1.2d Merge Sort — Edexcel 1CP2

What is Merge Sort?

Merge sort is an efficient sorting algorithm that uses a divide and conquer strategy. It works by recursively splitting the list into halves until each sub-list has one element, then merging the sub-lists back together in sorted order.

How Merge Sort Works

Merge sort has two phases:

Split phase: Divide the list in half repeatedly until each sub-list contains only one element (a single element is always sorted).
Merge phase: Merge pairs of sorted sub-lists by comparing the front elements and picking the smaller one each time.

Worked Example

Sort [38, 27, 43, 3] using merge sort:

Split:

[38, 27, 43, 3] → [38, 27] and [43, 3] → [38] [27] [43] [3]

Merge:

Merge [38] and [27]: compare 38 and 27 → pick 27 → pick 38 → [27, 38]

Merge [43] and [3]: compare 43 and 3 → pick 3 → pick 43 → [3, 43]

Merge [27, 38] and [3, 43]: compare 27 and 3 → pick 3; compare 27 and 43 → pick 27; pick 38; pick 43 → [3, 27, 38, 43]

Comparing Merge Sort and Bubble Sort

Feature	Bubble Sort	Merge Sort
Worst case efficiency	O(n²) — quadratic	O(n log n) — much faster
Best case efficiency	O(n) if optimised	O(n log n) always
Extra memory needed?	No (in-place)	Yes — needs space for sub-lists
Practical use	Small lists only	Large datasets
Complexity to implement	Simple	More complex (recursive)

Exam tip: You will often be asked to trace through a merge sort split or merge step. Always show the complete split tree (down to single elements) before the merge phase. Show each merge step separately.

⚠️ Common Mistakes

Stopping the split phase too early — you must reach single-element sub-lists
In the merge step, not comparing front elements — always take the smaller of the two front elements
Saying merge sort uses less memory than bubble sort — it uses MORE memory (extra lists for sub-lists)
Confusing the split and merge phases in an exam trace

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Key points

Divide and conquer strategy explained
Complete traced example: split phase and merge phase
Merge sort vs bubble sort efficiency comparison
Why merge sort uses extra memory
Exam technique for tracing merge sort

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Worksheet — 1.2d Merge Sort

8 Edexcel-style questions · instantly marked

Q1State the two phases of merge sort.[2]

✅ Mark scheme

Split/divide phase [1] and merge phase [1].

Q2When does the split phase of merge sort stop?[1]

✅ Mark scheme

When every sub-list contains only one element (a single element is always sorted). [1]

Q3Show the complete split phase of merge sort on the list [8, 3, 5, 1]. Draw the splitting tree.[2]

✅ Mark scheme

[8,3,5,1] → [8,3] and [5,1] [1] → [8] [3] and [5] [1] [1]

Q4Show how the merge step combines [3, 8] and [1, 5] into one sorted list. Show each comparison.[3]

✅ Mark scheme

Compare 3 and 1 → pick 1 [1]; compare 3 and 5 → pick 3 [1]; compare 8 and 5 → pick 5; pick 8 → result: [1,3,5,8] [1]

Q5Give one advantage of merge sort over bubble sort.[1]

✅ Mark scheme

Merge sort is more efficient on large datasets (O(n log n) vs O(n²)). [1]

Q6Give one disadvantage of merge sort compared to bubble sort.[1]

✅ Mark scheme

Any 1: Merge sort requires more memory (extra space for sub-lists) [1] / It is more complex to implement [1].

Q7Describe the merge step: given two sorted sub-lists, how does merge sort combine them into one sorted list?[3]

✅ Mark scheme

Compare the front elements of both sub-lists [1]; take the smaller one and place it in the output list [1]; repeat until one sub-list is empty, then append the remaining elements of the other [1].

Q8Trace the complete merge sort on [5, 2, 8, 1, 9, 3]. Show all split and merge steps.[4]

✅ Mark scheme

Split: [5,2,8] and [1,9,3] → [5,2] [8] [1,9] [3] → [5] [2] [8] [1] [9] [3] [1]. Merge pairs: [2,5] [8] [1,9] [3] [1]. Merge: [2,5,8] and [1,3,9] [1]. Final merge: [1,2,3,5,8,9] [1]. Method clearly shown [1]. Award marks for correct working at each stage.

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What is Merge Sort?

How Merge Sort Works

Worked Example

Comparing Merge Sort and Bubble Sort

Key points

Worksheet — 1.2d Merge Sort

Mini Test — 1.2d Merge Sort

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