课程名称︰计算机程式 课程性质︰群组必修 课程教师︰谌玉真 开课学院：工学院 开课系所︰化工系 考试日期（年月日）︰2010/11/04 考试时限（分钟）：110分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.Letter grades are sometimes assigned to numeric scores by using the grading scheme commonly called grading on the curve. In the scheme, a letter grade is assigned to a numeric score, according to the following table: x=Numeric Score Letter Grade -------------------------------------------------------------- x < xm-(3/2)σ F xm-(3/2)σ≦ x < xm-(1/2)σ D xm-(1/2)σ≦ x < xm+(1/2)σ C xm+(1/2)σ≦ x < xm+(3/2)σ B xm+(3/2)σ≦ x A where xm is the mean score and σ is the standard deviation. Read a list of real numbers representing numeric scores, calculate their mean and standard deviation, and then find and display the letter grade corresponding to each numeric score. n variance = σ^2 = (1/n)Σ(xi-xm)^2 i=1 n standard deviation = σ =√((1/n)Σ(xi-xm)^2) i=1 The list of scores is 50, 61, 64, 69, 74, 77, 80, 83, 95 2.Write a program that reads triples of real numbers and assigns the appropriate value of true or false to the following logical variables: Triangle: True if the real numbers can represent the lengths of the sides of a triangle and false otherwise(the sum of any two of the numbers must be greater than the third) Equilateral: True if Triangle is true and the triangle is equilateral(the three sides are equal) Isosceles: True if Triangle is true and the triangle is isosceles(at least two sides are equal) Scalene: True if Triangle is true and the triangle is scalene(no two sides are equal) The output from your program should have a format like the following: Enter 3 lengths: 2,3,3 Triangle is: T Equilateral is: F Isosceles is: T Scalene is: F 3.In some situations, an exponential function y = b*e^(m*x) gives a better fit to a set of data points than does a straight line. One common method to determine the constants a and b is to take logarithms ln(y) = ln(b) + m*x and then use the method of least squares to find values of the constants m and ln(b). Write a program that uses this method to fit an exponential curve to a set of data points. Run it for the values in the following table, which gives the barometric pressure readings, in millimeters of mercury, at various altitudes. Test for yourself what is the value of pressure if altitude = 1750m and 2200m. Altitude(x) Barometric Pressure(y) (meters) (millimeters) -------------------------------------------------------- 0 760 500 714 1000 673 1500 631 2000 594 2500 563 Hint:for y'=b'+ m*x _ _ slope = m = ((Σ(xi*yi'))-(Σxi)y')/((Σxi^2)-(Σxi)x) _ _ intercept = b'= y'-m*x Note the difference between y and y'(=ln(y)), also b and b'(=ln(b)) in this problem. 4.A variable z may be represented by the series z = 1+1/(1*1!)+1/(2*2!)+1/(3*3!)+...+1/(n*n!) when n! represents the factorial of n (for example 5!=5*4*3*2*1). Write a program that computes the value of z to use a DO WHILE loop. The program should continue to add terms until the value of 1/(n*n!) becomes less than err where err can be any value such as 0.0005 or 0.00005. Print the final value of z. --

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