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Algebra

  1. Multiplying or dividing both sides of an inequality by a negative number reverses the inequality. That is, if x > y and c < 0, then cx < cy.
  2. Transitive Property: If x < y and y < z, then x < z.
  3. Like Inequalities Can Be Added: If x < y and w < z, then x + w < y + z .
  4. Rules for exponents:

     

    xa × xb = xa + b Caution, xa + xb ≠ xa + b

    (xa)b = xab

    (xy)a = xa × ya

    xya  = xaya

    xaxb = xa − b , if a > b. xaxb = 1xb-a , if b > a.

    x0 = 1

  5. There are only two rules for roots that you need to know for the GRE:

     

    xyn=xnyn     For example, 3x =  √3 ×  √x .

    xyn = xnyn     For example, x83 = x383 = x32

    Caution: x+ynxn+yn

  6. Factoring formulas:

     

    x(y + z) = xy + xz
    x2 − y2 = (x + y)(x − y)
    (x − y)2 = x2 − 2xy + y2
    (x + y)2 = x2 + 2xy + y2
    −(x − y) = y − x

  7. Adding, multiplying, and dividing fractions:

     

    xy + zy = x+zy and xy − zy = x-zy
    Example: 24 + 34 = 2+34 = 54 .

    wx × yz = wyxz
    Example: 12 × 34 = 1×32×4 = 38 .

    wx ÷ yz =  wx × zy
    Example: 12 ÷ 34 = 12 × 43 = 46 = 23 .

  8. x% = x100
  9. Quadratic Formula: x 

-b±b2-4ac2a are the solutions of the equation ax2 + bx + c = 0.





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