maths pure

• Trigonometry --> sohcahtoa
• what is the sine angle formula?


  $a^2=$$b^2+$$c^2-2bc(cosA)$
• $cos^2(θ) +$$sin^2(θ)=$$1$
• $tanθ=$$sinθ / cosθ$
• area of triangle?

  $1/2 (ab(sin)c)$
• what is factor theorem?

  The factor theorem states that if a polynomial f(x) has a factor (x - a), then f(a) = 0.
• when do you use pascal's triangle?

  for binomial expansions eg. $(x+1)^2 =$$x^2+$$2x+$$1$
• what is the formula for binominal expansions when the power is to big for pascal's triangle?


  $^ncr^2=$$n!/r!(n-r)!$

  example :

  $^6c2=$$6!/2!(6-2)! =$$6x5x4x3x2x1/2x1(4x3x2x1) =$$6x5/2 =$$15$

  c stands for pascels triangle

  n stands for the row in the triangle eg 6th row down which has the formula - 1 6 15 20 15 6 1

  r stands for the number across ( the first one is 0) therefore 6C2 is 15
• what is the complete the square formula?

  $(x + a)^2-b$
• what are the steps for completing the square?

  1. divide coefficent of x by 2
  2. put in $( ......)^2$
  3. subtract new number squared
  4. simplify

  example

  write $x^2 +$$8x+$5 _____in the form_____ (x-a)^2-b

  1. 8/2 = 4
  2. $(x+4)^2$
  3. $(x+4)^2-16+$$5$
  4. $(x+4)^2-11$
• what is the quadratic formula?

  $x=$$-b(+or-) √b^2-4ac/2a$
• when do you use the quadratic formula?


  for when u cant factorise quadratics
• what is the discriminat?


  b^2-4ac
• when do you use the discriminat?

  it is related to quadratic graphs and their roots

  >0 = 2 distinct roots

  <0 = no roots

  =0= repeated (1) roots
• what is the equation to find the gradient of a line from 2 cordinates?

  rise /run

  $y(2)-y(1)/x(2)-x(1)$
• what is the equation for the mid point when given 2 cordinates?


  $[x(1)+$$x(2)/2, y(1)+$$y(2) /2]$
• what is the equation of a line when given 2 cordinates?


  $√[(x(2)-x(1))^2+$$(y(2)+$$y(1))^2]$
• parallel lines have the same gradient
• perpendicular lines have the negative reciprocal gradient
• what are the 2 equations for strait lines?

  1. y=mx+c
  2. y-y(1)=m[x-x(1)]
• to find the intersection of 2 lines = simultaneous equations
• what is the equation of a circle?

  $x^2 +$$y^2 =$$r^2$

  (x,y) radius = r
• any triangle in a circle is a right angle trinagle where the line goes through the diameter
• a radius and tanget are perpendicular
• the perpendicualr bisector of a chord will always go through the center
• describe the transformation of the graph $y=$$x^2$to $y=$$(x+2)^2-4$


  it has moved -2 in the x direction and -4 in the y direction and has a vector of
• describe the transformation of the graph y=f(x) into a. y=-f(x) and b. y=f(-x)?


  A.reflection in the x axis

  b. reflection in the y axis
• describe the transformation of the graph y=sin(x) into a. y=sin2x and b. y=2 sinx ?


  a.stretch by 1/2 in the x axis

  b. stretch by 2 in the y axis
• why do you use differentiation? ( dy/dx)

  to find a gradient
• what are the steps for differentiation?

  mutliply the old power by number before the x

  reduce the power by 1
• what is the normal?

  perpendular to the tangent
• how do you find the range of value of x which are decreasing ?

  meaning negative gradient so when dy/dx <0
• how do you find the range of vaules of when a function is increasing?

  means when the gradient is positive and therefore when dy/dx >(or=)0
• what is the use of the second deritive?

  to find the nature of the curve and the change in gradient ...

  $d^2y/dx^2=$$negative$ then it is a max point

  $d^2y/dx^2=$$positive$ then it is a min point

  if it =0 then it is a inflection point
• negative powers are the same as fractions eg 1/x is the same as $x^(.^-.^1.^)$ ( ignore the dots they are there because of formating on the website)
• fractional powers are the same as square roots eg $√x =$$x^1.^/.^2$
• what is the equation of surface area of a cilinder?

  $sa=$$2πr^2+$$2πrh$
• what is the equation of volume of cilinder?

  $v=$$πr^2h$
• If you differentiate a derivative, you get the second derivative.
• If you start with an equation for y in terms of x, the first derivative is dy/dx and the second derivative is written 2nd derivative.