A level maths pure

• Sin2x = 2sinxcosx
• Cos2x = cos^2 x - sin^2 x
• Cos2x = 1 - 2sin^2x
• Cos2x = 2cos^2x - 1
• Tan2x = 2tanx / 1 -tan^2x
• Discriminant = b^2 + 4ac
• If the discriminant is positive, there are two real roots.
• If the discriminant is negative, there are no real roots.
• If the discriminant is zero, there is one repeated root (a double root).
• Ln 1/x = -lnx
• a^2 = b^2 + c^2 - 2bc(cosA)
• Arc length = r0
• Sector area = 0.5 x r^2x0
• Segment area = 0.5 x r^2 x (0-sin0)
• F(x) + a = y coordinate + a
• Af(x) = y coordinate x a
• -f(x) = flip and reflect In x axis
• |f(x)| = below the x axis flips up
• F(x + a) = x coordinate - a
• F(ax) = x coordinate x 1/a
• F(-x) = flip reflection in y axis
• F(|x|) = right of the y axis reflects in left side
• Small angle approx = sin0 and tan0 are 0
• Small angle approx = cos0 becomes 1 - 0^2/2
• Co functions: sin0/cos0 = cos/sin (90-0)
• Sin^2 + cos^2 = 1
• 1 + tan^20 = sec^20
• 1 + cot^20 = cosec^20
• Rearranged DAF sin^20 = 1/2 - 1/2cos20
• Rearranged DAF cos^20 = 1/2 + 1/2cos20
• If Rcosc : a and Rsinc : b = R : root of a^2 + b^2 and tanc : b/a
• Second derirative > 0 = convex/min
• Second derirative < 0 = concave/max
• Second derirative : 0 = point of inflection
• First derirative < 0 = decreasing
• First derivative > 0 = increasing
• dx e^x = e^x
• dx lnx = 1/x
• Dx sinx = cosx
• Dx cosx = -sinx