Pure

• A polynomial only has positive indices
• The degree of a polynomial is the highest power
• If f(a)=0 then (x-a) is a factor of f(x)
• if (2)^3-3(2)^2-10(2)+24=0 then x-2 is a factor
• if x-2=0 you would substitute 2 into a polynomial to check if it is a factor
• to divide a polynomial you divide x out of the first value then times this by the thing you are dividing by
• law of indices a^-n=1/a^n
• When sketching the polynomial y=2(x-2)(x-3)(x-4) the y intercept would be -48 and it would cross the x axis at 2,3,4.
• If you had (x-3)^2 when the 3 is plotted on the x axis you would draw it bouncing off the axis rather than it going through the axis.
• The discriminant is what is under the square root.
• If b squared-4ac>0 then there are 2 real solutions.
• If b squared-4ac=0 there is one repeated root.
• If b squared-4ac<0 it has no real roots
• If it asks about a tangent to the axes it has one solution.
• If it says the equation has real roots you use a > but also equal to sign
• Equation of line (y-y1)=m(x-x1)
• To find the distance between 2 points - square root of (x2-x1)^2+(y2-y1)^2
• Midpoint of 2 coordinates is (x1+x2/2),(y1+y2/2)
• dy/dx = nx^n-1
• second derivative >0 then it is a minimum point
• second derivative <0 then it is a maximum point
• second derivative = 0 then no conclusions can be draw
• translation (3/0) replace x with x-3
• translation (0/4) replace y with y-4
• stretch (x direction scale factor of 2) replace x with x/2
• stretch (y direction scale factor 3) replace y with y/3
• reflection in x axis replace y with -y
• reflection in y axis replace x with -x
• tan x = sin x /cos x
• cos^2 x + sin^2 x = 1
• When there is a different number of x need to change limits
• f'(x)=lim h to 0 f(x+h) - f(x)/h
• Wherever the tangent is flat on a curve the derivative is 0
• a=b^x ---> logb (a)=x
• the logarithm of a negative number or 0 is not a real number.
• log10 x is written as log x

  loge x is written as ln x --->natural log
• loga (a^x) =x a^log a^x =x

  when a=e

  ln(e^x) =x e^lnx =x
• loga xy = loga x +loga y

  loga x/y = loga x - loga y

  loga x^k = kloga x

  loga 1 = 0
• y = e^kx

  dy/dx = ke^kx
• To integrate a term you add one to the power and then divide by the power.