AQA A Level Maths: Pure復習筆記10.1.4 Newton-Raphson
Newton-Raphson The Newton-Raphson method The Newton-Raphson method finds?roots?of equations in the form?f(x)?=?0 It can be used to find?approximate solutions?when an equation cannot be solved using...
AQA A Level Maths: Pure復習筆記10.1.3 x = g(x) Iteration
x = g(x) Iteration What does xn + 1?= f(xn) mean? When an equation cannot be solved using the usual?analytical methods, we can still find?approximate solutions?to a certain degree of accuracy Itera...
AQA A Level Maths: Pure復習筆記10.1.2 Change of Sign Failure
Change of Sign Failure When can the sign change method fail? There are certain circumstances where a?change of sign?fails to appropriately reflect the number or existence of roots If the interval i...
AQA A Level Maths: Pure復習筆記10.1.1 Change of Sign
Change of Sign What does a change of sign mean? A?sign change?between f(a) to f(b) means there must be a?root?between a and b When an equation cannot be solved using the usual?analytical methods, w...
AQA A Level Maths: Pure復習筆記9.2.3 Modelling with Parametric Equations
Modelling with Parametric Equations What can be modelled with parametric equations? A common use for parametric equations is motion in two dimensions x = f(t)?– horizontal position, dependent on ti...
AQA A Level Maths: Pure復習筆記9.2.2 Parametric Integration
Parametric Integration How does integration work with parametric equations? Integration is used to find the area under a curve where the curve has been defined by parametric equations x = f(t) y = ...
AQA A Level Maths: Pure復習筆記9.2.1 Parametric Differentiation
Parametric Differentiation How do I find dy/dx from parametric equations? Ensure you are familiar with Parametric Equations – Basics first This method uses the chain rule and the reciprocal propert...
AQA A Level Maths: Pure復習筆記9.1.3 Parametric Equations - Sketching Graphs
Parametric Equations - Sketching Graphs How do I sketch a graph from parametric equations? Plotting?a graph is covered in Parametric Equations - Basics Still find the key features of a graph … … th...
AQA A Level Maths: Pure復習筆記9.1.2 Parametric Equations - Eliminating the Parameter
Parametric Equations - Eliminating the Parameter What does eliminating the parameter mean? In parametric equations,?x = f(t)?and?y = g(t) There is still a connection directly linking?x?and?y This w...
