Q BankQuestion BankDocsDocuments

14. Calculus

Understand the idea of a derived function.
Only an informal understanding of limits is expected; differentiation from first principles is not required.

Use notation for derivatives and increments, including f'(x), f''(x), dy/dx, d^2y/dx^2, delta y / delta x and the limiting notation as delta x -> 0.

Know and use derivatives of x^n for any rational n, sin x, cos x, tan x, e^x and ln x.
Includes constant multiples, sums and composite functions using the chain rule.
For trigonometric functions, angles are always in radians.

Differentiate products and quotients of functions.

Use differentiation to find gradients, tangents and normals.

Use differentiation to find stationary points.
Points of inflexion are not included.

Apply differentiation to connected rates of change, small increments and approximations.

Apply differentiation to practical problems involving maxima and minima.

Use first and second derivative tests to discriminate between maxima and minima.
Points of inflexion are not included.
Give full justification of conclusions.
Explain how to distinguish between a maximum point and a minimum point when required.
Unless specified otherwise, any valid method is allowed.

Understand integration as the reverse process of differentiation.
Solutions for indefinite integrals should include an arbitrary constant.

Integrate sums of terms in powers of x, including 1/x and 1/(ax + b).
Solutions for indefinite integrals should include an arbitrary constant.

Integrate functions of the form (ax + b)^n for any rational n, sin(ax + b), cos(ax + b), sec^2(ax + b) and e^(ax+b).
Includes the case where n = -1.
For trigonometric functions, angles are always in radians.
Solutions for indefinite integrals should include an arbitrary constant.

Evaluate definite integrals and apply integration to plane areas.
Plane areas include areas between a line and a curve, between two curves, and a sum of two areas.

Apply differentiation and integration to kinematics problems involving displacement, velocity and acceleration of a particle moving in a straight line with variable or constant acceleration.

Use the relationships in 14.14 to draw and use displacement-time, distance-time, velocity-time, speed-time and acceleration-time graphs.

Objective notes

15 learning objectives

ConceptIGCSE Additional Math