Additional Maths

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  • 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
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            • 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
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            • 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
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          • When the centre is at the origin (0,0) (Simplified version of other).
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        • 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
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        • For triangle ABC
          • Sine rule
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          • Cosine rule
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          • Area
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        • 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.
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      • Integration
        • Used to find area under graph
        • Definite
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        • Indefinite
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      • Kinetmatics
        • SUVAT
          • Variables
            • Acceleration = a, Initial velocity = u, at time =t, velocity = v and displacement = s.
          • Equations
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          • For General Motion
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