Maths C4

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  • CORE 4
    • Partial fractions
      • Involves writing an algebraic fraction as 2 or more simpler fractions
        • Substitution
        • Equating coefficients
    • Coordinate geometry
      • Parametric equation
        • Example: X=1+T     Y=T-2
        • Example:    X= Sin t + 9 Y= Cos 2t +4
        • find dy/dx by doing: dy/dt divided by dx/dt
        • Area under the curve:   {y dx/dt
      • Cartesian equation
        • Y= Mx + C
        • P --> C    Use:  trig identity Sin(2)t + Cos(2)t =1
    • Binomial Expansion
      • formula:        1+ nx +n(n-1)(x)^2 /2! ....
        • 'n' is a positive integer - the expansion is finite
    • Vectors
      • A quantity with both magnitude and direction
        • Equal vectors have the same magnitude and direction
        • Magnitude = Modulus [A]
          • The vector a has the same magnitude as -a but is in the opposite direction
      • PQ + QP = 0
        • AB= B- A or AB= AO + OB
      • A vector parallel to a is written by Xa where X is a non zero scalar
        • Vector parallel to the x, y and z axis =i+ j + k
        • A.B = 0       (parallel vectors)
      • Position vector = from the origin e.g. OA, OB, OC
        • Cos AOB = a.b/[A][B]
      • Vector equation:  r=a +tb
    • Differentiation
      • Chain rule
      • Product rule
      • Implicit: Y becomes dy/dx
      • Connected rates of change: da/db =  da/dc x dc/db
        • decrease: -k (k>0)
        • Increase: k
    • Integration
      • formulas
        • {1/x = ln[x]
        • {e(x) = e(x)
        • {a(x) =    1/ln[a] * a(x)
        • {Six = -Cos
        • {ln x= x ln[x] - x
        • {(ax+b)^n = 1/a * (ax+b) ^(n+1) / n+1
        • {1/ax+b =     1/a * ln[ax+b]
        • {sec(ax+b) = 1/a * ln[sec(ax+b) +tan(ax+b) ]
      • {f'(x)/f(x) =   ln[f (x)] +C
      • Integration by parts:            uv - {v du/dx

Comments

10jadoona

Nice

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