Paper 2: Algorithm Tracing and Trace Table Completion

Trace tables are used to track how variables change as an algorithm executes. Completing trace tables is a common exam skill in OCR J277 Paper 2, typically worth 3-6 marks. This lesson teaches you how to trace through code systematically and avoid common errors.

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What Is a Trace Table?

A trace table is a table with a column for each variable and each output. Each row represents one step of the algorithm (usually one line of code or one iteration of a loop). By filling in the table, you can see exactly how the algorithm behaves.

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How to Complete a Trace Table

1. Create columns for every variable mentioned in the code, plus an "Output" column
2. Start with the initial values of variables
3. Execute each line of code in order, updating the relevant column
4. For loops, create a new row for each iteration
5. Only update a variable when the code explicitly changes it
6. Record any output (e.g., print statements) in the Output column

OCR Exam Tip: Cross out each line of code as you trace through it (on the question paper) to keep track of where you are. For loops, use a tally to count iterations.

The trace-table construction flow — repeated for each line of code — is shown below:

flowchart TD
    A[Identify all variables] --> B[Add Output column]
    B --> C[Record initial values]
    C --> D[Read next line of code]
    D --> E{What kind of statement?}
    E -->|Assignment| F[Update changed variable only]
    E -->|Loop iteration| G[Add new row, update loop var]
    E -->|Print| H[Record value in Output column]
    E -->|If/else| I[Evaluate condition, follow branch]
    F --> J{More code lines?}
    G --> J
    H --> J
    I --> J
    J -->|Yes| D
    J -->|No| K[Final Output is the answer]

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Worked Example 1: Simple Loop

x = 1
total = 0
for i = 1 to 4
    total = total + x
    x = x * 2
next i
print(total)

Step	i	x	total	Output
Init	—	1	0
i=1	1	1	1
	1	2	1
i=2	2	2	3
	2	4	3
i=3	3	4	7
	3	8	7
i=4	4	8	15
	4	16	15
End				15

The output is 15.

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Worked Example 2: While Loop with Input

count = 0
total = 0
num = input("Enter a number (0 to stop): ")
while num != 0
    total = total + num
    count = count + 1
    num = input("Enter a number (0 to stop): ")
endwhile
print(total / count)

If the user enters: 10, 20, 30, 0

Step	num	count	total	Output
Init	—	0	0
Input	10	0	0
Loop 1	10	1	10
Input	20	1	10
Loop 2	20	2	30
Input	30	2	30
Loop 3	30	3	60
Input	0	3	60
End				20

The output is 20 (the average of 10, 20, and 30).

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Worked Example 3: Nested Selection

age = 17
hasTicked = true

if age >= 18 then
    if hasTicked == true then
        print("Entry allowed")
    else
        print("Must agree to terms")
    endif
else
    print("Too young")
endif

Trace:

1. age = 17, hasTicked = true
2. Is age >= 18? No (17 < 18), so go to else
3. Output: "Too young"

age	hasTicked	Output
17	true	Too young

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Worked Example 4: Array Processing

scores = [5, 8, 3, 9, 2]
highest = scores[0]
for i = 1 to 4
    if scores[i] > highest then
        highest = scores[i]
    endif
next i
print(highest)

Step	i	scores[i]	highest	Output
Init	—	—	5
i=1	1	8	8
i=2	2	3	8
i=3	3	9	9
i=4	4	2	9
End				9

The output is 9 (the highest value in the array).

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Common Trace Table Mistakes

Mistake	Correction
Updating variables that have not changed	Only write a new value when the code explicitly changes it
Getting loop boundaries wrong	Check whether the loop is inclusive (1 to 5 means 1, 2, 3, 4, 5)
Forgetting the initial values	Always fill in the starting values before the loop begins
Confusing = (assignment) with == (comparison)	x = 5 assigns the value 5 to x; x == 5 checks if x equals 5
Incorrect array indexing	Arrays start at index 0 in OCR pseudocode
Not recording outputs	Include a separate Output column and record every print statement

OCR Exam Tip: If the exam provides a partially completed trace table, fill in only the blank cells. Do not alter cells that are already filled in — they are correct and serve as a guide.

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Strategy for Trace Table Questions

1. Read the entire algorithm before starting the trace
2. Set up your table with all variables and an Output column
3. Go line by line, not trying to skip ahead
4. Use a pencil so you can correct errors
5. Check your final answer makes sense (e.g., is a total realistic?)
6. For loops, count the iterations to make sure you do not do too few or too many

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Summary