Further calculus
This chapter extends calculus knowledge by introducing advanced integration techniques. It covers the derivative of tan⁻¹x and its reverse…
What you'll learn
- Use the derivative of tan⁻¹x.
- Extend reverse differentiation to include the integration of 1/(a² + x²).
- Recognise and integrate functions of the form f'(x)/f(x).
- Use given substitutions to simplify and evaluate definite or indefinite integrals.
- Integrate rational functions by decomposition into partial fractions.
- Recognise when an integrand can be regarded as a product and use integration by parts.
Study tools for this chapter
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Guided lesson slides
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Flashcards
11 spaced-repetition cards
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MCQs
105 multiple-choice questions
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Exam questions
78 questions with mark schemes
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Revision notes
Structured notes with exam techniques and definitions
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About Further calculus on Nexelia Academy
Further calculus is chapter 8 of Nexelia Academy's Cambridge A-Level Pure Mathematics 2 & 3 course. This chapter extends calculus knowledge by introducing advanced integration techniques. It covers the derivative of tan⁻¹x and its reverse…
This chapter is mapped to the official Cambridge International AS & A Level Pure Mathematics 2 & 3 syllabus and includes 105 multiple-choice questions, 78 structured exam questions with full mark schemes, 11 spaced-repetition flashcards, guided lesson slides and access to an AI tutor trained on the Cambridge specification.
Frequently asked questions about Further calculus
How do I revise Further calculus for Cambridge A-Level Pure Mathematics 2 & 3?
Work through the guided lesson slides first to build a mental model, then drill the 105 MCQs for quick recall, attempt the 78 exam questions with mark schemes for technique, and use flashcards for spaced repetition. The AI tutor is available throughout if you get stuck.
How many practice questions does Further calculus include?
Further calculus on Nexelia Academy includes 105 multiple-choice questions, 78 structured exam questions with full mark schemes, and 11 flashcards.
Is Further calculus free?
Chapter 1 of Cambridge A-Level Pure Mathematics 2 & 3 is free for all registered users. Further calculus is included in Pro and Max plans, which unlock every chapter with unlimited practice.
Does Nexelia Academy cover Further calculus for Cambridge A-Level Pure Mathematics 2 & 3?
Yes. Further calculus is fully mapped to the official Cambridge International AS & A Level Pure Mathematics 2 & 3 syllabus and is one of Nexelia Academy's published chapters for this course.