Why students lose marks in integration and it has nothing to do with the mathematics
In 25 years of teaching IB Mathematics, I have never once seen a student fail an integration question because they did not know the technique. They fail because they make a decision too early. They look at an integral, pattern-match it to something familiar, and apply a method before they have truly read the question. Integration by parts gets applied where substitution was faster. Substitution is attempted where partial fractions were required. The mathematics inside is correct — but the method chosen was wrong, and marks disappear. The real skill in IB AA HL integration is not mechanical fluency. It is recognition before execution. These worksheets are designed to train that recognition.
Recognition Training
Integration by Substitution
Recognising when a composite function and its derivative both appear in the integrand. Includes standard and reverse chain rule cases. The most common error is substituting correctly in the integrand but forgetting to change the limits in a definite integral.
Integration by Parts
Applying the LIATE priority rule, handling repeated integration by parts, and navigating the cyclic case where the original integral reappears. The signature error: choosing u and dv incorrectly so that each application makes the integral more complex rather than simpler.
Integration by Partial Fractions
Decomposing rational functions into partial fractions for distinct linear, repeated linear, and irreducible quadratic factors, then integrating. The most commonly lost mark: setting up the decomposition correctly but using incorrect values when solving for the constants A, B, C.
The 4 Patterns Behind Every Lost Mark
Applying the method before reading the full expression
Students see ln x and immediately attempt integration by parts. They see a fraction and immediately decompose. Pattern-matching fires before the expression is fully read. Write down every feature of the integrand before choosing a method.
Forgetting the constant of integration
This costs one mark every time, and it costs it silently. Students who complete the hardest part of the question correctly lose a mark at the final step. Make +C a reflex, not a memory task.
Incorrect LIATE assignment in integration by parts
Choosing the wrong function as u makes the question dramatically harder. The signal: each application produces a new integral more complex than the previous one. Stop. Swap u and dv. Restart.
Carrying original limits through a substitution
u = g(x) is substituted, the limits in x must be converted to limits in u. Students substitute correctly in the integrand and then evaluate using the original x-values. The working is correct; the answer is wrong.
The Full Diagnostic Path
- 50 original exam-style questions across 4 sections
- Full worked solutions with M1/A1 IB mark scheme
- Mistake analysis on every question
- Sections: substitution, by parts, partial fractions, and mixed technique identification
- Examiner commentary per section
Need one-to-one help with integration?
Book a session with Abdul Wadood and work through the techniques that are costing you marks.