Do I have to draw a graph for function inequalities in IB Math?

Not always, but you should think graphically even when you solve algebraically. IB Math examiners reward solutions that clearly identify where the function is positive/negative or above/below another function. A quick sketch reduces sign errors because you can see where crossings happen and where the curve sits relative to the boundary. If you don’t sketch, you need a sign chart or test points to justify intervals. The key is that your final answer must describe the region of solutions, not just the boundary values. Graph thinking is often the difference between full marks and “method but incomplete answer.”

Why do I lose marks when my boundary points are correct?

Because boundary points are only the places where the inequality might switch truth value. In IB Math, the job isn’t to find where (f(x)=0) and stop; it’s to decide where (f(x)>0) or (f(x)\\le 0) across the entire domain. Students commonly forget to test an interval, or they miss a domain restriction that removes part of the interval. Another frequent issue is endpoint inclusion: strict inequalities exclude the boundary even if you found it correctly. Finally, the answer format matters: interval notation must be consistent and complete. Correct boundaries with an incomplete set is still incomplete.

Should I solve inequalities algebraically or with a GDC?

Use both strategically. Algebra is great for finding exact boundary points and showing method, which IB Math markschemes often expect. A GDC is excellent for checking your intervals visually, especially when functions are messy or when intersections are not “nice.” The safest approach is: do the algebra to find candidates, then confirm with a quick graph or table to verify which regions satisfy the inequality. If the question asks for exact values, rely on algebra for the final statement. If it asks for a solution set or region, use the graph to ensure you didn’t miss an interval.

IB Math: Why Function Inequalities Are Easy to Mess Up

IB Math

RevisionDojo Team

•12/21/2025•6 min read

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IB Math: Why Function Inequalities Are Easy to Mess Up

IB Math

RevisionDojo Team

•12/21/2025•6 min read

A tiny symbol, a big mark loss

The most painful IB Math mistakes are rarely “hard topic” mistakes. They’re “I knew this” mistakes.

Function inequalities are the perfect example. You’ll feel confident, do clean algebra, find the right boundary points... and still drop marks because your final answer isn’t a set of points, it’s a region of values. IB Math questions love this because it quietly tests whether you understand functions as behaviour (above, below, between), not just as something you rearrange.

If you’ve ever written an answer, circled it, and then realized you never checked the graph or the domain, you already know why these are easy to mess up.

The quick checklist before you touch the algebra (save this)

Before solving any function inequality in IB Math, run this mental checklist:

What exactly is the inequality asking: where is the function above/below something?
What are the boundary points (where the two sides are equal)?
Is it strict (<, >) or non-strict (≤, ≥)?
What is the domain restriction (denominators, roots, logs, given domain)?
Can you confirm intervals with a quick sketch or sign chart?

For targeted practice on the exact syllabus skill, use AHL 2.15 -- Solutions of inequalities and then drill the AHL 2.15 Questionbank.

Why function inequalities feel “unfair” in IB Math

In an equation, you’re hunting for a value of (x). In an inequality, you’re describing a landscape.

That landscape is made of intervals: places where a function sits above the axis, below another curve, or between two boundaries. And that’s where IB Math punishes autopilot.

A common pattern is comparing two functions:

Solve (f(x) > g(x))
Rearrange to (f(x) - g(x) > 0)
Find where the difference is positive

Students often stop after “find the roots” and forget the final step: deciding which intervals actually satisfy the inequality.

If functions still feel shaky, start with Understanding Functions in IB Math AA: A Beginner's Walkthrough to rebuild intuition.

The three traps that steal the most marks

Treating an inequality like an equation

In IB Math, getting the boundary points is often only half the method. You must also state the intervals that work. That means either:

a quick sketch, or
a sign chart / test value approach.

Boundary points tell you where things can change. They don’t tell you what happens between.

Forgetting domain restrictions

Domain issues quietly delete pieces of your answer.

Rational functions: values that make denominators zero are never allowed.
Roots: even roots require the radicand (\ge 0).
Logs: arguments must be (> 0).

The safest habit: write domain restrictions as a first line, and then intersect them with your interval solution at the end.

Endpoint confusion (the bracket problem)

Strict vs non-strict inequalities decide whether endpoints are included.

In exam pressure, students often flip (() and ([) accidentally. It feels small, but IB Math markschemes treat it as accuracy.

For structured review, RevisionDojo’s SL 2.7 Notes and SL 2.7 Questionbank are a clean way to practise boundaries plus notation.

A RevisionDojo way to practise this (without burning hours)

Function inequalities improve fast when practice is tight and feedback is immediate.

Use RevisionDojo like this:

Do 10 questions in the AHL 2.15 Questionbank or the modulus inequalities questionbank.
After each one, check: “Did I give intervals, handle domain, and choose the right endpoints?”
Reinforce the method with AHL 2.15 Flashcards.

Then, when you want exam pacing, use Mock Exams and Predicted Papers inside RevisionDojo to simulate the stress that causes these mistakes in real IB Math papers. If you’re stuck on why your interval is wrong, AI Chat can walk through the sign analysis step-by-step, and Grading tools help you match markscheme wording.

Conclusion: think in intervals, not answers

Function inequalities are easy to mess up in IB Math because they look like equations but behave like geography. You’re mapping regions, respecting borders, and checking what’s allowed to exist in the first place.

If you want this to become automatic, build a short practice loop in RevisionDojo: Notes for the method, Questionbank for repetition, Flashcards for the rules, AI Chat for the “why,” and Mock Exams to pressure-test your timing. Master the intervals, and IB Math starts to feel a lot less fragile.

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