# CORE 2

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• Created on: 24-05-16 10:26
• 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 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]