2.1.3e Trace Tables — OCR J277

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What is a Trace Table?

A trace table (also called a dry run) is a technique used to manually track the values of variables as an algorithm executes, line by line. It lets you verify that code produces the correct output without running it on a computer.

In OCR J277 exams, you will be asked to complete trace tables for given algorithms. Each column represents a variable or output; each row represents one iteration or key step.

Purpose of Trace Tables

Test an algorithm's correctness before coding it
Identify logic errors and bugs
Understand what a piece of code does
Communicate algorithm behaviour clearly

How to Complete a Trace Table — Step by Step

1. Read through the algorithm carefully before starting

2. Create a column for every variable referenced in the algorithm, plus an output column if needed

3. Initialise: write any starting values in the first row

4. Execute each line in order, updating only the variable that changes on that line

5. Leave other cells blank if their value did not change on that step

6. Continue until the algorithm ends or reaches the required condition

Exam tip: You do NOT need to fill in every cell every row — only the value that changes. Examiners award marks for each correct cell. Show every change, even temporary ones (e.g. a temp variable in a swap).

Worked Example 1 — Simple Loop with Counter

total = 0

FOR i = 1 TO 4

    total = total + i

NEXT i

OUTPUT total

i	total	OUTPUT
Initialise		0
i = 1	1	1
i = 2	2	3
i = 3	3	6
i = 4	4	10
Output			10

Worked Example 2 — Bubble Sort Trace (first pass)

List: [5, 3, 8, 1] — trace the first full pass

FOR j = 0 TO 2

  IF list[j] > list[j+1] THEN

    temp = list[j]

    list[j] = list[j+1]

    list[j+1] = temp

  END IF

NEXT j

j	list[0]	list[1]	list[2]	list[3]	temp	Swap?
Start	5	3	8	1
j=0: 5>3?	5	3			5	Yes
swap	3	5
j=1: 5>8?		5	8			No
j=2: 8>1?			8	1	8	Yes
swap			1	8
End pass 1	3	5	1	8

Worked Example 3 — Binary Search Trace

Sorted list: [2, 5, 9, 14, 21, 34, 42] — search for target = 21

low	high	mid	list[mid]	Action
0	6	3	14	14 < 21 → low = mid+1 = 4
4	6	5	34	34 > 21 → high = mid-1 = 4
4	4	4	21	Found! Return index 4

Exam tip: Always show the calculation for mid: mid = (low + high) DIV 2. E.g. (0+6) DIV 2 = 3. Showing your working can earn partial marks even if the final answer has a small error.

⚠️ Common Mistakes in Trace Tables

Copying the same value into a cell when it didn't change — leave blank if unchanged
Forgetting to update the loop counter (i, j) each iteration
Not showing the temp variable when tracing a swap
Using integer division (DIV) — make sure to floor, not round. E.g. (3+4) DIV 2 = 3, not 3.5
Stopping the trace too early — run all iterations unless told otherwise
Reversing the condition in binary search (confusing > and <)

Detecting Errors with Trace Tables

Trace tables are used to find logic errors — where the program runs but gives the wrong answer. Example: a loop starting at index 1 instead of 0 would skip the first element. Tracing reveals this because you can see when the expected value doesn't appear.

They can also detect infinite loops — if tracing shows a variable never reaches the loop exit condition, the loop will never terminate.

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Worksheet — 2.1.3e Trace Tables

8 questions · 20 marks

Q1What is a trace table and why is it used?[2]

✅ Mark scheme

A trace table tracks the value of each variable as an algorithm executes line by line [1]. It is used to test/verify a program's logic, identify errors, and understand what code does without running it on a computer [1].

Q2Trace the following algorithm and complete the table: x=10; y=3; z=x MOD y; OUTPUT z[3]

✅ Mark scheme

x=10 [1]; y=3 [1]; z = 10 MOD 3 = 1; OUTPUT = 1 [1]. (MOD gives the remainder: 10 ÷ 3 = 3 remainder 1)

Q3Trace this loop: count=0; FOR i=1 TO 5; count=count+i; NEXT i; OUTPUT count. Give the value of count after each iteration.[3]

✅ Mark scheme

i=1: count=1 [½]; i=2: count=3 [½]; i=3: count=6 [½]; i=4: count=10 [½]; i=5: count=15 [½]; OUTPUT=15 [½]. Accept all correct values [3 total].

Q4A swap routine uses: temp=a; a=b; b=temp. If a=7, b=2, trace these three lines showing the value of a, b and temp after each.[3]

✅ Mark scheme

After temp=a: a=7, b=2, temp=7 [1]. After a=b: a=2, b=2, temp=7 [1]. After b=temp: a=2, b=7, temp=7 [1].

Q5Trace one pass of bubble sort on [4, 1, 7, 2]. Show the list after each comparison and whether a swap occurred.[3]

✅ Mark scheme

j=0: 4>1? Yes → swap → [1,4,7,2] [1]. j=1: 4>7? No → [1,4,7,2] [1]. j=2: 7>2? Yes → swap → [1,4,2,7] [1]. Final state: [1,4,2,7].

Q6Perform a binary search trace on [3,7,12,18,25,30,45] for target=12. Show low, high, mid, and list[mid] for each step.[3]

✅ Mark scheme

Step 1: low=0,high=6,mid=3,list[3]=18 — 18>12 so high=2 [1]. Step 2: low=0,high=2,mid=1,list[1]=7 — 7<12 so low=2 [1]. Step 3: low=2,high=2,mid=2,list[2]=12 — Found at index 2 [1].

Q7What type of error can a trace table help detect? Give an example.[2]

✅ Mark scheme

Logic errors [1] — e.g. a loop starting at index 1 instead of 0 (skipping first element), or using > instead of >= in a condition, giving a wrong result without a crash [1].

Q8A student traces a loop and notices the variable controlling the loop never reaches the exit condition. What problem does this indicate?[1]

✅ Mark scheme

An infinite loop [1] — the loop will never terminate because the exit condition can never be met.

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Term	Definition

What is a Trace Table?

Purpose of Trace Tables

How to Complete a Trace Table — Step by Step

Worked Example 1 — Simple Loop with Counter

Worked Example 2 — Bubble Sort Trace (first pass)

Worked Example 3 — Binary Search Trace

Detecting Errors with Trace Tables

Worksheet — 2.1.3e Trace Tables

Mini Test — 2.1.3e Trace Tables