Mathematics Grade 10 September Test 2019 Paper & Memo

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Downloaded from hlayiso.com Mathematics 2 Common Test September 2019 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. ip This question paper consists of 6 questions. we Answer ALL the questions. a Clearly show ALL calculations, diagrams. graphs, etc. which you have used in determining your answers. 4. Answers only will NOT necessarily be awarded full marks. ay You may use an approved scientific calculator (non-programmable — and non-graphical), unless stated otherwise 6. Hf necessary, round off answers correct to TWO decimal places. unless stated otherwise. qh Diagrams are NOT necessarily drawn to scale. 8. Write neatly and legibly. Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 3 Common Test September 2019 NSC QUESTION 1 1.1 Mrs. Reyem wants to buy herself a new laptop. After completing her monthly budget she realises that she does not have the money to buy a new laptop right now. Mrs. Reyem decides to buy a laptop on a hire purchase agreement from a computer store that advertises the following special: Cash Price: R 4 999 OR Hire purchase: 12% Deposit and 24 equal monthly payments to the value of R 6 598,68 1.1.1 Calculate how much Mrs. Reyem would pay for the deposit. (2) 1.1.2 Calculate how much Mrs. Reyem will have to pay as her monthly instalment. (i) 1.1.3 Calculate the total amount that Mrs. Reyem will pay for her new laptop on the hire purchase agreement. (2) 1.1.4 Calculate the yearly interest rate charged on the laptop hire purchase agreement, if Mrs. Reyem had decided to pay a deposit of R600. (3) 1.2 The average price of a litre of petrol in the UK is now approximately £1.30. In the United States a litre of petrol costs about $0,85 while in South Africa we pay R16,57 per litre. Country Currency Exchange Rate United States (USA) Dollars ($) $1=R 14,75 United Kingdom (UK) Pounds (£) £1=R 18,77 Use the exchange rate table to calculate in which country the cost per litre 3 of petrol would be CHEAPEST. (3) 13 Amelia decides to invest some money at a compound interest rate of 14% p.a. How much money (to the nearest rand) should be invested if she wants to receive a final amount of R 85 000 in eight years time? (3) 1.4 The population of a city in South Africa increased by 5,25% for the year 2017. At the beginning of 2018 the population of the city was 2 560 000. Assuming that the population will continue to increase at a constant rate of 5,25% each year, estimate the population of the city at the beginning of 2020. Give your answer correct to the nearest whole number. (3) 17] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 4 Common Test September 2019 NSC QUESTION 2 2.1 A bag contains red, green, blue and yellow balls. There are 5 of each colour, numbered from | to 5. “The balls are placed in a bag and one is chosen at random. 211 Determine the probability that the ball selected is pink. 2.1.2 Determine the probability that the ball selected is blue. 2.1.3 Determine the probability that the ball selected is numbered 3. 22 The two events A and B are such that: P(A)=0,85 and P(B)=k. Determine: 22) P(A and B). if A and B are mutually exclusive events. 2.2.2 P(A and B), if A and B are non-mutually exclusive, exhaustive cvents and k=(),5. 28. Match the Venn diagrams in column A with the expressions in column B which best represents the shaded area. In your answer book write down the question number and the correct expression from column B only. e.g. 2.3.7) P(A or B) COLUMN A COLUMN B 23] A B C0) a 23.2 A B qe P(A and B) 235 A B CQ) “ae®) 2.3.4 A B CO) P(A and B)' Copyright Reserved Please turn over (4)

Downloaded from hlayiso.com Mathematics 5 Common Test September 2019 NSC 24 Last year, there were 38 pupils in a grade 10 class. Of these pupils: e 22 studied French (F) e 8 studied German (G) e 7 studied both French and German. 2.4.1 Represent the information above in a Venn diagram. 2.4.2 How many learners from the class studied neither French nor German? 2.4.3 Determine the probability that a learner selected at random from this class: (a) studied German ONLY (b) did NOT study French. QUESTION 3 Mr. Lembede asked each student in his Grade 10 Mathematics class how many minutes of homework they do each day. He drew this box and whisker diagram for the information he obtained. a {——— 0 20 40 60 80 100 Minutes 3.1 Using the box and whisker diagram determine: 3.1.1. the median for the data. 3.1.2 what percentage of these students do more than 50 minutes of homework each day. a2 Calculate: 3.2.1 the range for the data. 3.2.2 the interquartile range for the data. Copyright Reserved Please turn over (3) () (1) () [18] (1) (2) (2) (2) [7]

Downloaded from hlayiso.com Mathematics 6 Common Test September 2019 NSC QUESTION 4 The frequency table and histogram below provide information from a survey about the distances travelled by some teachers on a daily basis. Use the information provided to answer the questions which follow. Distance (x km) Frequency 0<x<10 15 10<x<20 a 20 <x S30 b 30< «S40 10 40 <x <50 10 Histogram showing distance travelled by a selection of teachers on a daily basis Bi ae Fa Bisa eal l] ii T i aaa ae OH aaTOa tate MOTI ERT ae i eunee i 30 ELE dL n | ¥ 25 ++ | =) iste B20} Lal a a ISHeEE fanae cr} 104 5 re 0) 10 20 30 40 50 DISTANCE (x km) 41 Is the above given data discrete or continuous? (1) 4.2 Determine the values of a@ and b from the frequency table. (2) 4.2 How many teachers participated in the survey? (1) 43 Identify the modal class for the data. (1) 4.4 Calculate an estimate the mean of the data. (3) 45 Calculate an estimate of the median daily distance travelled. (1) [9] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 7 Common Test September 2019 : NSC QUESTION 5 5.1 The diagram below shows a spotlight at point B, mounted 12 metres directly above a point C at the front edge of a field. The spotlight swings 44, 3° from the vertical to illuminate another point D, the midpoint of AC. B : 12m fn a m ia A + D tt Cc 5.1.1 Calculate the length of DC. (3) 5.1.2 Calculate through how many more degrees the spotlight must swing in order to illuminate point A (i.e. calculate @) (3) 2.2 The diagram below represents a pyramid with a square base of side 12 cm. The diagonals QS and TR meet at M. N is vertically above M.and NR =9cm. 12cm 5.2.1 Calculate the length of TR. (Leave your answer in surd form.) (3) 5.2.2 Calculate the length of MN, the perpendicular height of the pyramid. (2) 5.2.3 Calculate the size of NTR . (3) {14] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics, 8 Common Test September 2019 NSC QUESTION 6 6.1 The diagram below shows a sphere, with a diameter of 30cm, placed inside an empty cylindrical tank of radius 45cm and height 80cm. The cylinder is then filled with water. 4 Volume of sphere =F ar’ : 1, -|80cem Volume of cone oe Volume of a cylinder = 27h 6 i Calculate the volume of the metal sphere, indicated in the diagram as A, (2) 6.1.2 Calculate the volume of water required to fill the tank. (3) 6.1.3. The sphere is removed from the tank as seen in the diagram below. Calculate /, the height of the water remaining in the tank. (3) 6.2 The sphere is then melted down and the metal is made into a solid cone of height 25cm. Calculate the radius of the cone. (2) [10] TOTAL: = Copyright Reserved

education Department: Education PROVINCE OF KWAZULU-NATAL SENIOR CERTIFICATE Pieter ee tt er ee eueeuaees otsssnaes are, ¢ Seessess MARKS: = 75 TIME: 14 hours SEPTEMBER 2019 MARKING GUIDELINE NATIONAL GRADE 10 + MATHEMATICS COMMON TEST Sesseeeeessee eet * Peeeessesesseeees ess? This marking guideline consists of 6 Pages. Please turn over oft htayiso.com Mathematics 2 Common Test September 2019 NSC - MARKING GUIDELINE QUESTION 1 a Deposit 12 4999 = =x = 100 = R599, R599,98 tay 1.1.2 Monthly instalment = amas = R274,95 t15 113 Total paid =R 599,98 + R 6 598,68 = R7198,66 (2 114 A= R6598,68 | P= — R4399,00 n= 2years is? A=P(+ixn) an i= P ” 6598.68 _ ;- 4399 j=—4399__ 2 i=0,25 -- interest rate = 25% G3) 12 United States S1=R14,75 $0,85= R12,54 | United Kingdom £1= R18,77 £1,30= 224,40 | Petro! would be cheapest in the United States. By 13 A= R85000 P= ? n= 8years i= 14% A=P(I+iy" __A ati” _ _ 85000 (1+0,14)" P=R29797,52 (3) Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics: ‘Common Test Sc oer 2019 Mathematics Common Test September 2019 NSC - naneke GUIDELINE NSC ~ anente GUIDELINE 14 ? 2.4.1 2560000 S, F 2 years 5,25% A= P(1+i)" (+1) 15 A= 2s60000( 1+ 525 sas) 100 A=2835856 (3) ) 242 | 15 leamers a) 2.43 an © | peGeman only) = = 0,0263=2,63% a QUESTION 2 243 0 ©) | paid NOT study French) = 6-5 0,42 42% a 2.1.1 Fipinkl =. Q) [18] 212 P(blue)= <7 = 7 OR 25% OR 0,25 w QUESTION 3 2 4 =- yo see 2.13 P(numbered 3) = 55 = = OR 20% OR 0,2 a ag. P(A and B)=0 () 2223 Let P(A and By) =x _ 0 4 B 3.11 30 minutes: Q) 3.12 25% Q) 321 Range = 80-4 = 76 minutes (2) 3.22 IQR =50-20 = 30 minutes (2) 1 (0,85—x)+(x)+(0,5-x)=1 QUESTION 4 41 Continuous () 42. a=20 ‘Therefore P(A and B) = 0,35 b=30 (2) (4) fae “i 42 85 teachers a) PA) (i) 43 20<x<30 ay P(A and B)' a) 44 Estimated mean P(A and B) ay _ (155) -+(20%15) + (30x25) + (10X35) +(10x45) 85 = 22,65 (3) 45 Estimated median = 25km () 19 Copyright Reserved Please turn over Copyright Reserved Please tum over

Downloaded from hlayiso.com Mathematics: Common Test September 2019 NSC - MARKING GUIDELINE QUESTION 5 S11 DC tan44,3° = m “tan ratio DC =12tan44,3° = oannplification DC=11,7lm YA (3) 3.1.2 AC =2xXDC = 23,42m 23,42 tan’ MABE => CA based on DC (5.1.1) ABC = 62,87° CA value for ABC £0 = 62,87°=44,3° =18,57° ¥CA ( ABC—44,3°) therefore spotlight will need toswing 18,57° further (3) 5.2.1 TR°=TQ" + OR* (pythagoras) TR=N12? +12° TR =12V2.em 3 3.2.2 NM *=N&°-MR* — (pythagoras) NM = (6) NM =3em (2) 323 amNeae 6v2 NTR=19,47° Q) {14 QUESTION 6 6.11 4_, Volume of sphere 3 4 3 =—a(15) 5 (15) =14137,17cm* 2) 6.1.2 Volume of water =Viinage ~ Vege =nPh Sar =(45)*(80)—14137.17 =498800,84cm* a Copyright Reserved Please turn over Mathematics Common Test September 2019 NSC - Seam GUIDELINE 6.13 h _ Volume of water ar _ 498800,84 (45) h = 78,41cm (3) 6.2 1a V=—ar'h 3 @ {10} TOTAL: 75 Copyright Reserved