Department of Computer Science

University of Illinois at Urbana-Champaign

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

 


Name:                                                                         NetID:
 

Lab Section:                                                                Date: 2/24/11

 


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 9 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.



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

Deduction

Grader

1

6

 

 

2

6

 

 

3

8

 

 

4

8

 

 

5

6

 

 

6

6

 

 

7

8

 

 

8

6

 

 

9

6

 

 

10

8

 

 

11

7

 

 

12

8

 

 

13

6

 

 

14

6

 

 

15

8

 

 

16

6

 

 

17

8

 

 

18

8

 

 

Total

125

 

 

 

 

Exam Scoreΰ

 

A

 

1.      Given  A=[1;2], B=[3;4], circle the result MATLAB will return when you type the following  command in the MATLAB command window. There is only one correct answer.

 

>> A*B

 

 

a)

ERROR

b)

1

 

c)

2 2



d)

3 4

6 8

 

 

    2. You are given the following system in the standard form A*b = c.

 

            A =  b =  c =

 

Once A and c have been initialized in the MATLAB workspace, circle the command that will allow you to solve for the vector b. There is only one correct answer.

   

a)  c/A

 

b)  c./A


c)  A\c



d)  c\A

 

 

3.      Write the results Matlab returns if you type the following command at the Matlab prompt.

            >> [linspace(-2,2,5), 3:2:7]

 

 

 _____________________________________________________

 

 

 

 

 

4.      Given the array A = answer the following questions:

 

a)      Write the results Matlab returns if you type the following command at the Matlab prompt.

 

       >> A(1:2,:)

 

 

       _____________________________________________________

                

 

b)      Using subscripting, write a single Matlab command to extract all the values in the first column of A .



                 _____________________________________________________

               

         

a)      Write the results Matlab returns if you type the following command at the Matlab prompt.

 

               >> A'

 

 

                _____________________________________________________

5.      Write the results Matlab returns for the following commands typed in the Matlab command window.

 

>> A = [1; 2; 3];

>> B = A.*A.*A

   B =

 

 

 

     _____________________________________________________

 

 

 

6.      Write a single Matlab command to create the following matrix.

A 99 x 99 matrix as follows:

 

 

            (Hint: you might use the ones function and the cumsum function.)

 

 

 

>> _____________________________________________________

 

 

 

 

7.      For the given y and x values below, find the x values that correspond to the smallest value in y. The answer is [ 0.2   0.8   1.0]. Write the Matlab code to produce this answer. Your answer should work for any values of y and x, assuming y and x are of the same size. Hint: consider using subscripting and the Matlab function ‘min’.

 

>>  y = [  2   1    5    4    3    5    4    1    5      1 ] ;
>>  x = [ .1  .2   .3   .4   .5   .6   .7   .8   .9   1.0 ] ;

 

 

>>r = _____________________________________________________

 

  r =

0.2000      0.8000     1.0000

 

 

 

8.      Fill in the blanks to write a Matlab expression to display a row vector with 5 random integers in the range from -10 to 10 inclusive.

  >> random =ceil(______________+_____________* rand(1,5))

9.       We have two functions named f1 and f2 saved in two separate files f1.m and f2.m as follows:

      function y = f1(x)

 global g

 g = g + x.^2 + 3*x +1;

 y = g + 7;

 

      function y = f2(x)

 g = 50;

 y = g + 10*x;

 

 

The following sequence of commands is entered at the Matlab prompt. Fill in the blanks with the correct values that Matlab returns for the variables named a, b, and g.

 

  >> clear

>> global g

>> g = 0;

>> a = f1(5);

>> b = f2(g+2);

>> a

a = _____________________________________________

 >> b

b =  _____________________________________________

 >> g

g =  _____________________________________________

 

         

 

 

    

10.  Fill in the blanks below to use the built-in function fplot  to plot the function 

                         on the interval [1,2].

 

            >> fplot(__________________________________, _________________________________);

 

 

 

 

 

11.  Write a single Matlab command to find a root of the function

 

        

          near x = 2. Do NOT calculate the actual root, just write a Matlab command that would produce

         the root.

 

 

 

          >>   ___________________________________________________________

 

 

 

 

12.  We would like to plot the following 3D surface:

 

 

 

           Fill in the blanks to plot the surface above a grid of points in the x-y plane with 50 equally spaced 

          values for x between -5 and 5 and 50 equally spaced values for y between -3 and 3 .

 

 

>> x = linspace(-5, 5, 50);

 

 

>> y = linspace(-3, 3, 50);

 

 

>> [XMAT ,YMAT] = meshgrid(_______________,___________________);

 

 

>> ZMAT = exp(____________).*(_________________+_________________);

 

 

>> surf(_______________, ________________, ___________________)

 

 

 

13.   Given the code for the function named what ,

 

      function i = what(x, y)
                                

       i = x*(y >= x) + y*(x > y);

     

 

Write the output the function produces when it is called from the Matlab prompt with the arguments shown below.

 

 

      >> z = what(2,3);

        z =

 

            _____________________________________________________

 

 

      >> z = what(3,2);

        z =

 

            _____________________________________________________

 

 

     >> z = what(2,2);

        z =

 

 

            _____________________________________________________

 

 

 

 

 

 

 

 

14.   Consider a cylinder with length L and radius R. Fill in the blanks below to complete the code for a function that calculates the volume and area of a cylinder. Recall that for an opened ended cylinder area= 2* π *R*L   and   volume= π *R^2*L.

 

 function [volume, area] = cylinder(________,________)

 

 

 __________________ = pi*R.^2.*L;

 

 

 __________________ = 2*pi.*R.*L;

 

15.  Which of the following Matlab code fragments is a correct way of computing an approximation of

 the definite integral of the function f(x) = sin(x) on the real interval [0, π]? Circle each of the correct answers. (Note: there may be more that one correct answer.)

 

     a)

>> x = linspace(0,pi,100)

>> y = sin(x)

>> trapz(x,y)

 

 

     b)

>> quadl(@sin,0,pi)

 

 

     c)

>> trapz(@x,'sin(x)',0,pi)

 

 

     d)

>> x = linspace(0,pi,100)

>> y = sin(x)

>> quad(x,y)

 

 

 

16.   Write the result Matlab returns when the following sequence of commands are typed in
       the Matlab command window.

 

            >> r = [-10  1  7  0  6  9];

     >> s = [ 4  7  1  10  6  7];

     >> t = s(r <= min(s))

        t =

 

          _____________________________________________________

 

 

 

17.  Consider solving the following initial value ODE  problem using the  ode45 function:

 

                   

 

where x(0)=1,for 0≤t≤10. We create the following .m file called ex1.m:

 

function xprime=ex1(t,x)
xprime=x*sin(t); 

 

Fill in the blanks below to solve the above ODE.



>> [t,x] = ode45(‘___________’,[_________ ,__________], _______);

18.  Complete the code below for a function named convert that converts grams to pounds and 

       pounds to grams. Recall that each pound is approximately equal to 453 grams.

 

 

function [pound,gram] = convert(pound,gram)

if isempty( ________________________________ )

 

    pound = _______________________________ /453;

 

elseif isempty(________________________________)

 

    gram = ________________________________ *453;

 

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