| IB HL - Calculus |
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| Simple differentiation |
- Simple differentiation of powers of x.
- Derivatives of ln and e.
- Derivatives of trigonometric functions.
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| Tangents and normals |
- Understanding the differential represents the gradient function.
- Finding the equation of a tangent to a curve at a given point.
- Finding the equation of a normal to a curve at a given point.
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| Graphing derivatives |
- Graphing derivatives and matching with the original function.
- The second differential and it's graph.
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| Chain rule |
- Differentiating by use of the chain rule.
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| Product and quotient rules |
- Differentiation by use of the product rule.
- Differentiation by use of the quotient rule.
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| Turning points |
- Using differentiation to find maximum and minimum points on curves.
- Using the second differential to determine the nature of the maximum or minimum points.
- The point of inflexion.
- Solving real-life problems of maximum and minimum points.
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| Integration as anti-differentiation |
- Basic integration as anti-differentiation.
- Integration of logarithmic and trig functions.
- Solving the value of the constant when integrating.
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| Definite integration |
- Finding areas under graphs.
- Finding areas bounded between graphs.
- Finding volumes of revolution.
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| Kinetics |
- Understanding the relationship between displacement, velocity, and acceleration.
- Using calculus to find missing displacement, velocity, acceleration.
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| Implicit differentiation |
- Differentiate implicitly, linking with the chain rule.
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| Partial fractions |
- Split fractions into partial fractions.
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| Integration by substitution |
- Integration using substitution.
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| Integration by parts |
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| First order differential equations |
- Separating variables to solve first order differential equations.
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