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Date	May 2021	Marks available	8	Reference code	21M.1.HL.TZ0.14
Level	HL	Paper	1	Time zone	no time zone
Command term	Construct	Question number	14	Adapted from	N/A

Question

The following flowchart is intended to represent an algorithm in which numbers that are input cannot be negative.

The flowchart contains a logic error that will affect the algorithm’s functionality.

The algorithm is to be altered to restrict the values that are input to whole numbers between 0 and 1000.

Identify the logic error in the algorithm.

[1]

a.i.

Outline how the error in the algorithm identified in part (i) can be corrected.

[2]

a.ii.

State the name of the method that could be used to restrict the values that are input.

[1]

A further change has been requested for the algorithm to enable it to calculate the average of all the numbers entered. The average will be output when the algorithm terminates.

Based on the flowchart, construct this algorithm using pseudocode. You must include the required changes:

correction of logic error
only allow input of integers between 0 and 1000
calculation of average of all numbers entered
output of final average.

[8]

Markscheme

Award [1 max]

The algorithm will always output zero as the value of LOWEST, for any set of the input values (because all input values are greater than or equal to 0);
The LOWEST is initialized to 0 and negative inputs are not allowed, zero will be the permanently lowest number;

a.i.

Award [2 max]

Example 1:

Replace LOWEST = 0;
With LOWEST=99999999/ any very high number;

Example 2:

Before the loop/ Accept “at the beginning”;
The first number NUMBER should be inputted and LOWEST set to NUMBER / LOWEST=input(NUMBER);
Loop only 999 times (because 1 number already inputted)/ condition in the loop should be changed to COUNTER>998;

Example 3:

If statement should be used within the loop;
after the statement ‘input NUMBER’;
For example, if COUNTER==0 then LOWEST = NUMBER/ set LOWEST to the first inputted number;

a.ii.

Award [1 max]
Validation (check);
Data type check;
Range check;

Award [8 max]

Correct initialization of HIGHEST, LOWEST and TOTAL;
Correct use of loop for 1000 inputs (doesn’t have to be while loop);
Checking if NUMBER is between 0 to 1000(accept inclusive or exclusive range);
Checking if NUMBER is a whole number;
Running total of numbers (for average calculation);
Correct comparison and changing the value of HIGHEST if needed;
Correct comparison and changing the value of LOWEST if needed;
Appropriate calculation of AVERAGE;
Output of AVERAGE, HIGHEST and LOWEST (outside loop);

Example answer 1

HIGHEST = −1    //any value lesser than or equal to 0
LOWEST = 10000 //any value greater than or equal to 1000
COUNTER = 0
TOTAL = 0
loop while COUNTER < 1000 // allow COUNTER <= 999
    input NUMBER
    if NUMBER<0 or NUMBER>1000 or NUMBER div 1 ≠ NUMBER/1
                  //accept NUMBER<1 or NUMBER>999 or NUMBER mod 1 ≠ 0
               output " Your number is invalid, please try again"
    else
          if NUMBER > HIGHEST then
            HIGHEST = NUMBER
          end if
          if NUMBER < LOWEST then
            LOWEST = NUMBER
          end if
          TOTAL = TOTAL + NUMBER
          COUNTER = COUNTER + 1
     endif
end loop
AVERAGE = TOTAL / COUNTER // allow TOTAL / 1000
output HIGHEST
output LOWEST
output AVERAGE

Example answer 2: (the lowest and the highest are set to the value of the first inputted number)

input NUMBER
loop while NUMBER<0 or NUMBER>1000 or NUMBER div 1 ≠ NUMBER/1
    output " Your number is invalid, please try again"
    input NUMBER
end loop
HIGHEST = NUMBER
LOWEST = NUMBER
TOTAL = 0
loop COUNTER FROM 0 to 998
           input NUMBER
           loop while NUMBER<0 or NUMBER>1000 or NUMBER div 1 ≠ NUMBER/1
               output " Your number is invalid, please try again"
               input NUMBER
           end loop
           if NUMBER > HIGHEST then
             HIGHEST = NUMBER
           end if
           if NUMBER < LOWEST then
             LOWEST = NUMBER
           end if
           TOTAL = TOTAL + NUMBER

end loop
AVERAGE = TOTAL / 1000
output HIGHEST, LOWEST, AVERAGE

Example answer 3

HIGHEST = -1     //any value lesser than or equal to 0
LOWEST = 10000  //any value greater than or equal to 1000
C = 0
TOTAL = 0
loop while C<1000
    input NUMBER
    if NUMBER>=0 and NUMBER<=1000
        if NUMBER mod 1 == 0
             if NUMBER > HIGHEST then
                  HIGHEST = NUMBER
             else
                if NUMBER < LOWEST then
                      LOWEST = NUMBER
                endif
            end if
            TOTAL = TOTAL + NUMBER
            C=C+1
        endif
    else
       output(“invalid input, enter another number”)
   endif
end loop
output HIGHEST, LOWEST, TOTAL/1000

Examiners report

The term logic error was not always familiar to candidates. Many candidates correctly identified the logic error in Part(a)(i).

a.i.

A large number gave less precise or incorrect answers to Part(a)(ii).

a.ii.

A large number of candidates did not score any marks for question in Part (b) because they were not able to state the name of the method that could be used to restrict the values that are input.

In Part (c) candidates were required to produce an algorithm based on the flowchart given in the question. Most candidates achieved some marks for this algorithm, but full marks were rare.

Syllabus sections

Topic 4: Computational thinking, problem-solving and programming » 4.2 Connecting computational thinking and program design

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18M.1.SL.TZ0.12a:

The collection DATA contains the following data:

2, 4, 1, −2, −4, 1, 0

Consider the following pseudocode:

COUNTER = 0
SUM = 0
DATA.resetNext()
loop for X from 0 to 6
  if DATA.getNext() > 0
    ARRAY[X] = DATA.getNext()
    COUNTER = COUNTER + 1
    SUM = SUM + ARRAY[X]
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end loop
output SUM/COUNTER

Trace the pseudocode using the table below:

18N.1.SL.TZ0.7:

Construct a trace table for the following algorithm

A = 3
B = 7
loop while B >= A
  A = A + 1
  output(B − A)
  B = B − 1
end loop

19N.1.SL.TZ0.7:

Construct a trace table for the following algorithm.

K = 1
N = 1
M = 2
loop while K < 5
   output(N,M)
   K = K + 1
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   M = M * 2
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21M.1.SL.TZ0.8:

List the output from the given algorithm for the following input.

2, 6, 8, 9, 12, 15, 18, 20

loop for Count from 0 to 7
    input NUMBER
    if NUMBER div 2 = NUMBER / 2 then
        if NUMBER div 3 = NUMBER / 3 then
        output NUMBER
        end if
    end if
end loop

19N.1.SL.TZ0.10a:

Consider the following algorithm.

N = 372
X = N DIV 100
Y = X + 10 * (N MOD 100 DIV 10)
Z = Y + (N MOD 10) * 100

Determine the values of variables X, Y, and Z after execution of this algorithm. Show your working.

19M.2.SL.TZ0.4b:
Using the rules and initial values above, construct the pseudocode that would enable the area of the sea ice and the sea level rise to be calculated if there was an increase of 0.04 °C in the ocean surface temperature.

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Topic 4: Computational thinking, problem-solving and programming

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