# Mathematics Grade 12 Paper 1 Gauteng Mock 2016 Memo

> Grade 12 Mathematics Paper 1 memorandum from the Gauteng Mock Exam 2016, 15 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/2016-grade-12-math-trial-exam-paper-1-gp-memo/2c4e675b-5dba-4830-8ca6-c8c4a7f8bc09
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Memorandum
- Year: 2016
- Exam period: Gauteng Mock Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 15

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## About this document

Mathematics · Grade 12 · Gauteng Mock Exam · 2016. Memorandum, 15 pages. Read online or download the PDF.

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## Document text

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### Page 1

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                       $&_{$,THffiffi trSffiHfffi,Sffi
                       H€FU*LIC *S S*iJT16 A$ft1{A

           PREPARATORY EXAM I NATION
                              2416
                  MEMORANDUM

             MATHEMATTCS (F|RST pApER) (10611)

15 pages

### Page 2

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                                                                                      1061 1/1 6

                          GAUTENG DEPARTMENT OF EDUCATION
                                PREPARATORY EXAMINATION

                                                    MATHEMATICS
                                                    (First Paper)

                                                    MEMORANDUM

      QTTESTTON       I
1.1   1. 1.1   3x3 + 5x=2
               3x2 + 5x-2=0                                         / standard form
               (:r-t)(r+2)=s                                        / factors
                      I
               x = 1...OR..x = -2                                   / both x values
                     J
                                                                                            (3)
      L.t.z
               J;n-r=x
               J;n=x*l
               x+7 =(x + tf                                         { x+7:(x+l)2
               x*l=x-+'2x+L
                   -a
                                                                    /standard form
               x2+x-6=0
               (x +:)(x - 2)= o                                     /factors
               x=-3 OR x=2
                N/A.                                                /N/A
                .Jt-./-                                             { x=2
                                                                                            (s)
      1.1.3    x' -8"r=10
                                                                    /standard form
               x' - 8x - 10:0

               x: -brJu'-qac
                          2a
                                                                    /substitution
               x- -(-8) r             - +(r[- ro)
                                2Q)
               .[ = 9,1   OR x=-l.,1                                / x :9,1
                                                                    /x :-1,1
                                                                                            (4)

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      1"t.4       3-t + 3-r*I.5   -8
                  3'*3-5-B
                           3'
                  32' - 9.3" + 15=0             /standard form
                                                /lfactors
                  (r' - tXr' - :)= o
                  3'"   =5 OR J =J
                  x=logr5         x=1           / x:l
                  x =1,46
                                                / x:log 5 ORx = 1,46

                  OR

                  Let 3* =k

                   &*3'5=8
                         k
                                                y'substitute with
                   k2 -8k+15 =o
                                                /standard forrn
                   (* -z)(r, - 5)= o            y'factors
                    k=3 OR k=5
                   3* =3   3* =5
                                                { x:l
                   x=l             x = log:5
                                                / x:log 5 OR x:1,46
                                   x --1,46
                                                                          (s)
1.2      22015   + 22013
                71006
               .+
                                                /factors
              Zrrrr{2, + t)
                 2"0r?                          / 2zotz
        = z(s)
                                                /answer
        =10
                                                                          (3)
                                                                         t20l

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      QUESTTON 2

2.1   kxl +Ix+1=0
      L,= b2 - 4ac
        =(k)' - +(r[r)                                       /correct substitution rn
      ...= kz - 4k                                           A

           =t(t -+)
      for non- realroots
      a<0                                                    / L<A
                                                             la and4
      k(k - 4). o                                            / inequality signs
      :.a <k <4
                                                                                        gl
2.2   2**r = 4Y....                    2**' = 4Y.......1
      x? +2y=3                         xz + 2y =3......2

      1x+l _ 17y                       1.t+l _ e1?y

      x +l=2y                          r + 1= 2y-........3   / simplify equation
      x=2y-1.......3
      Substitute in 2                  Substitute tu 2
                                                             / substitute
      (zy -tY + 2y =3                  xn +x+1=3

      4y' -4y +1+ 21t - 3 = 0          x' + x -2=0
      4y' -Zy -2=o                     (x+z)(x-l)=o
      z{zy + t)(y - t)= o              x=-2...OR...J=l       / factors
                                       Substilute in 3
      ...y--LoR
        '2      v=t                                          / both y values
                                       -2+l-Zy...l+L=2y
      Substitute in 3
                                       ,=-1.........v=l
                                       "2
      , =,f-1l - r...... x = z(r)- r
            t2)
      x=   -2.          .-..J = I                            lboth x values

      OR
                                                                                        (s)
                                                                                        tel

### Page 5

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                                                                                 10611116

      QUESTTON 3

3.r   -8          -28                     22
                / \to-/\=14/
               \a ,/---.-4 ./

      3.1.1   40                                               /answer

                                                                                       (1)
      3.12    2a=4                     3a+l=6       a+b+c:-8   /second difference :4
              a=2                      t(z)+b --o   2+c---8    / a=2
                                                               {b=0
                                       b=0          c=-10      {c=-lO
                     =2n? -lO
              "'7,
                                                                                       &\
3.2

      3.2.1   a=5                                              / To=1AT.
              To =107.,

              a+5d:t0(a +2d)                                   la + 5d =l}(a +2d)
              5+5d:lo(5 +tul)
                                                               /simplification
              5d -ZM = 50- 5
                      d=-3                                     /d=1
                                                                                       AI
      3.2.2   s, =iP, + fu      -lal                           / correct formula
                                                               /conect substitution
              S.n   =fft ttl+ (zo- rX-r)l
                    =-470                                      /answer
                                                                                       (3)

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                   ..       /-\k
3.3   3.3.1
               tr{ I                )

              t4'lt)
                 I \.'
                   =               ./

              r. 1. 1.
               '2'4'
                        1                                  .l
                                                          rl y ---
                        2                                        2

              e-a                                         / correct substitution in,S*
               --            l-r
                               I
                                        I
                             t-         ^
                                        2
                    -2
                                                                                    (3)
      3.3.2

              .t,H.
              ).r. I
              u2        L)

                        1
              | --
                        2

              *un-'(" -r)
                               r-L
                                                          /n=8
                         ,[f1)' -,]                       /correct substitution in ,s,
                        =- [(2/ )
                                        1-1               y'S,,=a
                                                                "<< 9B3.93
                                        2
                                                                     64
                             255
                        =-64                ..oR...3,99

                                                                                    (3)
      3.3.3                        ?55
                                        64
                             t 63                         y'answer
                               &
              OR

              =--127
                        64
              OR
              = - 1,98
                                                                                    (1)

### Page 7

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                                                                   10611/16

3.4
      le: tsl:
            5)
               n?:
      u,t----
              4                                  { d =- A'
                                                            5
              5
      Tn = ct + (n     -tld
                  ' rfl).
                                                 /correct substitution in
          re + (n-             o
                     't5,/                       correct formula
                  AA
          19--n+-<0                              {7,<o
             55
              -4rr.-Lg!                          /inequality
               55                                y'answer
                                   .24,75
                              44
      .'.The 25th Tetm                           /conclusion

                                                                            (6)
                                                                         t2st
      OUESTION 4
4.t   P:4                                        / P=4
      cl=2                                       { q:2
      r(s;3) : y   =++2
                  3=a+2
                  a=1                            { a:l
                                                                            (3)
4.2
      &(-r) =
                  I +2                           /answer
                -x-4
      OR

      h(r)=*            t')

                                                                            (1)
4.3   y - - x + c........,{q;z)
                                                 /correct substitution of
      z: -(+)+ c
                                                 @;2)
      C:6                                        /answer

                                                                            t6t

### Page 8

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QITESTI{}N 5

f{:,-}   :ee"                                 roug}r t}re Point {*4, rf,J

                             * "tr-*ft               a                      /substitution

                                  .l         }#

                                             fl:*:
                                          t&u
                                          l-
                                         $"*
                                         d                                  /value of *

         jift
         \nJ
          {4* t"                                                            /intercirange:r ancl Y
         4!
          t*I                                                               /equation
         rtJ*46

                                                                            /shnpe ./"
                                                                            'rshap* l' '
                                                                            *'asyrnptotes of br:th graPhs

          1 t-rX
          t4i

                   / / \-
                   l+1
  I.ri r.l
  rit.r7-     - -l i -_ II
                   t\i
                   \* /

  Atrr:ut rhe line V ::.v

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      QUESTTON 6
              f
6.1
      !=a{                                      /substitution (i; -4)
      -4=   a(L)z

      -4=a                  ;x>0                lvalue of a
                                                /equation
      h(x)= 4*z

                                                                            (3)
62    ! = -4xz
      -9 = -4xz
                                                                        9
       "9                                       /simplification x2 =-
            4                                                           4

      ,=*{otr
                       lo    \
      x>o ..rll)'1:-91                          /answer
                                 I
                             /
                                                                            (2)
                             vz-!'
      Gradient of ST = !-
6_3

                       xz -Jt

          -       (-4)                          /substitution
      =-91,5-l
                                                /answer
      = -10
                                                                            (2\
6.4                                             /interchange x artdy
      x = -4t-' ;y >-A
                                                /restriction
      -.:         x
      v ----
      "4                                        y'the value of y'
           t-..
           II
      v ='i- z

      -1     l"\
                  t-
      h'=-l--                                   /equation
               \l4
                                                                            (4)
6-5                                             /shape inverse
                                                /point on inverse
                                                /axis of symmetry

                                                                             (s)
                                                                            IT4I

### Page 10

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      QUESTTON 7

7.1
          l+0.164:lt*l=,..l
          rrv,rw_L^,                                          /correct substitution into
                       D)                                     correct fonnulae
                        ;
          ,"{troq - 11'nont
          r,                12                                /ld.:,rp
          inon = 15,28o/o                                     /answer
                                                                                           (3)
      -                                                       r' 2 300 000
7.2

                                                              [(, - 9/2)" -,]
                                 .Y) -,                       L(   4) l
                                                              { n:32
                                  0,r2
                                   4                          /answer
          x = R43 807,22
                                                                                           (4)

7.3
          7.3.1         A= P(r+ i)'                           r'substitution
                                         (   o.t+ts\'
                        A=Rr35000[. o
                                                   )          / A: ft138 339,15
                        I = .R138 339,15
                                                                                           (2)
          7.3.2
                                                               /correct formula (P)

                                             -[,.T) '-]        /correct substitution

                                                               {n=L8
                                                 aJ475
                                                   12
                                                               /answer
                        x = R8 613"99
                                                                                            (4)
                                                                                           l13l

                                                         {o

### Page 11

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                                                                                10611/16

      QUESTTON 8

8.1
      .f(x)=4-3x?
      f(x+h)=4-3(x+h)z                                        /simplification of
                       =4-3x? -6xh-3hz                        .f(x+h)

                         f (x)                                /formula
       J,,$) _r*"f(x+h)-
                       Ir+0        h

       = lim
                  (4   - 3x2 - 6xh - 3h2 ) - (+ - 3x2)
         h-+A

                  - 6xh-3hz                                   /simplific ation - 6xh th?
       = lim
         h-+O            h
                  h(-6x -3h)
       = lim                                                  /common factor
           i-+0

      = lim(-6.r- 3i)

       =          -6x                                         / answer-6x
                                                                                       {5)
      8.2.t                                                   { 4x3
                        o.l *' -2* * 11                       /-2
                           L         J-J
                                                              / -z)i-l
                        =4x3 -2-2x-3
                                                                                       (3)
      8.2.2
                         1r:-
                                2x-3
                                 Vx
                                 1_1                          /simplification
                              =2xa -3x a
                        dv 3+ 3-:                             /both values of derivatives
                        dx2            4
                                                                                       (2\
8.3
      -f(x):x'-7x'                                            { f'{x)
      f'(x):3x2 -l4x
      f'(x) =5                                                / J-'k) = s
      3x2 -L4x = 5
      3x2 -14x-5=0
                                                              /factors
      (:x + t)(x - 5): o

      *=-1 oR J
                                   x=5                        /both answers
                                                              NOTE
                                                              NO PENALTY IF
                                                              CANDIDATE COMMITS
                                                              AN ERROR IN WRITING
                                                              AN ANSWER WITH
                                                              POSITIVE EXPONENTS.
                                                                                       (41
                                                                                      It4t
                                                         11

### Page 12

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      QUESTTON e

9.1                                                        /y-intercept

                                                           /y-intercept

                                                           /shape

                                                                                     (3)
9.2   J'$)=a(x+?Xx-1){x-6)                                 /corect f,ormulae
                                                           /substitution
        12= alo + \{a - 1}t0 - 6)
                                                           { a:L
            c=l
        .', .f(x) = (r + ?X, - 1)(.:r - 6)                 /expansion
                  =.r3-5x2-8x+12
                                                                                     (4)
9.3   f'(x) = o                                            /equating to zero
      .'.3x?-10x-8=0                                       /factors
      (3x+2){x-4J=0
                                                           y'ansrvers.x
      *:-Z3 oR r=4
                                                           /ansrvers y
      ,,-ooo oR v=-i6
      "27
      rurningpoints ** f- ,A         ,#) AND (a;   --36)   r'TPs

                                                                                     (s)
9.4     2                                                  /answer
      ---<x<4
        3
                                                                                     (r)
9.5   l'" t-*1: 6x - 1o                                    /second derivative
      6x-10>0                                              /6x-10>0
      jf>- 5                                               /ansrver
           30
                                                                                     (3)
                                                                                    II6I

                                               12

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        *ITESTION le

                                                                               f
                                                                              ff

                                                                          Y

                                     4s
10 I    Fl .= 128
                                                                                   /substirution
        4.u-.r.lr = 128
                .ft---- l?8                                                        /ansrver
                       4-r-
                                                                                                 f2'!
t{}"2                                       = 4..t:..r+ Zxh+&xh
                                                                                   /fonnula
                                             =,,$yi 110rft
                                                                     aa
        'I otal surf*ce &rea                                                       /siniplilication
                                             = 4xz + 10x.{
                                                                     x-
                                                    . ?i 320
                                                   ,il.v'                          y'answer
                                             -
                                                            --   x
                                                                                                   {s}
            /                trn\
         Dxl 4x'* --- l = 0
1*"3

            t                 .rl
                   ^         ,320                                                  /derivative
                   6J ----               ::::: U

                             --r''                                                 /equate lo zero
                 {3x'*320=*
                             8x3 =32*
                                         32!
                             ''t = x                                               /sirnplific.ati*n

                               '11EoI
                              1. = r i_

                               1"=ffi
                               *.- - e..li
                                     ri,r
                                                                                   / answer
                              t?
                              "l;
        Fleight: :                         :2,74
                        1' 1\-
                        l"-'
                        tk{
                                     I

                        \ )/
                                                                                                   {4}
                                                                                                   I9t

                                                                              13

### Page 14

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        QI]ESTION 11

11"1    Let S represert the participants for swinrming; G represent the gynuastics   ,/6
        participants and A for the athletics parlicipants.                           /21-x
                                                                                     /14-x
                                                                                     / all other
                                                                                     values in the
                                                                                     Venn diagram
                                                                                     correct
                                                                                     (CA }

                                                                                                   AI
n.2     2l- x+x + l4-.r+ 9+14+ 1 0+ 6+ I I = B0                                      y'equation
                                                85-x = 8O
                                                                                     /answer
                                                  -r=5
                                                                                                   0\
I 1.3                                             5+14+10+9                          u'equation
        P (Particip*nts in at least 2 events)              80                        /clivision by 80
                                                                                     /answer
                                                = 4,47 5
                                                                                                   (s)
                                                                                                   tel

                                                       14

### Page 15

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        QUESTION 12

        9! = 362 880
                               of the answer

                                                     /gt.
rzfiz                                                { 5t,
                                                     /aRswer
        =3024
        OR

        !.x 84Jx,6.                                  9x8x7x6
        :3 024                                       /answer

                                           {5

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