C1 - created from Mind Map

Simultaneous Equations & Disguised Quadratics Linear Quadratic Disguised Quadratics Add/ subtract the two equations to eliminate one variable Set one equal to y or x and substitute in Substitution Some equations- eg x^4-x^2-5=0 can be converted to quadratic equations to solve more easily If there are three orders, ie x^4, x^2, x^0 let A = the middle order, therefore highest order = A^2

Quadratics eg 4x^2+3x+7=0 Solving Inequalities Intersections of lines If the equation factorises If does not factorise... Each bracket = 0 eg.(4x+3)(x-2)=0 x = -3/4 or x = 2 Quadratic formula Complete the square x= (-b ± √(b^2-4ac) ) / 2a x^2 ± bx = (x±b/2)^2 - (b/2)^2 a(x+b)^2 + c Rearrange to find one or two values of x Vertex = (-b, c ) If multiplying or dividing by a negative number, REVERSE the sign Quadratic Set so that equation = 0 Factorise If equation > 0 it is where the graph is above the x axis If equation Set equal to eachother to eliminate y Remember to get the y values at the end by re-substituting the x values

Gradients, tangents and normals To find a gradient, differentiate the equation and then substitute in the x value The tangent to a curve has the same gradient as the point on the curve it touches y+y-value= m (x + x-value) Stationary points when dy/dx = 0 solve dy/dx=0 to find stationary points Differentiate dy/dx to give d^2y/dx^2 . Substitute in x values, if negative then it is a max point, if positive it is a min point

Coordinate Geometry, Lines and Circles Midpoints, gradients and distance between two points equation of a line through (a,b) with gradient m is y-b = m(x-a) Circles Point A => (x,y) Point B => (w,z) midpoint = ( (x+w)/2 , (y+z)/2 ) length of the line through AB = √{ (x+w)^2 + (y+z)^2 } Gradient = (x-w)/(y-z) Equation of a circle centre (a,b) radius r = (x-a)^2 + (x-b)^2 = r^2

Surds and indices Surds Indices a ^ (1/n) = n√a a^ (m/n) = n√a^m √m x √n = √mn √m / √n = √(m/n) To simplify k/√a multiply by √a / √a a^(-n) = 1/(a^n) a^n x a^m = a^(m+n) a^m / a^n = a^(m-n) (a^m)^n = a^(m x n) a^0 = 1

Curve sketching and transformations any graph of the form y=x^n pass through (0,0) and (1,1) y=f(x) y=f(x) + a is a transformation a units upwards y=f(x+a) is a transformation -a units to the right y = f(ax) is a stretch sf 1/a parallel to x axis y = af(x) is a stretch sf a parallel to y axis

C1