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Standard Integrals SL
In this page, we will look at some of the standard integration techniques that you need to know about involving x^n, \sin x, \cos x, \dfrac{1}{x}, e^x and the composite of these with the linear function...
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L'Hôpital's Rule HL
You will probably have already considered limits in work on the sum of a geometric series, rational functions and asymptotes and differentiation from first principles. On this page, we will take the idea...
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Related Rates of Change HL
This page is about finding related rates of change, otherwise known as connected rates of change. In questions on this topic, you will be given the rate of change of one quantity and be required to find...
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Implicit Differentiation HL
This page is all about implicit equations and how we find their gradients. Implicit equations are equations which are not written explicitly. Examination questions typically ask you to find the equation...
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Maclaurin Series HL
A Maclaurin series is a power series that enables us to find a polynomial that approximates a function that cannot be written algebraically. It is what calculators and computers use to work with transcendental...
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Optimisation
Optimisation questions involve finding the best solution to a problem. Usually, that is the maximum or minimum value of a function. Questions on this topic require you to take information from a practical...
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Equation of Tangent and Normal
On this page, we look at how to find the equation of a tangent and the equation of a normal to a curve. A tangent to a curve at a point is the straight line through that point whose gradient is equal...
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Product and Quotient Rule
The product rule is a formula that we can use to differentiate the product of two (or more) functions. The quotient rule is for the quotient of two functions (one function divided by another). The rules...
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Chain Rule
The chain rule is used to differentiate composite functions. The rule itself is quite simple, but it is important to recognise when it is needed and to become fluent in applying it. This can save time...
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Complex Numbers HL - Roots of Polynomials
The Conjugate Root Theorem states that if the complex number a + ib is a root of a polynomial in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial....