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```Assessment test
Unit 5 Algorithms
1.
(a) What is an algorithm?

A set of instructions for how to solve a problem or perform a task
(b) The following program simulates throwing two dice. What is the output from the
following program if:
(i)
Die1 = 3, Die2 = 4 7
(ii)
Die1 = 5, Die2 =5 20

Start
Die1 = Random(1,6)
Die2 = Random(1,6)
Score =
Die1 + Die 2
No
Die1 = Die2?
Yes
Score = Score*2
Output score
End
1
Assessment test
Unit 5 Algorithms
(c) Rewrite the flowchart as a pseudocode algorithm, making the following alterations:
If the user throws a “double”, they get another turn, and the score accumulates into a
total score. Their turn ends as soon as Die1 and Die2 have different values after a
“throw”. Print out the total score at the end of a turn.

TotalScore = 0
Repeat
Die1 = Random (1,6)
Die2 = Random (1,6)
Score = Die1 + Die2
If Die1 == Die2 then
Score = Score*2
End If
TotalScore = TotalScore+Score
Until Die1<>Die2
Output Score
(d) What is output if the user “throws” 3 times, getting 4 and 4, 3 and 3, 6 and 1 on the
three throws? 16 + 12 + 7 = 35

[9 marks]
2.
The following list of numbers is to be searched:
103, 118, 122, 134, 138, 149, 156, 159, 163, 171, 180, 193, 199
(a) List the numbers that will be examined if a linear search is carried out to find the
number 138.

103, 118, 122, 134, 138
(b) List the numbers that will be examined if a binary search is carried out to find the
number 138.

156, 122,138
(c) Using a binary search, how many items will need to be examined to find the
number 199?

4
(d) Give one advantage of the linear search method and one advantage of the binary
search method.

Linear search can be carried out on an unsorted list
Binary search is much faster for a large number of items
[7 marks]
2
Assessment test
Unit 5 Algorithms
3.
A sort is carried out on the following list of numbers.
15
6
43
21
8
17
11
3
(a) How many passes through the list will be required to sort the numbers into ascending
sequence using the bubble sort algorithm? 7

(b) Show how the numbers change after each comparison is made during the first pass,
and the position of the numbers after the first pass is complete. The first row is
completed for you.

6
15
43
21
8
17
11
3
6
15
43
21
8
17
11
3
6
15
21
43
8
17
11
3
6
15
21
8
43
17
11
3
6
15
21
8
17
43
11
3
6
15
21
8
17
11
43
3
6
15
21
8
17
11
3
43
(c) Using an insertion sort, what sequence are the numbers in after 1, 2 and 3 items have
been moved?

15
6
43
21
8
17
11
3
6
15
43
21
8
17
11
3
6
15
43
21
8
17
11
3
6
15
21
43
8
17
11
3
[10 marks]
3
Assessment test
Unit 5 Algorithms
4.
Explain the principle of the merge sort, using the numbers below to illustrate the procedure.
Show each stage of the process.
46
27
[8 marks]
33
21
18
28
43
13
The merge sort has two phases.
In the first phase the list is divided into sublists until there are 8 lists containing 1 item each
Sublists:
46, 27, 33, 21
18, 28, 43, 13
Then:
46, 27
18, 28
Then:
33, 21
46 27 33 21
18
(1 mark)
43, 13 (1 mark)
28 43 13
(1 mark)
In the second stage the sublists are merged in pairs, into ascending sequence: (1 mark)
27 46
21
27 33
21 33
46
18 28
13 43
13 18 28
(1 mark)
43
(1 mark)
43
(1 mark)
The final stage is to merge the two sublists
giving
5.
21
27 33
46
13 18 28
13
18 21
27 28
33 43 46
(1 mark)
Write a pseudocode algorithm which does the following:
Asks the user to input an integer between 0 and 23, representing the hours in a 24hour clock, and accepts the user’s input, which you can assume will be valid.
Outputs the equivalent time in 12 hour clock format. For example:
If the user inputs 0, the output will be 12am
If the user inputs 2, the output will be 2am
If the user inputs 12, the output will be 12pm
If the user inputs 23, the output will be 11pm
[7 marks]
hour = input (“Input hour between 0 and 23:”)
if hour = 0 then
print (12, “am”)
else
if hour < 12 then
print (hour, “am”)
else
if hour = 12
print (12, “pm”)
else
hour = hour – 12
print (hour, “pm”)
endif
endif
endif
4
Assessment test
Unit 5 Algorithms
Alternatively, use a switch/case statement:
hour = input (“Input hour between 0 and 23:”)
switch hour:
case 0:
print (12, “am”)
case <12:
print (hour, “am”)
case 12:
print (12, “pm”)
default:
print (hour, “pm”)
endswitch
6.
Below is an incomplete algorithm which is intended to check the username and password
entered by a user.
2 count = 1
4 …………………………………………………………………………………………
5
6
7
…………………………………………………………………………………………
else
8
9
……………………………………………………………………………………
10
count = count + 1
11
endif
12 endwhile
13 ……………………………………………………………………………………
14
print (“Welcome back”)
15 else
16
Lines 4, 5, 9 and 13 are missing from the algorithm above. Using four of the lines
of code below, complete this algorithm.
[4 marks]
if password == “AXcd35” Line 5
while count < 3 AND passwordOK == False
Line 4
while count < 3 OR passwordOK == False
Line 13
5
Assessment test
Unit 5 Algorithms
7.
Complete the trace table below to determine the output from the following algorithm:
total = 0
n = 1
while n < 6
if n mod 2 == 0
total = total + n
endif
n = n + 1
endwhile
print(total)
[5 marks]
total
n
n mod 2
n<6
0
1
1
Yes
0
2
0
Yes
2
3
1
Yes
2
4
0
Yes
6
5
1
Yes
6
6
No
OUTPUT
6
[Total 50 Marks]
6
```