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Try-Exam 2015
Notice that the total points of this exam are 75 but it will be graded from 70 points.
Making your answer clear and keeping your paper clean will be appreciated.
Answer the following questions:
Q1:[15 points]
Q2:[15 points]
a) The graph of the function
=
+
+
+
+
passes through the points (–4, –7.6), (–2, –17.2), (0.2, 9.2), (1, –1.6), and (4, –36.4).
Determine the constants a, b, c, d, and e using a MATLAB program.
b) Given the two following polynomials: (x-7)(x+5)(2x-3)(x+4)(x-6) and (3x-3)(x+2)
Write MATLAB commands to add and multiply them.
Q3:[15 points]
Given the following data:
Year
1750 1800 1850 1900 1950 1990 2000 2009
Population 791 980 1260 1650 2520 5270 6060 6800
a) Determine the exponential function that best fits the data. Use the function to estimate the population in
1980. Generate one figure window with two plots: the estimated exponential equation (with the data
points with circles) and the data points using solid line.
b) Estimate the population in 1975 with linear and spline interpolations.
Page 1 of
Q4:[15 points]
The file Store.txt contains the data of 50 products in a factory. The data are arranged in rows and
columns. Each row represents the following data for each product: product id, unit price, number of
available units.
Write a MATLAB program to:
a) Display the total credit value (total price) of the products.
b) Display the number of most expensive products (unit price >= 150).
c) Plot the histogram of the number of available units.
d) Export the following statistics to a text file with name Output.txt: the most expensive product
and the product with smaller available amount. (id and value)
Q5:[15 points]
Mention briefly what the following program does. Mention its output for each of the following
inputs: a) 2, 3, -19, 10, 20
b) -11, 17, 33, 5, 0
A=zeros(5,1);
for i=1:5
A(i)=input('Enter an integer value: ');
end
c=1;
pos=1;
while (c<=5)
y=A(c);
for k=c:5
if(A(k)>=y)
y=A(k);
pos=k;
end
end
temp=A(c);
A(c)=A(pos);
A(pos)=temp;
fprintf('%i
',y)
c=c+1;
end
Page 2 of 2
Model Answer
Q1:[15 points]
e='V=(1/3)*pi*h*(R1^2+(1.2*R1)^2+R1*(1.2*R1))';
R1=solve(e,R1);
V=1000;
h=8:2:16;
R1=subs(R1,V);
R1=subs(R1,h);
R2=1.2*R1;
S=pi*(R1+R2).*sqrt((R2-R1).^2+h.^2)+pi*(R1.^2+R2.^2);
S=double(S);
fprintf('\n The results are grouped as follows:\n')
fprintf('\n R1 \t\t R2 \t\t S \n')
fprintf('\n %6.3f \t %6.3f \t %6.3f ',R1,R2,S)
Q2:[15 points]
(a)
xs=[-4;-2;0.2;1;4];
ys=[-7.6;-17.2;9.2;-1.6;-36.4];
coeff_a=xs.^4;
coeff_b=xs.^3;
coeff_c=xs.^2;
coeff_d=xs;
coeff_e=[1; 1; 1; 1; 1];
X=[coeff_a, coeff_b coeff_c, coeff_d, coeff_e];
C=inv(X)*ys
Q2:[15 points]
(b)
sym x
p1=(x-7)*(x+5)*(2*x-3)*(x+4)*(x-6);
p2=(3*x-3)*(x+2);
p1=expand(p1)
p2=expand(p2)
A=p1+p2
M=expand(p1*p2)
Q3:[15 points]
Year=[1750
1800
1850
1900
1950
1990
2000
2009];
Population=[791 980 1260
1650
2520
5270
6060
6800];
p=polyfit(Year,log(Population),1)
m=p(1);
b=exp(p(2));
%estimate the population at 1980
EP=b*exp(m*1980)
%one figure for two plots
x=Year;
y=b.*exp(m*x);
subplot(2,1,1)
plot(Year,Population,'o',x,y)
subplot(2,1,2)
plot(Year,Population)
% interpolations using linear and spline
Ent_P1=interp1(Year, Population,1975,'linear')
Ent_P2=interp1(Year, Population,1975,'spline')
Q4:[15 points]
S=load('Store.txt')
Price=S(:,2)
Units=S(:,3)
% the total value of the products
TV=Units.*Price;
TV=sum(TV);
fprintf('The total value is %8.3f\n',TV)
% the number of most expensive products
count=sum(Price>=150);
fprintf('The total value is %i\n',count)
%the histogram of the number of available units
hist(Units);
% to export the most expensive product and the product with smaller
% available amount.
ID=S(:,1);
mx=max(Price)
mx_index=find(Price==mx)
mx_id=ID(mx_index)
mn=min(Units)
mn_index=find(Units==mn)
mn_id=ID(mn_index)
fid=fopen('Output.txt','w')
fprintf(fid,'Most expensive item: id= %d \t price=%5.3f \n',mx_id,mx)
fprintf(fid,'Less available item: id= %d \t units=%d \n',mn_id,mn)
fclose(fid)
‫]‪Q5:[15 points‬‬
‫أو ‪ :‬وم ا ر‬
‫‪ :‬ا رج !‬
‫ل ‪ 5‬أ داد‬
‫اد ل ا و‬
‫م وم ر‬
‫م ر ن ر‬
‫ز ‪.‬‬
‫‪:‬‬
‫‪20, 10, 3, 2, -19‬‬
‫‪a) 2, 3, -19, 10, 20‬‬
‫‪33, 17, 5, 0, -11‬‬
‫‪b) -11, 17, 33, 5, 0‬‬