AS Pure Mathematics - P2

This is only to be used as a rough guide and is not the official specification

1. Algebra

Modulus Functions

Algebraic Long Division

Factor Theorem

Remainder Theorem

2. Logarithmic and exponential functions

Exponential functions

Logarithms

Exponential Function ex

Natural Log Functions

Modelling Curves of the form y=kxn and y=kax

3. Trigonometry

Secant, Cosecant and Cotangent

Identities

• A cos x ± B sin x and A sin x ± B cos x type

Solving Equations using:

• the identities : sin²x + cos²x ≡1 ; 1 + tan²x ≡ sec²x ; 1 + cot²x ≡ cosec²x
• Examples: 1 | 2 | 3

• the identities for sin2A, cos2A and tan2A
• Examples: 1 | 2 | 3

• the identities for A cos x ± B sin x and A sin x ± B cos x

Miscellaneous Exam Practice

4. Differentiation

Differentiating the exponential function ex

Differentiating the natural log function, ln(x)

Differentiating the trig. functions, sin(x), cos(x) and tan(x)

The Chain Rule

The Product Rule

The Quotient Rule

A Special Result

Miscellaneous Exam Practice

Parametric Functions

Implicit Functions

5. Integration

(ax+b)n types

The exponential functions : ex, eax and e(ax+b)

Reciprocal Functions : 1/x and 1/(ax+b)

Integrals of the form : f'(x)/f(x)

Integrals of the form : f'(x)ef(x)

Trigonometric types

Trapezium Rule

Specification and Modules

Specification

P1 | P2 | P3 | M1 | M2 | S1 | S2