Mathematics Grade 11 Paper 2 North West June 2018 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE/GRAAD 11 MATHEMATICS P2 (MEMO)/ WISKUNDE V2 (MEMO) MID YEAR EXAMINATION/ HALF-JAAR EKSAMEN 2018 MARKS/PUNTE: 100 JUNE EXAMINATION 2012 This markingguidelines consists of 10 pages./Die merkriglyne bestaan uit 10 bladsye. Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION/VRAAG 1 1.1.1 (2) mAB  mBC 0 1 p  0  2 1 5  2 1 p  1 p  3 3  3 3 p 1  answer/antw 1.1.2 mAB  mBC  1 (3)  setting an equation/vergelyking 1  0 p  0   1 1  2 5  2  simplification/vereendiging 1 p   1 3 3 p  answer/antw  1 9 p  9 1.1.3  x2  x1    y2  y1   d 2 (3) 2 2  substitution/substitusie  5  2    p  0   52 2 2  simplification/vereenvoudig 9  p 2  25 p   25  9  both answers/beide antw  4 1.2 S  x; y y P  4;5 M  2; 2  Q  4;1 x O R  1;  4  Demo NW/JUNE/MATH/ EMIS/6******* 2

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 1.2.1 5 1 (2) mPQ   substitution/substitusie 4  4 1   answer/antw 2 1.2.2 4  2 (3) mRM  1  2  2 2 1 1 mPQ  mRM    2  2 2  2  1  1  PM  RS 1.2.3  x1  x2 y1  y2  (3)  ;   2 2   1  x 4  y   ;   2 2  1  x 4  y 2 2  setting equations/verg 2 2 1  x  4 4 y  4  x5 x5 y 8  y 8 1.2.4 (3)  Substitution/substitusie  1  4    4  1 2 2 RQ   50 5 2  RQ  50 or 5 2  5  4   8  1 2 2 SQ   50  SQ  50 or 5 2 5 2 QRS is isosceles 1.2.5 (5)  4  4    5  1 2 2 PM  4 5  PM  4 5  5  1  8  4  2 2 RS  6 5  RS  6 5 1 Area PRS   base  height  Formula/form 2 1  Substitution/substitusie  6 54 5 2  Answer/antw  60 unit 2 [24] Demo NW/JUNE/MATH/ EMIS/6******* 3

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION/VRAAG 2 (3) 17 sin   15  0 15 sin   17 17 15   correct sketch/korrekte sket x2  y 2  r 2 x 2  152  17 2 x   17 2  152  8 Ans : x  8  8 15 tan    8  Answer/antw 2.1.2 (2) cos   180    cos    cos   8      17  8  Answer/antw  17 2.2.1 (2) tan 70  p tan110  tan 180  70    tan 70   tan 70  Answer/antw  p Demo NW/JUNE/MATH/ EMIS/6******* 4

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 2.2.2 (3) r x y 2 2 2 r 2  p 2  12 r  1  p2 1  p2  sin 290  sin  360  70    sin 70   sin 70 p  Answer/antw  1  p2 2.3 (6) sin150.tan 225 sin  30  .sin 420 sin 180  30  .tan 180  45  sin30    sin 30.sin  360  60   tan 45  sin 30   sin 30  tan 45   sin 60    sin 30  sin 60  1   1  correct    2 substitution/korrek  1  3  te subs      2  2  2  3  answer/antw [16] QUESTION /VRAAG3 3. (8 1 cos 390 )  cos30  tan  360  x  .cos 180  x  .cos  x  90   tan x cos(30)    cos x cos 30     tan x   cos x  sin x   sin x cos 30 cos30   sin x     cos x  sin x   1   sin x   cos x   cos x  1  sin 2 x  Simplification/vereenv..  Answer/antw  cos 2 x Demo NW/JUNE/MATH/ EMIS/6******* 5

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 3.2 (6) 2 cos x.tan x LHS   cos x 1 1 cos x  sin 2 x  cos x   sin 2 x  cos 2 x  2   cos x  cos x 1  cos x cos x 1  cos x  sin x  cos x 2  cos x    cos x  cos x  1  cos x sin 2 x  Simplification/vereenv..   cos x 1  cos x 1  cos 2 x  1  cos x 2   cos x 1  cos x  1  cos x 1  cos x   cos x  Factoring/fakt.. 1  cos x  1  cos x  cos x  Simplification/vereenv... 1  LHS=RHS 3.3 (6) 4 6 cos x  5  cos x  std form/std vorm 6 cos x  5cos x  4  0 2  factors/faktore  3cos x  4  2 cos x  1  0 4 1  values of cos x /waarde van cos x  or cos x   3 2 1  selection of answer/antw cos x   2  answer/antw x  120  360.k ; k  OR  k Z x  120  360.k or 240  360.k [20] Demo NW/JUNE/MATH/ EMIS/6******* 6

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION/VRAAG 4 Statement (S) Reason (R) 4.2.1 (2) ˆ  DEC BCA ˆ  26 equal chords; equal s  S  R 4.2.2 (2) Â1  53  at centre  2   at  S circumference  R 4.2.3 ˆ  180 D̂  A opp s quad supp (6)  S 1  R D̂  180  53  127  127 Ĉ4  26  127  180 sum of s in   S/ R Ĉ4  27 2Cˆ  180  106 3 s opp equal sides  S/ R Ĉ3  37 OCDˆ  37  27  Answer/antw construction  64 [10] Demo NW/JUNE/MATH/ EMIS/6******* 7

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 QUESTION/VRAAG 5 5.1 (1)  Answer/antw 90 or right  5.2 Complete the proof: ˆ  PBM Required to proof : MPT ˆ Construction: Draw diameter PA and join AM Statement (S) Reason (R) 5.2 (5) ˆ  90 PMA  in semi-circle  S/ R ˆ  Pˆ  180  90  90 s in   S/ R A 1  S/ R ˆ  ˆP  90 MPT tangent  diameter/ radius  S 1 ˆ A  MPT ˆ  S/ R ˆ ˆ PBM  A s in same segment ˆ  PBM  MPT ˆ Demo NW/JUNE/MATH/ EMIS/6******* 8

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 OR Statement (S) Reason (R) 5.2 ˆ  90 APT chord  tan (5)  S/ R MPT  90  Pˆ1 ˆ PMA  90  S diameter subtends right  ˆ A  90  ˆP1  S/ R ˆ PBM  A ˆ s in same segment  S ˆ  PBM  MPT ˆ  S/ R 5.3 M A 1 2 x 1 B 1 2 4 C 2 3 1 S4 2 3 Q 2 3 1 1 2 R P Statement (S) Reason (R) 5.3.1 (8)  S R ˆ x B̂1  A tan chord theorem 2  SR ˆ ˆ A B x s opp equal sides 1 1 Qˆ B ˆ x corresp s; BC // PQ  S R 1 B̂  ˆ 2 A x 1 tan chord theorem  S R Pˆ2  B ˆ x alt s; BC // PQ  S R 2 Demo NW/JUNE/MATH/ EMIS/6******* 9

Downloaded from hlayiso.com Mathematics/ P2/WISKUNDE/V2Half-jaar EksamenMid-Year Examination NW/ Jun 2018 NSC- Grade 11 5.3.2 ˆ P̂2  A (2) 1 both  x  S/ R  ABRP is a cyclic quad BR subtends equal s  conclusion/konk.. 5.3.3 (3) AP = BP sides opp equal s  S/ R BQ = BP sides opp equal s S/ R AP = BQ both = BP  S/ R [19] QUESTION/VRAAG 6 Statement (S) Reason (R) 6.1 K̂1  90 diameter subtends right  (5) S R Uˆ K ˆ  90 s in the same seg. 1 1 or Û1  90  S/ R diameter subtends right  S/ R ˆ  180  90  90 NUP PUS is straight  R  PUNK is a cyclic quad ext   int opp  opp s supp 6.2 Sˆ 1  Pˆ1 alt s; OS // PN (6) S R Kˆ  Pˆ s in the same seg. 2 1 K̂ 2  ˆS1 converse tan chord theorem S R S R  SO is a tangent [11] TOTAL: [100] Demo NW/JUNE/MATH/ EMIS/6******* 10