A-level Mathematics/OCR/C2/Appendix A: Formulae

< A-level Mathematics‎ | OCR‎ | C2

By the end of this module you will be expected to have learnt the following formulae:

Contents

Dividing and Factoring PolynomialsEdit

Remainder TheoremEdit

If you have a polynomial f(x) divided by x - c, the remainder is equal to f(c). Note if the equation is x + c then you need to negate c: f(-c).

The Factor TheoremEdit

A polynomial f(x) has a factor x - c if and only if f(c) = 0. Note if the equation is x + c then you need to negate c: f(-c).

Formula For Exponential and Logarithmic FunctionEdit

The Laws of ExponentsEdit

  1. where c is a constant

Logarithmic FunctionEdit

The inverse of is which is equivalent to

Change of Base Rule: can be written as

Laws of Logarithmic FunctionsEdit

When X and Y are positive.

Circles and AnglesEdit

Conversion of Degree Minutes and Seconds to a DecimalEdit

where X is the degree, y is the minutes, and z is the seconds.

Arc LengthEdit

Note: θ need to be in radians

Area of a SectorEdit

Note: θ need to be in radians.

TrigonometryEdit

The Trigonometric Ratios Of An AngleEdit

Function Written Defined Inverse Function Written Equivalent to
Cosine
Sine
Tangent

Important Trigonometric ValuesEdit

You need to have these values memorized.

0 0 1 0
1 0 -

The Law of CosinesEdit

The Law of SinesEdit

Area of a TriangleEdit

Trigonometric IdentitiesEdit

IntegrationEdit

Integration RulesEdit

The reason that we add a + C when we compute the integral is because the derivative of a constant is zero, therefore we have an unknown constant when we compute the integral.

Rules of Definite IntegralsEdit

  1. , F is the anti derivative of f such that F' = f
  2. Area between a curve and the x-axis is
  3. Area between a curve and the y-axis is
  4. Area between curves is

Trapezium RuleEdit

Where:

Midpoint RuleEdit

Where: n is the number of strips.

and

This is part of the C2 (Core Mathematics 2) module of the A-level Mathematics text.


Dividing and Factoring Polynomials / Sequences and Series / Logarithms and Exponentials / Circles and Angles / Integration

Appendix A: Formulae