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[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

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]


Midpoint Rule[edit | edit source]

Where: n is the number of strips.