Maths Formule

Maths Formule

1. Pythagoras Theorem

   • A2 + B2 = C2

2. Percentage Increase

   • Price x Multiplier to the power of years

3. Cumulative Frequency

   • Addition of Frequencies (ongoing)

4. Trigonometry

   • SOHCAHTOA
     • Sin, Opposite, Hypotenuse
     • Cos, Adjacent, Hypotenuse
     • Tan, Opposite, Adjacent
     • Theta= cos/tan/sin to the -1 (fraction)

5. Area and Volume of Similar Shapes

   • Area Scale Factor= (length scale factor)2
   • Volume Scale factor= (length scale factor)3

6. Direct Proportion

   • y oc x
   • y= kx
   • Inverse Proportion
     • y oc 1/x
     • y= k/x

7. Negative and fractional indicies

   • 2 to the power of -1= 1/2 to the power of 1= 0.5
     • Rule: a to the -n= 1/a to the power of n
     • 5, square root, n= n 1/5

8. Equation of a straight line

   • y= mx + c
     • m= gradient
     • c= where it crosses the y axis (y intercept)

9. Factorise expressions of the form x2-b2

   • Rule: x2-a2 factorises to (x+a)(x-a)

10. Reverse Percentages

    • Original amount= new amount/ multiplier
    • New amount= original amount x multiplier

11. Midpoint of a line

    • For coordinates (a,b) and (c,d)...
      • (a+c divided by 2, b+d divided by 2)

12. Quartiles

    • median= half way
    • upper quartile= 3/4
    • lower quartile= 1/4

13. Difference between two points

    • (all in a square root) --> (change in x)2 + (change in y)2 + (change in z)2

14. Frequency Density

    • Frequency/ width of group

15. Upper and Lower bounds

    • When multiplying--> to find upper bound= multiply the upper bounds. To find lower bound, multiply by lower bounds
    • 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

16. Sine Rule

    • a/ SinA= b/SinB= c/SinC
    • SinA/a = SinB/b = SinC/c
    • Cosine Rule
      • c2= a2 + b2 - 2abCosC
        • CosC= a2 + b2 - c2/ 2ab

17. Area of a triangle

    • 1/2 base x height
    • Area of triangle ABC= 1/2 acSinB, 1/2 bcSinA, 1/2 abSinC

18. The length of an arc

    • Theta/ 360 x pie x diametre
    • Area of a sector
      • Theta/ 360 x pie x radius squared

19. Volume of a prism

    • area of cross section x height
    • Volume of a cone
      • 1/3 pie x radius squared x height
      • Volume of a sphere
        • 4/3 x pie x radius cubed

20. Surface area of a cone

    • Curved surface area= pie x radius x length
    • Total surface area= (pie x radius x length) + (pie x radius squared)