Section Two - Algebra

Section Two - Algebra

1. Basics

   • Negative Numbers
     • + + makes +
       • + - makes -
         • - + makes _
           • - - makes +
   • letters multiplied
     • abc = a x b x c
       • gn2 = g x n x n
         • (gn)2 = g x g x n x n
           • p(q-r)3 = p x (q-r) x (q-r) x (q-r)

2. Powers and Roots

   • Rules
     • When multiplying, you add the powers
       • When dividing, you subtract the powers
         • When raising one power to another, you multiply them
           • Anything to the power of 1 equals itself
             • Anything to the power of 0 is 1
               • 1 to any power is still 1
                 • Fractions - Apply the power to the top and bottom
   • Tricky rules
     • Negative powers - turn it upside down (Reciprocal)
       • Fractional powers - 1/2 = Square root, 1/3 = Cube root, 1/4 = Fourth root
         • Two-stage Fractional powers - with powers like 64 5/6, always split the fraction into a root and power,

3. Brackets

   • Single Brackets
     • The number outside the brackets multiplies each term inside the bracket
     • 4a(3b-2c)
       • 12ab - 8ac
   • Double Brackets
     • Multiply everything in the first bracket by everything in the second bracket
       • FOIL method
         • First - multiply the first term in each bracket together
           • Outside - multiply the outside terms
             • Inside - multiply the inside terms
               • Last - multiply the second term in each bracket together
     • (2p - 4)(3p + 1) = 6p2 + 2p -12p -4
       • 6p2 - 10p -4
   • Triple Brackets
     • Multiply the first two brackets
       • Then multiply the product by the third bracket