Mathematics Grade 11 Paper 2 Gauteng June 2016 Memo

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION 2016 GRADE 11 MATHEMATICS Second Paper MEMORANDUM 11 pages 1

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS (Second Paper) INFORMATION: A – Accuracy C.A. – Continued Accuracy S – Statement R – Reason S and R – Statement and Reason 2

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 QUESTION 1 MARKS : 16 1.1 KT =  Distance formula =  subst. in corr. formula  answer = [2/3 if answer not in surd form] (3) 1.2  answer =  subst. (-5 ; 1) into str. line eq.  answer (C.A) OR OR  answer =  subst. (7 ;-2) into str. line eq.  answer (C.A) (3) 1.3 =  answer (A)  eq. of Line KT. (A) OR y-int A (0 ; ) of line KT. B (0 ; - ) 1 1 AB = 5  6 4  add of y co-ord. of A and B 5 65  answer (A) =5 OR 5,42 OR (4) 12 12 3

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 1.4 β = 39,81° β = 39,81°  = α= ........ext. of ∆ =   answer ANY other valid solution (PENALISE once for rounding off , either α or β) (6) QUESTION 2 MARKS : 14 2.1 Let M (x ; y) ...... radii   corr. Subst. in dist. formula  simplification (C.A)  answer (4) Answer only 0 2.2 A( subst. in midpt. formula y=0  co-ord. of A A(0 ; 4) [2/3 if not in co-ordinate form] (3) 2.3  Eq. of line OK:  corr. subst. in str. line formula answer (C.A) (3) 4

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 2.4 Let T (x ; y) ......⟘ lines  ...................(1)  Eq. of line OK ....................(2)  equating (1) and (2) =  answer (C.A) (4) Any other valid method QUESTION 3 MARKS 28 3.1 13sinα = -5 sinα = -  sinα = - y α x  cartesian plane with terminal arm in 3rd quad. = –12  x = –12 3cosα = 3(  subst. cosα = =  answer (5) 5

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 3.2.1  -sin θ ;  -tan θ ;  cos θ ;  = – tan = – = =  or (6) 3.2.2  -sin 50 =  – sin 30 ; =  cos 40 ;  – cos 40 or cos 40 = sin 50 = -1  – cos 60  answer (6) 3.3  factorization (4 θ – 8) sin 30° = (θ – 2) (2) sin 30° =  factorization of denominator =  answer = 6

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 60o 2 1 30o 3 tan 240° = tan (180° + 60°) = tan 60°  tan 60 = 3  answer Full marks if tan 60° = 3 or Show sketch to determine sol. Answer only max 1 mark(surd form) (5) 3.4.1 1 L.H.S: (sinα tan α  cos α) tan x cos  sin α + cos tan  = sin α + tan  cos  sin = sin α +  subst. tan α = sin  cos cos  cos 2   cos 2  sin  = sin α + sin  sin 2   cos 2  sin 2   cos 2 sin  = sin  (4) 1 = =R.H.S sin Any other valid method 3.4.2 α = {0°; 90°; 180; 270° ; 360°}  0 ; 180°; 360°  90°; 270° (2) 7

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 QUESTION 4 MARKS 12 4.1 180  answer (1) 4.2  -1 ;1  corr. brackets OR OR R  -1 ;1  corr. inequalities (2) 4.3 θ = 40  a =2 2 (2) 4.4 g(180 ) = – 0,77  answer (C.A) (1) 4.5.1  -180 ; -103,3 -180 OR  corr. inequality OR [-180 ; - 103,3°) corr. bracket OR (16,7 ; 130 ) or (136,7 ; 180 ] (2) 4.5.2 [–130° ;- 90°] OR  [-130° ; -90°] –130° ≤ x ≤ –90° corr brackets OR corr. inequalities [0 ;50 ] or [90 ;180] (2) 4.6 =  = OR  answer = (2) 8

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 QUESTION 5 MARKS 8 5.1 is perpendicular to the chord  answer (1) 5.2.1 AD = ... th. of pyth.  Subst. = = 28,84 cm  answer (2) 5.2.2 OD = x + 16  answer (1) 5.2.3 ......... th. of pyth OC = OD .....radii =   x = 10  simplification  answer (4) QUESTION 6 MARKS 8 6.1 PT = KT ...... line from centre ⟘ to ch. S R (2) 6.2 ....... th. of pyth. S but ..... th. of pyth.  but OK = OC ..... radii  subst. OK = OC = \  subst.OP = OC – PC  = PC  OC  OC  2OC.PC  PC2 2 2 2   simplification = 2(OC.PC) = 2(x + y)(y) =  subst. for OC and PC (6) 9

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 QUESTION 7 MARKS 14 7.1 .......... ⎿ at centre = 2 ⎿ on circum.  Reason = = 55  answer (2) 7.2 S ....... ⎿s opp = sides, radii R =  answer = 35 Answer with reason full marks (3) 7.3      R2  R3  R2  R3 ⎿s opp = sides  R 2  35  20  answer = 15  S and R ........ ⎿s in same seg = 15  answer = 45 (3) 7.4 ......... vert opp. ⎿s = 90  S and R  answer ........ ⎿s of a ∆ =  S and R = OR  answer OR ........ ⎿s of a ∆  S and R = = 45  answer ......... ⎿s in the same seg. = 45  S and R  answer (4) 10

Downloaded from hlayiso.com MEMORANDUM Mathematics P2 7.5  R TR ⫽ PQ ....... alt. ⎿s = OR OR    TRP  45  TRP  P   R TRP  P  45 TR ⫽ PQ ....... alt. ⎿s = (2) 11