Mathematics Grade 11 September Test 2019 Paper & Memo

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Mathematics Downloaded from hlayiso.com Common Test September 2019 NSC - GRADE 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions: i. 2s 10. Copyright Reserved This question paper consists of 6 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, et cetera, which you have used in determining the 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 to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. TWO DIAGRAM SHEETS for QUESTION 2.2, QUESTION 2.3 AND QUESTION 5.1.1 are attached at the end of this question paper. Detach the DIAGRAM SHEETS and hand in together with your ANSWER BOOK. Write neatly and legibly. Please turn over

Mathematics QUESTION 1 Downloaded from hlayiso.c NSC - GRADE II 1.1 The box and whisker diagram below shows the marks obtained by a class of 19 learners in a mathematics test. The test was out of 100 marks. QM. Test September 2019 o— +e I I I I I I TT d I I 10 20 30, 40 SO 60 70 75 80 90 100 1.1.1 Describe the skewness of the data. (1) 1.1.2 Determine the interquartile range of the data. (2) 1.1.3. If the pass requirement for the test is 30% and only one learner obtained 30% in the test, estimate the number of learners in the class who failed the test. (2) 1.2. The table below shows the price in Rands of I litre of petrol for each month in 2017. Months in the year Jan Feb Mar | Apr | May | Jun Jul Aug | Sep Oct Nov | Dee (2017) Price of 1 litre of petrol 13.09 | 13.38 | 13.30 | 13,08 | 13.57 | 13.32 | 12.63 | 12.82 | 13.49 | 13,74 | 13,78 | 14.49 (in Rands) 1.2.1 Determine the mean price of petrol in 2017. (2) 1.2.2 Write down the standard deviation of the data. (1) 1.2.3. In how many months during 2017 was the price of | litre of petrol outside ONE standard deviation of the mean? (3) (11) Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics Common Test September 2019 NSC - GRADE I QUESTION 2 The amount of data, in megabytes, that a student used browsing the internet each day was recorded. The information is given in the frequency table below. | Amount of data used (in megabytes) | Number of days 100< ds 200 2 200< d < 300 5 300< d < 400 Ul 400< d< 500 25 S00< d < 600 37 600< ds 700 21 700< d < 800 15 800< ds 900 14 2.1 Calculate the estimated mean amount of data used per day. (3) 2.2. Complete the cumulative frequency column in the table provided on DIAGRAM SHEET I. (2) 2.3. Use the grid provided on DIAGRAM SHEET | to draw an ogive (cumulative frequency curve) to represent the data. (4) [9] QUESTION 3 3.1 Two bags, A and B, are filled with coloured balls. It is equally likely that Jade will choose bag A or bag B. Bag A is filled with 5 green balls (G) and 3 yellow balls (Y). Bag B is filled with 2 green balls (G) and 6 yellow balls (Y). Jade randomly selects a bag and draws a ball from it. 3.1.1 Draw a tree diagram to represent the above information. Show the probabilities associated with each branch as well as the possible outcomes. (3) 3.1.2. Write down the probability that Jade will select bag A and draw a green ball from it. qd) 3.1.3. Calculate the probability of Jade choosing a yellow ball. (3) 3.2. Aand B are two events ina sample space. P(not A)=0,48 and P(B) = 0,32. 3.2.1 Determine P(A). dl) 3.2.2 Determine P(A and B) if A and B are independent events. (2) Copyright Reserved Please turn over

Mathematics Copyright Reserved Downloaded from hlayiso.com Common Test NSC - GRADE I1 During the Olympic Games in 2016, complaints about a certain hotel fell into 3 main categories: Reception (R), Food (F) and Accommodation (A). A total of 173 complaints were received about this hotel. There were: 115 complaints about the Reception. 55 complaints about the Food. 63 complaints about the Accommodation 23 complaints about the Reception and the Food but not the Accommodation. 12 complaints about the Reception and the Accommodation but not the Food. 17 complaints about the Food and the Accommodation but not the Reception. Let the number of complaints about all 3 categories be x. 3.3.1 Draw a Venn Diagram to represent the information above. 3.3.2 Determine the value of x, September 2019 3.3.3. Determine the probability that a complaint, selected at random from those received, was about: (a) The Accommodation only. (b) At least two of the categories. (1) (2) [18] Please turn over

Downloaded from hlayiso.com Mathematics. ‘ommon Test September 2019 NSC - GRADE 11 QUESTION 4 4.1 The sketch below shows APQR with PQ = 32 mm, QR = 60 mm and P= 50°, 60 mm Calculate the size of R . (3) 4.2. ADEF is shown in the sketch below. G is a point on DF and EG is drawn. DG=DE=.x, FG= = and EG = V3x. 3x = F 2 E 4.2.1 Calculate the size of D. (4) 4.2.2 Calculate the area of AGEF in terms of xx, in its simplest form. (5) {12} Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics Common Test September 2019 NSC - GRADE II QUESTION 5 5.1 Given f (x)= 2cos3x. 5.1.1 Use the grid on DIAGRAM SHEET 2 and draw a sketch graph of f for the interval x €[—-90° ; 90°}. Clearly show all intercepts with the axes and turning points of the graph. (3) 5.1.2 Write down the period of /- (1) 5.1.3. Write down the range off. (1) 5.2 Inthe diagram below the graphs of g(x)=sin(v+a) and A(x)=btanex are drawn in the interval «e[-180° ; 180°]. g and A intersect at D and E. The coordinates of D are (—135° ; =1) and the coordinates of E are approximately (—22,3° : 0,4). 5.2.1 Write down the values of a, b and c. (3) §.2.2 Write down the equations of the asymptotes of /i in the interval [-180° ; 180°). Q) 5.2.3 Solve for vif g(+)—h(.)>0 in the interval [-180° ; 0°]. (4) 5.2.4 Describe the transformation of g to m if m(x)=cosx-1. (2) [16] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics Common Test September 2019 NSC - GRADE 11 QUESTION 6 6.1 The sketch below shows a pyramid on a square base. The length of a side of the base is 10 em and the perpendicular height of the pyramid is 15 cm. Volume of pyramid =4 x area of base x perpendicular height Total surface area of pyramid = area of base + sum of areas of the triangular faces 6.1.1 Calculate the volume of the pyramid. (2) 6.1.2 Calculate the total surface area of the pyramid. (4) 6.2. Achild is given some modelling clay to play with, At first, he uses all the clay to make a single sphere (ball). Thereafter, he uses all the clay to make identical smaller spheres. If the diameter of each of the smaller spheres is exactly half the diameter of the original sphere, how many smaller spheres will he be able to make? 4 Volume of sphere = wer | Total surface area of sphere =471r° | GB) [9] TOTAL MARKS: 75 Copyright Reserved

Downloaded from hlayiso.com Mathematics Common Test September 2019 NSC - GRADE 11 : NAME & SURNAME: i DIAGRAM SHEET 1 ? QUESTION 2.2 : Amount of data used (in megabytes) | Number of days | Cumulative frequency : 100< d < 200 2 : 200< d < 300 5 : 300< d = 400 1 : 400< ds 500 25 : 500< d < 600 37 : 600< d < 700 21 : 700< d < 800 15 i 800< d < 900 14 i UESTION 2.3 i 130 she =o He} in 120 = 110 ; 100 : 90 : 80 : = : = 70 s a z i . o < 60 . wv ; 3 50 : E : 3 : 40 : 30 i 20 : 10 ; 0 100 200 300 400 500 600 700 800 900 i Amount of data used (in megabytes) i Copyright Reserved Please turn over

Common Test September 2019 iso.com yiso 10 NSC - GRADE Tt Downloaded from hla Mathematics NAME & SURNAME: DIAGRAM SHEET 2 QUESTION 5.1.1 30° 15° ~75° 60° \ 30° -15° (09 ~90° 50 4 dAdO YUVAL i a3 Copyright Reserved Ae ee nen cee nee neneeseeen nes werseenemeeseenaseaneee

hlayiso.com Mathematics 2 Common Test September 2019 GRADE 11 Marking Guideline - QUESTION 1 education 1.1.1 | Data is skewed to the left or negatively skewed ¥ answer | Department: | (} Education } 11.2 |IQR = 75-30 ¥ both quartifes | PROVINCE OF KWAZULU-NATAL = 45 Answer only: Full marks || “ answer o AB - We 1 ~ 30 marks is at position gsr) | | =5 Y position 5 | NATIONAL <4 failed the test Answer only: Full marks || ~ answer | SENIOR CERTIFICATE @)) 120 | 160, Y 160,69 | 12 =RI3,39 Answer only: Full marks ¥ answer Q) | 1.22 [oo Y ans GRADE 11 o=R0,47 answer - 1.2.3 | (1339-047; 13,39 + 0,47) = (12,92 ; 13,86) YY interval -.3 months ~ answer SW SSS Se Pec cca e esc e eee SSB esceSesccErES, QB) MATHEMATICS _ (| COMMON TEST SEPTEMBER 2019 MARKING GUIDELINE Sssseesesseseast % MARKS: 75 This marking guideline consists of 8 pages. Please turn over Copyright Reserved Please tum over

Downloaded from hlayiso.com Mathematics Common Test September 2019 GRADE I Marking Guideline QUESTION 3 3d Bags Balls | Outcomes G 5 AG 8 x A 2 3 branches Y AY | ¥ probabilities on branches G BG ¥ outcomes 1 # z 8 B 8 3 ¥ BY (3) 342 P(green ball from bag A) = 3 = Zor 031 % answer qa) 3.1.3 3) (16 13 (5 x8) P(yellow ball xs |+| x= ea (>) G q “(» a 2°8 = — OR 0,56 ¥ answer 16 G3) 32.1 | P(A)=1-048 = 0,52 ¥ answer dy) wis P(A and B) = P(A) x P(B) = 0,52 x 0,32 ¥ correct substitution into formula =0,17 or 14 Y answer 625 Q) Mathematics Commo. st September 2019 GRADE Marking Guideline QUESTION 2 2.1 | (150% 2) + (250%5) + (350%11) + (450%25) + (550%37) + (650% 21) + (750%15) + (85014) 130 =~ 23800 ¥ 73800 130 ¥ 130 = 567,69 megabytes Y answer (3) 22 | Amount of data used (in megabytes) | Number of days _| Cumulative frequency | 100< ds 200 2 2 200< d < 300 5 7 300< ds 400 ul 18 400< d < 500 25 B ¥ 2,7, 18,43 500< d< 600 37 80. 600< ds 700 21 101 700< d= 800 15 16 ee S00< d< 900 4 130 : Le (2) 2.3 130 | a = ' ; 0 | = 1 100 = 80 — ¥ grounded _ -_ at (100 ; 0) = 70 2 Y upper £ 60 limits |g | a 5 ¥ cums (2 S= | 6 ¥ shape: | smooth curve | = == i | 0 & ° = 0 100 200 300 «400» $00 600-700» 800-900 ‘Amount of data used (in megabytes) [91 Copyright Reserved Please turn over Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics. Common Test September 2019 oxabe u Marking Guideline 33.1 ¥ 80-x ,23 Vv 15-x ,17 Y 34—x .12 QB) 3.3.2. 80—x+234+15—x4+12+x417434—x=173 ~ sum of values in Venn 181-2x=173 diagram +173 xed Y answer (2) 30 3 3.3.3(a) | P(A only) = — answer 173 a) 23+ 12444 17= 56 3.3.3(b) | P(at least two categories) = aa = a OR 0,32 ¥ answer (2) [18] QUESTION 4 41 | sink _ sinP | rp sinR _sin50° Y applying sine rule in APQR 32.0. anR= ae # sink the subject of the formila R=24,11° Y answer | (3) Copyright Reserved Please turn over Mathematics Common Test September 2019 okADE I Marking Guideline 4.21 EG? = DE’ + DG? -2.DE.DG.cosD (v3x) =x°+x?-2.xx.cosD 3x? =2x* —2x* cosD #42xrcosD=0 OR 2x*cosD= ¥ applying cosine cule in ADEG ¥ simplification x (1+2cosb) = cosD= -} Y value of cosD D=120° ¥ answer (4) . e130 4.22 pée=80-E {sum of 2s of isosceles A] = 30° ¥ size of DGE EGF=180°-30° [Zs on a straight line] . = 150" Y size of EGF Atea of AGEF = 4(GE)(GF) {sin EGF) Y applying area rule in AEGF =5 (vie Bx)( =] (ints0) ¥ substitution 3x -3(F 3) 3p aa oa ¥ answer (5) OR Area of AGEF = Area of AEDF - Area of AEDG =3(s) (é x] in120")—L(a)(a)( (sin 120°) ¥ Area of AEDF—Area of AEDG Y applying area rule in AEDF ¥ applying area rule in AEDG Y substitution ¥ answer (5) 121 Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics: Comm «st September 2019 GRADE 1 Marking Guideline QUESTION 5 S.LL ¥ x— intercepts v y— intercept Y turning points @) $1.2 Y answer a 5.1.3 Y answer () 5.2.1 v a=45° ¥ b=-1 Y cal (3) S22! v x=-90° Y x= 90° (2) 5.2.3 | -135°<.x<-90° or -22,3°<x<0° Vv -135°Sx<-90° vv -22,3°Sxs0° (4) 5.2.4 | Shift the graph of g 45° to the left and 1 unit downwards Y shift 45° to the left © shift 1 unit downwards (2) [16] Copyright Reserved Please turn over Mathematics Common Test September 2019 Ripe iu Marking Guideline QUESTION 6 6.11 1 - V=3%area of base x height 1 2 3 x 10° x15 Y substitution = 500 cm* Y answer Q) 6.12 Rr Slant height = V5? +15? = J250 = SV10 v V3?+15" or ¥250 OR sv10 TSA of pyramid = area of base + 4(area of a triangle) Y substitution into correct formula 1 100 + 4{Zx10xsVi0} w pxloxsvi0 = 416,23 cm? ¥ answer (4) 6.3 1 Let Fsingle sphere = and Fsmalier sphere = a 4 Then: Vsingle sphere = yer And: Vsmailer sphere ~4e(5-) 2 wi a(t ? } 3 \8 =1(4 ay Zefa, ‘) =i(3") (fxr Therefore 8 smaller spheres can be made using the same ¥ answer modelling clay. GB) OR OR The radius of a smaller sphere is 2 times smaller than vr =2 times smaller radius of the single sphere. Because the volume of a sphere depends on r°, the ¥ V= 2° times smaller volume of the smaller sphere will be 2° =8 times smaller than the volume of the single sphere. Therefore 8 smaller spheres can be made from the Y answer modelling clay. @G) TOTAL: 75 Copyright Reserved