Algorithms Exam Practice

This lesson provides comprehensive exam practice for the Algorithms topic, covering the key content from OCR J277 Section 2.2 that appears on Paper 2: Computational Thinking, Algorithms and Programming. This lesson brings together searching algorithms, sorting algorithms, trace tables, and algorithm design.

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Paper 2 Overview for Algorithms

The OCR J277 Paper 2 exam is worth 80 marks and lasts 1 hour 30 minutes. The algorithms section typically accounts for approximately 15–25 marks. Questions range from 1-mark recall questions to 6-mark extended response questions.

Common question types include:

Question Type	Typical Marks	What You Need to Do
Define/State	1–2 marks	Give a precise definition (e.g. "What is an algorithm?")
Describe	2–4 marks	Explain how an algorithm works step by step
Compare	3–4 marks	Identify similarities and differences between algorithms
Trace table	3–5 marks	Complete a trace table for given pseudocode
Write/Complete pseudocode	3–6 marks	Write or complete an algorithm in pseudocode/Python
Evaluate/Recommend	4–6 marks	Justify which algorithm is best for a given scenario

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Practice Question 1: Definitions (2 marks)

Question: Define the term "algorithm" and give one reason why algorithms are used in program development.

Model Answer: An algorithm is a step-by-step set of instructions designed to solve a specific problem or complete a task (1 mark). Algorithms are used in program development to plan the solution before writing code, ensuring the logic is correct and allowing programmers to identify potential issues early (1 mark).

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Practice Question 2: Linear Search Trace (4 marks)

Question: The array data contains: [12, 5, 8, 3, 15, 7]. Trace the following algorithm when searching for the value 15.

target = 15
for i = 0 to data.length - 1
    if data[i] == target then
        print("Found at " + str(i))
    endif
next i

Model Answer:

i	data[i]	data[i] == 15?	Output
0	12	No
1	5	No
2	8	No
3	3	No
4	15	Yes	"Found at 4"
5	7	No

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Practice Question 3: Binary Search Description (3 marks)

Question: Describe how binary search would find the value 42 in the sorted list [10, 20, 30, 42, 50, 60, 70].

Model Answer:

1. Find the middle element: index 3, value 42.
2. Compare 42 with target 42 — they are equal.
3. The item is found at index 3 after one comparison.

(In this case the target happens to be the middle element. For a harder example where multiple steps are needed, always show low, high, mid at each step.)

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Practice Question 4: Sorting Comparison (4 marks)

Question: A company needs to sort a database of 100,000 customer records. Compare the suitability of bubble sort and merge sort for this task.

Model Answer:

• Merge sort is more suitable because it has a time complexity of O(n log n), requiring approximately 100,000 × 17 ≈ 1,700,000 operations in all cases.
• Bubble sort has a worst-case time complexity of O(n²), requiring up to 10,000,000,000 operations — approximately 5,880 times more than merge sort.
• However, merge sort requires O(n) extra memory to store the sub-lists during sorting, whereas bubble sort sorts in place with O(1) extra memory.
• For 100,000 records, the speed advantage of merge sort far outweighs its additional memory usage, making it the better choice.

OCR Exam Tip: For comparison questions, always state the time complexity with numbers, explain the practical impact, and consider both time and space. A balanced answer that acknowledges drawbacks of your recommended algorithm will score higher.

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Practice Question 5: Write an Algorithm (5 marks)

Question: Write an algorithm in pseudocode that takes a list of 10 test scores and finds the highest score. Output the highest score.

Model Answer:

scores = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

for i = 0 to 9
    scores[i] = int(input("Enter score: "))
next i

highest = scores[0]
for i = 1 to 9
    if scores[i] > highest then
        highest = scores[i]
    endif
next i

print("Highest score is: " + str(highest))

Python equivalent:

scores = []
for i in range(10):
    scores.append(int(input("Enter score: ")))

highest = scores[0]
for i in range(1, 10):
    if scores[i] > highest:
        highest = scores[i]

print("Highest score is:", highest)

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Practice Question 6: Bubble Sort Trace (5 marks)

Question: Show the state of the list [7, 3, 5, 1] after each complete pass of bubble sort.

Model Answer:

Pass 1: Compare 7&3 (swap), 7&5 (swap), 7&1 (swap) → [3, 5, 1, 7] Pass 2: Compare 3&5 (no swap), 5&1 (swap) → [3, 1, 5, 7] Pass 3: Compare 3&1 (swap) → [1, 3, 5, 7] Pass 4: No swaps — list is sorted. Final: [1, 3, 5, 7]

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Key Revision Checklist

Topic	Can I...
Algorithms	Define an algorithm and explain why they are used?
Linear search	Describe, write in pseudocode, and trace it?
Binary search	Describe, write in pseudocode, and trace it? State it needs sorted data?
Bubble sort	Describe, write in pseudocode, and show passes?
Merge sort	Describe the divide and merge phases?
Insertion sort	Describe how elements are inserted into the sorted portion?
Comparing algorithms	Compare time complexity, space complexity, and suitability?
Trace tables	Complete a trace table accurately for any given pseudocode?

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Final Exam Tips

1. Read the question carefully — "describe" means explain step by step; "state" means a brief answer; "compare" means discuss both algorithms.
2. Use OCR pseudocode conventions in your answers unless the question specifies Python.
3. Show your working in trace tables — partial marks are available.
4. Use specific numbers when comparing efficiency (e.g. "10 comparisons vs 1,000").
5. Manage your time — do not spend 15 minutes on a 3-mark question.

OCR Exam Tip: Before the exam, practise completing trace tables under timed conditions. Many students understand the algorithms but make careless errors under time pressure. The more you practise, the fewer mistakes you will make.

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Practice Question 7: Merge Sort Stages (6 marks)

Question: Show the stages of a merge sort applied to the list [8, 2, 5, 1, 7, 3]. Show both the divide phase and the merge phase.

Model Answer:

Divide phase:

graph TD
  N0["[8, 2, 5, 1, 7, 3]"] --> N1["[8, 2, 5]"]
  N0 --> N2["[1, 7, 3]"]
  N1 --> N3["[8]"]
  N1 --> N4["[2, 5]"]
  N2 --> N5["[1]"]
  N2 --> N6["[7, 3]"]
  N4 --> N7["[2]"]
  N4 --> N8["[5]"]
  N6 --> N9["[7]"]
  N6 --> N10["[3]"]

Merge phase:

• Merge [2] and [5] → [2, 5]
• Merge [8] and [2, 5] → [2, 5, 8]
• Merge [7] and [3] → [3, 7]
• Merge [1] and [3, 7] → [1, 3, 7]
• Merge [2, 5, 8] and [1, 3, 7]:
  • 2 vs 1 → take 1 → [1]
  • 2 vs 3 → take 2 → [1, 2]
  • 5 vs 3 → take 3 → [1, 2, 3]
  • 5 vs 7 → take 5 → [1, 2, 3, 5]
  • 8 vs 7 → take 7 → [1, 2, 3, 5, 7]
  • Append remaining [8] → [1, 2, 3, 5, 7, 8]

Final sorted list: [1, 2, 3, 5, 7, 8].

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Practice Question 8: Trace Table Exam Standard (5 marks)

Question: Complete the trace table for the algorithm below when num = 12.

num = 12
count = 0
i = 1
while i <= num
    if num MOD i == 0 then
        count = count + 1
    endif
    i = i + 1
endwhile
print(count)

Model Answer:

i	num MOD i	Divisor?	count
1	0	Yes	1
2	0	Yes	2
3	0	Yes	3
4	0	Yes	4
5	2	No	4
6	0	Yes	5
7	5	No	5
8	4	No	5
9	3	No	5
10	2	No	5
11	1	No	5
12	0	Yes	6

Output: 6 (the number of divisors of 12: 1, 2, 3, 4, 6, 12).

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Practice Question 9: Algorithm Recommendation (6 marks)