COMMON PAPER CAPE WINELANDS EDUCATION DISTRICT GRADE 12 2015 SEPTEMBER EXAMINATION MATHEMATICAL LITERACY PAPER 1 MARKS: 150 Time : 3 hours This question paper consists of 15 pages and 3 annexures.
INSTRUCTIONS AND INFORMATION 1. This question paper consists of FIVE questions. Answer ALL the questions. 2. QUESTION 1.4.6 needs to be answered on the attached ANNEXURE A and QUESTION 4.4.2 on ANNEXURE C. Write your name in the space provided on the ANNEXURES and hand in the ANNEXURES together with your ANSWER BOOK. 3 Number the answers correctly according to the numbering system used in this question paper. 4. Start EACH question on a NEW page. 5. You may use an approved calculator (non-programmable and non-graphical), unless stated otherwise. 6. Show ALL the calculations clearly. 7. Round off ALL final answers appropriately according to the given context, unless stated otherwise. 8. Indicate units of measurement, where applicable. 9. Write neatly and legibly. 2
QUESTION 1 [45] 1.1 The information on main sources of income tax for South Africa for the financial years 2009/10 and 2013/14 is given below. Use the given information to answer the following questions. Main Sources of Income Tax 2013-2014 2009-2010 Other VAT 19.8% 17.20% 26.4% 24.70% R813,8 milliard collected in tax 2013-2014 Company Tax 19.8% 26.70% 16,8% more tax collected in 2013-2014 than in 2009-2010 Personal income tax 34.0% 31.40% 1.1.1 What percentage of South African income tax for 2013/14 was Personal income tax? (2) 1.1.2 Calculate the actual amount in rand of Personal income tax collected in 2013/14. (3) 1.1.3 Which source of income tax decreased between the 2009/10 and 2013/14 financial years? (2) 1.1.4 What was the total income tax collected in 2009/10? (2) 3
1.2 The following newspaper article compares the selling prices of certain items at different shops. The shops are: Shoprite (Worcester); Pick n Pay(Stellenbosch); Spar(Montagu); Woollies(Paarl); Nomane (General Dealer in Wellington) and Monani Super Market in Ceres. 4
1.2.1 Which store would you say is the most expensive? (2) 1.2.2 The price of 2kg sugar at Monani Supermarket in Ceres is VAT inclusive. Calculate the VAT exclusive price of 2 kg sugar at Monani Supermarket on May 6. (3) 1.2.3 Determine the probability of finding the most affordable brown bread among the six shops on January 29. (2) 1.2.4 The price of Blossom Margarine at Pick n Pay increased from R8,00 on January 29 to R14,99 on May 6. Determine the percentage increase by using the following formula: Percentage increase = difference in price price on Jan 29 100% (4) 1.3 Study the price of maize meal in the table below and answer the following questions. 1.3.1 At which shop(s) did the price of maize meal remain unchanged from January to May? (2) 1.3.2 Which shop had the highest percentage increase in the price of maize meal between January and May? (2) 5
1.4 Maggie bakes gingerbread cakes and sells them at R1,50 each. She uses the following recipe to make the cakes. Ingredients (bakes 12 cakes) 6 oz self raising flower 4 oz soft brown suger 1 teaspoon bicarbonate of soda 1 teaspoon grind ginger 1 teaspoon golden syrup (1oz = 30g) (1dozen = 12 cakes) 1.4.1 How many ounces of soft brown sugar are needed for 2 dozen cakes? (2) 1.4.2 To bake perfect cakes, the temperature of the oven must be 350. The cakes must be baked for 15minutes. If Maggie takes the cakes from the oven at the time indicated on the watch, what time did she put the cakes in the oven? (2) 1.4.3 Convert 350 degrees Celcius. You may use the following formulae: = ( 32 ) 1,8 Round your answer to the nearest10. (3) 1.4.4 Write down a formula Maggie can use to calculate her total income from the sales of the cakes she bakes. The formula is: Total Income (R) =. (2) TABLE 1: Total income from the sales of her cakes Number of cakes 0 20 40 60 80 120 P 160 Total Income (R) 0 30 60 90 120 Q 210 240 1.4.5 Calculate the missing values P and Q. (4) 1.4.6 The line graph of Maggie s expenditure for baking the cakes is given on ANNEXURE A. Use this line graph to calculate the fixed cost. (2) 1.4.7 Draw another line graph on the same set of axis to indicate the total income from the sales of the different number of cakes as indicated in TABLE 1. (4) 1.4.8 What happens at the point at which the two graphs meet? (2) [45] 6
QUESTION 2 [24] The sports organiser of Mzila Secondary School conducted a survey on weight status of girls at the school. He calculated the Body Mass Index (BMI) of a sample of the girls population at the school. There are 365 girls at the school. The table below shows the age, height, mass and BMI of the sample. TABLE 2: The age, mass and height of surveyed female learners LEARNER Age (Years) Height(m) Mass (kg) BMI Luvo 14 1.65 65 23,9 Glynis 18 1,7 72 P Doris 16 1,62 68 25,9 Yolanda 16 1,5 65 Q Qutsa 18 1,55 72 29,96 Tsakane 15 1,56 66 27,1 Refelwe 16 1,55 62 25,8 Nora 17 1,58 63 25,2 Siba 15 R 69 27 Sive 16 1,55 53 22,1 Yonela 17 1,66 81 29,4 Amanda 19 1,63 71 26,7 2.1 Answer the following questions. 2.1.1 Is the sample representative? Justify your answer. (3) 2.1.2 Determine the range of ages of girls in the sample. (2) 2.1.3 Use the formula: BMI = (a) P (b) Q (c) R weight (kg) Height (m) 2 to calculate: (2) (2) (3) 7
2.2 The BMI is used to determine the weight status of individuals. The sports organizer used the following BMI age growth chart for girls to determine the weight status for this sample. Use TABLE 2 and the BMI age growth chart below to answer the following questions. BMI age growth chart for girls 2.2.1 Determine Tsakane s weight status. (2) 2.2.2 Determine the number of 16 year old girl(s) whose weight status lies beteen the 5 th and the 85 th percentile. (2) 2.2.3 What is the weight status of girl(s) in 2.2.2 above? (2) 2.2.4 Amanda is worried about her weight status. She wants her status to be normal. (a) What is Amanda s current weight status? (b) Calculate the minimum number of kilograms Amanda must lose to get a normal weight status. (2) (4) [24] 8
QUESTION 3 [20] 3.1 Refer to the map of wine cellars in the Western Cape on ANNEXURE B and answer the questions that follow. 3.1.1 On which road does the Le Roux and Fourie wine farm lie? (2) 3.1.2 What river is adjacent to the Bon Cap wine farm? (2) 3.1.3 Name TWO farms where a restaurant is indicated. (2) 3.1.4 Which national road is indicated on this map? (2) 3.1.5 The actual distance between Ashton and Robertson is 17,3 km. On this map the distance between Ashton and Robertson is 6,4cm. Determine the scale of the map. Round your answer correct to the nearest 10 000. (4) 3.1.6 A family arrived in Robertson at 10:15. What time did they leave from Ashton if they travelled for 52 minutes? (2) 3.2 RDP houses are built with bricks to assist low income people with proper houses. Fig 1 is an example of one of these houses. Fig 1 Study the floor plan below and answer the questions that follow. N 9
QUESTION 4 [38] 3.2.1 How many windows and doors have an eastern elevation? (2) 3.2.2 How many doors are indicated on this plan? (2) 3.2.3 Which elevation (view) is illustrated in figure 1? (2) 4.1 The composite bar graph below shows the number of learners in each grade at Mama Lumka s aftercare: [20] 4.1.1 How many learners are there in Grade 2 in the aftercare? (2) 4.1.2 How many more boys than girls are in Grade R? (2) 4.1.3 What percentage of the learners in Mama Lumka s aftercare is in Grade 4? (4) 4.1.4 What is the average number of boys per grade? (3) 10
4.2 Tshawe uses seashells to make ornaments as shown alongside. He then sells these to tourists near the beach. He measured the widths, in millimetres, of a few seashells and recorded his findings as follows: 11 8 11 13 10 9 7 14 12 13 12 8 7 9 10 12 13 12 13 14 12 10 10 9 15 12 11 10 12 14 11 12 10 4.2.1 What is the average width per shell? (3) 4.2.2 Determine the modal width of the shells. (2) 4.2.3 Calculate the range of the width of the shells. (2) 4.3 A comparison of monthly salaries of call centres between urban and rural areas was done by comparing monthly salaries of two call centres, one in Cape Town and one in Worcester. A sample of monthly salaries for the two call centres are given below. The accompanying box-and- whisker plot shows monthly salaries for both centres. Worcester: 4 200; 4 320; 4 500; 4 650; 4 650; 4 650; 5 500; 5 650; 7 250 Cape Town: 5 600; 5 650; 6 250; 6 250; 6 250; 6 300; 7 800; 8 200; 8 900 A B 4000 4400 4800 5200 5600 6000 6400 6800 7200 7600 8000 8400 8800 9000 Use the information on salaries for the call centres and the box-and-whisker plots to answer the following questions. 4.3.1 Which call centre does box-and-whisker plot B represent? (2) 4.3.2 Determine the value of Quartile number 3 (Q 3 ) for the Worcester call centre. (2) 4.3.3 Calculate the interquartile range of the Cape Town call centre. (2) 4.3.4 Write TWO statements comparing the rural and urban salaries at call centres. (4) 11
4.4 The table below shows salary increases for public servants in South Africa from 2007 to 2012. Year 2007 2008 2009 2010 2011 2012 Salary increase as a percentage 7.5 6.4 6.8 6.2 6.8 7 On ANNEXURE C a graph showing food inflation for the same period is given. Use the information in the table and the graph on ANNEXURE C to answer the following questions. 4.4.1 Briefly explain the meaning of the term food inflation. (2) 4.4.2 On ANNEXURE C a graph showing food infation is South Africa for the period 2007 2012 is drawn. On the same set of axes draw a graph showing salary increases for public servants in South Africa during the same period. (4) 4.4.3 In which year was food inflation the highest? (2) 4.4.4 Describe the relationship between food inflation and salary increases for public servants between 2010 and 2012. (2) [38] 12
QUESTION 5 [23] 5.1 Nomsa applied for a personal loan at a local bank to start her own business. Use the information below to answer the questions that follow: 5.1.1 What is the total amount of the loan? (2) 5.1.2 What will her monthly instalment be? (2) 5.1.3 For how many years will she pay off this loan? (2) 5.1.4 Show how the total repayable amount was calculated as R142 194,00. (3) 5.1.5 Calculate the total of interest, fees and credit life insurance added to this loan. (3) 13
5.2 Mama Lumka uses an old tractor tyre to build a sand pit for the children at her créche to play in. The tyre has a diameter of 1,6 m and a height of 0,45 m. 5.2.1 Calculate how much sand this tyre can hold. Use the formula: Volume = π (radius) 2 height (π = 3,142) (3) 5.2.2 Mama Lumka will fill the tyre only ¾ of its capacity in order to leave enough space for the children to play in the sand pit. How much sand must she buy? (2) 5.2.3 How far from the top of the tyre will the level of the sand be if he only fills the tyre ¾ of its capacity? Give your answer in centimetre. (2) 5.3 During a rainy day, a family decided to play a game of Snakes & Ladders. The idea of the game is to start at 1 and end at 100 by rolling either one or two dice. If one die (dice) is used, the player moves the number of spaces that appears on the topside of the dice. If two six sided dice are used, the player would move the number of spaces which is the sum of both dice. For example: if a player rolls a 3 on the one dice and a 5 on the other dice, the player moves eight spaces forward. 14
5.3.1 If the game was played with one dice, determine the probability of Peter rolling a 5 on the dice. (2) 5.3.2 When playing with two dice, what is the probability of Peter landing on number 37 if he is currently on number 36? Explain your answer. (2) TOTAL:150 [23] 15
NAME: GRADE 12: ANNEXURE A QUESTION 1.4.6 Expenditure Amount in Rand (R) Number of cakes 16
ANNEXURE B QUESTION 3.1
percentage increase NAME: GRADE 12: ANNEXURE C QUESTION 4.4 Salary increases vs food inflation: SA, 2007 2012 12 Salary increase vs food inflation: SA 2007-2012 10 8 6 4 2 0 [2007] [2008] [2009] [2010] [2011] [2012]