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OCR H446 2.3.1 Big O growth

Part 3 of 16 · H446 2.3.1 · Algorithms

Big O is where H446 2.3.1 students most often reach for the right words with the wrong meaning. This worksheet builds constant, logarithmic, linear, polynomial and exponential growth from what actually happens to the work when the input size changes, and asks students to read growth from code structure and from a graph.

Students will:

  • classify expressions and code shapes into the five growth families
  • explain a curve by saying what happens when the input size doubles
  • trace a counter and use the count to identify the growth family
  • repair common misstatements about exponential and logarithmic work
  • explain why a growth class alone does not predict runtime on small inputs

Inside: 6 explanation cells, 1 multiple-choice question, 1 fill-in-the-blanks cell, 3 written answers and 1 trace table. 26 marks, about 25 to 35 minutes.

Series: H446 2.3.1 · Algorithms, part 3 of 16.

Shared by Coding PathwayVerified teacher

  • 12 cells
  • About 30 minutes
  • CC BY-SA 4.0
  • Shared 31 Aug 2026
  • Updated 3 Sept 2026

Preview

The whole resource, exactly as a class sees it. Answers and marking are held back.

Big O growth

Big O describes how work grows as input size n grows. It suppresses constant factors and lower-order terms to compare scalability.

By the end, you will be able to

  • interpret O(1), O(log n), O(n), polynomial and exponential growth;
  • match code/algorithms to growth families;
  • explain graphs using what happens when n changes;
  • avoid confusing n², 2n and 2ⁿ.

Reactivate: nested dependent loops multiply possible iterations.

Worked model: growth families

Big O growth familiesinput size nwork / timeO(1)O(log n)O(n)O(n²)O(2ⁿ)

O(1): work is bounded independently of n. O(log n): each step removes a constant fraction, so extra work gets progressively smaller relative to n. O(n): doubling n roughly doubles dominant work. O(n²): doubling n roughly quadruples it. O(2ⁿ): each added input can roughly double possibilities.

Multiple choice1 mark

Which expression models exponential growth?

  • An + n
  • Bn²
  • C2ⁿ
  • D2n
Written answer4 marks

Give Big O for: (a) 7 operations, (b) 3n + 20, (c) n² + n, (d) repeatedly halving n.

State the dominant growth family.

Students type their answer here.

Trace table6 marks

Trace the count and use it to identify the growth family.

Enter a value only when it changes. Record output in order.

Use one row for each pass through the loop. Fill in a box only when that value changes on that row, and leave the rest blank.

ProgramPython
  1. n = 4
  2. count = 0
  3. for row in range(n):
  4. for column in range(n):
  5. count = count + 1
  6. print(count)
Trace table with 5 columns
RowncountrowcolumnOutput
1
2
3
4
5
6
7
8

Guided graph explanation

Do not merely name a curve. Use a change: if n doubles, linear work approximately doubles, quadratic work approximately quadruples, while logarithmic work adds about one step for base-two halving.

Written answer8 marks

Compare O(log n), O(n²) and O(2ⁿ) as n grows. Include the mechanism behind each shape and correct two claims: '2n is exponential' and 'logarithmic means no growth'.

Use doubling/halving language.

Students type their answer here.

Independent transfer

Classify direct array access, linear search, binary search, two full nested loops and exhaustive binary choices. Then rank them for large n and explain why Big O alone may not predict small-input runtime.

Written answer8 marks

Give classifications, ranking and qualification.

Use O notation and one small-input caveat.

Students type their answer here.

Closed-book checkpoint

Complete each sentence from memory. There is no answer bank and correctness is held for teacher review.

Fill in the blanks5 marks
Work independent of n is completion 1 complexity. Repeated halving is completion 2. One full pass is completion 3. A fixed power such as n² is completion 4. Growth such as 2ⁿ is completion 5.

Review your understanding

Before submitting, check that you can explain the central distinction in your own words, expose the intermediate state that supports your answer and apply the method in an unfamiliar context.