Maths-Grade-11-SEPT-2022-QP-and-Memo.pdf

Downloaded from Stanmorephysics.com | Ce HEE Gy I” KWAZULU-NATAL PROVINCE raNi, EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE MARKS: 75 TIME: 1% hour This question paper consists of 8 pages and 1 diagram sheet.

Matlaganealoaded From Stanmorephysics. COM Common Test September 2022 Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 2. 10. 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, etc. which you have use@® determining your answers. rey Answers only will NOT necessarily be awarded full marks. a ani You may use an approved scientific calculator (non-program: Ne d non-graphical), unless stated otherwise. XN If necessary, round off answers correct to TW! imal places, unless stated otherwise. Diagrams are NOT necessarily drawn to sa A DIAGRAM SHEET for QUESTION 33.1 and QUESTION 4.1 is attached at the end of this question paper. Detachthe DIAGRAM SHEET and hand it in together with your ANSWER BOOK. e) Write neatly and legibly Copyright Reserved Please turn over

Matlagunealoaded from Stanmorephysics. Com Common Test September 2022 Grade 11 QUESTION 1 1.1 A survey was conducted among 560 drivers about the number of accidents they were involved in during one calendar year. The results are summarised in the table below. a 4 Number of accidents wey Of driver Two or fewer More than two Total 30 years and younger 157 51 208 Older than 30 years 304 48 352 Total 461 99 SAO 1.1.1 Use the information in the table to calculate the probability that a driver selected at random from this group: oy CO (a) is older than 30 years. (2) (b) was involved in more than two sei the year. (1) (c) is older than 30 years and wonifiSer in more than two accidents in the year. & (2) 1.1.2 Are the events “being invo w more than two accidents in the year” and “being older than 3 rs” independent of each other? Motivate your answer by “oo ‘vant calculations. (3) 1.2 For two events, A and B se sample space §S, it is given that: e P(A) =0,55 ° P(B)=0,6 g@ e P(Aand 25 1.2.1 aw a Venn diagram to represent this information. (4) (@) Determine P[not(A or B)]. dd) 1.2.3 Determine P[A and (not B)]. qd) 1.3 During a virus pandemic Khanyi decides to visit her friend Nozipho. Neither of them knew that Nozipho had contracted the virus. e The probability that both of them will be wearing masks during the visit is 82%. e Ifthey are wearing masks during the visit, the probability that Khanyi will contract the virus is 8%. e Ifthey are not wearing masks during the visit, the probability that Khanyi will not contract the virus is 27%. What is the probability that Khanyi will contract the virus because of the visit to Nozipho? (5) [19] Copyright Reserved Please turn over

Matlpganeloaded From Stanmorephysics. COM Common Test September 2022 Grade 11 QUESTION 2 A tyre manufacturer collected data on how far cars could travel using one set of tyres. The distances, in 1000’s of kilometres, covered by cars using one set of tyres are shown in the ogive (cumulative frequency curve) below. Ogive (cumulative frequency curve) showing the distances travelled by cars using one set of tyres 120 110 100 B90 5 3. 80 5 oO & 70 oO = 60 8 =I 2 50 5 40 30 20 10 0 t 10 615) «6©200«25 80's 8S Oss SZ 5855S CSC CS 8 Distance travelled in 1000's of kilometres 2.1 What is the total number of Cars’on which data was collected? = ie 2.2 Write down the modal class of the data. 2.3 Use the ogive to determine the median number of kilometres travelled before new tyres were required. 2.4 In the survey, what percentage of the cars travelled more than 50 000 km with one set of tyres? Copyright Reserved Please turn over () (2) (2) (3) [8]

Matixeaiwaloaded from Stanmorephysics. CoM Common Test September 2022 Grade 11 QUESTION 3 The data listed below shows the distance (in kilometres) travelled by cyclists on each day of a twelve day cycle tour: 3.1 3.2 3.3 3.4 82 89 94 100 113 121 123 128 128 132 135 140 Determine 3.1.1 the mean distance travelled per day 3.1.2 the standard deviation of the data On how many days do the cyclists travel a distance that is outside of one standard deviation from the mean? Show all your calculations. The 5-number summary for the data is as follows: (82 ; 97 ; 122 ; 130 ; 140). 3.3.1 Use the scaled line on the DIAGRAM SHEET to draw a box-and-whisker diagram for this set of data. 3.3.2 Comment on the skewness of the data. Before the start of each day’s section of the tour, the cyclists had an additional warm- up ride of x km. If this is also taken into account, write down, in terms of x (where applicable) 3.4.1 the mean distance travelled per day 3.4.2 the standard deviation Copyright Reserved Please turn over (2) (1) (3) (3) (1) (2) (1) [13]

Matineaiwaloaded from Stanmorephysics. CoM Common Test September 2022 Grade 11 QUESTION 4 41 Draw the graph of, vy =—2sinx, for x e[—90° ;270° ] on the set of axes provided on the DIAGRAM SHEET. Clearly indicate all intercepts with the axes, turning points and end points. (4) 4.2 In the diagram, the graphs of f(x)=tanbx and g(x) =cos(x—30°) are drawn on the same set of axes for x €[—180° ;180°]. P(90°; 1) lies on f and Q lies on g, such that PQ is parallel to the y-axis. A is a turning point of g. cd aq a \ 2 S / ne, A ae o 2 Use the diagram to answer the following questions: 4.2.1 Write down the value of b. () 4.2.2 Write down the coordinates of A, the turning point of g. (2) 4.2.3 Write down the coordinates of Q. (2) 4.2.4 Write down the equation of the asymptote of y=tanb(x+20°) for x €[-180° ;180°]. (1) 4.2.5 Determine the range of hif A(x) = g(x)+3. (2) 4.2.6 For which values of x, in the interval x €[0°,.:0u°y, will f(x).g(x) <0? (3) [15] Copyright Reserved Please turn over

Matineaiwaloaded from Stanmorephysics. com Common Test September 2022 Grade 11 QUESTION 5 5.1 In the diagram below, F=35°, E=90°, GDF =14° and FG =7m. D 2 LI 35° E G Tm F 5.1.1 Write down the size of EGD. (1) 5.1.2 Calculate the length of DE. (5) 5.2 The diagram below shows a regular octagon inscribed in a circle of radius r cm and with centre O. A and B are two vertices of the octagon. AO, BO and AB are drawn. — A B Se 5.2.1 Show that the area of the octagon is 2V27? cm’. (4) 5.2.2 If r=5 cm, calculate the perimeter of the octagon. (3) [13] Copyright Reserved Please turn over

Matineawaloaded from Stanmorephiysics. COM Common Test September 2022 Grade 11 QUESTION 6 The solid below was made by drilling a right circular cone out of a right rectangular prism (i.e. the cone is removed from the prism). P, Q, Rand S are vertices of the prism such that PQ = 20 cm, QR = 15 cm, RS = 12 cm. The radius of the cone, 7, is 4,5 cm and the height of the cone, A, is 6 cm. The slant height ofthe cone is /. Total surface area of a cone = zr? +r S | | | | | | 12 cm | N / | \ ec M | * “ 7 ‘ pot dt R / \ / / ys / \ if \l/ / v 15cm / / / / P 20cm Q Calculate the total surface area of the solid. [7] TOTAL: 75 Copyright Reserved

Matineaiwaloaded from Stanmorephysics. com Common Test September 2022 Grade 11 NAME & SURNAME: DIAGRAM SHEET QUESTION 3.3.1 I T T T I T I T I y T 1 1 80 90 100 110 120 130 140 QUESTION 4.1 gle 3 2 1 —90° 0 ' 90° : j 180° : 270° 4 i i i i i i ~a'- ae ne ae | ee et nana Copyright Reserved

Downloaded from Stanmorephysics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE This marking guideline consists of 7 pages.

Mathefagwrdoaded from Stanmorephysics.com GRADE 11 Marking Guideline QUESTION 1 Common Test September 2022 P(older than 30 years) = 352 ¥ 352 (as numerator) . 560 ¥ 560 (as denominator) a . : (a) = 0,63 Answer only: full marks (2) . 99 1.1.1 | P(more than 2 accidents) = —— 99 (b) 560 v answer (——or 0,18) =0,18 560 0) . 48 i P(older than 30 years and more than 2 accidents) = 560 Y 48 in numerator fe = 0,09 v answer (2) 1.1.2 P(older than 30 years) x P(more than 2 accidents) 2 = 352 x 2 Y calculating P(older than 560 560 30 years) x P(more than 2 _ 1089 or 0,11 accidents) 9800 .. P(older than 30 years) x P(more than 2 accidents) # V reasoning P(older than 30 years and more than 2 accidents) v . Therefore: the events are not independent conclusion G) 1.2.1 P(S) P(A One mark each for the (A) P(B) following values placed correctly: v 0,3 v 0,25 v 0,35 v0,1 0,1 (4) 1.2.2 | P[not(A omB)] = Ogi V0,1 Q) 1.2.3 | P[A and (not B)] =0,3 ¥0,3 Q) Copyright Reserved Please turn over

Mathehaowrdoaded from Stanmorephysics.com Common Test September 2022 GRADE 11 Marking Guideline 1.3 A tree diagram may be drawn to represent all the possible outcomes with their probabilities: Contract 0,08 Masks 0,82 0,92 Not Contract Contract 0,73, 0,18 No masks 0,27 Not Contract P(mask and contract) + P(no mask and contract) ¥¥ 0,82 0,08 = 0,82 x 0,08 + 0,18 x 0,73 vv 0,18 0,73 =0,20 or 20% ¥ answer after addition (accept 19,70%) (5) [19] QUESTION 2 2.1 120 cars v answer Q) 2.2 45000 < x < 55000 vv answer Y (2) OR fr J 45000<x<55000 vv answer 0) 2.3 46 500 km vv answer (accept from 46 000 to 47 000) (2) 2.4 120 — 77 = 43 cars Y 77 (accept 76 to 78) vo 9 Percentage: 8 = 35,83% 43 (accept 42 to 44) 120 VY 35,83% (accept 35,0% to 36,67%) (3) [8] Copyright Reserved Please turn over

Mathehaowrdoaded from Stanmorephysics.com GRADE 11 Marking Guideline Common Test September 2022 QUESTION 3 3.1.1 1385 vy 1385 12 12 = 115,42 v Answer only: full marks answer (2) 3.1.2 | 18,67 km v answer dQ) 3.2 | Interval: —(115,42—18,67 ; 115,42 +18,67) = (96,75 ; 134,09) Y 96,75 Outside of this interval: (82; 89; 94; 135; 140) ¥ 134,09 Therefore: on 5 days Y answer (3) 3.3.1 v whiskers —______ |__1 ending at 82 and 82 97 722 730 140 ee + +‘ + + + box from 97 I q I T I T J I ' T 1 to 130 80 90 100 110 120 130 140 | Q, at 122 (3) 3.3.2 | The data is skewed to the left OR negatively skewed v answer () 3.4.1 New mean = 1385+12x y 1385+ 12x 12 Answer only: full marks 12 =115,42+x Vv 115,42+x (2) 3.4.2 | 18,67 km vv answer dQ) [13] QUESTION 4 41 (-90°;2) (270°;2 v x-intercepts t and y-intercept Y turning point Vv : oD 0° x end points an (90°:-2) v shape (4) Copyright Reserved Please turn over

Mathefagwrdoaded from Stanmorephysics.com Common Test September 2022 GRADE 11 Marking Guideline 1 Y answer 4.2.1 == 2 Q) 42.2 | AGo':1) Y 30° vor (2) 423 (90:5) v . vo 2 (2) 4.2.4 | x=160° v answer dd) 42.5 | 2<y<4 ¥ endpoints Y correct notation OR (2) ye[2; 4] Y¥ endpoints Y correct notation (2) 4.2.6 | »=0° or 120° <x <180° VY x=0° Y endpoints of interval OR Y correct notation G3) x=0° or xe[120° ; 180°) vx=0 Y¥ endpoints of interval Y correct notation GQ) [15] QUESTION 5 5.1.1 | 49° v answer dd) s12| DG_ GF — a“ sinF sinFDG Y applying sine rule in triangle DGF DG 7 ae : =— Y substitution sin35° sinl4° DG= 7xsin35 sin 14° _ 7xsin35° sin 14° Vv = 16,60 m length of DG DE = sin EGD DG DE — . aoe Y substitution in correct trig —— =sin 49 : 16,60 ratio DE=16,60xsin 49° -1253m ¥ answer (5) Copyright Reserved Please turn over

Matheaowrdoaded from Stanmorephysics.com Common Test September 2022 GRADE 11 Marking Guideline A 360° ° . A 5.2.1 | AOB =—— = 45 [ Zs around a point] ¥v AOB=45° AOQ=BO=r Area of AAOB= 5AO-BOssin AOB = 1 sins” Y substitution into area rule -lp _ OR 1p ve vip? tL or 1? v2 2 \V2 2 (2 2 \W2 2 | 2 Area of the octagon = 8x Area of AAOB 1 2 -( 35) OR (2 )2 ¥ 8xArea of AAOB = 4 2 2 2 -(4} OR (2v2)r cm _| 2x V2xV/2 2 V2 =2/2r? cm? (4) 5.2.2 | AB’ =AO’ +BO*=2.A0,BO.cos AOB =57 +57 —2(5\(5)cos 45° Y substitution into cosine rule =14,64 - AB=3,83 cm Y length of AB .”. perimeter = 8 x 3,83 = 30,61 cm v answer G) [13] Copyright Reserved Please turn over

Mathefagwrdoaded from Stanmorephysics.com GRADE 11 Marking Guideline QUESTION 6 Common Test September 2022 TSA of prism = 2(12x20)+2(12x15)+2(15x 20) =480+360+600 =1440cm? Area of circular base of cone = 2x1? =2x4,5° = 63,62 cm? Slant height of cone (@) = Vh? +r = 6° +4,5° =7,5cm Lateral surface area of cone = 7 xrx =71x4,5x7,5 = 106,03 em? TSA of solid =1440 +106, 03 — 63, 62 =1482,41 cm? ¥ 2(12x 20) + 21215) +2(15x 20) v answer Y 63,62 cm? Y using Theorem of Pythagoras v¥ 7,5 cm ¥ 106,03 cm? v answer [7] Copyright Reserved TOTAL: 75