MATHEMATICS
Grade 11
MORE EXERCISES
Quadratic number patterns, quadratic patterns.
  
        Question  1
     Study the following quadratic number
     sequence : 8 ; 13; 20; 29; . . .
     1.1  Write down the following two
            terms.                                            [ A 1.1 ]
     1.2  Determine the general term,
            Tn.                                                 [ A 1.2 ]
     1.3  Calculate the value of the
            twenty first term, T21                     [ A 1.3 ]
     1.4  Which term is equal to 148?         [ A 1.4 ]

        Question  2
     Study the following quadratic number
     sequence : ─2 ; ─1; 4; 13; . . .
     2.1  Write down the following two
            numbers.                                    [ A 2.1 ]
     2.2  Determine the general term,
            Tn.                                              [ A 2.2 ]
     2.3  Calculate the value of the
            fifteenth term, T15.                     [ A 2.3 ]

     2.4  Which term is equal
            to 494?                                      [ A 2.4 ]

        Question  3
     The following numbers form a quadratic
     quadratic sequence : ─5;   5;   17;   31;   . . .
     3.1  Write down the following two
            nubers.                                           [ A 3.1 ]
     3.2  Determine the general term,
            Tn.                                                   [ A 3.2 ]
     3.3  Calculate the value of the
            nineth term,   T9.                             [ A 3.3 ]
     3.4  Determine the value of n
            if Tn = 355.                                      [ A 3.4 ]

        Question  4
    Given the quadratic sequence :
                 12;   7;   ─2;   ─15;   . . .
  
     4.1  Write down the following two
            numbers.                                     [ A 4.1 ]
     4.2  Determine the general term,
            Tn.                                               [ A 4.2 ]
     4.3  Calculate the value of the
            eleventh term,   T11.                    [ A 4.3 ]
     4.4  Determine the value of n
            if Tn = −617.                                [ A 4.4 ]

        Question  5
       The following numbers form a quadratic
       sequence : x;   y;   8; . . .
       The second difference of the sequence
       is 2 and the second first difference 6.
       Determine x and y.                                 [ A 5. ]

        Question  6
        Given the quadratic sequence :
             1;   p;   21;   q; . . .
  
       The second differences are equal to 4.
       Calculate the values of p and q.
                                                                  [ A 6. ]

        Question  7
       The sequence    ─ 2;   x;   y;   . . .   is a
       quadratic sequence with a constant
       second difference of 2. The difference
       between the second term and the third
       term is 7. Determine the values of x and y.
                                                                 [ A 7. ]

        Question  8
          Given the quadratic sequence
                  4;    9;    x;    37;   . . .
  
        8.1  Calculate x.                               [ A 8.1 ]
        8.2  Determine the nth term.            [ A 8.2 ]

        Department of Education, Grade 12,
        Paper 1, November 2010
  
        Question  9
         A quadratic sequence has a second term
         equal to 0, a third term equal to 6
         and a fifth term equal to 24.

        9.1  Calculate the second difference.
                                                                   [ A 9.1 ]
        9.2  Determine the first term.
                                                                   [ A 9.2 ]
  
        Question  10
              Given the quadratic sequence
               6;    7;    12;    p;    . . .
  
        10.1  Calculate the value of p.
                                                                  [ A 10.1 ]
        10.2  Determine the nth term.
                                                                  [ A 10.2 ]
        10.3  The first difference between
                  two consecutive terms of the
                  sequence is 53. Calculate the
                  value of these two terms.
                                                                  [ A 10.3 ]

        Question  11
         The general term of a quadratic
         sequence is given by
         Tn = 3(n + 2)2 ─ 4   Determine the first
         first difference. the constant second
         difference and the first term.            [ A 11. ]

        Question  12
       The pattern  −7;  −8;  −11;  −16;
       is a quadratic number pattern.
      12.1  Determine the nth term
               Tn.                                           [ A 12.1 ]

      12.2  Determine the seventeenth
               term, T17.                                [ A 12.2 ]

      12.3  Determine the value of n
               if Tn < −313.                            [ A 12.3 ]

      12.4  Between which TWO terms of
               the quadratic number pattern
               will there be a difference
               of −43?                                    [ A 12.4 ]

        Question  13
       The general term of a quadratic number
       pattern is given by −n2 + bn − 150 and the
       first term of the first difference is 15.
      13.1  Show that b = 18.                      [ A 13.1 ]
      13.2  Determine the value of T16.
                                                                 [ A 13.2 ]
      13.3  Which term is equal
                to −598?                                   [ A 13.3 ]

      13.4  Which term is the first term
                that is less than −270?             [ A 13.4 ]

      13.5  Determine the general term
               for the sequence of the first
               difference of the quadratic
               number pattern.                         [ A 13.5 ]

      13.6  Which TWO consecutive terms
               in the quadratic number pattern
               have a first difference of −5?
                                                                 [ A 13.6 ]

        Question  14
       The general term of a quadratic number
       pattern is given by 3n2 − 4n + c and the
       first term of the patern is −14.

      14.1  Show that c = −13.                    [ A 14.1 ]

      14.2  Determine the value of T7.
                                                                 [ A 14.2 ]
      14.3  Which term is the first term
               that has a value greater
               than 300?                                  [ A 14.3 ]
      14.4  Which TWO consecutive terms
               in the quadratic number pattern
               have a first difference of 125?
                                                                  [ A 14.4 ]
  
  
  
  
  
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