A Level Mathematics Syllabus Statement

Syllabus Content

Carry out simple cases of integration by substitution and integration by parts; understand these methods as the inverse processes of the chain and product rules respectively (Integration by substitution includes finding a suitable substitution and is limited to cases where one substitution will lead to a function which can be integrated; integration by parts includes more than one application of the method but excludes reduction formulae)

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Integration Exercises on indefinite and definite integration of basic algebraic and trigonometric functions.

Integration Video You can't possibly learn all about integration from a 28 minute video so all that this resource can do is provide a quick revision to help you do the online exercise.

Integration Flowchart This flowchart will only be of use to those who have already learnt the techniques mentioned in the IB AA Syllabus.

Here are some exam-style questions on this statement:

"The acceleration, \(a\) ms^-2 , of an object at time \(t\) seconds is given by" ... more

"Given that \( \frac{dy}{dx} = \sin(x + \frac{\pi}{3})\) and \(y = 5\) when \(x = \frac{8\pi}{3}\), find \(y\) in terms of \(x\)." ... more

"(a) Using a suitable substitution, or otherwise, find" ... more

"Find \(f(x)\) if:" ... more

"Let \(f(x) = \frac{ln3x}{kx} \) where \( x \gt 0\) and \( k \in \mathbf Q^+ \)." ... more

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Calculus It is said that the word calculus comes from the Latin word for the small pebble used for counting and calculations. The two major branches, differentiation and integration, are studied by pupils only towards the end of their school days but does then form a major part of their studies. A course in calculus is a prerequisite for other, more advanced courses in mathematical analysis. Isaac Newton is best known for developing calculus. He was born in England in 1642 and is considered one of the most influential scientists and mathematicians in history.

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