luisnorth
Mind Map by , created over 5 years ago

A Levels Maths Mind Map on C1, created by luisnorth on 02/25/2014.

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luisnorth
Created by luisnorth over 5 years ago
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C1
1 Simultaneous Equations & Disguised Quadratics
1.1 Linear
1.1.1 Add/ subtract the two equations to eliminate one variable
1.1.2 Set one equal to y or x and substitute in
1.2 Quadratic
1.2.1 Substitution
1.3 Disguised Quadratics
1.3.1 Some equations- eg x^4-x^2-5=0 can be converted to quadratic equations to solve more easily
1.3.2 If there are three orders, ie x^4, x^2, x^0
1.3.3 let A = the middle order, therefore highest order = A^2
2 Quadratics
2.1 eg 4x^2+3x+7=0
2.2 Solving
2.2.1 If the equation factorises
2.2.1.1 Each bracket = 0
2.2.1.2 eg.(4x+3)(x-2)=0
2.2.1.2.1 x = -3/4 or x = 2
2.2.2 If does not factorise...
2.2.2.1 Quadratic formula
2.2.2.1.1 x= (-b ± √(b^2-4ac) ) / 2a
2.2.2.2 Complete the square
2.2.2.2.1 x^2 ± bx = (x±b/2)^2 - (b/2)^2
2.2.2.2.1.1 Rearrange to find one or two values of x
2.2.2.2.2 a(x+b)^2 + c
2.2.2.2.2.1 Vertex = (-b, c )
2.3 Inequalities
2.3.1 If multiplying or dividing by a negative number, REVERSE the sign
2.3.2 Quadratic
2.3.2.1 Set so that equation = 0
2.3.2.2 Factorise
2.3.2.3 If equation > 0 it is where the graph is above the x axis
2.3.2.4 If equation < 0 it is where the graph is below the x axis
2.4 Intersections of lines
2.4.1 Set equal to eachother to eliminate y
2.4.2 Remember to get the y values at the end by re-substituting the x values
3 Gradients, tangents and normals
3.1 To find a gradient, differentiate the equation and then substitute in the x value
3.2 The tangent to a curve has the same gradient as the point on the curve it touches
3.3 y+y-value= m (x + x-value)
3.4 Stationary points
3.4.1 when dy/dx = 0
3.4.2 solve dy/dx=0 to find stationary points
3.4.3 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
4 Coordinate Geometry, Lines and Circles
4.1 Midpoints, gradients and distance between two points
4.1.1 Point A => (x,y) Point B => (w,z)
4.1.1.1 midpoint = ( (x+w)/2 , (y+z)/2 )
4.1.1.2 length of the line through AB = √{ (x+w)^2 + (y+z)^2 }
4.1.1.3 Gradient = (x-w)/(y-z)
4.2 equation of a line through (a,b) with gradient m is y-b = m(x-a)
4.3 Circles
4.3.1 Equation of a circle centre (a,b) radius r = (x-a)^2 + (x-b)^2 = r^2
5 Surds and indices
5.1 Surds
5.1.1 √m x √n = √mn
5.1.2 √m / √n = √(m/n)
5.1.3 To simplify k/√a multiply by √a / √a
5.2 Indices
5.2.1 a^(-n) = 1/(a^n)
5.2.2 a^n x a^m = a^(m+n)
5.2.3 a^m / a^n = a^(m-n)
5.2.4 (a^m)^n = a^(m x n)
5.2.5 a^0 = 1
5.3 a ^ (1/n) = n√a
5.4 a^ (m/n) = n√a^m
6 Curve sketching and transformations
6.1 any graph of the form y=x^n pass through (0,0) and (1,1)
6.2 y=f(x)
6.2.1 y=f(x) + a is a transformation a units upwards
6.2.2 y=f(x+a) is a transformation -a units to the right
6.2.3 y = f(ax) is a stretch sf 1/a parallel to x axis
6.2.4 y = af(x) is a stretch sf a parallel to y axis

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