Mathematics Grade 12 Paper 2 KwaZulu Natal Mock 2020 Memo

Mathematics P2 NSC Preparatory Examination September 2020 1 NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS P2 PREPARATORY EXAMINATION SEPTEMBER 2020 MARKING GUIDLINES MARKS: 150 TIME: 3 hours This marking guideline consists of 12 pages.

Mathematics P2 NSC Preparatory Examination September 2020 2 QUESTION 1 NUMBER OF RED NUMBER OF MIDPOINT OF f. x CARDS COUNTRIES (f) INTERVAL (x) 0< x≤ 2 27 1 27 2< x≤ 4 15 3 45 4< x≤ 6 5 5 25 6< x≤ 8 5 7 35 8 < x ≤ 10 3 9 27 TOTAL 55 159 1.1 CA 159 Estimated mean = red cards CA  55 CA  Answer only full marks answer (3) 1.2 Full The red cards issued to countries during a marks for soccer competition 6 correct points 60 CUMULATIVE FREQUENCY 50 2 40 marks for 30 4correct points 20 10 1 mark 0 for 2 0 2 4 6 8 10 12 correct NUMBER OF RED CARDS points (3) 1.3 Q3  4 and Q1  1 IQR  4  1  3 red cards CA  Q1 Answer only full marks and Q3 CA answer (2) [8]

Mathematics P2 NSC Preparatory Examination September 2020 3 QUESTION 2 2.1 A  for A A for B A For equation Answer only full marks (4) 2.2 Estimated monthly income CA substitution CA answer R25598,89 (2) If 9000 is used only 1 mark 2.3 r = 0,94 CA (2) 2.4 Very strong positive relationship between the monthly rent and the monthly CA  strong income. CA  positive (2) [10]

Mathematics P2 NSC Preparatory Examination September 2020 4 QUESTION 3 3.1.1 A sub into correct formula 1 A  3 A Sub into correct formula A (4) 3.1.2 KM  4  42  10  02 CA subst  100 CA 10 units  10 units (2) Answer only full marks 3.1.3 1 CA tan   2 CA    26,570 provided acute angle Answer only full marks (2) 3.1.4  x1  x2 y1  y2  Acorrect substitution  ;   2 2  1 8 1 2   ;   2 2  9 3  ;  Aanswer (2) 2 2 3.2 Asubst A3 Aproduct = −1 (3) 3.3 AMKN -2 AKN  MN ASum of 180o is cyclic quadrilateral (converse, opp of a cyclic 1 1 M MN    2     1 quad are supplementary) 2 2 A reason (4) [17]

Mathematics P2 NSC Preparatory Examination September 2020 5 QUESTION 4 4.1 A A (2) 4.2 CA into equation CA CAequation For CA marks coordinates of M must be in second quadrant (3) 4.3 A or A Aproduct of gradients = -1 A900 is a tangent (conv. tangent and diameter) Areason (5) 4.4.1 CA CAequation Subst. (3; 2): CAsubst of (3; 2) or (2; -2) CAequation (4) 4.4.2 Let C(x; y) CAequation of circle At C; CAsubst x = 0 CAy values CAco-ordinate CAgradient Now CAequation (6) 4.5 Lines AT and BT intersect at C CAequations equal CAvalue of a CAvalue of b, For CA marks A and B are points in the 4th quadrant (3) [23]

Mathematics P2 NSC Preparatory Examination September 2020 6 QUESTION 5 5.1 Acos 49 0 A sin 79 0 Acos 30 0 A answer (4) Answer only no marks, used calculator 5.2 Aexpansion Alike terms added Adivide : A (4) 5.3.1 LHS: A A Anumerator Aanswer (4) RHS

Mathematics P2 NSC Preparatory Examination September 2020 7 5.3.2 A Astandard quadratic OR form A  Factors ref CA900 OR CA228.59 CA311.41 (6) QUESTION 6 6.1 A A A A (4) 6.2 A (1) 6.3.1 AAvalues and notation (2) 6.3.2 AAA values and correct notation (3) [11]

Mathematics P2 NSC Preparatory Examination September 2020 8 QUESTION 7 7.1 n   ASubst. into Area rule Asin2x Aanswer (5) 7.2 AUse of sine rule Asubst into sine Rule Asin 2x A2 sin x cos x (4) In 7.3 A ASP = PQ tan y (2)

Mathematics P2 NSC Preparatory Examination September 2020 9 QUESTION 8 8.1 h k R.T.P KP KQ  PL QM CONSTRUCTION: Aconstruction In ΔKPQ , draw perpendicular heights, h from Q to KP and K from P to KQ 1 Amethod KP  h Area of Δ KPQ 2  Area of ΔLPQ 1 PL  h 2 KP A KP PL = PL 1 KQ  k Area of KPQ Amethod  2 Area of MQP 1 QM  k 2 KQ KQ = A QM QM But area of  PLQ = Area of  MPQ Same base, same height Area of ΔKPQ Area of ΔKPQ   Area of ΔLPQ Area of ΔMQP Amethod KP KQ   PL QM (6)

Mathematics P2 NSC Preparatory Examination September 2020 10 8.2.1 In ΔAPQ: AB AC AS AR BC PQ  . ; conv prop AP AQ A S/R BC A S/R (4) 8.2.2 In A S/R A S/R A S/R A S/R (4) 8.2.3 AS AR A S is cyclic conv. A S/R (4) 8.2.4 AS AR AS AS/R AS/R (5) [23] QUESTION 9 9.1 In ΔMBC: B̂2  B̂3 = x BE bisects MB̂C AS  MB̂C  2 x MB̂C  MĈB  2 x angles opposite equal sides AS/R In ΔBEC : Ê 2  180o  ( x  x) Sum of angles of a Δ AS/R = 180o –2x AAnswer (4)

Mathematics P2 NSC Preparatory Examination September 2020 11 9.2 In ΔMBC: BM̂C  180o  (2 x  2 x) Sum of angles of a Δ = 180o – 4x AS AR 1 But BÂC  BM̂C  at centre twice angle 2 AS/R 1 = (180o  4 x) 2 = 90 – 2x (3) 9.3 In ΔABE : Ê1  Ê 2  180o Straight line AS/R Ê1  180o  E 2 = 180o – ( 180o – 2x) = 2x AS In ΔABE : AB̂E  BÂC  Ê  180o Sum of  s of Δ AS/R AB̂E  180o  (BÂC  Ê1 ) = 180o  (90o  2 x  2 x) = 90o AS  AE is a diameter of circle ABE (Subtends)  90o AR (5) [12]

Mathematics P2 NSC Preparatory Examination September 2020 12 QUESTION 10 10.1.1 Let and A S/R AS AR A S/R bisects AS (5) 10.1.2 In and is common AS/R AS AR remaining AR AR similar ’s A S/R (6) 10.2.1 XY = XT AS AR Aanswer (3) 10.2.2 A LHS A RHS ASimplification mm AAnswer (4) [18] TOTAL: 150