Mathematics Grade 11 Free State March Test 2022 Paper & Memo

Downloaded from hlayiso.com education Department of Education FREE STATE PROVINCE Downloaded from testpapers.co.za [ GRADE 11 ♦ ,� �----------------------------- �------------� ,, � MATHEM II II II II II II II II II II II ,,II -----------------------------�� #/ This question paper consists of 6 pages Copyright reserved Please turn over

Downloaded from hlayiso.com FS/MARCH 2022 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of THREE questions. 2. Clearly show ALL calculations, diagrams, graphs, etc. that you have used to determine your answers. 3. Answers only will NOT necessarily be awarded full marks. 4. If necessary, round off answers to TWO decimal places, unless stated oth se. � 5. Diagrams are NOT necessarily drawn to scale. c,O 6. You may use an app roved scie n tific calculato r (n�;ramm able an d ated ot e ise � h � r a u � 7. :�:: ::::: :d � :::1: 2

Downloaded from hlayiso.com FS/MARCH 2022 NSC QUESTION 1 1.1 Solve for x. 1.1.1 (x-2)(x+7)=0 (2) 1.1.2 x(5x-3)=1 (Correct to TWO decimal places) (4) 1.1.3 X 2 -X-6<0 (3) 1.1.4 (4) 1.1.5 .J2x-1 + 2 = X (4) � 1.2 Solve for x and y simultaneously x+6 = 2y ♦ 2 x2 + 2xy = 3 y (6) [23] QUESTION 2 2.1 Simplify the following without using a calc�{;/.� gx+l _ 5_32x 2.1.1 C:J \) (4) ( ✓3 x+l )4 2.1.2 R-� ✓x (4) 2.2 Determine the valu�'fk for which the equation ! � x' - x + 1 k * where k o Qal roots. � ( 5) [13] 3

Downloaded from hlayiso.com FS/MARCH 2022 NSC QUESTION 3 Give reasons for your statements and calculations in Question 3 3.1 Complete the following statement 3.1.1 Oppositeangles of a cyclic quadrilateral are.................................. (1 ) 3.2 In the diagram below, O is the centre of the circle. A, B and C are points on the circumference of the circle. AB, AC and OC are drawn. A Prove the theorem which states that BOC= 2x BAC (5) 4

Downloaded from hlayiso.com FS/MARCH 2022 NSC 3.3 In the diagram, O is centre of the circle. Points A, B, C and D lie on the circumference of the circle. BOD is a diameter. 'f:\ = 51' and 131 = 29-·. A line is drawn from Oto F such that the length of BC= 24m and radius of the circle centred Ois 13m. A 3.3.1 Determine the size of COB (2) 3.3.2 Determine the size of A2 . (2) 3.3.3 Determine the size of 5. (1 ) 3.3.4 Determine the length of OF. ( 3) [14] TOTAL [50] 5

Downloaded from hlayiso.com FS/MARCH 2022 NSC INFORMATION SHEET -b± b -4ac X=----- ✓ 2 2a A= P(l+ ni) A= P(l-ni) A=P(l-i) n A=P(l+it S n =�[2a+(n- l)d] 2 a r n -1) ;r:;i=l a Tn = ar -i Sn = ( S =-· -l<r<l n r -1 1-r' 00 F = x[( l+ it -1] p = x[l - (1+i t n] i i f(x+h)- f(x) f'(x)= lim h➔ O h y = mx+c m=-- Y2 -Yi m=tan0 x2 -Xi 2 a b c (x-a) +(y-b)2 = r2 ln.dABC: --=--=-- sin A sin B sin C a 2 = b 2 + c 2 -2bc.cos A area MBC =.!ab.sin C 2 sin(a + JJ)=sin a.cos fJ+cos a.sin fJ sin(a-�)=sin a.cos�-cos a.sin� cos(a+JJ)=cos a.cos /J-sin a.sin fJ cos(a- JJ)=cosa.cosjJ+sin a.sin fJ cos 2 a-sin 2 a cos2a = {1-2sin 2 a sin 2a = 2sin a.cos a 2cos 2 a -l I<xi -x) 0-2 =-i=�l___ 2 n(A) P(A) = P(A or B) = P(A) + P(B) -P(A and B) n(s) y =a+ bx b= =I"=x( =--_xX_Yx)_-2 _Y) I<x- 6

Downloaded from hlayiso.com education Department of Education FREE STATE PROVINCE [ GRADE 11/GRAAD 11 ] �-------�--------------�-----------------------� '# ,: M #fr"i ��MATICS/WISKUNDE �:, • 1-J;,:.j,�-- II II rARCH 2022 ,� RKING f;UIDELINE/NASIENRIGL YN II " - - - - - - - - - - - - - - - - -- - - --- - - . - - ........ - - ._.... - - ti #1 .-... � MARKS: 50 PUNTE: 50 These marking guidelines consists of 6 pages. Hierdie nasienriglyne bestaan uit 6 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com FS/March 2022 Marking Guicfeline NOTE: • If a candidate answers a question TWICE, only mark the FIRST attempt. • CA applies in all aspects of the marking guideline. LET WEL: • lndien 'n kandidaat 'n vraag TWEE keer beantwoord, sien slegs die EERSTE paging na. QUESTION/VRAAG 1 1.1.1 x=2 or x=-7 ✓ X=2 ✓ X=-7 (2) 1.1.2 2 5x -3x-1=0 ✓ standard form ✓ -b ± b 2 -4ac X=----- 2a ✓ 2 _ -(-3)± (-3) - 4(5)(-1) nto the correct 2(5) = 3± ✓-29 10 =0.84 or x=-0.24 ✓ both answers (4) 1.1.3 (x- 3)(x+2)<0 ✓ factors C.V x= 3 or x= -2 ✓ critical values -2< X<3 ✓ answer (3) Copyright reserved/Kopiereg voorbehou

Downloaded from hlayiso.com FS/March 2022 Mark"inq Gu1·cfer e ine 1.1.4 2x +2x .t = 48 ✓ expansion 2x (1+2) =48 ✓ common factor ✓ simplification 2x =16 2x = 24 ✓ answer :.x =4 (4) 1.1.5 (.J2x-1)2 =(x-2)2 ✓squaring both sides 2x-1=x2 -4x+4 ✓standard form x2 -6x+5=0 ✓factors (x-5)(x-1)=0 ✓answer with selection X=5 or X:;t:l (4) 1.2 X=2y-6 ✓ X = 2y-6 (2y-6)2 +2y(2y-6) =3y2 ✓subst 4y2 -24y+36+4y2 -12y-3y2 =0 ✓simplification 5y2 - 36y + 36= 0 (5y-6)(y-6)=0 ✓factors 6 Y=- or y=6 ✓bothy values 5 X=2(�)-6 or X =2(6)-6 18 =-- =6 ✓ both x values 5 (6) Copyright reserved/Kopiereg voorbehou

Downloaded from hlayiso.com FS/March 2022 Marking Guicfeline Question 2 2.1.1 3 2 (x+l) _6.3 2 x ✓ prime factors 3l ( f' 32x+2 _ 5_32x = ✓ simplification 3 2x+� 2 3 2 x 32-6 3" 3l J = ( ) ✓common factor ( 3 1 32 =32 =✓3 1 ✓answer (4) 2.1.2 2ffx-4ffx = 2ffx-4 ffx ✓X ✓ ✓x 2x4 ./x-4x4 ✓X 2X ✓X-4X ✓X 4 4 = ✓x ✓ ✓X = -2x ./x 4 -2x ./x4 ✓X ✓ ✓x =-2x4 ✓answer (4) 2.2 1= kx2 -kx+k 0 = kx2- kx + k-1 ✓ standard form fi=O b2-4ac =O Copyright reserved/Kopiereg voorbehou

Downloaded from hlayiso.com FS/March 2022 Mark"inq Gu1·cfer e ine 2 ( -k ) -4 ( k) ( k -1) = 0 ✓correct subt k2 -4k2 +4k = 0 -3k2 +4k = 0 k(-3k +4) =0 ✓factors 4 k =O or k =- 3 ...�>0 ✓�>0 4 O<k<- 3 ✓answer (5) Question 3 3.1.1 Supplementary or sum up to 1so· ✓answer 3.2 ✓Construction Join AO A Join AO In MOB Copyright reserved/Kopiereg voorbehou

Downloaded from hlayiso.com FS/March 2022 Mark"inq Gu1·cfer e ine 61 =Ai +B ext L. of� ✓S/R But A.1 = B = radii(OA=OB) :. 61 = 2Ai ✓S Similarly in�AOC - ~ - 02 =A 2 + C ext L. of� ButA 2 =C - - .-.6 2 =2A2 .-. .-. �-· ,-. :. 01 + 02 = 2Ai +2A 2 ✓s BOC =2 (A 1 +A2 ) ✓S :. BOC = 2xBAC (5 ) 3.3.1 COB= 2(51') =102' L..at theu = 2 x L..at ci rcum ✓S ✓R 3.3.2 . 1 ✓S A 2 = 39" L..m-J 2 ✓R 3.3.3 15 =180'-(90 ° +29 ° ) = 61 ° sum of L. in� ✓S/R 3.3.4 In �COB 1 CF=-(24 ) line from centre to midpoint 2 ✓S/R OC 2 = CF 2 +OF 2 pyth theorem 13 2 = 12 2 +OF 2 ✓Subst intopyt OF 2 =169-144 OF 2 = 25 OF=Sm ✓answer Copyright reserved/Kopiereg voorbehou