IB+Standard+Level+-+Calculus

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There have been some additions to the syllabus here, they are highlighted in bold

7.1

Informal ideas of limit and convergence.


 * Limit notation**

Definition of derivative as

//f'(x)// = lim// h->0 ((f(x+h)-f(x))/h)//

Derivative of //x n (neQ), sin x, cos x, tan x, e x and// In //x.// **(6.2 in new syllabus)**

Derivative interpreted as gradient function and as rate of change.

7.2

Differentiation of a sum and a real multiple of the functions in 7.1.

The chain rule for composite functions.

The product and quotient rules.

The second derivative.


 * Extension to higher derivatives**

7.3

Local maximum and minimum points.


 * Testing for maximum or minimum**

Use of the first and second derivative in optimization problems.


 * Graphical behaviour of functions including the relationship between the graphs of //f, f' and f''.//**


 * Optimization**

7.4

Indefinite integration as anti differentiation.

Indefinite integral of //x n (neQ), sin x, cos x, 1/x and// //e x //

The composites of any of these with the linear function //ax + b//


 * Integration by inspection, or substitution of the form S //f(g(x))g'(x)dx//**

7.5

Anti-differentiation with a boundary condition to determine the constant term.

Defining integrals. **//(both analytically and using technology)//**

Areas under curves (between the curve and the x-//axis//), areas between curves.

Volumes of revolution.

7.6

Kinematic problems involving displacement, //s//, velocity, //v//, and acceleration, //a//.


 * Total distance travelled**

7.7

Graphical behaviour of functions: tangents and normals, behaviour for large |//x//|, horizontal and vertical asymptotes. **(6.3 in new syllabus)**


 * Tangents and normals, and their equations (6.1 in new syllabus)**

The significance of the second derivative; distinction between maximum and minimum points. **(6.3 in new syllabus)**

Points of inflexion with zero and non-zero gradients. **(6.3 in new syllabus)**

Pages relating to Calculus
to be found to quadratics. || 7.7 || J. Gregg ||
 * **Page Name** || **Description** || **Chapter ref.** || **Added by** ||
 * Finding Tangents || A GeoGebra file that generates questions thaht require tangents