MATHS

MATHS

1. NUMBERS

   • FRACTIONS
     • Adding/Subtracting-BOOM BOOM POW
       • 1/4 + 7/10
         • 4 X 7 = 28 and 1 x 10 = 10
           • 4 x 10 = 40, so 28 + 10 = 38/40-19/20
     • Multiplying
       • Multiply numerators together
         • Multiply denominators together
           • Simplify if possible
     • Dividing
       • Multiply the reciprocal of the fracton and continue working out like you would with multiplying
     • Recurring decimals to fractions
       • Let x equal the number being converted
         • x = 0.45454545...
         • multiply by 10 then 100
           • 10x =4.54545... and 100x =45.4545...
           • Subtract x from 100x as they have the same 1st decimal
             • 100x - x = 45= 99x
             • divide both sides by 99 and simplify if possible
               • x = 45/99 or 5/11
   • INDICIES
     • Laws of indicies
       • a^b x a^c = a^b+c -Multiplying
         • a^b/a^c = a^b-c -Dividing
           • (a^b)^c -Power to power
     • Negative indicies
       • a^-b = 1/a^b
       • a^0 = 1
     • Fractional indicies
       • The power of 1/2 means the square root
         • 25^1/2 = 5
       • A power of a fraction like 2/3 means 1st root the number, 2nd square it
         • 27^2/3 = 9
           • Cube root 27 = 3
             • 3^2 = 9
   • STANDARD FORM
     • 134000 = 1.34 x 10^5
     • 0.000765 = 7.65 x 10^-5
   • PERCENTAGES
     • Percentage change
       • change/original x 100
         • Eg- car bought for £4000 then sold for £3500, calc % decrease
           • 500/4000 x 100
             • 0.125 x 100
               • 12.5%
     • Reverse percentages
       • Divide by % then x by 100
         • Car sold for £7650, 15% less than what he bought it as, what was original price
           • 100%-15% = 85%
             • 85% = £7650
               • /85
               • 1% = £90
                 • x 100
                 • 100% = £9000
     • Compound interest
       • Initial x multiplier^time
         • 8000 x 1.05^3 = £9261
           • Multiplier for a 5% increase
           • Initial amount invested
           • Money invested for 3 years
   • DIRECT AND INVERSE PROPORTION
     • Direct
       • C is directly proportional to D when C=200, D=2 find C when D=5
         • Can be to the square/cube etc
         • C ~ D
           • C = K x D
             • K= the constant of proportionality
             • 200 = K x 2
               • Substitute in C and D
               • 200/2 = K = 100
                 • Work out K
                 • So to find C when D = 5 the formula is
                   • C = 100 x 5
                     • C = 500
     • Inverse
       • P is inversely proportional to Q when P=10, Q=2 find P when Q=4
         • Can be to square/cube etc
         • P ~ 1/Q
           • P = K/Q
             • 10 = K/2
               • Substitute in P and Q
               • 10 x 2 = K = 20
                 • Work out K
                 • So to fine P when Q= 4 the formula is
                   • P=20/4
                     • P=5