NATIONAL CERTIFICATE (VOCATIONAL) MATHEMATICAL LITERACY (First Paper) NQF LEVEL 3 SUPPLEMENTARY EXAMINATION 2010 (10401023) 25 February (X-Paper) 09:00 12:00 Calculators may be used. This question paper consists of 11 pages.
(10101023) -2- NC1560(E)(F25)V TIME: 3 HOURS MARKS: 150 INSTRUCTIONS AND INFORMATION 1. 2. 3. 4. 5. 6. This question paper consists of NINE questions. Answer ALL the questions. Read ALL the questions carefully. Clearly show ALL calculations, diagrams, graphs, etcetera you have used in determining the answers. Number the answers according to the numbering system used in this question paper. Diagrams are not necessarily drawn to scale. Write neatly and legibly.
(10101023) -3- NC1560(E)(F25)V QUESTION 1 1.1 Calculate the following: 1.1.1 325 36,3 0,3 1.1.2 7,5 % of R450 1.1.3 0,8 of 250 students 1.1.4 The area of a square with a sides' length of 6 cm 1.1.5 The diameter of a circular flower bed if the radius is 1,5 m 1.2 11 Rewrite as a percentage. 20 1.3 Convert 2,5 km to meters. 1.4 Re-arrange the following temperatures from the highest to lowest: 0 ºC ; 12 ºC ; -3 ºC ; 3 ºC ; -0,5 ºC 1.5 The costs of 1 kg of sugar is R8,90. How much will you pay for 12,5 kg of sugar? 1.6 The ratio of mixing milk for a baby is: 3 teaspoons of milk powder for every 150 ml of warm water. How much milk powder should be mixed with 450 ml of warm water? 1.7 An athlete started running a marathon at 07:00:00 and finished it at 11:53:06 the same day. How long did it take the athlete to complete the marathon? 1.8 What would the exchange rate for changing rand to dollars be if you get R425 for $50? 1.9 The price of a bicycle is R765.00 without value added tax (VAT) of 14%. What is the price of the bicycle with VAT? 1.10 Decrease R128 by 5 %. 1.11 Determine the perimeter of a rectangular below. 5,2 m 3,8 m 1.12 A 10 litre bucket is filled with soup. If cups with capacity of 250 ml are used, estimate how many cups of soup could be served? [36]
(10101023) -4- NC1560(E)(F25)V QUESTION 2 A company received the following bank statement. Study the statement and answer the questions that follow. Transaction details Date Credits Debits Balance Balance 01/05/2009 50 018, 98 Rent 01/05/2009 3 000, 00 47 018, 98 Bank fees 01/05/2009 11, 24 47 007, 74 Telkom SA 02/05/2009 6 789, 43 40 218, 31 Bank fees 02/05/2009 11, 15 40 207, 16 Branch withdrawal 03/05/2009 2 000, 00 38 207, 16 Bank charges 03/05/2009 (a) 38 197, 06 ATM withdrawal 05/05/2009 1 000, 00 37 197, 06 Bank fees 05/05/2009 9, 45 37 187, 61 Debit order EWC 06/05/2009 6429, 95 30 757, 66 Bank fees 06/05/2009 11, 20 30 746, 46 Manie Stols Transfers 07/05/2009 890, 54 31 637, 00 Salaries Internet transfers 15/05/2009 19 000 12 637, 00 Credits Transfers Vodacom 15/05/2009 43 432, 72 56 069, 72 Service fees 30/05/2009 (b) 55 988, 72 Transfer & Statement Balance 30/05/2009 123 000,00 (c) 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 What is the period covered by this statement? What is the opening balance of this statement? Explain in your own words, what it means to debit an account by R1 000,00. Calculate the bank charges of 03 May 2009, the value of (a). Calculate the total credits of this statement. Calculate the value of (b), the service fee on 30 May 2009. Calculate the value of (c), the closing balance on 30 May 2009. If the company employs two workers' one worker gets 42,5% and the other one 57,5%, what is the salary of each employee if their salaries in total are R18 789,99? (4) [16]
(10101023) -5- NC1560(E)(F25)V QUESTION 3 3.1 Tables 3.1.1 3.1.4 consist of data which forms a relationship. Do the following with each of the tables: (i) (ii) Complete the tables by determining the missing values of (a) (d). Determine whether the relationship in each table is an example of direct or indirect proportion. 3.1.1 Number of pens 1 2 3 4 5 Cost in rand R5, 00 R10, 00 R15, 00 R20, 00 (a) 3.1.2 Number of harvesters 50 40 25 20 10 Number of days to harvest 40 50 80 100 (b) 3.1.3 Speed in km/h 40 60 90 100 120 Time in hours to complete a distance of 180 km 4,5 3 2 1, 8 (c) 3.1.4 Mass in kilogram 1 2 3 4 5 Price in rand R17, 00 R34, 00 R51, 00 R68, 00 (d) 3.2 An artisan earns R960 for normal working day of 8 hours. 3.2.1 3.2.2 How much does the artisan earn for a one-hour work? How much does the artisan earn for a normal working week of 5 days without overtime? [17]
(10101023) -6- NC1560(E)(F25)V QUESTION 4 Below is a map indicating various positions of cities in South Africa. Use the map to answer the questions that follow. 4.1 Which cities are situated in the following blocks: 4.1.1 4.1.2 4.1.3 B3 C6 D2 4.2 Describe the grid position (block) of Polokwane. 4.3 What is the direction from Durban to Richards Bay? 4.4 Use the scale on the map to determine how far in kilometers Richards Bay approximately is from Durban. [9]
(10101023) -7- NC1560(E)(F25)V QUESTION 5 The following graph illustrates the number of crimes committed in a certain area of South Africa over a period of two weeks. Study the graph carefully and then answer the questions that follow. Crimes committed over two week period 35 30 Number of crimes reported 25 20 15 10 5 0 Theft Assualt Assault Rape Fraud Arson Murder Types of crimes 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Which is the most common crime and what was the number of cases reported for this particular crime? Which is the least common crime and what was the number of cases reported for this particular crime? How many crimes were committed altogether over the two-week period? What was the mean number of crimes committed per day over this two-week period? Arrange these crimes in descending order from the highest to the lowest. What is the probability of a person being assaulted? Give your answer as a percentage to the total number of crimes. Express the number of fraud cases to the total number of crimes as a percentage. [18]
(10101023) -8- NC1560(E)(F25)V QUESTION 6 The graph below shows Sam's journey with his taxi, where the speed in kilometre per hour (km/h) to the distance in kilometre (km) is shown. Study the graph and answer the questions that follow. Sam's journey with his taxi Speed in km/h 110 100 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 120 140 160 180 Distance in km 6.1 6.2 6.3 How long was the journey in km? What was the top speed in km/h during this journey? What was the speed in km/h along the following distances: 6.3.1 6.3.2 30-45 km 130-150 km 6.4 Determine for how long in km did Sam drove at a speed of 80 km/h. (4) [12]
(10101023) -9- NC1560(E)(F25)V QUESTION 7 In 2006 Sipho's company had an average monthly income of R123 700. At the end of the financial year the company's annual expenditure was R1 090 000. They will also invest R50 000 of the annual/yearly profit and have two options. 7.1 7.2 7.3 7.4 Calculate the total annual (yearly) income. Calculate the total annual profit. Calculate the average monthly profit. OPTION 1: The company invests R50 000 of the total annual profit at 11% per year compounded annually. Calculate the value of the investment after three years. A = P( 1 + i) n A = accumulated final amount P = principal amount or initial amount invested i = interest rate = 11 100 n = number of years the money was invested (4) 7.5 OPTION 2: The company invests the R50 000 of the total annual profit at 11% per year on simple interest monthly. Calculate the value of the investment after three years. A = P( 1+ i. n) (4) 7.6 Which option will generate the most interest, OPTION 1 or OPTION 2? [16]
(10101023) -10- NC1560(E)(F25)V QUESTION 8 Each year a country produces more than 236 million ton of garbage. About 72 million ton of that garbage gets recycled. Study the pie graph and then answer the questions that follow. Rubber/leather/textiles 7% Plastics 11% Metal 8% Wood 6% Glass 5% Other 4% Food scraps 12% Paper 35% Garden refuse 12% 8.1 8.2 8.3 8.4 8.5 8.6 Reduce ~ Reuse Recycle ~ Respect Which item do the citizens throw away the most? Which TWO categories together make up 24 % of the garbage? What percentage of garbage make up plastic, wood and glass? What percentage of the garbage is not made up of paper? Express the amount of garbage that gets recycled as a percentage of the total amount of garbage. Calculate the tons of plastics that the years' garbage contains. [15]
(10101023) -11- NC1560(E)(F25)V QUESTION 9 Study the drawing of a concrete cylindrical dirt bin below and answer the question that follow. 0, 06 m 0, 7 m 1, 2 m V = π r 2 h OR V = π r r h where π = 3, 14 V = volume r = radius h = height 9.1 9.2 9.3 9.4 What is the diameter of the outer circle of the dirt bin? What is the radius of the inner circle of the dirt bin? How thick is the rim of the dirt bin in cm? Calculate the volume of the inner part of the dirt bin. NB: The base is 0, 06 m thick. (4) [11] TOTAL: 150