Form 2 Maths

2008-06-03 2:59 am

Find the values of A and B in the identities

1. (x-3)^2 ≡ x^2+Ax+(A+B)

2.Charles wants to know the thickness of a piece of paper by first measuring the thickness of a pile of 500 pieces of paper to be 58mm (correct to the nearest mm) and then dividing his measured value by the total number of pieces of paper.

(a)(i)Find the maximum error of the thickness of a piece of paper;
(ii) Find the thickness of each piece of paper;
(iii) Find the percentage error, correct to the nearest 0.1%.

(b) Will he get a larger or smaller error if he uses less pieces of paper?

回答 (1)

NCY

2008-06-03 3:26 am

✔ 最佳答案

1)(x﹣3)2 ≡ x2 + Ax + (A + B)
x2﹣6x + 9 ≡ x2 + Ax + (A+B)
We have：
A = -6 and
A + B = 9
-6 + B = 9
B = 15

2ai)the maximum error of the thickness of 500 pieces of paper
= (1/2)(1) mm
= 0.5 mm
the maximum error of the thickness of a piece of paper
= 0.5 / 500
= 0.001mm
ii)the thickness of each piece of paper
= 58/500
= 0.116 mm
iii)the percentage error
= maximum absoulte error / measured value X 100%
= 0.001/0.116 X 100%
= 0.9% (correct to the nearest 0.1%)
b)When the less pieces of paper is used, as the measurement error remain unchange = 0.5mm
the error for a piece of paper = error of total number of paper / number of paper
will then increase.
Hence,he will get a larger error.

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