NATIONAL CERTIFICATE (VOCATIONAL) MATHEMATICAL LITERACY (Second Paper) NQF LEVEL 3 NOVEMBER 2010 (10401023) 24 November (Y-Paper) 13:00 16:00 Drawing instruments including rulers, pairs of compasses and protractors may be used. Calculators may be used. This question paper consists of 8 pages and 2 answer sheets.
(10401023) -2- NC1640(E)(N24)V TIME: 3 HOURS MARKS: 100 INSTRUCTIONS AND INFORMATION 1. 2. 3. 4. 5. 6. 7. Answer ALL the questions. Read ALL the questions carefully. Number the answers according to the numbering system used in this question paper. Clearly show ALL calculations, diagrams, graphs, et cetera you have used in determining the answers. Diagrams are NOT necessarily drawn to scale. Write your examination number and centre number on the attached ANSWER SHEET and hand the completed ANSWER SHEET in with the ANSWER BOOK. Write neatly and legibly.
(10401023) -3- NC1640(E)(N24)V QUESTION 1 1.1 The overtime worked by a worker was recorded for a month. The data below shows the hours the worker worked overtime: 3 2,5 4 3 1 2 2,5 3,5 4 1,5 3 2 4 3 2 1.1.1 Determine the median. (3) 1.1.2 Determine the mean/average hours that the worker worked overtime. (4) 1.1.3 If the worker is paid R65,00/hour for overtime, what did she earn for working overtime for that month? (3) 1.2 The prize money for a lottery stands at R3 million. If there is more than one winner, the winners will share the prize money equally. The table below shows the equal share (in thousands of rand) that each winner will receive if there is more than one winner. Number of winners 1 2 4 5 8 (c) 20 Equal share (in R1 000s) 3 000 (a) 750 (b) 375 300 150 Formula: Equal Share Prize money = No. of winners 1 000 This formula was developed by the competition coordinator to share the prize money equally in thousands of rands. 1.2.1 Use the formula to calculate the values of (a), (b) and (c). (8) 1.2.2 Complete: If the number of winners increase, the (2) 1.2.3 Is the relationship an example of a DIRECT or an INVERSE proportion? Choose the correct answer. (2)
(10401023) -4- NC1640(E)(N24)V 1.3 A consultant uses the table below to assist clients in calculating monthly instalments on funeral cover that suits their needs. INSURED Life insured up to the age of 59 Life insured age 60 64 Spouse up to the age of 59 Spouse age 60 64 Children up to the age of 24 Parents/In-laws, extra spouses, extended family members - Up to the age of 64 - Age 65 69 - Age 70 74 MINIMUM MAXIMUM MONTHLY COVER COVER PREMIUM R5 000 R15 000 R1,25 per R1 000 R5 000 R15 000 R3,95 per R1 000 R5 000 R15 000 R1,25 per R1 000 R5 000 R15 000 R3,95 per R1 000 R1 000 R5 000 R1,10 per R1 000 R1 000 R1 000 R1 000 R8 000 R8 000 R8 000 Per R1 000 per person R3,40 R11,90 R16,80 Show how the consultant will calculate the monthly instalment of the following clients: 1.3.1 A man and his spouse at the age of 38 and 33 respectively for minimum cover (3) 1.3.2 A woman with the information given in the table below for maximum cover: Persons to be Their ages in insured years Herself 34 Her spouse 41 Her son 19 Her daughter 16 Her father 60 Her mother-in-law 66 (8) 1.4 Phuti runs a small bakery from home. She bakes muffins and sells them at a college. She keeps her sugar in a rectangular tin with the following dimensions: Length: 250 mm Breadth: 190 mm Height: 60 mm 1.4.1 Calculate the volume of the sugar in the tin in cm 3. (3) 1.4.2 Determine the mass of the sugar in the tin if 1,12 g = 1 cm 3. (2) 1.4.3 A recipe for baking 12 muffins requires 33,6 g of sugar. Determine the number of muffins you can bake with the sugar in the tin. (2) 1.4.4 Determine the number of tins required to bake 600 muffins. (3) [43]
(10401023) -5- NC1640(E)(N24)V QUESTION 2 2.1 The Student Representative Council (SRC) receives a portion of the student registration fees every year. Every student will contribute to the SRC fund which is normally used for various student activities. The table below shows two types of students enrolled at a college in 2010. Study this table carefully and answer the questions that follow. Type of student Number of students enrolled in January 2010 Contribution to SRC Fund at enrolment Fees paid in a year Number of enrolment periods (When?) Year course 660 R50,00 Once off Once (In January) Semester course 350 R25,00 Two payments Twice (In January and in July) 2.1.1 How much will a semester student contribute to the SRC fund per year? (2) 2.1.2 Calculate the income of the SRC fund for January 2010. (4) 2.1.3 Calculate the total income for the whole year if only 328 students enrolled for the second semester. (4) 2.2 The table below shows how the SRC track their annual budget and how the money was spent up to the end of the second quarter. Expenses: First Quarter Expenses: Second Quarter ACTIVITY BUDGET Jan Feb Mar Apr May Jun TOTAL Educational Tours R50 000 R12 000 R12 000 R12 000 (a) Petty cash R3 000 R300 R300 R300 R300 R300 R1 500 Cultural Activities R10 000 R5 000 R5 000 Sports Trips R50 000 R10 000 (b) R11 000 R30 000 Cultural Day R17 000 R0 Valentine's Day R10 000 R11 000 R11 000 Administration R10 000 R500 R500 R500 R500 R500 (c) Other R2 000 R0 TOTAL (d) TOTAL EXPENSES (e) SURPLUS/DEFICIT (f) 2.2.1 Calculate the value of the following: (a) Expenditure on educational tours (2) (b) Sports trips for March (2)
(10401023) -6- NC1640(E)(N24)V (c) Expenditure on administration (2) (d) Total budget (2) (e) Total expenditure (2) (f) Surplus or deficit (Surplus = Budgeted Expenses) (2) 2.2.2 In which TWO months were the expenses the lowest and what could be the reasons for it? (3) 2.2.3 Evaluate if the SRC will (under-spend/break even/over-spend) at the end of the year. Justify your choice. (2) [27] QUESTION 3 Siphiwe sells products for an insurance company and she earns commission for every new client. The table below shows what her total commission would be for the number of clients to whom she sells the products. Number of clients (x) 5 10 15 (a) 26 (b) 40 Commission earned (R) (y) 525 1 050 1 575 2 100 (c) 3 150 (d) 3.1 What is the independent variable in this table? (2) 3.2 How much commission (R) does Siphiwe earn per client? (2) 3.3 Write down a formula that can be used to calculate the commission. (2) 3.4 Calculate the values of (a), (b), (c) and (d). (8) 3.5 Use the completed table to plot a graph on ANSWER SHEET 1 (attached). (5) 3.6 After Siphiwe reached her target of 50 clients, the company doubled her commission for every new client. Calculate the total commission that she will earn if she manages to sell products to 58 clients in one month. (5) [24]
(10401023) -7- NC1640(E)(N24)V QUESTION 4 The stacked bar graph below shows the causes of death of both males and females in homicide cases in one particular year. At least 18 000 people were killed in that year. A police officer needs to further analyse the data. Study the graph and answer the questions that follow. 4.1 What percentage of females were killed by fire arms? (2) 4.2 What percentage of males were killed by sharp objects? (2) 4.3 Determine the number of females killed if 10 600 males were killed. (2) 4.4 Determine the number of females killed by fire arms. (2) 4.5 Determine the number of males killed by strangulation. (2) 4.6 More males than females were killed with sharp objects. Is the statement TRUE or FALSE? Motivate your answer. (3) 4.7 Fewer males than females were killed by poisoning. Is the statement TRUE or FALSE? Motivate your answer. (3) 4.8 Give ONE example that could be represented by 'other' on the graph. (2) 4.9 Give a title for the graph. (2) 4.10 Consider only the information for females to draw a bar graph. Use the attached graph paper on ANSWER SHEET 2 and submit it with your ANSWER BOOK. (6) [26]
(10401023) -8- NC1640(E)(N24)V QUESTION 5 The sketch below shows property that need to be renovated and rented to tenants. Section A is a rectangular lawn with a circular swimming pool. The swimming pool is 1 metre deep and it has a radius of 1,8 m. Section B is the floor plan of a bachelor flat. Study the sketch and answer the questions that follow. SECTION A SECTION B 4 m 4 m 2,5 m Swimming pool 3,6m 3,6 m 3 m Bathroom room 2 m 5 m Bedroom 1 m Lawn Veranda Kitchen Lounge 2 m 2,5 m 2,5 m 5.1 Calculate the area of the swimming pool. 2 Use the formula: A = πr where r = radius and π = 3,14. (3) 5.2 Determine the cost of replanting the entire lawn at R53,75/m 2. (6) 5.3 Calculate the volume of the swimming pool. 2 Use the formula: V = πr h where r = radius, h = height and π = 3,14. (3) 5.4 Determine the cost to fill the swimming pool with water up to 10 cm from the top at R6,90 per kilolitre. HINT: 1 000 cm 3 = 1 l. (7) 5.5 Calculate the area of the veranda. (3) 5.6 Determine the cost to tile the kitchen, lounge and the bathroom at R102,95/m 2. Consider the following: The bath, toilet and basin's total area are 3,2 m 2. (8) [30] TOTAL: 100
(10401023) -9- NC1640(E)(N24)V ANSWER SHEET 1 Complete and submit with your ANSWER BOOK. Examination No Centre No 9 9 9 9 QUESTION 3.5 7500 6750 6000 ------------------------------------------------------- 5250 4500 3750 3000 2250 1500 750 0 0 5 10 15 20 25 30 35 40 45
(10401023) -10- NC1640(E)(N24)V ANSWER SHEET 2 Complete and submit with your ANSWER BOOK. Examination No Centre No 9 9 9 9 QUESTION 4.10 100 90 80 70 60 50 40 30 20 10 0 Fire arm Sharp Object Strangulation Poisoning Other