Download Functional Equations IOQM PYQs — free PDF
All 6 previous-year questions on Functional Equations, each with the official answer and a worked solution. Free to download, print and share — no sign-up needed. Prefer to solve first? The questions-only edition has the same paper without solutions, with the answer key on the last page.
Functional Equations in IOQM: previous year question analysis
Functional Equations has appeared 6 times in IOQM between 2012 and 2025, making it the 12th most-asked of 14 chapters and about 1.7% of the bank. Over the last 4 years it has averaged 1.5 questions per year.
Answers checked against the official answer keys.
How many Functional Equations questions appeared each year
| Year | Questions | Relative volume |
|---|---|---|
| 2012 | 1 | |
| 2014 | 1 | |
| 2024 | 1 | |
| 2025 | 3 |
Which Functional Equations sub-topics are asked most
Every question in this chapter is tagged to a sub-topic, so you can see exactly where the marks sit before you revise.
- multiplicative strictly increasing function on naturals1 questions
- completely multiplicative injective function on $\mathbb{N}$1 questions
- substitution $x \to 3 - x$ and elimination1 questions
- functional equation over the integers plus a summation bound1 questions
- piecewise integer function, solving f(f(n))=991 questions
- substitution x -> 3-x to solve for f1 questions
Question formats used in Functional Equations
- Numerical / integer answer6
How Functional Equations compares with nearby chapters
- #10Inequalities12
- #11Modular Arithmetic9
- #12Functional Equations6
- #13Graphs, Games & Sets6
- #14Pigeonhole & Invariants6
Counts are computed from AcadXL’s own IOQM question bank, tagged chapter- and sub-topic-wise and checked against official answer keys. Sign in to attempt the 6 Functional Equations questions with solutions.