The first question regarding to "list" won't appear in our exam.

a.(5pts) Provide the header for a method that takes an array of ints and returns the percentage of elements that are perfect squares.  A perfect square is an integer number whose square root is also an integer number. (You have to give this method a name.) 

public static double percentOfPerfectSquare(int[] a)

b.(5pts) How would you check to see whether an element of the array (say, at index i) is indeed a perfect square? (Use the method double Math.sqrt(double x) to compute a square root.)

One possible solution:
int sqrtInt = (int)Math.sqrt(a[i]);
if( sqrtInt * sqrtInt == a[i] )
    CONDITION = true;

Another possible solution:
int sqrtInt = (int)Math.sqrt(a[i]);
if( (double)sqrtInt = Math.sqrt(a[i]))
    CONDITION = true;

c.(10pts) Assume that b is solved with the boolean CONDITION.  Write the body of this method.

int totalCount = 0;
for(int i = 0; i < a.length; i++){
    // calculate CONDITION
    if (CONDITION)
        totalCount++;
}
return (double)totalCount /  a.length;