Maths

Maths

Surds
1. Rather than rounding we can use surds
  1. x^2=4^2+2^2 =16+4 =20=root of 20= root4xroot5=2root5
  2. Surd basic rule; rootA/b=rootA/rootB
2. Rationalising the denominator
  1. Convention in maths is not to have surds on the bottom of any fractions
    1. e.g 2/root3 =2/root3 x root3/root3 =2root3/3
Arc length; ArcAB=x/360 x 3.14D
Area and volume
1. Sphere; 4/3 x 3.14 xr^3
2. Cone; 1/3 x 3.14 xr^2h
3. Cylinder; 3.14xr^2xh
4. Pyramid; 1/3AH
Function notation
1. In maths a function is a rule which tells you how to take a number as an INPUT and get a number as an OUTPUT
  1. If we call the function f the input x gives us f(x)
    1. e.g f(x)=x+5...f(3)=8 as (3)+5 as the input is x
Quadratic equations
1. Basic principal is you multiply 2 numbers together to get zero, then one of them must be zero
  1. e.g x(x-3)... x=0 or x=2
2. Factorising quadratics
  1. Remeber basic steps; 1.common factor, 2difference of squares, 3trinomals
    1. Difference of squares
      1. e.g x^2-9=(-3)(x+3)
    2. Trinomals
      1. e.g x^2+8x+12=(x+2)(x+6)
    3. e.g x^2+9x= (X-3)(x+3)
Vectors
1. Vectors are simple addition and subtraction of numbers within a bracket
  1. (3)+(-2)=(1)
Completing the square
1. It is sometimes useful to express trinomals in a squared form
  1. The most basic form is (x+p)^2+q
    1. Changing this is called completing the square
      1. Half the x term gives you the number in brackets, then subtract that number squared
        e.g x^2+8x =(x+4)^2-16
Gradient
1. M=y^2-y^1/x^2-x^1
  1. e.g 3-5/4-0 =-2/4 =-1/2
Algerbraic operations
1. Simplifying fractions
  1. 2x/8y =x/4y
    1. advanced e.g (x-4)^3(x+2)/(x+2)^4(x-4) =(x-4)^2/(x+2)^3
2. Cancelling factors
  1. You can only cancel terms in a numerator and demoninator if both involve multiplication, you cant cancel addition or subtraction
    1. e.g a+b/b+c =a/c
      1. advanced e.g x+3/x^2+4x+3 =x+3/ (x+3)(x+1) =!/x+1
3. adding or subracting
  1. As with normal fractions, we need a common denominator
    1. e.g 2/x+1/y =2y/xy+x/xy =2y+x/xy =2
Quadratic formula
1. If we have the quadratic equation ax^2+bx+c=0 the solutions can be found using this formula
Determining the nature of roots
1. We can use the discriminant to help us determine the nature of the roots
2. There are 3 possibilites
  1. If the discriminant>0 then we have 2 distinctive roots
    1. If the discriminant=0 then we have no real roots
      1. If the discriminant is<0 then we have no real roots
3. THE DISCRIMINANT
Solving Trig equations
1. To solve trig equations for angles use ASTC which stand for acute angle, Sin, Cos and Tan
5 Figure summaries
1. for a set of data a five figure summary consists of the following values; L-lowest value, Q-lower quartile, median, Q3- upper quartile, H-highest value
Standard Deviation
1. This is to work out the mean
2. n= number of data

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