# 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

• Pythagorean type: sin²x + cos²x ≡1 ; 1 + tan²x ≡ sec²x ; 1 + cot²x ≡ cosec²x
• Examples : 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8

• Addition type: sin(A±B), cos(A±B) and tan(A±B)

• 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

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