题目

Problem

The circumference round the trunk of a large tree is measured and found to be $5.00\text{ m}$ . After one year the circumference is measured again and found to be $5.02\text{ m}$ .

(a) Given that the circumferences at yearly intervals form an arithmetic progression, find the circumference 20 years after the first measurement.

(2)

(b) Given instead that the circumferences at yearly intervals form a geometric progression, find the circumference 20 years after the first measurement.

(3)

题目中文翻译

测得一棵大树树干的周长为 $5.00\text{ m}$ 。一年后再次测量，周长为 $5.02\text{ m}$ 。

(a) 已知每隔一年测得的周长构成等差数列，求第一次测量 20 年后的周长。

(2)

(b) 若改为假设每隔一年测得的周长构成等比数列，求第一次测量 20 年后的周长。

(3)

原卷通用作答要求

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

解答

(a)

解法一

思路

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第一次测量是第 $1$ 项。经过 $20$ 年共增加 $20$ 次公差。

答题过程

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The yearly difference is $5.02-5.00=0.02$ m. After $20$ years the circumference is $5.00+20(0.02)=5.40$ m.

(b)

解法一

思路

展开

用相邻两次的读数求公比。经过 $20$ 年要乘以公比的 $20$ 次方。

答题过程

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The yearly ratio is $5.02/5.00=1.004$ . The circumference after $20$ years is

5.00(1.004)^{20}=5.41557\ldots\,\mathrm m,

which is $5.42$ m to three significant figures.

CIE 9709 2023 March Paper 12 Q4

题目

解答

(a)

解法一

思路

答题过程

(b)

解法一

思路

答题过程