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

From Wikibooks, open books for an open world
Jump to navigation Jump to search

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

Dividing and Factoring Polynomials[edit | edit source]

Remainder Theorem[edit | edit source]

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 Theorem[edit | edit source]

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 Function[edit | edit source]

The Laws of Exponents[edit | edit source]

  1. where c is a constant

Logarithmic Function[edit | edit source]

The inverse of is which is equivalent to

Change of Base Rule: can be written as

Laws of Logarithmic Functions[edit | edit source]

When X and Y are positive.

Circles and Angles[edit | edit source]

Conversion of Degree Minutes and Seconds to a Decimal[edit | edit source]

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

Arc Length[edit | edit source]

Note: θ need to be in radians

Area of a Sector[edit | edit source]

Note: θ need to be in radians.

Trigonometry[edit | edit source]

The Trigonometric Ratios Of An Angle[edit | edit source]

Function Written Defined Inverse Function Written Equivalent to
Cosine
Sine
Tangent

Important Trigonometric Values[edit | edit source]

You need to have these values memorized.

0 0 1 0
1 0 -

The Law of Cosines[edit | edit source]

The Law of Sines[edit | edit source]

Area of a Triangle[edit | edit source]

Trigonometric Identities[edit | edit source]

Integration[edit | edit source]

Integration Rules[edit | edit source]

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 Integrals[edit | edit source]

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

Trapezium Rule[edit | edit source]

Where:

Midpoint Rule[edit | edit source]

Where: n is the number of strips.

and