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

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

Dividing and Factoring Polynomials

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Remainder Theorem

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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

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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

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The Laws of Exponents

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  1. where c is a constant

Logarithmic Function

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The inverse of is which is equivalent to

Change of Base Rule: can be written as

Laws of Logarithmic Functions

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When X and Y are positive.

Circles and Angles

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Conversion of Degree Minutes and Seconds to a Decimal

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

Arc Length

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Note: θ need to be in radians

Area of a Sector

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Note: θ need to be in radians.

Trigonometry

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The Trigonometric Ratios Of An Angle

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Function Written Defined Inverse Function Written Equivalent to
Cosine
Sine
Tangent

Important Trigonometric Values

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You need to have these values memorized.

0 0 1 0
1 0 -

The Law of Cosines

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The Law of Sines

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Area of a Triangle

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Trigonometric Identities

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Integration

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Integration Rules

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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

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  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

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Where:

Midpoint Rule

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Where: n is the number of strips.

and