MATHS

• How the trapezium rule can be used to give more accurate area?

  increase no. Of trapezium
• How can a model be refined?

  with context, include thickness, model shape more accurately
• Why wouldn’t a function have an inverse?

  If it is a many to one function (there are more than one inputs with same output)
• If y = a^x

  Dy/dx = a^x ln(a)
• What makes a solution including small angles valid?

  If the angle answer is small; less than or equal to 0.26 rad or 15°
• 1 + t^2 = sec^2
• 1 + ct^2 = cosec ^2
• Dy/dx cosx ?

  -sinx
• Dy/dx sinx?

  cosx
• Intergral of sinx?

  -cosx
• Intergral of cos x?

  sin X
• Intergral of 1/x?

  ln (x)
• Increasing function?

  f’(x)>0
• Decreasing function?

  f(x)<0
• Minimum point?

  f“(x)>0
• Maximum point?

  f”(x)<0
• POI?

  f”(x)=0
• one real root?

  b^2 -4ac = 0
• Two real roots?

  b^2-4ac >0
• No real roots?

  b^2-4ac <0
• Product rule is differentiation and used when there is a product.
• Product rule?

  UV‘ + VU’
• Chain rule?

  dy/dx = dy/dt x dt/dx
• Quotient rule?

  vu’ - uv’/ v^2
• Intergrating parametrics?

  dy/dx = dy/dt / dx/dt
• Newton raphson formula

  X n+1 = Xn - f(xn) / f’(xn)
• when does the newton raphson method not work?

  when theres a turning point to what x =, and so f’(x) = 0.
• Rational number can be written as

  a / b
• Domain is the set of all possible inputs
• Range is the set of all possible outputs
• One to one and many to one are both mappings that are functions
• fg(x) =?

  f (g(x))
• The domain of f(x) is the range of f-1(x)
• The range of f(x) is the domain of f-1(x)
• The graph of |f(x)| reflects in the x axis and deletes any sections below the x axis
• F(x +a) is translation by vector (-a , 0) (all x values - a)
• F(x) + a translation by vector (0,a) all y values + a
• F(-x) is a reflection in the y axis
• -f(x) reflects in x axis
• F(ax) is a horizontal stretch of scale factor 1/a