Department of Computer Science

University of Illinois at Urbana-Champaign

Computer Science 101: Mid Term Exam I (60 minutes)

 


Name:                                                                         NetID:
 

Lab Section:                                                                Date: September 28, 2006

 


No questions will be answered during this examination.  If you do not understand a question, read it again.  If you still do not understand it, make reasonable assumptions and write them down. (Points will be deducted if unreasonable assumptions are made.)

DO NOT CHEAT: Cheating includes not only copying from another person but also allowing someone to copy from you.  Anyone who copies or allows someone to copy will receive a score of zero.  So be defensive and protect your work.

 

This examination contains 10 pages including this page. Check that your copy is complete, and ask for a replacement if it is not. Do all your work on these pages. For your own protection, in case pages come apart, write your NetID at the TOP of each page before beginning work.

The number of points for a question is roughly proportional to the amount of time you may need for it. Don’t spend too much time on any one question.

Do not forget to sign the attendance list. If your exam is misplaced and you did not sign the attendance list then you will receive a zero score for the exam.

You may not use any electronic devices, book, notes or other references during this examination.


DO NOT WRITE IN THIS SPACE

Section

Possible Score

Score

Grader

1

4

 

 

2

8

 

 

3

6

 

 

4

6

 

 

5

6

 

 

6

8

 

 

7

8

 

 

8

9

 

 

9

6

 

 

10

6

 

 

11

6

 

 

12

8

 

 

13

6

 

 

14

6

 

 

15

6

 

 

16

6

 

 

17

12

 

 

18

8

 

 

Total

125

 

 

A

1. Assume the vector v has been created as follows:

     >> v = [6 7 8 9];

    Write the output of the following Matlab command:

    >> v([3 1 4 2])

    ______________________________________________________

 

 

 

2. Write a single Matlab command to produce the vector  [ 1 3 5 7 … 999] , all the odd integers

     from 1 to 999:


    >> ____________________________________________________

 

 

 

3. Assume that x has been declared a symbolic value as follows:

  >> syms x

   Write a single Matlab command to find the second derivative of the function sin(x).

    Do not write the answer ‘-sin(x)’, write the Matlab command that will give you the correct result.

 

    >> ___________________________________________________

 

 

 

 

4. Write a single Matlab command to find the root of cos(x) nearest to 2.  Do not write the root.

 

  >> _________________________________________ ________

5. Write Matlab command(s) to create a 100 by 100 matrix named mat with the vector

    [1 2 3 … 98 99 100] (a vector with the integer values from 1 to 100) along on the main diagonal  

    and 100 along the bottom row and zeros everywhere else:

   

 

 

 

 

 

 

 

 

6. Given vectors v1, v2 :

    >> v1 = [1; 2; 3];

    >> v2 = [1 2 3];

 

     which of the following is a legal expression, that is, will NOT produce a Matlab error? There may be  

     more than one legal expression. Circle each expression that is legal. Do not compute the value of the

     expression.

 

a)      v1 + v2


 

 

b)      v1 – v2’


 

 

c)      v1 * v2


 

 

d)      v1 .* v2

7. Given

 

     >> mat1 = [ 1 2 ; 3 4 ; 5 6 ];

 

     write the output the following Matlab commands produce.

 

>> size(mat1)

 

ans =  ________________________________________

_

>> mat1(1:2 , : )

                                 
                            

ans = ________________________________________

 

 

 

 

 

8. Transform the following system of linear equations into a Matlab matrix and vector. Matrix A should contain the coefficients of the equations and column vector c should contain the right hand side of the equations.

 

 

>> A =  ____________________________________________________

 

>> c =  ____________________________________________________

 

Write a single Matlab command to solve the system of equations using matrix A and vector c.

 

>> ________________________________________________________

 

9. Assume the vector x has been created as follows:

      >> x = [4 2 -1 3];

     Write the output of the following expressions.

      >> min(x)  

 

     ans =

 

                     ______________________________________________________________________

 

      >>  max(x.^2)

 

 

     ans =

 

                     _____________________________________________________________________

 

 

 

10. Assume that matrix A has been declared as follows:

   >> A = [1 2 3; 2 4 6];

 

      Write the result of the following expression.

 

   >> A(1,:) .* A(2,:)

 

   ans =

 

                    _____________________________________________________________________

 

 

 

 

 

 

 

 

11. Given a vector v, write a single Matlab expression to obtain the truncated vector of v, that is, the

      vector whose ends are truncated from the original vector v.

      (For example, if the vector v is [1 2 3 4 5] then the truncated vector is [2 3 4], but your   

       Matlab expression should work for any length vector.)

 

             >> ____________________________________________________________________

 

12. Given

    

   >> x = [1 3 5 7 9 11 13];

 

     which one of the expressions below (choices a thru d) is equivalent to the following Matlab command?

 

       >> y = [13 9 5 1];

 

      That is, which of the Matlab commands below assigns the vector of values [13 9 5 1] to y?

      There may be more than correct answer. Circle each correct answer.

 

 

a)      y = x(end:-2:1);


 

 

 

 

     b) y = x(length(x):-2:1);

 

 

 

 

 

 

    c) y = x([13 9 5 1]);

   

 

 

 

 

 

    d) y = x(13:-4:1);

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

13. Write a single Matlab command to find all the roots of the polynomial y = x3 - 5x2 + 5x  .

      (Don't write the roots.)

 

 

  >> ____________________________________________________________________

 

 

 

 

 

 

 

14.  The file data.m contains the script,

 

       x = 2;

   y = 1;

 

      The file f.m contains the function code,

 

      function y = f(x)

    global z

    z = [z, x];

    y = x * 3;

 

      At the Matlab prompt you type the following commands. Fill in the blanks with the correct values that  

      Matlab would return.

 

       >> clear

   >> global z

   >> f(1);

   >> who

 

               ________________________________________________________________

 

 

       >> data

   >> who

        

             _________________________________________________________________

 

 

 

 

 

 

 

 

 

 

 

15. Write the values of v, w and x after entering the following sequence of Matlab commands.

   >> v = 2*ones(4,1)
 
   v =     


                 _____________________________________________________
   
   >> v = [ 1 2 3 4];
   >> w = cumsum(v)
 
   w =
 
                _____________________________________________________

       >> w = [5 4 3 2 1];   
       >> x = diff(w)
  
   x =
 

             ______________________________________________________

 

 

 

 

 

 

 

 

 

 

16. Using the built-in function quadl complete the Matlab command by filling in the blanks, to compute
      the definite integral :

        


>> quadl( _______________________________________ , ______________ , _____________ )

 

 

17. Assume that you have a script in the file named tower_data.m with the contents:

 

        HL =  10;

        HR =  20;

 

      Write a complete Matlab function named appendvalues. The function has one input parameter, h

      that will hold a row vector. The function appendvalues will run the script named tower_data

      and then prepend the value of HL to the vector h and append the value HR to h. The function

      appendvalues has one return value, this modified row vector.

      For example, at the Matlab prompt if we assigned h the following values then we would get the

      results as shown below:

    >>  h = [ 3   4   5   4   3];

 

    >>  newh = appendvalues(h)

    newh    =

              10   3   4   5   4   3   20

 

 

      Of course the code you write for appendvalues should work not just for the example above but for

      any vector h.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18. The function named diff_L  has the following properties:

 

·        diff_L has two input parameters x and y that hold vectors of equal lengths.

·        diff_L calls the function xy_length and passes this function x and y.

·        diff_L computes and returns the difference between the target value L = 10 and the value returned from the function xy_length.

      Assume that you have a function named xy_length in the file xy_length.m with contents:

 

      function calc_length = xy_length(x,y)       

       calc_length = sum( sqrt( diff(x).^ 2 +  diff(y).^ 2 ) );

 

 

      For example, at the Matlab prompt if we assigned x and y the following values then we would get the

      results as shown below:

    >>  x = [ 0   1   2];

 

    >>  y = [ 2   0   3];

    

    >>  delta_L = diff_L(x,y)

 

        delta_L =

                    4.6017

 

     Which of the choices below satisfy the properties for diff_L as described above and would return the

     results as shown above? There may be more than one correct answer. Circle each correct answer.

 

a) 

function delta_L = diff_L(x,y)

L = 10;

xy_length(x,y)

delta_L = L - calc_length;

 

 

b) 

function delta_L = diff_L(x,y)

L = 10;

delta_L = L – xy_length(x,y);

 

 

c) 

function delta_L = diff_L(x,y)

L = 10;

calc_length = xy_length(x,y);

      L - calc_length

 

d) 

function delta_L = diff_L(x,y)

L = 10;

calc_length = xy_length(x,y);

delta_L = L - calc_length;