Mathematics Grade 11 KwaZulu Natal June 2021 Paper & Memo

Downloaded from hlayiso.com \ KWAZULULNAT EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE MATHEMATICS COMMON TEST JUNE 2021 This question paper consists of 6 pages and 1 diagram sheet.

Downloaded from hlayiso.com Mathematics 2 Common Test June 2021 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. 10. This question paper consists of 5 questions. Answer ALL the questions. Number the answers correctly according to the numbering system used in this question paper. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. A DIAGRAM SHEET for QUESTION 3.2 is attached at the end of this question paper. Detach the DIAGRAM SHEET and hand it in together with your ANSWER BOOK. Write neatly and legibly. Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 3 Common Test June 2021 NSC QUESTION 1 The first three terms of a quadratic number pattern are 50; 35 and 24. 1. Write down the next two terms in this number pattern. 1.2 Determine the general term of this number pattern in the form 7), = an’ +bnt+c. 8) Calculate the value of the 30" first difference of this number pattern. QUESTION 2 Given: f(x)=-2x? —4x+30 2.1 Determine the x-intercepts of f 2.2 Determine the equation of the axis of symmetry of f 2.3 Determine the range of f. 2.4 Graph g is obtained by reflecting graph fin the x-axis and then translating it 4 units to the right. Determine the equation of graph g, in the form g(x) = a(x + py +q. Copyright Reserved Please turn over (2) (4) (3) 19] Q) (2) (2) (3) {10}

Downloaded from hlayiso.com Mathematics 4 Common Test June 2021 NSC QUESTION 3 The diagram below shows the graph of hyperbola f passing through the point - 334) and having asymptotes intersecting at (— 2;1). (2:1) 3.1 Determine the equation of fin the form f(x) Ss q- (3) x+pD 3.2 The graph fis drawn on the grid on the diagram sheet. On the same grid, sketch the graph of g(x)= 2~*-—-4. Clearly label all the intercepts that g makes with the axes and show any asymptotes of g. (5) 3.3 If itis given that f and g intersect at (-3;4) and (-1;- 2), determine the values of x for which g(x)> f(x). (3) [11 Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 5 Common Test June 2021 NSC QUESTION 4 4.1 P(—4;3)and Q(2;k) are two points in the Cartesian plane such that the gradient of PQ is positive and the distance PQ is2V10 units. y] Q2 sh) P(-4 ; 3) a1 Show that k =5. GB) 4.1.2 Determine the equation of PQ. (4) Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 6 Common Test June 2021 NSC 4.2 In the diagram A(-1 ; 4) and C(4 ; -1) are points in a Cartesian plane. B is a point on the x- axis such that BAC = 54,46". A134) y 54,46° > B x C(4 3-1) y 4.2.1 Calculate the size of (0), angle of inclination of AC. (3) 4.2.2 Calculate the coordinates of B. (4) [14] QUESTION 5 Consider the following equation: 3sin? x +cos* x-5=7sinx. 5.1 Show that the equation 3sin? x + cos? x5 =7sinx can be written as 2sin? x—7sinx—4=0. a) 5.2 Hence, or otherwise, determine the general solution of 3sin* x +cos* x-5 =7sinx. (5) [6 TOTAL: 50 i Copyright Reserved Please turn over

3 N 5 & : S 7: oO > VY fo} a >= S cS Eg . = 2 (ra nN me) 4 Zz s S iS S 3 Se 2 & D = & a E 2 3 = Ze Copyright Reserved AdO UVAL

Downloaded from hlayiso.com Mathematics 2 Common Test June 2021 GRADE 11 Marking Guideline QUESTION 1 KWAZULU-NATAL PROVINCE REPUBLIC OF SOUTHAFRICA 7 2 ] 7 iu ~~ i ~~ < N\ : 4 ~ | A ~~ 4 NATIONAL 17 14 v17 SENIOR CERTIFICATE : a C 12 2a=4 a=2 v value ofa 3a+b=-15 3(2)4+b=-15 ¥ value of b at+b+c=50 - 2+(-21)+c=50 a o : “ % c= 69 . MATHEMATICS: ‘a 7, =2n? -21n+ 69 vt, a 2 1" (4) . i COMMON‘ TEST ” 13 First —— pattern: i fo Pel Poet : : heme a n= : JUNE 2021 : 7 416 v 7, =4n-19 ‘ 4 A MARKING GUIDELINE : T, =4(30)-19 Y substitution 7 ane 7 =101 v answer Pritt Q) [9] MARKS: 50 This marking guideline consists of 7 pages. Copyright Reserved Please turn over Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 3 Common Test June 2021 GRADE I1 Marking Guideline QUESTION 2 Pl For x-intercepts, substitute 7 =0 : y=~2x? —4x 430 2x? -4x+30=0 ¥ substitute y=0 x? +2x-15=0 (x +5x-3)=0 Y factors x=—-5 or x=3 Y both answers @) 22 ait : 2a one) Y substituti 2-2) substitution =-1 v answer (2) OR OR ~ substitution v answer Q) 23 fE1)=-2(-1) -4(-1)+30 =32 Range: y<32 OR Y&(—00 32] Y substitute y=—1 Y y<32 OR ye (-«:32] Q) 24 S(x)=-2x +1)? +32 — f(z) = 2x41) -32 e(x)=2(x+1-4) -32 e(x)=2(x-3)? -32 S(x)=-2(e +1)? +32 Y for reflection in x-axis ¥ translation of 4 units right Y g(x)=2(x-3)? -32 @) OR OR Tuming point of f (-1;32) Turing point of g: (3 ;—32) : Y for a=2 © 9x) 2x-3P -32 g(x)=2(e-3P va es) Y for minimum value of -32 (3) [10] ] Copyright Reserved Please turn over Mathematics 4 Common Test June 2021 GRADE II Marking Guideline QUESTION 3 3.1 a ya 49 xtp a =—L41 are) Substitute (-3;4) 4-41 -342 -3 V y= 41 if x42 (3) 32 For x-intercept, substitute y= 0: 0=2%-4 a*=4 Vv x=2 ¥ shape g Indicating the: Y x-intercept v y-intercept f Y asymptote C2) 24 I () 23) xS-3 or -2<xs-l ¥xs-3 vv -2<xs-l (3) OR OR xe(-0;-3] U-2;-1] ¥ (-0:-3] vv(-2,-1] 3) (1) Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 5 Common Test Sune 2021 GRADE 11 Marking Guideline QUESTION 4 4] 2i0= Va = a) +O. F 2V10 = RT| 2-(-4)F +(k-3 Y substitution 40 =(k-3) +(2+4)* ¥ squaring both sides 40 =k? —6k +9436 ik? -6k4+5=0 (k-1fk~-5)=0 ¥ factorisation kelork=5 412 & : aaa x-% ¥ substitution . Y value of m y—y =m(x-x,) yemxtc Substitute (— 4:3) and m= ; : 1 i ada’ (x-C4)) OR 3= re 4)+e | v substitution 14 13 -3ssx42 apt y cae ce i 3 ie v Saxe ee answer ir) aD 4) Copyright Reserved Please turn over Mathematics Gg Common Test June 2021 GRADE i! Marking Guideline 42.1 Y tig =-1 Reference angle: 45° v reference angle: 45° Angle of inclination =180° — 45° = 135° v answer: 135° GB 4.2.2 | Angle of inclination of AB =135° —54,46° = 80,54" ¥ 80,54" os mtgg = tan80,54° =6 Y my =6 Y equating “2 3 (4) OR OR Angle of inclination of AB = 135° —54,46° = 80,54" ¥ 80,54" J. Mg = tan80,54° =6 Y yy =6 Equation of AB: y==6x+¢ Substitute (— 1,4): ¥ equation of AB Substitute y = 0: 5 wean V xen : Af 5 0) U3 (4) {14} Copyright Reserved Please tum over

Downloaded from hlayiso.com Mathematics 7 Common Test June 2021 GRADE 11 Marking Guideline QUESTION 5 SA 3sin? x + 00s? x— 3sin? x+1—sin? x-5=7sinx Y cos’ x=1-sin? x 2sin? x—7sinx—-4=0 a) $2 2sin? x-7sinx-4=0 (2sin x +1Xsinx-4)=0 Y factors : v = et inx=4 sinx=—5 or sinx=4 sinx=—> or sinx Ref. 2: 30° no solution ¥ no solution x= 180° +30° +4.360° (third quadrant) = 210° +4360" or x= 360° —30° +%.360° (fourth quadrant) ¥ x=210° or x=330" = 330° + 4.360" ¥ +k360° :keZ keZ (3) [6] TOTAL: 50 Copyright Reserved