**Approximation and errors**

Approximation and Errors

- The length and breadth o a rectangular room are 15cm and 12 cm respectively. If each of these measurements is liable to 1.5% error, calculate the absolute error in the perimeter of the room (3 mks)
- The length and width of a rectangle are stated as 18.5cm and 12.4cm respectively. Both measurements are given to the nearest 0.1cm.
- Determine the lower and upper limit of each measurement. (1 mark)
- Calculate the percentage error in the area of the rectangle. (3 marks)
- The top of a table is a regular hexagon. Each side of the hexagon measures 50.0cm Find the maximum percentage error in calculating the perimeter of the top of the table (3mks)
- A rectangular room has length 12.0 metres and width 8.0 metres. Find the maximum

percentage error in estimating the perimeter of the room.

- In this question mathematical tables or calculator should not used. The base and perpendicular

height of a triangle measured to the nearest centimeters are 12cm and 8cm respectively;

Find ;

(a) the absolute error in calculating the are of the triangle

- b) the percentage error in the area, giving the answer to 1 decimal place

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**Approximation and errors**

- A rectangular plate has a perimeter of 28cm. determine the dimensions of the plate that

give the maximum area

- A wire of length 5.2m is cut into two pieces without wastage. One of the pieces is

3.08m long. What is the shortest possible length of the second piece?

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- The dimensions of a rectangle are 10cm and 15cm. If there is an error of 5% in each of the

Measurements. Find the percentage error in the area of the rectangle.

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- Find the products of 17.3 and 13.8. Find also the percentage error in getting the product.

- The mass of a metal is given as 14kg to the nearest l0g. Find the percentage error in this

measurement.

- Complete the table below for the functions y = cos x and y = 2 cos (x +30°) for 0° ≤ X ≤ 360°

X | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° | 270° | 300° | 330° | 360° |

Cos X | 1 | 0.87 | 0.5 | -0.5 | 0.87 | -1.0 | 0.5 | 0 | 0.87 | 1 | |||

2 cos (x+ 30°) | 1.73 | 0 | -1.0 | -2.0 | -1.73 | -1.0 | 1 | 1.73 | 2.00 | 1.73 |

- a) On the same axis, draw the graphs of y = cosx and y = 2 cos (x + 30°) for 0°≤ X≤ 360° b) i) State the amplitude of the graph y = cos x°
- ii) State the period of the graph y = 2cos (x + 30°)
- c) Use your graph to solve

cos x = 2 cos (x + 30°)

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- Given that 8≤ y ≤ 12 and 1 ≤ x ≤ 6, find the maximum possible value of:

__y + x__

y – x

**Read Also: Area of the Circles: Sector, Arc. Segment and Chord**