Mathematics Grade 12 P2 KwaZulu Natal Mock 2020 QP

Downloaded from hlayiso.com education Department: Education PROVI N CE OF KWAZULU-NATAL GRADE 12 z^aa-.. - - - - -. -. -. - -. -. -.. - - - =. - - -. - - - -.. -... -; = -a\ ta '. |l MATHEMATICS P2 '.1 tt 'a ,a t' '.'ttt PREPARATORY EXAMINATION :i at a, |l '.ll t! SEPTEMBER 2O2O :i ll tt \l s\--r -e1 ! - ! = ! = ! ! ! ! ! ! ! ! = ! r ! = = ! = ! ! = = = ! = ! ! = ! : ! ! = ! = ! r ! = = 2)' MARKS: 150 TIME: 3 hours This question paper consists of 11 pages and an information sheet. ght reserved Please turn over

Downloaded from hlayiso.com Mathematics P2 2 Preparation Examination September 2020 NSC - Grade 12 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions: l. This question paper consists of 10 questions. 2. Answer ALL the questions, 3. Clearly show ALL calculations, diagrams, graphs, et ceter4 which you have used in determining the answers. Answers only will not necessarily be awarded fulI marks. 5. You may use an approved scientific calculator (non-programmable and non-graphical), unless $tated otherwise. 6. If necessary, round off answers to TWO decimal places, unless stated otherwise. '.7. Diagrams are NOT necessarily drawn to scale. 8. Number the answers correctly according to the numbering system used in this question paper. 9. Write neatly and legibly. Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics P2 3 Preparation Examination September 2020 NSC - Grade 12 QUESTTON I The total number of red cards issued per country to players during a soccer competition are given in the table below: NUMBER OF' NUMBER OF MIDPOINT OF INTERVAL (x) f.x RED CARDS COUNTRIES (fl 0<x<2 LI 2<x<4 l5 4<x<6 5 6< 16 I 8 5 8< x< l0 a J TOTAL 1.1 Calculate the estimated mean of the number of red cards per country. (3) t.2 Draw an ogive crrrve to represent the above data. (3) 1.3 Calculate the interquartile range of the number of red cards issued per country in the competition. (2) I8I QUESTION ? The table below shows a relationship between the monthly rent (x) a person pays for an apartment and the person's monthly income (y). Both are given in thousands of rands. YEAR 2003 2004 2005 2006 2007 2008 Rent (x) 2 3 15 \) 5.6 6 Income (v) 9 13,5 l5 16,5 t7 20 2.1 Determine the equation of the regression line. (4) 2.2 Determine the estimated monthly income if the rent per month is R9000. (2) 2.3 Calculate the value of the correlation coefficient. (2) 2.4 Describe the relationship between the monthly rent and the monthly income. (2) l10l Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics P2 1 Preparation Examination September 2020 NSC - Grade 12 QUESTTON 3 ln the diagram KLMN is a quadrilateralwith K(4; l0), L(l; t), M(4; 0) and N(S; 2). K(a; 10) 3.1 Determine the: 3.1.1 gradient of LM and MN (4) 3.1.2 length of KM. (2) 3.1.3 value of 0 (2) 3.1.4 midpoint of LN (2) 3.2 Show that KL I LM (3) J.J Prove that KLMN is a cyclic quadrilateral. (4) IrTl Copyright Reserved Please furn over

Downloaded from hlayiso.com Mathematics P2 5 Preparation Examination September 2020 NSC - Grade 12 QUESTTON 4 In the sketch below, AB is a diameter with coordinates A(3;2) and B(-5; 4) of circle ABC. M is the centre of the circle. BC produced meets AT in T. N(2; -2) is a point on the line TA. C is the y - intercept of the circle. B(-5; a) (3;2) N(2; -2) 4.r Determine the co-ordinates of M the centre of the circle (2) 4.2 Write down the equation of the circle in the form (x - p)2 + (y - d' : I (3) 4.3 Prove that TA is a tangent to the circle at A. (s) 4.4 Determine the equations of the lines 4.4.1 TA and (4) 4.4.2 BT (6) 4.5 If the coordinates of T are (a; b), calculate the values of a and b. (3) I23l Copyright Reserved Please furn over

Downloaded from hlayiso.com Mathematics P2 6 Preparation Examination September 2020 NSC - Grade 12 QUESTTON s 5.I Without using a calculator, evaluate Cos 79o cos 3l lo + sin l01o sin 49o (4) 5.2 Given: sin (x + y) : 3 sin (x -y) Prove that: tan x : 2tanv (4) E ^ J.J Ulven: cosx cos2x : Slnx sin 2x 2stnx 5.3.1 Prove that losr - cos2x = sinx (4) stn2x 2stnx 5.3.2 Hence, solve forx where x e[0";360"]: | + 2cos2x : cos 2x cos.r (6) 2stnx stn2x l18l QUESTTON 6 In the diagram, the graphs of f (x): a sin bx and, g (x) : c cos dx are drawn for the interval xe[-90'; 360"] 6.1 Determine the values of a, b, c and d. (4) 6.2 Write down the period of g. (1) 6.3 Determine the value(s) ofx in the interval xe [-90' ; 360"], for which 6.3.1 "f (x) < s @) (2) 6.3.2 f'(x) g'(") > 0 where S(r) > 0 (3) Copyright Reserved " Please tum over

Downloaded from hlayiso.com Mathematics P2 Preparation Examination September 2020 NSC - Gnde 12 l10l QUESTTON 7 In the diagram P, Q and R are three points in the same horizontal plane. PR = QR= z, QpR = x. SP is perpendicular to PQ. The angle of elevation of S from Q is y. o 7.1 Express the area of APQR in terms of x andm. (5) 7.2 Showthat PQ:2mcosx (4) 7.3 Hence, prove that SP :2m cos xtany (2) 111l Copynght Reserved Pleaee tum over

Downloaded from hlayiso.com Mathematics P2 8 Preparation Examination September 2020 NSC - Grade 12 QUESTTON 8 8.1 In the diagram below A KLM is givon, with P and Q lying on KL and KM respectively such that PQ il fU. PM and LQ are drawn. Prove that *="Q (6) PL QM Copynght Reserved Please tum over

Downloaded from hlayiso.com Mathematics P2 9 Preparation Examination September 2020 NSC - Grade 12 8.2 In the diagram, SBT, SA and TC are tangents to the circle at B, A and C respectively. AB is produced to P and AC is produced to Q such that T lies on the line PQ. AB AC. In aAPo.--AP- AQ Use the above information to prove: 8.2.r -A, rr, (4) 8.2.2 AABC ll/ LTCQ (4) 8.2.3 ABTQ is a cyclic quadrilateral. (4) 8.2.4 Prove that TQ is a tangent to circle TBC at T. (5) I23l Copyright Reserved Please tum over

Downloaded from hlayiso.com Mathematics P2 l0 Preparation Examination September 2020 NSC - Grade 12 QUESTION 9 In the diagtam, M is the centre of the circle through A, B and C. E is on AC. AC bisects frrfeg and EB bisects frrmC . fr,: x Determine the size of E" in terms ofx. (4) 9.1 (3) . 9.2 Show BAC = 90" - 2x 9.3 Prove that AE is a diameter of circle ABE. (s) Ir2l Please turn over Copyright Reserved

Downloaded from hlayiso.com Mathematics P2 1l Preparation Examination September 2020 NSC - Grade 12 QUESTTON 10 l0.l In the diagram XMN is a straight line and XT is a tangent tothe circle. Y is a point on XN so that XY : XT. Prove that: : 10.1.1 YTbisect MtN. (5) XM _ XT (6) IO.I.2 XT XN I0.2 Given that MY:20 mm. YN: 50 mm and XT : kmm; " 10.2.1 Express XM in terms of k. (3) 10.2.2 Calculate the length of k. (4) l18l TOTAL MARKS: 150 Copyright Reserved

Downloaded from hlayiso.com Mathematics P2 t2 Preparation Examination September 2020 NSC - Grade 12 -b! 2a A= P(7+ni) A= P(l-ni) A= P(l-i)' A= P(l+i)" Tn = e+(n-l)d d S^= * T, = ar'-r l-r i -l<r<l p- fll=- lt-lt m=tan9 !=mx+c /-h=m(x-x) xz-xl (*-o)'+0-b)'=r' o c o2 =b2 +c2 -2bc.c'osA areaMBC =!ab.snC In AAB1: =-b-= sin r4 sin B sin C 2 sin(a + F): srna.oos B + cosa.stn B sin(a - B) = srna.cns B - cns a.stn B cos(a + F) = cns a.cns B - sin a. sin B cos(a - B)= cosa-eos P +sna.sn B sinz a d stn2a =2sina.cnsa -1 st / -\ _ L\x'-x) i=l -2 n P(A or B) : P(A) + P(B) - P(A and B) Please tum over Copyright Reserved