Mathematics Grade 11 KZN September Test 2024 Paper & Memo

‘anmorephysics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFIC > a ” Sseseensene?® “ a cy cy o o “ a o J J ° feseesesseses MARKS: 75 TIME: 1% hours This question paper consists of 8 pages and 2 diagram sheets. Please Tum Over

madoaKenl oaded from Stanmor ephy sics.com Septomber 2024 Common Teat NSC — Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions, 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 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. TWO DIAGRAM SHEETS for QUESTION 2.1, QUESTION 2.2, QUESTION 6.1, and QUESTION 6.2 are attached at the end of this question paper, Detach the DIAGRAM SHEETS and hand it in together with your ANSWER BOOK. Write neatly and legibly. Copyright Reserved Please Turn Over

M tics “Bownloaded from Stanmoxepliyaics.com Sepsonmiber 2024 Conamen Test QUESTION 1 The table below shows the marks, as a percentage, scored by 10 learners in a Maths Olympiad. MARKS OBTAINED (AS A PERCENTAGE) 65 | 59 | 79 | 86 | 48 | 94 | 77 | 51 | 66 | 80 1.1 Calculate the mean mark of the data. (2) 1.2 Write down the standard deviation for the above data. (1) 1.3 Calculate the number of marks that lie within one standard deviation of the mean. (2) 1.4 Two learners were omitted from the original set of data. Their scores were x and 58. When the scores of these two leamers are included with the original set of data, then the new mean is now 67,5. Calculate the value of x. (2) [7] QUESTION 2 The ages of people who attended a musical concert was recorded. The information was summarised in the frequency table below. 2.1. Complete the cumulative frequency column in the table provided on DIAGRAM SHEET 1. (2) 2.2 Use the grid provided on DIAGRAM SHEET | to draw an ogive (cumulative frequency graph) to represent the data. Q) 2.3. Write down the modal class of the data. (1) 2.4 Youth are regarded as people below the age of 35. What percentage of youth attended the concert? (2) Copyright Reserved [8] Please Turn Over

MiQeuwaloaded from Stanmorephysics.com September 2024 Common Test NSC - Grade 11 QUESTION 3 3.1 3.2 A and B are two events such that: © P (mot A) = 0,55 * P®)=0,4 © P(A or B) = 0,67 Are events A and B independent events? Justify your answer with relevant calculations. (5) A survey was done among a group of 100 tourists to find out which city in South Africa they loved during their visit. They chose from Johannesburg (J), Durban (D) and Cape Town (C). The results of the survey are listed below: 17 said they loved all three cities 30 said they loved Durban and Cape Town 27 said they loved Johannesburg and Cape Town 52 said they loved Durban 9 said they loved only Johannesburg and Durban 12 said they loved Johannesburg only 9 said they loved Cape Town only The above information is represented in the partially completed Venn Diagram below: Ss 3.2.1 Write down the values of a, 5, e and f. . (4) 3.2.2 Calculate the probability that a tourist selected at random loved Cape Town or both Johannesburg and Durban. (3) Copyright Reserved Please Turn Over

MahemQwnloaded from Stanmgrephysics.com 3.3 Nelisiwe had a small box of 80 Smarties sweets. 40% of the Smarties are green, = of them are blue and the remainder are red. Nelisiwe picks a Smartie out of the box, takes note of the colour and then eats it. She then picks out a second Smartie and notes the colour before eating it. 3.3.1 How many red Smarties were in the box at the beginning? 3.3.2 Represent the above situation by means of a tree diagram. Indicate the probabilities associated with each branch and the possible outcomes. 3.3.3. Calculate the probability that Nelisiwe will pick two Smarties of the same colour. September 2024 Common Test (2) (3) G) [20]

Pownloaded from Stanmorephysics.com September 2024 Common Test NSC — Grade 1] QUESTION 4 ank was 5591 at the end of 2014. At the end of 2022, the 4.1. The population of fish in a t A average annual rate at which the population of fish grew to 6423. Calculate the population of fish grew over these 8 years. GB) 4,2- ~ Convert the nominal interest rate of 9% p.a. compounded half-yearly to an effective - interest rate. business that makes built-in cupboards. Today, he bought a board- 4.3. MrKheswa owns a chine is expected to last for 6 years. cutting machine for R250 000. The ma lepreciates 4.3.1 Calculate the scrap value of the machine in 6 years’ time if it d annually at 12% p.a. on a reducing-balance method. (2) increases at the rate of 11% p.a. 43.2 The cost of a new similar machine . he cost price of a new board-cutting compounded quarterly. Calculate t! machine in 6 years’ time. in the old machine and replace it with a new similar 4.3.3. Mr Kheswa will trade- machine in 6 years’ time. Calculate how much more will Mr Kheswa have to a) pay if he bought the new machine for cash. G) Mr Kheswa opened an investment account that pays interest at the rate of 12,25% p.a., compounded monthly. How much should he invest in this account today so that it will accumulate to the cash amount required to buy the new machine in 6 years’ time? 43.4 (3) Exactly seven years ago, Krish deposited R25 000 in a bank account. The bank paid interest at the rate of 8% p.a., compounded monthly for the first 4 years and then changed to 12% p.a., compounded quarterly for the next 3 years. Krish withdrew R10 000 three years after making the initial deposit. This is illustrated in the time-line below. 44 8% p.a. compounded monthly 12% p.a. compounded quarterly IN A | | jl -R 10,000 , T 0 il ) 1 ol ee 2 K 6) Calculate how much Krish has in the account today. [20] Copyright Reserved

Mporttoaded from Stanmorephysics. com September 2024 Common Test QUESTION 5 The sketch below shows the graphs of f(x)=sin(x+45°) and g(x) =coshx+g for x €[-90°;180°].. 5.1 Write down the values of 6 and g. (2) $2 Write down the period of g. (1) 53 Write down the equation of A, if h(x) = g(x)+1. (1) 5.4 Calculate the values of x for which f(x)—A(x) =0 if 0°< x <180°. (5) 5.5 Use the sketch to write down the value(s) of x for which ; S(x)x4g(x)==2. Q) {1] Copyright Reserved Please Tum Over

° tanMorephySics.COM serrerber 2024 Common Test Monimloaded from S ore ply: “ QUESTION 6 6.1 Inthe diagram below, AABC is drawn with C at the origin. Use the diagram on DIAGRAM SHEET 2 to Prove that c* =a? +5? —2abcosC. (4) 6.2 Inthe diagram below, SABC is right-angled at B, ACLCD. AC=15V5 , CD=10 and BCA =26,57°, Calculate the length of BD, (5) 19] TOTAL MARKS: 75 Copyright Reserved Please Tum Over

TEAR OFF iMDewrHoaded from Stanmorephysics.com eee ea NAME & SURNAME: DIAGRAM SHEET 1 QUESTION 2.1 Age group (x) Number of people yell 18<x<22 2 22<x<26 6 26<x<30 12 30<x<34 24 34<x<38 36 38<x<42 24 42<x<46 16 46<x<50 10 QUESTION 2.2 OGIVE Cumulative frequency ese rh aSeeeestrevnesrexraesress 4 18 2 26 30 M 38 a2 46 50 54 Age groups Copyright Reserved Please Tum Over

meguagloaded from Stanmorephysics.cCOM september 2024 Common Test NSC - Grade 11 NAME & SURNAME: DIAGRAM SHEET 2 QUESTION 6.1 QUESTION 6.2 A 15/5 D 26,57° Copyright Reserved

Downloaded from Stanmorephysics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE MARKS: 75 This marking guideline consists of 9 pages. Copyright Reserved Please Turn Over

Mathenati syn I loa di le d from Sta nae replys GSin fa om September 2024 Common Test QUESTION 1 11 || 65+59+ 79+86+48+94+77+51+66+80 10 _ 105 YA 705 10 =I 5 ¥ CA answer Answer only 2/2 (2) ¥ A 14,38 (1) ¥CA interval dard deviation of ¥ CA answer (2) 1.4 705+X+58 _ 67 5 VCA (sum of 10 marks) +X+58 _ 67 5 12 12 xX=47 ¥CAx=47 (2) [7] Copyright Reserved Please Turn Over

“aeGwnloaded from Stanperenhysiasneom September 2024 Common Test QUESTION 2 2.1 Age group (x) | Number of people | Cumulative frequency 18<x<22 2 2 22<x<26 6 8 YA 8 26<x<30 12 20 30<x<34 24 44 34<x<38 36 80 38<x<42 24 104 ae ae 42<x<46 16 120 46<x<50 10 130 (2) 2.2 Ogive 132 i 120 116 108 104 100 g || & S| 7 V . “|| 2 A grounding e 3 at (18 ; 0) S 60 3 Fd YA minimum of B ‘a 4 points O| 4 correct 2 28 ¥CA smooth 20 increasing 16 curve 8 4 0 14 (3) 2.3 | 34<x<38 YA 34<x<38 (1) = v 2.4 | No. of youth (under 35 years) = 52 Accept 50 to 54 CA 52 52 Percentage = eee Accept 38,46% to 41,54% v CA answer =~ 40% (2) [8] Copyright Reserved Please Turn Over

“aeBGwnloaded from Stanperenhysiasneom QUESTION 3 September 2024 Common Test 3.1 P(A) =1—P(not A) =1-0,55 = 0,45 .. Aand B are independent since P(A and B) = P(A)xP(B) YA 0,45 ¥CA substitution ¥CA 0,18 YCA P(A)xP(B) ¥CA conclusion (5) 3.2.1 | a=10 YA a=10 b=13 YCA b=13 e=13 YCA e=13 fei VCA f=17 (4) 3.2.2 10+17+13+9 9 49 9 P|C Jand D) | =———_——— + — ¥CA — YCA — [Cor (and D) 100 100 100 100 58 =73, oF 0,58 ¥CA answer 100 (3) mae Number of green sweets = 80x 2 32 100 Number of blue sweets = x80 =12 AY 32and 12 Number of red sweets = 80— 44 = 36 YCA 36 (2) Copyright Reserved Please Turn Over

wateBSwnloaded from Stanmerenhysigs.com September 2024 Common Test 3.3.2 Ww OUTCOMES 77-B BB 32 B » ¢& BG 2 80 BR GB G G GG ¥CA branch at first pick with probabilities ¥ CA branches at second pick with probabilities 2"¢ CA mark applies only if without replacement is considered ¥ CA outcomes 79 (3) 3.3.3 | P(same colour) = P(BB)+P(GG)+P(RR) ¥CA any two -R, 11 422, 31 36. 35 ites = xy SxS yx probabilities of 80 79° 80 79° 80 79 same colour = 49 oF 038 ¥CA 3" probability of 395 same colour ¥_CA answer (3) [20] Copyright Reserved Please Turn Over

“aeGwnloaded from Stanperenbysiasneom QUESTION 4 September 2024 Common Test 41 A=P(1+i)" 6423 = 5591(1+i)" vA correct substitution into correct formula ti = 9/9423 YA Li = e238 5591. 5591 i=0,01749... r=1,75%p.a. ¥ CA answer (3) 4.2 Ling -{1+te =) VA formula asic =l4 aT VA correct substitution + leg =| 4+ into correct formula = ooo o, a) »} x100 =9,20% p.a. ¥CA answer (3) 4.3.1 | 4 =P(1-i)" a 5 vA correct substitution = 250 000(1--0,12) into correct formula = R116 101,02 ¥CA CA only if iandn are correct (2) 4.3.2 | A=P(1+i)" cont YA f= =R250 ooo( +924)" 4 oo 4 ¥CA correct substitution into = R479 406, 53 correct formula ¥CA_ answer (3) 4.3.3 | Top-up amount = R479 406, 53 — R116 101, 02 = R363 305, 51 CA answer (1) Copyright Reserved Please Turn Over

vateBSwnloaded from Stanmerenhysigsncom September 2024 Common Test 4.3.4 A=P(1+i)" YA i= — and n=72 0.1225 \" ¥CA correct substitution So peop P(t 12 } into correct formula P = R174 857,32 ¥ CA answer (3) 44 8% p.a. compounded 12% p.a. compounded f —R10 000 4 i I | | ! ! | | I T T T T T 1 0 ai 2 3 4 5 6 (yéars) A=P(1+i)" 0,08 \*"* 32 =25 000( + coal VA 0 soa na 12 A; = R31 755,93— R10 000 YCA R31 755,93—R10 000 = R21 755, 93 12 A, = R21 755, 99(1+ oe) 12 = R23 561, 66 3x4 A, =R23 561,66(1+922) = R33 593, 29 OR | E 3a2 12 2x4 0,08 \*"” A=R|| 25 ovo{a+ 92) —10 000 [+92] x49?) Ay 25 o0o{ 1+ 9. 12 12 4 12 iA =R33593, 29 avai 000 rm (12922) 12 3x4 vA (+3?) 4 ¥CA R33593, 29 (5) [20] Copyright Reserved Please Turn Over

“aeGwnloaded from Stanperenhysiasneom September 2024 Common Test QUESTION 5 5:1. be2 VA b=2 gett YA q=-1 (2) 5.2 | Period = 180° vA Answer (1) 5.3 h(x) = cos 2x-1+1 = cos 2x ¥CA cos 2x (1) 54 f(x) =h(x) sin(x+45°) =cos 2x sin(x+45°) =sin(90°-2x) YA. co-ratio X+45° =90°— 2x +k.360° or x + 45° =180° — (90° — 2x) + k.360° ¥ CA both equations 3x = 45° + k.360° or — x = 45° + k.360° Ven Denccene X=15°+k.120 or x=-45°-k.360°;k eZ VA keZ JX =15° or x=135° (5) OR OR Y Aco-ratio _ ¥ CA both equations ap Sa eee Bee” ¥CA general solution -3x 0° — 45° + k.360° YCA both values of x ikeZ YA keZ (5) 5.5 1 = f (x)x4g(x) =-2 2 (x)490%) NOTE: =| Correct answer only: F£O)xg09) =—1 award full marks. VA (X)x g(x) =—1 — VA X= 45° (2) [14] Copyright Reserved Please Turn Over

“aeBGwnloaded from Stanperenhysiasneom QUESTION 6 September 2024 Common Test 6.1 B(acosC ; asinC) C(0; 0) A(b; 0) AB’ =(% Xe) +(Va -Ya) ? = (b—acosC)’ +(0—asinC)’ =b* —2abcosC +a’ cos*C +a’ sin? C * =b? +a? (cos*C +sin’ C)-2abcosC a c? =a? +b? —2abcosC VA B(acosC ; asinC) and A(b ; 0) “A substitution into distance formula vA Expansion YA cos?C+sin?C=1 (4) 6.2 In AABC: a BC cos ACB = AC YA Correct ratio and BC substitution cos 26,57° = —— 155 BC =15V5 x cos 26,57° BC = 29, 998.../30 units. YA BC=29,998.../30 units In ABCD: BD? = BC’ + CD’ - 2(BC)(CD)cos BCD 2 2 3 = (30) +(10)° -2(30)(10)cos116.57 VA 116.57° =1268,374509 ¥CA correct substitution into BD = 35, 61units correct formula ¥ CA Answer (5) [9] TOTAL MARK: 75 Copyright Reserved ver