Mind Map by , created over 5 years ago

national 5 Maths Mind Map on Maths, created by reeceyboy.victor on 01/23/2014.

Created by reeceyboy.victor over 5 years ago
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1 Surds
1.1 Rather than rounding we can use surds
1.1.1 x^2=4^2+2^2 =16+4 =20=root of 20= root4xroot5=2root5
1.1.2 Surd basic rule; rootA/b=rootA/rootB
1.2 Rationalising the denominator
1.2.1 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
3.1 Sphere; 4/3 x 3.14 xr^3
3.2 Cone; 1/3 x 3.14 xr^2h
3.3 Cylinder; 3.14xr^2xh
3.4 Pyramid; 1/3AH
4 Function notation
4.1 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
4.1.1 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
5.1 Basic principal is you multiply 2 numbers together to get zero, then one of them must be zero
5.1.1 e.g x(x-3)... x=0 or x=2
5.2 Factorising quadratics
5.2.1 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
6.1 Vectors are simple addition and subtraction of numbers within a bracket
6.1.1 (3)+(-2)=(1)
7 Completing the square
7.1 It is sometimes useful to express trinomals in a squared form
7.1.1 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
8.1 M=y^2-y^1/x^2-x^1
8.1.1 e.g 3-5/4-0 =-2/4 =-1/2
9 Algerbraic operations
9.1 Simplifying fractions
9.1.1 2x/8y =x/4y advanced e.g (x-4)^3(x+2)/(x+2)^4(x-4) =(x-4)^2/(x+2)^3
9.2 Cancelling factors
9.2.1 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
9.3 adding or subracting
9.3.1 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
10.1 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
11.1 We can use the discriminant to help us determine the nature of the roots
11.2 There are 3 possibilites
11.2.1 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
12 Solving Trig equations
12.1 To solve trig equations for angles use ASTC which stand for acute angle, Sin, Cos and Tan
13 5 Figure summaries
13.1 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
14 Standard Deviation
14.1 This is to work out the mean
14.2 n= number of data