Maths

Maths

1. Surds

   • Rather than rounding we can use surds
     • x^2=4^2+2^2 =16+4 =20=root of 20= root4xroot5=2root5
     • Surd basic rule; rootA/b=rootA/rootB
   • Rationalising the denominator
     • Convention in maths is not to have surds on the bottom of any fractions
       • e.g 2/root3 =2/root3 x root3/root3 =2root3/3

2. Arc length; ArcAB=x/360 x 3.14D

3. Area and volume

   • Sphere; 4/3 x 3.14 xr^3
   • Cone; 1/3 x 3.14 xr^2h
   • Cylinder; 3.14xr^2xh
   • Pyramid; 1/3AH

4. Function notation

   • 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
     • If we call the function f the input x gives us f(x)
       • e.g f(x)=x+5...f(3)=8 as (3)+5 as the input is x

5. Quadratic equations

   • Basic principal is you multiply 2 numbers together to get zero, then one of them must be zero
     • e.g x(x-3)... x=0 or x=2
   • Factorising quadratics
     • Remeber basic steps; 1.common factor, 2difference of squares, 3trinomals
       • Difference of squares
         • e.g x^2-9=(-3)(x+3)
       • Trinomals
         • e.g x^2+8x+12=(x+2)(x+6)
       • e.g x^2+9x= (X-3)(x+3)

6. Vectors

   • Vectors are simple addition and subtraction of numbers within a bracket
     • (3)+(-2)=(1)

7. Completing the square

   • It is sometimes useful to express trinomals in a squared form
     • The most basic form is (x+p)^2+q
       • Changing this is called completing the square
         • Half the x term gives you the number in brackets, then subtract that number squared
           • e.g x^2+8x =(x+4)^2-16

8. Gradient

   • M=y^2-y^1/x^2-x^1
     • e.g 3-5/4-0 =-2/4 =-1/2

9. Algerbraic operations

   • Simplifying fractions
     • 2x/8y =x/4y
       • advanced e.g (x-4)^3(x+2)/(x+2)^4(x-4) =(x-4)^2/(x+2)^3
   • Cancelling factors
     • You can only cancel terms in a numerator and demoninator if both involve multiplication, you cant cancel addition or subtraction
       • e.g a+b/b+c =a/c
         • advanced e.g x+3/x^2+4x+3 =x+3/ (x+3)(x+1) =!/x+1
   • adding or subracting
     • As with normal fractions, we need a common denominator
       • e.g 2/x+1/y =2y/xy+x/xy =2y+x/xy =2

10. Quadratic formula

    • If we have the quadratic equation ax^2+bx+c=0 the solutions can be found using this formula

11. Determining the nature of roots

    • We can use the discriminant to help us determine the nature of the roots
    • There are 3 possibilites
      • If the discriminant>0 then we have 2 distinctive roots
        • If the discriminant=0 then we have no real roots
          • If the discriminant is<0 then we have no real roots
    • THE DISCRIMINANT

12. Solving Trig equations

    • To solve trig equations for angles use ASTC which stand for acute angle, Sin, Cos and Tan

13. 5 Figure summaries

    • 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

14. Standard Deviation

    • This is to work out the mean
    • n= number of data

Images and files in the map