Additional Maths

Created by: A.B.
Created on: 27-03-13 20:11

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Additional Maths
- Algebra
  - 1 (Recapping)
    - Linear Expressions
    - Quadratic Expressions
      - To Solve
        Factorise
        
        Quadratic Formula
        
        Complete the Square
        Halve b then square it and add it on inside the brackets. Minus this number after +c. Factorise the values inside the bracket. Rearrange to solve, giving 2 values due to the square root.
    - Simultaneous Equations
      - Substitution
        When y is subject (or other unknown).
      - Elimination
        Add or subtract to eliminate variables
        Substitute into first equation.
        
        When y is not the subject.
  - 2
    - Linear Inequalities
      - Do the same to both sides.
      - Open circles show that the number is not included
      - Closed circles show the number is included
      - Quadratic Inequalities
        Sketch a graph
        
        Draw a table showing values of x
        
        Terms MUST be collected to one side
    - Algebraic Fractions
      - When multiplying, only multiply the numerator
    - Simplifying expressions containing square roots
      - Rationalise the denominator
  - 3 (polynomials)
    - Factor Theroem
      - If (x-a) is a factor of f(x) then f(a)=0.
        Can be found through division of polynomials.
    - Remainder Theorem
      - f(a) is the remainder when f(x) is divided by (x-a)
  - 4 (Bionomials)
    - Bionomial Distribution
      - In probability...
        The probability of a successful outcome is 'p'
        
        The probability that the outcome is a failure is 'q'
        
        There are 'n' trials
        
        The number of successes is 'X'
- Co-ordinate Geometry
  - 1 (Straight lines and circles)
    - To find the distance between a and b
      - Use Pythagoras
    - Circles
      - With centre (h,k) and radius r
      - When the centre is at the origin (0,0) (Simplified version of other).
    - The co-ordinates of the point of intersection of two lines are found by solving their equations simultaneously.
  - 2 (Inequalities)
    - Represent boundaries that are < or > as a dotted line whereas if they are also equal to as a solid line.
    - Region where inequalities satisfied simultaneously called the feasible region.
    - Objective function is the quantity wanted to be maximised or minimised (e.g. profit)
      - Will lie at, or near to the vertex of the feasible region.
- Trigonometry
  - 1 (Review)
    - SOHCAHTOA,for right angled triangles.
    - For angle theta, in right angled triangle
    - For triangle ABC
      - Sine rule
      - Cosine rule
      - Area
    - Sin theta and Cos theta can only take values between 1 and -1
  - 2 (Applications)
    - In 3D
      - Plane = flat surface
      - 2 lines may meet, be parallel or be skew
      - Untitled
- Calculus
  - Differentation
    - Used to find whether point is maximum, minimum or point of inflection.
  - Integration
    - Used to find area under graph
    - Definite
    - Indefinite
  - Kinetmatics
    - SUVAT
      - Variables
        Acceleration = a, Initial velocity = u, at time =t, velocity = v and displacement = s.
      - Equations
      - For General Motion

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Additional Maths

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