CORE 2

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  • Core 2
    • Algebra & Funtions
      • Factor  Theorem
        • If r=0  (cx+d) is a factor
      • Choosing Factors
        • Coefficient of highest power and constant.
      • If f(x) is polynomial and f(p)=0. x-p is factor of f(x).
      • If f(x) is divided by (ax-b) then the remainder is f(b/a)
    • Sine & Cosine Rule
      • a/sinA = b/sinB = c/sinC  (length)
      • sinA/a = sinB/b = sinC/c  (angle)
      • 1/2absinC
      • sin(180-x) = sinx
      • a^2 = b^2 + c^2 - 2bc cosA
      • CosA = (b^2 + c^2 - a^2) / 2bc
    • Exponentials & Logarithms
      • LOGaN = x     a^x = N
      • Multiplication law - LOGaXY = LOGaX + LOGaY
      • Division law - LOGaX/Y = LOGaX - LOGaY
      • Power law - LOGaX^k = kLOGaX
      • Changing base - LOGaB = LOGcB / LOGcA
        • E.G. LOG 4 29 = LOG 10 29 / LOG 10 4
    • Coordinate Geometry
      • Midpoint: (x1+x2/2 , y1+y2/2)
      • Distance: /(x2-x1)^2 + (y2-y1)^2
      • Equation: (x-a)^2 + (y-b)^2 = r^2
    • Binomial Expansion
      • nC0xa^n + nC1xa^n-1xb + nC2xa^n-2xb^2 ...
      • n! / (n-r)!r! = NCR = (n r)
        • E.G. 4th term in row 15. 15C4 = (15 4) = 15!/(15-4)!4! =1365
      • Coefficient
        • E.G. coefficient of x^3 in (3-2x)^5  x^3=5C3x3^2x(-2x)^3 10x9x(-8x^3)=-720x^3 coefficient of x^3 = -720
    • Radians
      • Radians to degrees              x 180/pi
      • Degrees to radians            x pi/180
      • area of sector: 1/2r^2Q
      • length of arc: rQ
    • Geometric Sequences & Series
      • a - first term.   r - common ratio.
      • Common ratio: u2/u1
      • Sn =             a (1-r^n)/1-r or                 a (r^n-1)/r-1
      • S(infinity) = a/1-r
    • Graphs of Trigonometric Functions
      • sin = o/h       cos = a/h      tan = o/a
      • CAST
      • sin(-Q)= -sinQ cos(-Q)=cos Q tan(-Q)=-tanQ
      • sin(90-Q)= cosQ    cos(90-Q)= sinQ
    • Differentiation
      • y is increasing function if gradient is positive    dy/dx > 0
      • y is increasing function if gradient is negative  dy./dx < 0
      • Gradient at max & min = 0
      • 1st - differentiate and find x when dy/dx =0
      • 2nd -  second derivative and sub in x  positive=max negative=min
      • 3rd - sub in x to find y
    • Trigonometric Identities
      • tanA = sinA/cosA
      • sin^2x + cos^2x = 1
        • 1 - sin^2x = cos^2x
        • 1 - cos^2x = sin^2x
    • Intergration
      • area under curve - points curve cross x axis. (put into integration with limits)
      • area between line (equation y1) and curve (equation y2)
        • [b/a (y1 - y2)
      • trapezium rule: [b/a dx = 1/2 h[y0+2(y1+y2...+yn-1)+yn]

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