Problem 3 – Multiple Choice from T-Square
which of the following is the value of vec after the following code is run?
a= 1:3:7
b= 2:2:6
c= mod(a,2)
vec= zeros(1,7)
vec([a b])= [c a(b/2)]
A. [0 2 0 4 0 6 0]
B. [1 1 0 4 0 7 1]
C. [1 2 1 4 1 6 1]
D. [1 2 3 4 0 6 7]
E. [0 1 0 4 0 7 0]
If there is a vector, vec=[1 2 3 4 5] which of the following will NOT output the value 5?
A. length(vec(end:-1:1))
B. vec(max(vec))
C. vec(vec(1:4)=[])
D. vec(~[true true true true false])
E. vec(mod(vec,2)~=0 & mod(vec,5)<=0)
Which of the follwing will give a vector of evenly spaced integers from 1 to 7?
A. 1:7
B. linspace(1,7)
C. sort(rand(1,7))
D. mod(9:1:15,8)
E. Two answers are correct
If vec= [1 4 3 7 2 9] which of the following will remove the odd indices from vec?
A. vec([1 3 4 6])=[ ]
B. vec([1 3 2])=[ ]
C. mod(vec,2)=[ ]
D. vec(1:2:6)=[ ]
E. Two answers are correct
Which of the following will output a value of 1, if vec= [ 1 5 4] ?
A. vec(~(~[false true]))
B. vec(vec<2 | mod(vec,2)~=0)
C. vec(logical(-1))
D. vec(~[false true true true true])
E. Two answers are correct
vec = [ 2,6,7,3]
b= vec([ 1 0 1 1])
What is the error MATLAB gives for this statement?
A. Error: Matrix Dimensions must Agree
B. Error : Subscript indices must either be real positive integers or logicals.
C. Error : Index exceeds matrix dimensions
D. Error: Undefined function or variable a
E. Error : The input character is not valid in MATLAB statements or expressions.
vec = [ 2,6,7,3]
b= vec(vec)
What is the error MATLAB gives for this statement?
A. Error: Matrix Dimensions must Agree
B. Error : Subscript indices must either be real positive integers or logicals.
C. Error : Index exceeds matrix dimensions
D. Error: Undefined function or variable a
E. Error : The input character is not valid in MATLAB statements or expressions.
vec1 = [ 2, 6, 7, 3];
vec2 = [3, 4];
vec4 = vec1.*vec2;
What is the error MATLAB gives for this statement?
A. Error: Matrix Dimensions must Agree
B. Error : Subscript indices must either be real positive integers or logicals.
C. Error : Index exceeds matrix dimensions
D. Error: Undefined function or variable a
E. Error : The input character is not valid in MATLAB statements or expressions.
Which of the following concatenations will return the string 'cs1371'?
A. ['cs' char(1371)]
B. ['cs' char(1) char(3) char(7) char(1)]
C. ['cs' str2num(1371)]
D. ['br'+1 '1371']
E. None of the above
Which of the following will NOT return a string with the alphabet in capital letters?
A. linspace('A','Z',26)
B. 'A':'Z'
C. ('a':'z')+'A'-'a'
D. char( double('A'):('A' + 25))
E. None of the above
A=[1 9 3
527
4 2 6]
Which of the following will remove the 7 from A?
A. A(2,3)= [ ]
B. A(3,2)= [ ]
C. A(A~=7)
D. A=A(mod(A,7)>=0)
E. None of the above
If str1 is a word or phrase with no punctuation, which of the following does NOT find whether
str1 is a palindrome?
A. all(str1 == str1(end:-1:1))
B. strcmpi(str1, str1(end:-1:1))
C. strcmp(str1(1:end/2), str1(end:-1:end/2+1))
D. all(str1./ str1(end:-1:1) == 1)
E. None of the above
Which of the following are NOT valid conditionals for an if statement? (Which one will allow
NOT the statement to run)
A. 'true or false'
B. strcmp(str1, str2)
C. [1 2 3]
D. double(false)
E. two of the above are incorrect
if a>3
if a< 10
a=2*a-5;
elseif mod(a,2)==1
a=a-2;
end
else
a=a-1;
end
If a=6 before the above code is run, what will be its value afterwards?
A. a= 2
B. a= 4
C. a= 5
D. a= 7
E. None of the above
switch str
case {'a' 'b' 'c'}
out=str(1:end-1)
case double('abc')
out=str(1:end-2)
case {'abc'}
out=str(1:end-3)
end
If str= 'abc' before the above code is run, what is the value of out afterwards?
A. out= 'ab'
B. out= 'a'
C. out= ''
D. out= 'abc'
E. Error
Which of the following is a variable that cannot be safely run through a switch statement?
A. linspace( 'A', 'Z', 26)
B. [65 97 65]
C. 659765
D. 'A'
E. None of the above
Which of the follow evaluates to true if a=true and b=false?
A. (~a | (a & b)) & ((~b & a) | (b & a))
B. ~ (a & b) & (b | (b & ~a))
C. ((a & b) | (b & (b | a))) | (~a | (a & ~b))
D. ~ ((b & (a | b)) | (a & (a | b)))
E. None of the above
a=[];
for i=length(z):-1:1
if mod(i,2)==0
a=[z(i) a];
else
z(i)=[];
end
end
If z is a vector of doubles and the above code is run, how will a and z relate?
A. a has the even values from z and is reversed
B. a and z are the same vectors
C. a has the same number of values as z but is reversed
D. a has half the values of z and is reversed
E. None of the above are correct or the code errors
Problem 3 – Multiple Choice [50 Points]
1. What is the effect of the function imager given the image matrix img?
function [ret] = imager(img)
img = double(img);
val = uint8((img(:,:,1)+img(:,:,2)+img(:,:,3))/3);
ret(:,:,1) = val;
ret(:,:,2) = val;
ret(:,:,3) = val;
A.
B.
C.
D.
E.
ret is a black and white image
ret is a grayscale image
ret is twice as large as img
ret is the same as img
None of the above
2. Given the following lines of code, which of the following operations would produce the same
sound?
[x, fs] = wavread('mysound.wav')
sound(x, fs)
A.
B.
C.
D.
E.
x = x(round(linspace(1, length(x), 2*length(x))))
sound(x, fs/2)
x = 2*x
sound(x, fs/2)
x = sound(x, fs*2)
sound(x, fs/2)
x = x(round(linspace(1, length(x), 2*length(x))))
sound(x, fs*2)
x = x/2
sound(x, fs/2)
3. Given the following Matlab code:
A = true;
B = false;
C = (A || B) && ~(B && B)
if C
output = 'almost there'
else
output = 0
end
What is the class of output?
A. char
B. double
C. logical
D. cell
E. Error
4. Given the following:
x = [0 1 2 3 4]
y = [0 2 4 6 8]
plot(x, y, 'ro')
What would the plot look like?
A. A solid red line connecting the given x and y values
B. A plot of red circular points with the given x and y values
C. A curved fit for the given x and y values
D. Error
E. None of the above
5. Convert the following while loop to a for loop.
vec = [1 2 3 4];
sum = 0;
while length(vec)>0
sum = sum + vec(1);
vec(1) = [];
end
A.
for vec
sum = sum + vec(i);
end
B.
for i = vec
sum = sum + vec(i);
end
C.
for i < length(vec)
sum = sum + vec(i);
i = i + 1;
end
D.
for i = vec
sum = sum + i;
end
E.
for i = length(vec)
sum = sum+vec(i);
end
6. Which of the following is a valid function header? (mark all that apply)
A. function = fx(input)
B. function ret1, ret2 = fx(input)
C . function ret = fx(34)
D. function fx
E. [ret1, ret2] = fx(input1, input2)
7. Given:
vec = [5 9 6 3 6 8]
Which of the following will NOT return the vector v2 = [5 6 3 6 8]?
A. v2 = vec(vec < 9)
B. v2 = vec([1 3:6])
C. v2 = vec;
v2(vec == max(vec))=[]
D. v2 = vec(vec ~= 9)
E. v2 = vec;
v2(vec > 9)=[]
8. Given :
x = linspace(1,10,100)
y= x.^3
y1 = diff(y)./diff(x)
Which of the following will plot the second derivative?
A. plot(x(2:end), diff(y1)./diff(x(2:end)))
B. plot(x(3:end), diff(y1)./diff(x(2:end)))
C. plot(x(2:end), diff(y1)./diff(x))
D. plot(x(2:end), diff(y1(2:end))./diff(x(2:end)))
E. plot(x, diff(y1)./diff(x(2:end)))
9. Which choice below is NOT true about the following line of code?
f1 = fopen('index.txt', 'w')
A. The file handle for ‘index.txt’ is stored in the variable f1
B. The text from ‘index.txt’ is stored in the cell array f1
C. The file has been opened with read only permission
D. Both A and C
E. Both B and C
10. Given:
cell = {'cool', 1:4, false}
cell{2} = []
What is the final value of cell?
A. {'cool', [], false}
B. {'cool', false}
C. {'cool', {}, false}
D. {'cool', [1 3 4], false}
E. Error
Problem 3 – Multiple Choice [50 Points]
1. B
2. D
3. A
4. B
5. D
6. D
7. E
8. B
9. A
10. A
Problem 7 – Miscellaneous [20 Points]
1. You are given the following information:
A = true
B = false
Evaluate:
i) (A && B) || (A && B)
________________________________________________
ii) (A || B) && (A || B)
________________________________________________
iii) (~(A || B)) || (A && B)
________________________________________________
2. Ackermann's Function is "a function to end all functions."
The work done by the function ack grows much faster than polynomials or exponentials.
Given the following recursive method:
function ret = ack(x,y)
if (x == 0)
ans = y + 1;
elseif (y == 0)
ans = ack(x - 1, 1);
else
ans = ack(x - 1, ack(x, y - 1));
end
What is the result of ack(1, 4)?
3. Given a vector of coefficients a, mark the code fragments below that will evaluate the
following function for a single value of x (not a vector):
y = a(1) + a(2) * x + a(3) * x2 + ... a(n) * xn-1.
A. polyval(x, a)
B. n = 1:length(a)
a(n) * x.^(n-1)'
C. polyval(a, x)
D. polyval(a(end:-1:1), x)
4. Which of the following correctly solves for X in the equation AX = B, knowing that A is a
4x4 matrix of known values, B is a 4x1 column vector of known values, and X is a 4x1
column vector of unknown values?
A.
B.
C.
D.
X
X
X
X
=
=
=
=
inv(B)*A
B\A
inv(A)*B
A/B
Problem 7 – Miscellaneous [20 Points]
1. (i) False
(ii) True
(iii) False
2. 6
3. C
4. C
Criteria
- 5 points each (All or nothing)
Problem 6 – Miscellaneous [20 Points]
1. Read the following code and answer the question that follows:
ch = 'Ann';
ch = ch + 'a';
ch = [ch 'na'];
len = length(ch);
What is the value of len at the end?
A. 3
B. 4
C. 5
D. 6
2. Read the following code and answer the question that follows:
A
a
b
c
d
=
=
=
=
=
{'cat', [7 6 9], {'dog'}}
A{3}
A{1}(1)
A{2}
A(2)
After the code above is executed, what is the data type of the following variables:
A = ____________________________________________________________________
a = ____________________________________________________________________
b = ____________________________________________________________________
c = ____________________________________________________________________
d = ____________________________________________________________________
3. Read the following code and answer the question that follows:
x = [9 3 0 6 3]
y = mod((sqrt(length(((x+5).*[1 2 3 4 5]))*5)),3)
What is the value of y?
A. 0
B. 3
C. 2
D. 5
2. You are given the following equations:
3x + 2y – z = 5
6x + z = 7
5x - 2y + z = 12
Write a script in MATLAB to solve the values of x, y, and z.
Problem 6 – Miscellaneous [20 Points]
1. C
2.
A = { 'cat' [7 6 9]
a=
'dog'
b= c
c=
[7
6
d=
{[7 6 9]}
9]
3. C
4.
A = [3 2 -1; 6 0 1; 5 -2 1]
{‘dog’}
B = [5; 7; 12]
C = inv(A)*B
x = C(1);
y = C(2);
z = C(3);
%If they don’t split C into x y and z separately, ignore it
Criteria
- 5 points each (All or nothing)
Problem 7 – Miscellaneous [20 Points]
1. List the three conditions required for a function be recursive:
1.
2.
3.
2. Which one(s) evaluate to a logical(boolean) 'true' ?
I. ( 5 > 4 ) & ( ( 8 + 4 ) < 11 )
II. ~( ( ( 6 + 4 * 3 ) > 20 ) )
III. ~( ( 4 ~= 4 ) | (~( 6 < ( 4 * 2 / 8 + 4 ) ) ) )
A. I only
B. II only
C. III only
D. I and III
E. II and III
3. If the following command is typed in the Matlab command window, what is returned?
>> 4%2
A.
B.
C.
D.
error
2
4
0
4. You have x-data and y-data points which best fit a 4th order polynomial. You now want to
evaluate the same polynomial at different x-data points. Which function(s) will you need to
obtain the above?
Problem 7 – Miscellaneous [20 Points]
1. Call to clone, terminating condition, move towards termination
2. B
3. C
4. polyfit(), polyval()
Criteria:
- 5 points each for complete correct answer for each part
10. Multiple Choice (20 points)
A) For the answers below, choose the best answer from the following possibilities:
F: filter; I: insert; L: fold; M: map; R: sort; S: search; T: traverse
__ raising all employees’ salaries by 2%
__ looking for a file in a file drawer
__ finding all the vehicles traveling faster than the speed limit
__ adding a note to a music score
__ finding the heaviest package on a truck
__ reading all the data from an Excel spread sheet into Matlab
B) Consider the following code:
(x & (~y | (x & ~y)))
What values for x and y will make the above expression evaluate TRUE?
a) x = 0;
y = 0
b) x = 0;
y = 1
c) x = 1;
y = 0
d) x = 1;
y = 1
C) True or false:
a) True False
b) True False
c) True False
d) True False
Functions must return a result
To create a 3D plot, the function mesh must be used
A parent class cannot be a child class
A Queue is a First-In-First-Out (FIFO) data structure
D) Your job is to create a sine wave in MATLAB. Given the four lines of code below that
create your x-values, what command will give the most accurate representation of the curve?
x1
x2
x3
x4
=
=
=
=
linspace(0, 2*pi);
linspace(0, 2*pi, 10);
[0:0.1:2*pi];
[0:1:2*pi];
a) plot(x1, sin(x1))
b) plot(x2, sin(x2))
c) plot(x3, sin(x3))
d) plot(x4, sin(x4))
Problem 10
A) M, S, F, I, L, T
- 6 pts, 1 for each
B) c
C) a) false, b) false, c) false, d) true
D) a
- 5 pts
- 4 pts, 1 for each
- 5 pts
10. Multiple Choice (20 points)
A)
For the answers below, choose the best answer from the following possibilities:
F: filter; I: insert; L: fold; M: map; R: sort; S: search; T: traverse
__ the annual process of changing all employee records to update their age and time of
employment
__ moving all the cars off a ferry
__ looking up a telephone number
__ the IRS setting aside all the tax returns containing checks
__ returning a book to the library
__ finding the median income of the population of a country
B) Consider the following code:
(~x & (~y | (x & y)))
What values for x and y will make the above expression evaluate TRUE?
a) x = 0;
y = 0
b) x = 0;
y = 1
c) x = 1;
y = 0
d) x = 1;
y = 1
C) Which of the following is NOT a characteristic of a recursive function?
a) Calls itself recursively
b) Has a terminating condition
c) Calls a helper function
d) Moves solution closer to the termination condition
D) Your job is to create a sine wave in MATLAB. Given the four lines of code below that
create your x-values, what command will give the most accurate representation of the curve?
x1
x2
x3
x4
=
=
=
=
linspace(0, 2*pi);
linspace(0, 2*pi, 50);
[0:0.2:2*pi];
[0:1:2*pi];
a) plot(x1, sin(x1))
b) plot(x2, sin(x2))
c) plot(x3, sin(x3))
d) plot(x4, sin(x4))
Problem 10
A) M, T, S, F, I, L
B) a
C) c
D) a
- 6 pts, 1 for each
- 5 pts
- 4 pts
- 5 pts
10. Multiple Choice (20 points)
A)
For the answers below, choose the best answer from the following possibilities:
F: filter; I: insert; L: fold; M: map; R: sort; S: search; T: traverse
__ finding the oldest player on the team
__ selecting the team MVP
__ finding all the players who have scored more than 3 goals
__ adding a player to the team roster
__ updating all the players’ statistics after a game
__ saving all your player info to a disk file
B)
Consider the following code:
(x & (y | (x & y)))
What values for x and y will make the above expression evaluate TRUE?
a) x = 0;
y = 0
b) x = 0;
y = 1
c) x = 1;
y = 0
d) x = 1;
y = 1
C) True or false:
a) True False
b) True False
c) True False
d) True False
Functions must have an input variable
To create a 3D plot, the function mesh must be used
Object Oriented Programming can be done in MATLAB
A Stack is a First-In-First-Out (FIFO) data structure
D) Your job is to create a sine wave in MATLAB. Given the four lines of code below that
create your x-values, what command will give the most accurate representation of the curve?
x1
x2
x3
x4
=
=
=
=
linspace(0, 2*pi);
linspace(0, 2*pi, 500);
[0:0.1:2*pi];
[0:1:2*pi];
a) plot(x1, sin(x1))
b) plot(x2, sin(x2))
c) plot(x3, sin(x3))
d) plot(x4, sin(x4))
Problem 10
A) L, L, F, I, M, T
- 6 pts, 1 for each
B) d
C) a) false, b) false, c) true, d) false
D) b
- 5 pts
- 4 pts, 1 for each
- 5 pts
10. Multiple Choice (20 points)
A) For the answers below, choose the best answer from the following possibilities:
F: filter; I: insert; L: fold; M: map; R: sort; S: search; T: traverse
__ finding the largest number in a matrix
__ looking for a Ford Thunderbird on autotrader.com
__ finding all the employees under 30 years old
__ entering a new friend in your address book
__ adding 5% to the price of all items under $25 in a store (leaving the other prices
unchanged)
__ copying all the Students in a Class to a data file
B) Consider the following code:
( ~x & (y | (x & y)))
What values for x and y will make the above expression evaluate TRUE?
a) x = 0;
y = 0
b) x = 0;
y = 1
c) x = 1;
y = 0
d) x = 1;
y = 1
C) Which of the following is NOT a characteristic of a recursive function?
a) Calls itself recursively
b) Has a terminating condition
c) Calls a helper function
d) Moves solution closer to the termination condition
D) Your job is to create a sine wave in MATLAB. Given the four lines of code below that
create your x-values, what command will give the most accurate representation of the curve?
x1
x2
x3
x4
=
=
=
=
linspace(0, 2*pi);
linspace(0, 2*pi, 50);
[0:0.001:2*pi];
[0:1:2*pi];
a) plot(x1, sin(x1))
b) plot(x2, sin(x2))
c) plot(x3, sin(x3))
d) plot(x4, sin(x4))
Problem 10
A) L, S, F, I, M, T
B) b
C) c
D) c
- 6 pts, 1 for each
- 5 pts
- 4 pts
- 5 pts
Problem 6 – Miscellaneous [30 Points]
I. You are given the following linear equations:
x - 3y = 1
3x - y = 2
Now let’s say you wanted to solve the equations simultaneously using MATLAB and store the
solution vector in the variable named solution using the following code:
solution = A1\A2;
How must the variables A1 and A2 be defined in order to get the correct solution?
A.
B.
C.
D.
E.
A1
A1
A1
A1
A1
=
=
=
=
=
[1 -3; 3 -1];
[2;1];
[3 -1; 1 -3];
[1;2];
[1 -3; 3 -1];
A2
A2
A2
A2
A2
=
=
=
=
=
[2;1];
[1 -3; 3 1];
[2;1];
[1 -3; 3 -1];
[1 2];
II. Given the following code:
function output = rec(x, y)
if(x == 0 || y == 0)
output = x + y;
else
output = rec(x-1,y) + rec(x, y-2)
end
answer = rec(2,2)
What is the value of answer?
A. 2
B. 4
C. 5
D. 8
E. None of the above
III. You are given the following code:
[snd, Fst] = wavread('Sound.wav');
Which of the following lines of code will play an amplified version of ‘Sound.wav’?
A.
B.
C.
D.
sound(snd, Fst*3);
sound(snd(round(1:half^2:end)), Fst)
sound(snd*3, Fst);
z= fft(Snd)
z(1:floor(length(z)/2)) = 255;
sound(ifft(z), Fst);
IV. Given the following piece of code:
a.price = 10;
b = a.price;
What is the data type of the variable b?
A.
B.
C.
D.
E.
struct
logical
cell
char
double
V. The following code is executed in MATLAB:
ABCD = 0;
testV = [ 3 -5 6 -8 9 11]
for i=1:length(testV)
if testV(i) > 0
ABCD = ABCD + mod(testV(i),2);
else
ABCD = ABCD + 5;
end
end
What is the final value of the variable ABCD?
A. 4
B. 24.5
C. 13
D. 14
E. None of the above
VI. Given: A = [3 7 5 2 6 1]
Circle each of the following choices that would produce an error when executed (circle all that
apply).
A. A(A)
B. A(10) = []
C. A([true false true])
D. A(0) = 3
E. A(linspace(2,6,5)) = 0
Problem 6 – Miscellaneous [30 Points]
I. C.
II. C.
III. C.
IV. E.
V. C
VI. A, B, D
Criteria
- 5 points each
- All or nothing except for VI: -2 for each missing answer or extra answer circled
Problem 3 – Vector Manipulation [20 Points]
I.
Read the code below and answer the questions that follow
a = [3:7];
b = a>5;
a(3:4) = 0;
c = find(a > 2);
d = sum(ones(size(a)));
e = mod(c,(max(a)-d));
What is the value of the following variables when the code above is executed?
b = _________________________________________________________
c = _________________________________________________________
e = _________________________________________________________
II.
Which of the following are valid function headers? (Circle all that apply)
A. function
B. function
C. function
D. function
E. function
ret = myFunction(X)
myFunction (X)
ret = myFunction()
= myFunction (X)
myFunction (234)
Problem 3 – Vector Manipulation [20 Points]
I.
b = [0
c = [1
e = [1
0
2
0
0 1
5]
1]
1]
Criteria:
- 5 points each (All or nothing)
- If one of them is wrong, but the remaining are correct with erroneous vector carried forward,
give them credit for the rest
II. A, B, C
Criteria:
- 5 points (All or nothing)
Part 2 – Multiple Choice [20 points]
For each of the following problems, write the letter of the best answer choice in the box adjacent
to the problem statement.
1. Given:
s= struct('Name',{'Bobby', 'Susan', 'Elaine'}, 'Age', [19 21 17],…
'Year',{ 'Jr', 'Sr', 'Fr'})
fld = 'Age';
avg = mean(s(2).(fld));
Which one of the following is the value of avg?
A. 17
B. 19
C. 21
D. []
E. Error
2. Given:
[num txt raw] = xlsread('Excel.xls')
Which one of the following is a true statement?
A. The dimensions of num are always equal to the dimensions of raw
B. The dimensions of txt are always equal to the dimensions of num
C. The dimensions of num are always equal to the dimensions of txt
D. txt has a data type of char
E. None of the above
3. Which one of the following is NOT a valid function header?
A. function A
B. function [out1, out2] = A(in)
C. function A(in)
D. function (out1, out2) = A(in)
E. function out = A
4. Given the following line of code:
[data, fs] = wavread('sound.wav');
Which one of the following represents the time between consecutive samples?
A. inv(data)
B. 1/fs
C. fs
D. length(data)/fs
E. data(1:end/2) / length(data)
For each of the following terms below, select the short definition on the right that best describes
the term. Write the corresponding letter in the box to the left of the question. Only answers in the
boxes will be graded.
A. a method for solving simultaneous
linear equations
5. use of the AND (&&) logical operator
6. the global operator
B. method of drawing a sphere with a
map image
C. allows recursive computation to
wrap itself on the stack
D. proper way to store towels in a
linen closet
7. matrix multiplication
E. a way of storing homogenous data
accessed by field names
F. can be used to rotate individual
objects for plotting
8. folding
G. extracting a single result from a
collection
9. wrapper function
H. a way of storing homogeneous data
accessed by indexing
I. can be used to check for bad inputs
to a recursive function
10. cell arrays
J. a way of storing heterogeneous data
accessed by indexing
K. to check if all of the chained
logical expressions are true
L. method for avoiding passing large
data collections into a function
M. to check if any of the chained
logical expressions are true
Part 2 – Multiple Choice [20 points]
1. B. 19
2. E. None of the above
3. D. function (out1, out2) = A(in) - round not square on
output vars
4. B. 1/fs
5. K. to check if all of the chained logical expressions are
true
6. L. method for avoiding passing large data collections into a
function
7. F. can be used to rotate individual objects for plotting
8. G. extracting a single result from a collection
9. I. can be used to check for bad inputs to a recursive
function
10 J. a way of storing heterogeneous data accessed by indexing