# C1

Mind Map by , created over 5 years ago

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

53
4
0
 Created by luisnorth over 5 years ago
Maths C4 Trig formulae (OCR MEI)
Maths Revision- end of year test
GCSE Maths Conversions
How to Develop the Time Management Skills Essential to Succeeding in IB Courses
How does Shakespeare present villainy in Macbeth?
Transforming Graphs
Indices and Surds
C1 - Algebra And Functions
GCSE Maths Symbols, Equations & Formulae
Maths GCSE - What to revise!
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
1.2.1 Substitution
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
2.1 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...
2.2.2.1.1 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
2.3.2.1 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