Directions: Fill in answers on the pages below. Don't spend too much time on any one problem. All questions below ask for a code segment, which does not need to be a complete program. You never need any #include statements, or the main function, but you should declare the variables that you use.
Points for each problem: 1-15, 2-15, 3-15, 4-20, 5-35.

1. Write a single printf statement that will print the value of an integer n and then the square of n in exactly the following form (no matter what the value of n is):
   n: [value of n], n squared: [value of n squared]

   For example, in case n == 6 it should print: n: 6, n squared: 36
   Similarly, in case n == 11 it should print: n: 11, n squared: 121
   And so forth for any n.

2. Write a segment of code that uses an extended if-else statement to print the proper message based on the value of a variable IQ, using on the following table. [You don't have to read a value for IQ.]

   IQ	What to print
   > 120	High
   90 - 120	Normal
   > 0 and < 90	Low
   < 0	Invalid

3. Write a program segment that will use scanf to read an integer n and then will use a loop to print the integers from 1 to n inclusive, with a blank between each one. Finally print a newline to skip to the next line.

4. Insert code into the C program below so that the program will print the Centigrade temperature corresponding to an input value for the Fahrenheit temperature. You need to supply the prototype and definition of a function ftoc, which takes a double representing Fahrenheit as its input parameter and returns the Centigrade temperature using the formula: C = (5/9)(F - 32).

   
   #include <stdio.h>
   
   
   
   /* insert prototype for function ftoc here*/
   
   
   int main() {
      double f, c;
      scanf("%lf", &f);
      c = ftoc(f);
      printf("Fahrenheit: %.2f = Centigrade: %.2f\n", f, c);
   }
   
   /* insert definition of ftoc here */
   
   
   
   

5. In this problem you will use a random number generator like the generator rand_double() that we used in class. Suppose that it returns a uniformly distributed random double between 0.0 and 1.0. (Do not worry about #include statements, or about initializing the RNG with srand.)

   double rand_double() {
      return rand()/(double)RAND_MAX;
   }
   

   1. Write a segment of code which will use this random number generator and a loop to print 10 random real numbers between 0.0 and 1.0.

   2. Write a code segment that will use rand_double() to simulate flipping a coin. Your segment should print out HEADS half the time and TAILS half the time. [Hint: Remember that half the time rand_double() will return a double that is less than 0.5.]

   3. Write a segment of code that will use rand_double() to produce two numbers, and put these numbers into variables x and y, where both numbers are uniformly distributed in the range from -0.5 to 0.5. [Hint: Just subtract a constant from the numbers returned by the RNG.]

   4. Put the previous segment into a loop that will repeatedly produce two new numbers x and y and will count those pairs of numbers generated that satisfy the condition x² + y² < 0.25. Suppose this count is stored in a variable count. Your segment should repeat for N pairs, where N is 1000, say. After N pairs altogether, the segment should finally print the ratio count/N as a double. (This ratio is a monte-carlo approximation to pi/4.)