IB+Higher+Level+-+Calculus

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

7.1

Informal ideas of limit and convergence.

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.

Derivatives of reciprocal circular functions. Derivatives of //a// x and //log// a //x//. Derivatives of arcsin //x//, arccos //x//, arctan //x//. **(6.2 in new syllabus)**

7.2

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

The chain rule for composite functions. Applications of chain rule to related rates of change.

The product and quotient rules.

The second derivative.

Awareness of higher derivatives

7.3

Local maximum and minimum points.

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 problems**

7.4

Indefinite integration as anti differentiation.

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


 * Other indefinite integrals using results from 6.2**

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.

Definite integrals.

Areas between a curve and the //x-axis// or //y-axis// in a given interval, 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//|; asymptotes. **(6.3 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)**

7.8

Implicit differentiation **(including in 6.2 in new syllabus)**

7.9

Further integration:

integration by substitution **(included in 6.7 in new syllabus)**

integration by parts. **(included in 6.7 in new syllabus)**

7.10

Solution of first order differential equations by separation of variables.**(not covered 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 to generate questions that require tangents