two similar iron bars were given as 12.5 cm and 9.23 cm. Calculate the maximum possible difference in length between the two bars.

2m 22s - 15.
The length and width of a rectangular piece of paper were measured as 60 cm and 12 cm respectively. Determine the relative error in the calculation of its area.

4m 7s - 16.
A tailor intended to subdivide a piece of cloth into 7 equal parts. She approximated #1/ 7# m to 0.14m.Calculate the percentage error in the approximation.

1m 44s