# Maths C4

• 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