12600
Spring ENGINEERING 2009
Exam 3
INSTRUCTIONS:
Duration: 60 minutes
Keep your eyes on your own work!
Keep your work covered at all times!
1. Each student is responsible for following directions. Read carefully.
2. Excel and MATLAB commands are provided on the next page.
3. This exam consists of 10 questions on 7 pages (4 sheets front AND back). Check to be sure
that you have all of the pages.
4. Write your name on the answer sheet.
5. Closed book and notes.
6. No calculators.
7. Please make sure you return the answer sheet.
ENGR 12600 Spring 2009
EXAM 3 Formula Sheet for Written Exam
Statistics Equations
Linear Regression
MATLAB Commands
+-*/^
=
.* ./ .^
%
' (transpose)
:
;
< > <= >=
~ ~= = =
& | && ||
() [ ]
... (ellipsis)
abs
acos
all
asin
atan
ans
axis
clc
clear
close
cos
csc
disp
else
elseif
end
eval
exit
exp
factorial
figure
floor
fminbnd
for
format
fplot
fprintf
function
fzero
grid
help
helpbrowser
hist
hold on
hold off
i, j
if
Inf
input
legend
length
linspace
load
log
log10
loglog
logspace
lookfor
max
mean
median
min
mode
NaN
ones
pi
plot
polyfit
polyval
prod
quit
round
sec
semilogx
semilogy
sin
size
sort
sqrt
std
subplot
sum
tan
text
title
while
who
whos
xlabel
xlsread
xor
ylabel
zeros
Excel Functions
+-*/^=
$
ABS
AVERAGE
COS
Linear
y = mx + b
EXP
LN
LOG10
MAX
MEDIAN
MIN
MODE
PI
SIN
SQRT
Exponential
y = b emx
y = b 10mx
Logarithmic
x = b emy
x = b 10my
2
STDEV
SUM
TAN
Power
y = b xm
x = b ym
ENGR 12600 Exam 3
April 21, 2009
RECORD ALL ANSWERS ON THE ANSWER SHEET
Problem 1 (6 points)
A morphological analysis was performed for a device that could be used to store and keep food
cool - a replacement for a common refrigerator. The overall function is determined to be to
preserve food. A list of items was generated during the morphological analysis of subfunctions and means. A sample of the items are listed below with the sub-functions and means
mixed up. Check the appropriate category for each to separate the sub-functions from the means.
Check only the ONE category for each item that is the most appropriate given the list of items.
Item
SubMeans
Function
Passive heat exchanger for cooling
Cool food
LEDs (Light Emitting Diodes) for lighting
Store vegetables
Sliders to move shelves
Insulation made from recycled plastic
Problem 2 (6 points)
The following commands were executed in MATLAB. What is the value of y if a=1, b=2, c = 4
and d = 5?
A. y= 3<d<4
B. y=~(xor(d>=b,a<b))&((a+b)==(c -1))
C. y=((d>=b|a<b)&((a+b)==c |d<=b*a)|(a+d<=b+c))&a>d
Problem 3 (6 points)
The following MATLAB code is executed:
for a = 5:2:5
c = a+2;
end
disp(c)
What appears on the screen?
a) 4
b) 5
c) 7
d) 9
e) Undefined function or variable 'c'
Problem 4 (12 points)
The following MATLAB code is executed twice for two different set of inputs. For each set of
inputs for x and y (in parts A and B below), circle the value of z that appears on the screen after
the following MATLAB commands are executed:
clear
x = input(Enter x:
y = input(Enter y:
);
);
ENGR 12600 Exam 3
April 21, 2009
RECORD ALL ANSWERS ON THE ANSWER SHEET
if x<8 | y< 8
if x>=6
z=x+y;
elseif x<6 & y>=12
z=x*y;
end
else
z=y-x;
end
disp(z)
A. First, the input x is assigned a value of 10 and the input y is assigned a value of 5. On your
answer sheet, circle what would appear on the screen for the value of z.
a) 5
b) 10
c) 15
d) 50
e) Undefined function or variable 'z'
B. The commands are run a second time with the input x assigned a value of 5 and the input y
assigned a value of 10. On your answer sheet, circle what would appear on the screen for the
value of z.
a) 5
b) 10
c) 15
d) 50
e) function Undefined or variable 'z'
Problem 5 (6 points)
The following MATLAB code is executed. What appears on the screen?
a=0
b=0
c=0
for a = 5:2:8
for b = 1:2
c = a-b;
end
end
disp([a b c])
Problem 6 (6 points)
The following MATLAB code is executed.
x=2;
y=4;
z=20;
while z <= 10
z=0;
x=x+1;
y=y+1;
z=x+y;
ENGR 12600 Exam 3
April 21, 2009
RECORD ALL ANSWERS ON THE ANSWER SHEET
end
disp(z)
On your answer sheet, circle what would appear on the screen for the value of z.
a) 8
b) 10
c) 12
d) 20
e) Undefined function or variable 'z'
Problem 7 (15 points)
A user-defined function called test_unitcircle has been written to test the trig identity:
The function as shown below has errors.
1
2
function [TorF] = test_unitcircle(angle)
% test_unitcircle Tests the trig identity sin^2(a) +
cos^2(a) = 1
% INPUT
% angle = angle in degrees
% OUTPUT
% TorF = 1 (true) if trig identity is verified or
%
0 (false) if trig identify is not verified
3
4
5
6
7
8
9 sincos = sin^2(alpha) + cos^2(alpha)
10 test_unitcircle = (sincos = 1)
Identify FIVE (5) mistakes in the code using the table on the answer sheet. Clearly indicate the
line number of the mistake, describe the mistake and how it could be fixed. Each mistake counts
as one, even if there are multiple mistakes on the same line. Mistakes of a similar type may only
be counted once.
Line
Numbe
r
What is the error?
How can the error be fixed?
Problem 8 (6 points)
Data is taken during a test that recorded displacement as a function of angular rotation. The
phenomena that was measured is plotted below and can be modeled by the equation
Where y is the displacement in centimeters and (theta) is the rotational angle in radians.
Write the MATLAB code that will
1) Plot the function shown above for angles between 0 and 6 radians
ENGR 12600 Exam 3
April 21, 2009
RECORD ALL ANSWERS ON THE ANSWER SHEET
2) Display the value of the minimum displacement between 0 and 6 radians using an
fprintf command
You do NOT have to add comment statements nor recreate the problem template. Comment
statements may be added to clarify your steps but no points will be deducted for not including
comments statements.
Problem 9 (30 points)
Write a MATLAB user-defined function to compute the exponential function directly from the
Taylor series:
The series should not end until the last term is less than 10-6.
The function should output:
the computed value of using the Taylor series,
the number of terms used in the Taylor series computation,
and the absolute difference between the Taylor series computed value of and the value
returned by MATLABs built-in exponential function.
Term
Last Term
Taylor Series
Value for
Value for
1
1
1
2
1
2
3
0.5
2.5
4
0.16666667
2.66666667
5
0.04166667
2.70833333
6
0.00833333
2.71666667
7
0.00138889
2.71805556
8
0.00019841
2.71825397
9
0.00002480
2.71827877
10
0.00000276
2.71828152
11
0.00000028
2.71828180
MATLAB Built-in value for = 2.71828182
Take for example as shown in the table on the right.
Eleven (11) terms are used in the Taylor series computation, the computed Taylor series value is
2.71828180, and the absolute difference between this value and the MATLAB computed value is
2.7131 x 10-8.
ENGR 12600 Exam 3
April 21, 2009
RECORD ALL ANSWERS ON THE ANSWER SHEET
Your code should contain proper commenting for a user-defined function.
Problem 10 (7 points)
Using the variable time, demonstrate how to use your user-defined function to compute the
exponential using the Taylor series. Write the code you would need to enter at the MATLAB
command window to generate all required outputs.
>> time = 3
>> __________________________________________________________________________