Mathematics Grade 11 P2 Gauteng June 2023 Memo (English)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION JUNE 2023 GRADE 11 MARKING GUIDELINES MATHEMATICS (PAPER 2) 10 pages

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 INSTRUCTIONS AND INFORMATION: A – ACCURACY CA – CONSISTENT ACCURACY S – STATEMENT  R – REASON S & R – STATEMENT with REASON NOTES:  If a candidate answered a question TWICE, mark only the FIRST attempt.  If a candidate crossed out an answer and did not redo it, mark the crossed-out answer.  Consistent accuracy applies to ALL aspects of the marking guidelines.  It is unacceptable to adopt values/answers in order to solve a problem. 2

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 1 1.1 10; 13; 17; 21; 21; 23; 27; 29; 31; 34; 37; 38; 42; 43; 46; 48  Correct Min. Q1 and Max. Min. =10 ; Q1 = 21 ; Max. = 48  Correct Q 2 29  31 38  42 Q2   30 ; Q3   40 2 2  Correct Q 3 (3) 1.2  Correct Min. plot/lower Grade 11A whisker  Correct Max. plot/upper 10 21 30 40 48 whisker Grade 11B  Correct box (3) 1.3 480  Fraction x  Answer 16 x  30 NB: Answer only full marks (2) 1.4 σ = 11,46  Answer (2) 1.5 1σ interval: (30 – 11,46 ; 30 + 11,46)  Interval (18,54 ; 41,46)  Answer 4 learners achieved over 41,46 marks. (2) 1.6 There is no difference in the IQR. IQR = 19 for both classes.  Comment However, the middle 50% for Grade 11B was between 21 and 40  IQR value compared to only 11 and 30 for Grade 11A. The box for 11B is shifted to the right. Thus, Grade 11B generally performed better. (2) 1.7 75%  Answer (1) [15] 3

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 2 2.1 Equation of EG:  Gradient  Answer 3x – y + 6 = 0 y = 3x + 6 then mEG = 3 tan β = 3 β = 71,57° (2) 2.2 x + 3(0) = 8  x=0  Coordinate form x=8  (8 ; 0) (2) 2.3 M DF  M GE diagonals bisect  M DE  M GE   10  8) 6  0   Coordinates of K K ;   x-value  2 2   y-value K( 1 ; 3) x 1 y9 1  3 2 2 x  3 y  3  E( 3 ;  3) (4) 2.4 mDF  mGE  mDF  DF  GE 1  Reason =  3 3 = –1 DF  GE DGFE is a rhombus. (diagonals bisect perpendicularly) (3) [11] 4

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 3 3.1  Substitution d x  x )  ( y  y ) 2 1 2 2 1 2 AC  1  (2) 2  5  (1) 2  Answer AC  3 5 (2) 3.2 54  Substitution m BC   Answer 1  ( 3 ) 1 m BC  4 (2) 3.3 m BC  m BD  mCD  Equal gradients 1 y 5 1 y4  Substitution  or   y=6 4 5 1 4 5  ( 3) y6 (3) 3.4 m AH  4 ( AH  BC )  m AH y  ( 1)  4 x  ( 2)   Substitute A  Equation y  4 x  9 (3) [10] QUESTION 4 4.1 4.1.1 x 2  ( 24) 2  25 2  Substitute into Pythagoras x  7  Answer (2) 4.1.2 (a) sin   Answer 24  25 (1) (b) cos(180   )  Reduction   cos   Simplified answer 7     25  7  25 (2) 5

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 (c) tan 2 (   )  Reduction  Simplified answer  tan 2  2   24     7  576  49 (2) 4.1.3 (a)  24 y sin    sin   25 15 y  24  Equate sine ratios  15 25 x  cos    72 15 y 5  Equate cosine ratios 7 cos   25 x 7  15 25  21 x 5 (4) (b) 1  72   Formula for area Δ AreaROT  (12)   Base = 12 2  5 72 AreaROT = 86,4 units2  Height = 5 ALTERNATIVE  Area OT  15 OR  12  OT length  106,26°   253,7397...  Substitute sine area 1 formula Area ROT  (15) (12) sin (106,26) 2  Area Area ROT  86,4 units 2 (4) 6

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 4.2 tan 225  sin (180   ) cos (90   )  tan 225° = 1 cos (90   ) sin (   540)  sin (180° – θ) = sin θ 1  sin  .  sin  cos (90° + θ) = –sin θ   sin (–θ –540°) = sin θ sin  .sin   1 – sin2 θ = cos2 θ 1  sin 2  cos 2   sin 2    tan 2  sin  2 cos 2   sin 2   tan 2  (6) [21] QUESTION 5 y 2 1 x O −240º −180º −120º −60º 60º 120º 180º 240º f -1 g -2 5.1 A=2  Answer (1) 5.2 Period = 720°  Answer (1) 5.3 a = –1  Value of a p = –60°  Value of p (2) 5.4 –120° ≤ x ≤ 60° or x = –240° or x = 240°  Interval  –240°; 240° (2) 5.5 p = 30°  Value of p (2) [8] 7

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 6 6.1   r  Substitution tan    2 R  Manipulation   R. tan    r 2 (2) 6.2 1 4 1 Vhemisphere  . R 3  Volume Sphere 2 3 2 2  Substitute r from 6.1 Vhemisphere  R 3 3  Subtract volumes 1 (Method) Vcone  r 2 R  Factors 3 2 1     Vcone    R. tan    R 3   2  2   Vcone   .R 3 tan 2   3 2 2 1   Vremaining  R 3   .R 3 tan 2   3 3 2 R 3     Vremaining   2  tan 2    3   2  (4) 6.3 1   1   Vcone   .R 3 tan 2    Vcone  π.R3 tan 2   3 2 3 2 1  36   Substitute Vcone   11 tan 2  3  R  11 and   36 3  2   Volume of wax Vcone  147,15 cm 3 (3) [9] QUESTION 7 7.1 7.1.1 Ĉ 2  40 tan chord theorem  S  R (2) 7.1.2 K̂ 1  90 ' s in a semi circle  S  R (2) 7.1.3 P̂1  25 ext  of a Δ  S  R (2) 7.2 T̂1  65 ext  of Δ  R  R TC  QC sides opp equal ' s (2) [8] 8

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 QUESTION 8 T U 1 O 2 V 8.1 Construct UO and extend.  Construction In ΔTOU Ô1  T̂  Û 1 exterior  of   SR T̂  Û 1 ' s opp equal radii  SR  Ô1  2Û 1 Similarly in TOU  Ô 2  2Û 2  S  Ô1  Ô 2  2Û 1  2Û 2   Ô1  Ô 2  2 Û 1  Û 2   Conclusion TÔV  2TÛV (5) 9

Downloaded from hlayiso.com MATHEMATICS MARKING GUIDELINES (PAPER 2) GRADE 11 A B 1 2 3 O 2 2x C F 1 1 2 2 M 1 D 8.2 8.2.1 Two pairs of adjacent sides equal.  R (1) 8.2.2 (a)  at centre = 2   at circumference  R (1) (b) ext  of cyclic quad  R (1) (c) corr ' s, OD MB  R (1) (d) opp ' s, rhombus  R ALTERNATIVE alt ' s, OB DM (1) 8.2.3 D̂ 2  x  90 tan  rad  R D̂ 2  90  x B̂3  90 tan  rad  S Ĉ  90  x int s of   SR  D̂ 2  Ĉ both 90  x  Conclusion (4) 8.2.4 F̂2  90 corr s, FB DM  SR  S AF  FD line from centre  chord  R AB  BC line through midpt to 2 nd side  R (4) [18] TOTAL: 100 10