Calculus
Informal ideas of limit, continuity and convergence. Definition of derivative from first principles.
The derivative interpreted as a gradient function and as a rate of change. Finding equations of tangents and normals.
Identifying increasing and decreasing functions.
The second derivative. Higher derivatives.
Derivatives of xn , sin x , cos x , tan x ,
and ln x . Differentiation of sums and multiples of functions.
The product and quotient rules. The chain rule for composite functions.
Related rates of change. Implicit differentiation.
Derivatives of sec x , csc x , cot x ,
, loga x ,arcsin x , arccos x and arctan x .
Local maximum and minimum values. Optimization problems. Points of inflexion with zero and non-zero gradients.
Graphical behaviour of functions, including the relationship between the graphs of f , f ′ and f ′′ .
Indefinite integration as anti-differentiation. Indefinite integral of x^n , sin x , cos x and .
Anti-differentiation with a boundary condition to determine the constant of integration. Definite integrals.
Area of the region enclosed by a curve and the x-axis or y-axis in a given interval; areas of regions enclosed by curves.
Volumes of revolution about the x-axis or y-axis.
Kinematic problems involving displacement s, velocity v and acceleration a. Total distance travelled.
Integration by substitution. Integration by parts.
http://www.ibmaths4u.com
Informal ideas of limit, continuity and convergence. Definition of derivative from first principles.
The derivative interpreted as a gradient function and as a rate of change. Finding equations of tangents and normals.
Identifying increasing and decreasing functions.
The second derivative. Higher derivatives.
Derivatives of xn , sin x , cos x , tan x ,
and ln x . Differentiation of sums and multiples of functions.The product and quotient rules. The chain rule for composite functions.
Related rates of change. Implicit differentiation.
Derivatives of sec x , csc x , cot x ,
, loga x ,arcsin x , arccos x and arctan x .Local maximum and minimum values. Optimization problems. Points of inflexion with zero and non-zero gradients.
Graphical behaviour of functions, including the relationship between the graphs of f , f ′ and f ′′ .
Indefinite integration as anti-differentiation. Indefinite integral of x^n , sin x , cos x and
.Anti-differentiation with a boundary condition to determine the constant of integration. Definite integrals.
Area of the region enclosed by a curve and the x-axis or y-axis in a given interval; areas of regions enclosed by curves.
Volumes of revolution about the x-axis or y-axis.
Kinematic problems involving displacement s, velocity v and acceleration a. Total distance travelled.
Integration by substitution. Integration by parts.
http://www.ibmaths4u.com
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