WISKUNDE
GRAAD 11
NOG OEFENINGE
  
Oplos van kwadratiese vergelykings, vierkantsvergelykings.
  
MATHEMATICS
GRADE 11
MORE EXERCISES
  
Solving quadratic equations.
  
  
A
  
                                 Los onderstaande vergelykings op deur faktore te gebruik :                 Solve the following equations by using factors :
  
          1.  x 2 + 4x + 3 = 0                                          [ 1 ]
  
          3.  y 2 - 3y + 2 = 0                                           [ 3 ]
  
          5.  a 2 + a - 2 = 0                                             [ 5 ]
  
          7.  3p 2 - 3p - 4 = 0                                         [ 7 ]
  
          9.  x 2 - 4x - 21 = 0                                          [ 9 ]
  
        11.  3y 2 - 11y + 10 = 0                                  [ 11 ]
  
        13.  15z 2 + 3z - 6 = 0                                    [ 13 ]
  
        15.  35b 2 - 22b - 24 = 0                                [ 15 ]
  
        17.  −p 2 - 2p + 5 = 0                                      [ 17 ]
  
  
  
          2.  x 2 + 7x + 10 = 0                                   [ 2 ]
  
          4.  y 2 - 10y + 21 = 0                                 [ 4 ]
  
          6.  b 2 - b - 6 = 0                                        [ 6 ]
  
          8.  q 2 + 2q - 15 = 0                                  [ 8 ]
  
        10.  2x 2 + 3x + 1 = 0                               [ 10 ]
  
        12.  6z 2 + 13z + 6 = 0                             [ 12 ]
  
        14.  6a 2 - 7a - 20 = 0                               [ 14 ]
  
        16.  −y 2 + 3y - 2 = 0                                 [ 16 ]
  
        18.  -3y 2 + 11y - 10 = 0                           [ 18 ]
  
  
  
  
B
  
                                 Los die volgende vergelykings op deur die formule                        Solve the following equations by using the formula
                                 formule te gebruik en gee jou antwoord korrek                                 and give your answer correct to two decimals
                                 tot 2 desimale :                                                                                    where necessary :
  
        19.  x 2 + x ─ 3 = 0                                         [ 19 ]
  
        21.  z 2 + 4z + 1 = 0                                       [ 21 ]
  
        23.  b 2 + 7b ─ 4 = 0                                      [ 23 ]
  
        25.  3b 2  ─ 4b ─ 5 = 0                                   [ 25 ]
  
        27.  5x 2  ─ 3x ─ 2 = 0                                    [ 27 ]
  
        29.  −3z 2  ─ 4z = ─ 9                                     [ 29 ]
  
        20.  y 2  ─ y ─ 5 = 0                                    [ 20 ]
  
        22.  a 2  ─ 5a + 2 = 0                                  [ 22 ]
  
        24.  2a 2  ─ a + 1 = 0                                  [ 24 ]
  
        26.  4p 2  ─ p ─ 7 = 0                                 [ 26 ]
  
        28.  ─ 2y 2 + 8y = 7                                     [ 28 ]
  
        30.  ─ 4a 2 + 1 = 3a                                     [ 30 ]
  
  
C
  
                                 Los die volgende vergelykings op deur die vierkant                        Solve the following equations by completing the square
                                 te voltooi en gee jou antwoord korrek tot 2 desimale,                     and give your answer correct to two decimals
                                 indien nodig :                                                                                       where necessary :
  
        31.  q 2  ─ 2q ─ 3 = 0                                     [ 31 ]
  
        33.  y 2  ─ 2y ─ 8 = 0                                      [ 33 ]
  
        35.  2a 2  ─ 3a + 4 = 0                                    [ 35 ]
  
        37.  ─ p 2  ─ 3p + 7 = 0                                  [ 37 ]
  
        39.  ─ 3x 2 + 4x = 7                                         [ 39 ]
  
        32.  x 2 + 3x ─ 4 = 0                                    [ 32 ]
  
        34.  3z 2 + z ─ 2 = 0                                    [ 34 ]
  
        36.  5b 2 + b + 6 = 0                                   [ 36 ]
  
        38.  ─ 2q 2 + 5q ─ 6  =  0                           [ 38 ]
  
        40.  ─ x 2 + 2x + 8 = 0                                 [ 40 ]
  
  
  
  
  
  
  
  
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