Maths Formule

Maths Formule

Pythagoras Theorem
1. A2 + B2 = C2
Percentage Increase
1. Price x Multiplier to the power of years
Cumulative Frequency
1. Addition of Frequencies (ongoing)
Trigonometry
1. SOHCAHTOA
  1. Sin, Opposite, Hypotenuse
  2. Cos, Adjacent, Hypotenuse
  3. Tan, Opposite, Adjacent
  4. Theta= cos/tan/sin to the -1 (fraction)
Area and Volume of Similar Shapes
1. Area Scale Factor= (length scale factor)2
2. Volume Scale factor= (length scale factor)3
Direct Proportion
1. y oc x
2. y= kx
3. Inverse Proportion
  1. y oc 1/x
  2. y= k/x
Negative and fractional indicies
1. 2 to the power of -1= 1/2 to the power of 1= 0.5
  1. Rule: a to the -n= 1/a to the power of n
  2. 5, square root, n= n 1/5
Equation of a straight line
1. y= mx + c
  1. m= gradient
  2. c= where it crosses the y axis (y intercept)
Factorise expressions of the form x2-b2
1. Rule: x2-a2 factorises to (x+a)(x-a)
Reverse Percentages
1. Original amount= new amount/ multiplier
2. New amount= original amount x multiplier
Midpoint of a line
1. For coordinates (a,b) and (c,d)...
  1. (a+c divided by 2, b+d divided by 2)
Quartiles
1. median= half way
2. upper quartile= 3/4
3. lower quartile= 1/4
Difference between two points
1. (all in a square root) --> (change in x)2 + (change in y)2 + (change in z)2
Frequency Density
1. Frequency/ width of group
Upper and Lower bounds
1. When multiplying--> to find upper bound= multiply the upper bounds. To find lower bound, multiply by lower bounds
2. When dividing--> to find upper bound= divide the upper bound by the lower bound. To find lower bound= divide the lower bound by the upper bound
Sine Rule
1. a/ SinA= b/SinB= c/SinC
2. SinA/a = SinB/b = SinC/c
3. Cosine Rule
  1. c2= a2 + b2 - 2abCosC
    1. CosC= a2 + b2 - c2/ 2ab
Area of a triangle
1. 1/2 base x height
2. Area of triangle ABC= 1/2 acSinB, 1/2 bcSinA, 1/2 abSinC
The length of an arc
1. Theta/ 360 x pie x diametre
2. Area of a sector
  1. Theta/ 360 x pie x radius squared
Volume of a prism
1. area of cross section x height
2. Volume of a cone
  1. 1/3 pie x radius squared x height
  2. Volume of a sphere
    1. 4/3 x pie x radius cubed
Surface area of a cone
1. Curved surface area= pie x radius x length
2. Total surface area= (pie x radius x length) + (pie x radius squared)

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