Grade 12 NSC Mathemetical Literacy P1 10601 (Afrikaans) Preperatory 2016 Oquestion Paper hlayiso.com

Downloaded from hlayiso.com 15 new 15 7 Formatted: Font: 10 pt 16 Formatted: Font: 10 pt Formatted: Font: 48 pt Start page 7 Formatted: Font: 48 pt, English (South Africa) GAUTENGSE DEPARTEMENT VAN ONDERWYS VOORBEREIDENDE EKSAMEN 2016 Formatted: Font: 16 pt, Afrikaans 10601 Formatted: Font: 16 pt, Afrikaans Formatted: Font: 16 pt, Afrikaans WISKUNDIGE GELETTERDHEID Formatted: Font: 16 pt, Afrikaans Formatted: Font: 16 pt, Afrikaans EERSTE VRAESTEL TYD: 3 uur PUNTE: 150 15 14 bladsyepages ++ 2 1 antwoordbladAnnexures en ʼn Formatted: Afrikaans addendum met 3 bylae Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans 1 b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 2 2 (Eerste Vraestel) 10601/16 GAUTENGSE DEPARTEMENT VAN ONDERWYS VOORBEREIDENDE EKSAMEN – 2016 WISKUNDIGE GELETTERDHEID (Eerste VraestelFirst Paper) PROOFREAD DATE ___________ SIGNATURE _________________ TYDTIME: 3 uurhours PROOFREAD DATE ___________ SIGNATURE _________________ PUNTEMARKS: 150 INSTRUCTIONS AND INFORMATION 1. This question paper consists of FIVE questions. Answer ALL the questions. 2. The Addendum is as follows: - Use ANNEXURE A to answer Question 1 - Use ANNEXURE B to answer Question 1.1.3 - Use ANNEXURE C to answer Question 2.4 3. Use the ANSWER SHEET at the back of your Question paper to answer Question 4.4.1 4. Number the answers correctly according to the numbering system used in this question paper. 5. Start the answers to each question on a NEW page. 6. You may use an approved calculator (non-programmable and non-graphical), unless stated otherwise. 7. Show ALL calculations clearly. 8. Round off ALL final answers appropriately to the given context, unless stated otherwise. 9. Indicate units of measurement, where applicable. 10. Maps and diagrams are NOT necessarily drawn to scale, unless stated otherwise. 11. Write neatly and legibly. b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 3 3 (Eerste Vraestel) 10601/16 QUESTION 1 1.1 Robert is the HR Officer of Bettie’s Best Boutique and Mrs. April is a 48-year-old sales manager who is a single mother with one child. Robert is preparing Mrs.April’s payslip for the month of October 2015. The total contribution towards the Unemployment Insurance Fund (UIF) is 1% from the employee’s Gross Salary and a matching 1% from the employer. Annexure A contains Mrs. April’s payslip for October 2015 and Annexure B contains the tax table for individuals for the tax year 2015/2016. Use the information of Mrs. April’s payslip on ANNEXURE A and the tax table on ANNEXURE B to answer the questions that follow. 1.1.1 Calculate the value of A. (2) 1.1.2 Calculate Mrs. April’s annual taxable income. Use the formula: Taxable income = Annual income – Annual Pension Fund contribution (4) Formatted: Left 1.1.3 (a) Medical Tax credits are deducted from the annual tax payable to determine the tax she needs to pay. Calculate the annual medical tax credits that she can deduct from her annual tax payable. (2) (b) Use the 2015/2016 tax table provided on ANNEXURE A to calculate Mrs. April’s annual tax payable. Formatted: Indent: Left: 0", Hanging: 0.42" Use the formula: Annual Tax Payable = Annual Tax-Rebate-Medical Tax Credit (2) Formatted: Left (c) Determine the value of B on Mrs. April’s payslip. (2) 1.1.4 (a) Show that Mrs. April’s total deductions amount to R3 803,45. (2) (b) Determine, the value of C, Mrs. April’s nett monthly income. Use the formula: Nett Income = Gross Income – Total Deductions (2) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 4 4 (Eerste Vraestel) 10601/16 1.1.5 (a) Write down the percentage used to calculate Mrs. April’s UIF (Unemployment Insurance Fund) contribution. (2) (b) Determine the total amount of UIF to be paid over to SARS at the end of the month of October by Bettie’s Best Boutique. (2) 1.1.6 Mrs. April is getting married in February 2016. She intends adding her future husband as a member of her medical aid scheme. Determine her annual medical tax credit for the 2015/16 tax year. (2) 1.1.7 Mrs. April’s child is in Grade 11 and intends to enrol for further studies after matric. To be able to have her child registered for the first year of study, Mrs. April decided to save R3 000 per month starting from the end of November 2014 to November 2015. The total amount at the end of November 2015 was then invested in a bank offering her a 32-day Call Account at 3,4% simple interest per annum. (a) Determine the total amount saved after one year. (1) (b) Hence, calculate the amount that Mrs. April will have in her account at the end of November 2016. (2) Formatted: Indent: Left: 0", Hanging: 0.5" b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 5 5 (Eerste Vraestel) 10601/16 1.2 During the December holiday, Mrs. April was involved in a road accident on her way back from Port Elizabeth. The insurance company informed her that her vehicle was damaged beyond repair. Mrs. April decided to replace the vehicle. She saw the advertisement below in a local newspaper. Formatted: Afrikaans Formatted: Afrikaans Almal moet gaan! R104 995 Spaar R11 000 Formatted: Font: Times New Roman, 15 pt, Bold Luikrug / Handrat / 2010 / 119 830 km Formatted: Font: Times New Roman, 15 pt, Bold, English (South Africa) Formatted: Font: Times New Roman, 9 pt Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 11 pt Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 11 pt Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 5 pt Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 9 pt, Bold, English (South Africa) Mrs. April was offered a hire purchase agreement from Brothers Bank. She was offered two options: Option 1 Option 2 Deposit: R10 500 No Deposit required Term: 5 years Term: 5 years Interest: 10,5% compounded bi-annually Interest: 12% compounded annually Admin fee: R1 010 Admin fee: R1 010 Registration/Licence: R788 Registration/Licence: R788 Use the information above to answer the following questions. 1.2.1 Calculate the amount to be financed by Mrs. April if she decided to choose Option 1. (3) 1.2.2 Calculate the amount that Mrs. April will owe the bank after two years on Option 2, without any payments made towards the hire purchase account. (5) 1.2.3 Determine the deposit as a percentage of the purchase price. (4) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 6 6 (Eerste Vraestel) 10601/16 1.3 Mrs. April is concerned about the impact that the projected inflation rate and increase in municipal rates and fees will have on her disposable income. Table 1 below shows the increased projected tariffs. Table 1: Increase on tariffs for 2017 Rates and services 2016 % increase 2017 charged Refuse removal R140,00 A R157,50 Sanitation R179,39 13% R202,71 Water consumption R170,86 10,5% R188,80 Electricity consumption (non- R584,79 14,3% R668,41 prepaid) Property rates R380,98 15% R438,13 Subtotal excluding B R1 655,55 VAT VAT on services R203,84 R231,78 Total R1 668,86 R1 887,33 Use the information above to answer the questions that follow. 1.3.1 Explain the meaning of interest rate. (2) 1.3.2 Determine the value of A, the percentage increase for refuse removal. Use the formula: Nuwe bedrag - Ou bedrag Formatted: Afrikaans Percentage increase =  100 % (3) Ou bedrag Formatted: Afrikaans Formatted: Afrikaans 1.3.3 Determine the value of B. (2) Formatted: Afrikaans 1.3.4 Through calculations show how the VAT amount of R231,78 was calculated. (2) 1.3.5 Calculate the additional amount per month for which Mrs. April will have to budget, on her municipal account for 2017. (2) [47] b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 7 7 (Eerste Vraestel) 10601/16 QUESTION 2 2.1 Parents at Kings Primary School are part of the feeding scheme at the school. They prepare sandwiches for the less fortunate learners and hand the sandwiches out at break time. The sandwiches are packed in plastic triangular plastic containers and then stacked in pairs on the slant sides of the triangular containers into a cardboard box as shown below. Formatted: Afrikaans 12” 5 cm WidthBreedte Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans 24” Lengteength 10 cm 10" Diepepthte 24" 12" LengteLengt 10 cm BreedteWidth h Formatted: Afrikaans Maatteseasurements: MaattesMeasurements: Formatted: Afrikaans Formatted: Afrikaans LengteLength = 10 cm Lengteh = 24 duiminches Verpakking Formatted: Afrikaans BreedteWidth = 10 cm Width Breedte = 12 soos van bo Formatted: Afrikaans inchesduim gesienPack Formatted: Afrikaans DiepteDepth 1 inch = 2,54 = cm5 cm Volume = Diepteepth Length ×= 10 Width × Depth aging as inchesduim seen from above Use the information above to answer the questions that follow. Formatted: Afrikaans 2.1.1 (a) Convert the length, width and depth of the cardboard box to cm. (3) Formatted: Font: 28 pt (b) Begin hier Calculate the volume of the cardboard box in cm . 3 (3) Formatted: Font: 28 pt, English (South Africa) Formatted: Tab stops: 0.42", Left + Not at 0.38" Formatted: Tab stops: 0.42", Left 2.1.2 Determine how many plastic containers can fit into: Formatted: Tab stops: 0.42", Left (a) The length of the cardboard box (3) Formatted: Tab stops: 0.42", Left Formatted: Tab stops: 0.42", Left (b) The width of the cardboard box (2) Formatted: Tab stops: 0.42", Left 2.1.3 If a total of 144 triangular plastic containers can fit into one cardboard box, calculate how many boxes will be needed if there are a total of 1 500 learners in the school who participate in the feeding scheme. (2) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 8 8 (Eerste Vraestel) 10601/16 2.2 When preparing the sandwiches, parents randomly put three spreads on the sandwiches: Sandwich Spread, Cheese Spread and Marmite. A box was randomly chosen and the spreads on the sandwiches were found to be in the following ratio: 5 Sandwich Spread, 59 Marmite and 80 Cheese Spread sandwiches. 2.2.1 Write down the ratio of Cheese Spread sandwiches to Sandwich Spread Formatted Table sandwiches in the simplest form. (2) 2.2.2 Write down the probability (as a percentage) of a learner getting a Sandwich Spread sandwich (3) 2.3 Mrs. Madiba, one of the parents, needs to deliver the sandwiches to Kings Primary School. The school is 25,3 km from Mrs. Madiba’s home. It takes her 45 minutes to reach the school. If Mrs. Madiba leaves her home at 10:50, at what time will she reach the school? (2) 2.4 Mrs. Madiba is concerned about her daughter’s general health and takes her to the local clinic to be examined. Her daughter, Suzy, is 12 years old, 150 cm tall and has a body- mass-index of 27 kg/m2. The nurse at the clinic provides her with a BMI (Body-Mass- Index) chart (ANNEXURE B). Use the information above to answer the questions that follow. 2.4.1 Write down the percentile into which Mrs. Madiba’s daughter falls. (2) 2.4.2 Mrs. Madiba told the nurse that she is concerned that her daughter is Formatted: Left overweight for her age and height. Substantiate Mrs. Madiba’s opinion by calculations. Massa (kg) Formatted: Afrikaans Use the formula: BMI = (5) (Lengte in m) 2 Formatted: Afrikaans Formatted: Afrikaans 2.4.3 Suzy needs to lose weight. If she loses enough weight to fall into the 85th Formatted: Afrikaans percentile, write down her new BMI. (2) Formatted: Left [29] b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 9 9 (Eerste Vraestel) 10601/16 QUESTION 3 Formatted: Afrikaans Formatted: Afrikaans 3.1 Formatted: Font: Times New Roman The Comrades Marathon is an ultra-marathon run between Durban and Pietermaritzburg. The race starts at 05:30 and finishes at 17:30. Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 8 pt, Bold, English Profile of the Marathon between Pietermartizburg and Durban. (South Africa) Hoogste punt Formatted: Font: Times New Roman, 8 pt, Bold Drummond 810 m Polly Shorts 11:30 afsny Bokant van Formatted: Font: Times New Roman, 8 pt, Bold, English Fields Hill (South Africa) Hoogte in meterHeight in metres 900 Formatted: Font: Times New Roman, 8 pt, Bold, English 750 Pinetown (South Africa) Durban 600 Grens Formatted: Font: Times New Roman Umlaas- weg Formatted: Font: Times New Roman, 8 pt, Bold, English 450 Inchanga Berea (South Africa) Camper- Bothas Hill down Winston Formatted: Font: Times New Roman Cato Ridge Tumble Inn Park Cowie Hill 150 Hoofweg Formatted: Font: Times New Roman 10 20 30 40 50 60 70 80 89 Formatted: Font: Times New Roman Afstand in Distance in km Formatted: Font: Times New Roman, 8 pt, Bold, English (South Africa) Source: www.crescentsofbrisbane.org Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 8 pt, Bold, English Use the information above to answer the questions that follow. (South Africa) Formatted: Font: Times New Roman 3.1.1 Write down the total distance of the Comrades Marathon. (2) Formatted ... Formatted: Font: Times New Roman 3.1.2 A cut-off point is a certain point which the runners must reach within a Formatted ... prescribed time so that they may continue their participation in the Comrades Formatted: Font: Times New Roman Marathon. Formatted ... Formatted: Font: Times New Roman (a) Write down the cut-off point and time for the marathon runners. (2) Formatted: Font: Times New Roman (b) Write down the approximate distance from the cut-off point to the end Formatted ... of the marathon. (1) Formatted ... Formatted: Font: Times New Roman 3.1.3 Write down the two points between which the steepest downhill slope lies, Formatted: Font: Times New Roman when the marathon will be run downhill. (2) Formatted: Font: Times New Roman 3.1.4 Thebogo participated in the Comrades Marathon and finished the marathon in Formatted ... a time of six and a half hours. Calculate Thebogo’s average speed in km/h. Formatted: Font: Times New Roman Formatted ... Afstand Formatted ... Use the formula: Average Speed = Tyd (2) Formatted ... Formatted: Font: Times New Roman 3.1.5 Describe in detail the marathon from Drummond to Pinetown, as indicated on Formatted: Font: Times New Roman the map. Use words like uphill, downhill, slope and steep. (5) Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans Formatted: Afrikaans b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 10 10 (Eerste Vraestel) 10601/16 3.2 Study the floor plan of the house below and answer the questions that follow. Formatted: Afrikaans Formatted: Afrikaans Formatted: Font: Times New Roman, 8 pt Formatted: Font: Times New Roman, 10 pt, Bold, English (South Africa) oond Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 10 pt, Bold, English KOMBUIS (South Africa) Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 10 pt, Bold, English KAMER (South Africa) wasbak Formatted: Font: Times New Roman, 8 pt leer Formatted: Font: Times New Roman, 10 pt, Bold, English (South Africa) Formatted: Font: Times New Roman elektriese warm- kas water- Formatted: Font: Times New Roman, 8 pt, Bold, English stort wasbak (South Africa) toestel BADKAMER Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 8 pt, Bold, English BUITEKAMER water- (South Africa) tenk was- Formatted: Font: Times New Roman toilet masjien Formatted: Font: Times New Roman, 8 pt, Bold, English (South Africa) Formatted: Font: Times New Roman, 8 pt ONDERSTE VERDIEPING BOONSTE VERDIEPING Formatted: Font: Times New Roman, 10 pt, Bold, English (South Africa) Formatted: Font: Times New Roman, 8 pt, Bold, English Scale 1 : 500 (South Africa) Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 10 pt, Bold, English Use the floor plan above to answer the following questions: (South Africa) Formatted: Font: Times New Roman 3.2.1 Identify the scale of the floor plan. (2) Formatted: Font: Times New Roman Formatted: Font: Times New Roman, 10 pt, Bold, English 3.2.2 Explain what the scale means in terms of the measurements on the plan and (South Africa) actual dimensions. (2) Formatted: Font: Times New Roman, 8 pt, Bold, English (South Africa) 3.2.3 Measure the South-Western wall of the house. Give your answer in cm. (2) Formatted: Font: Times New Roman, 8 pt [20] Formatted: Font: Times New Roman, 8 pt, Bold, English (South Africa) Formatted: Font: Times New Roman, 8 pt, Bold, English (South Africa) Formatted: Font: Times New Roman Formatted: Centered Formatted: Font: Times New Roman, 10 pt, Bold, English (South Africa) Formatted: Font: Times New Roman Formatted: Centered Formatted: Font: Times New Roman, 10 pt, Bold, English (South Africa) Formatted: Font: Bold, Afrikaans b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 11 11 (Eerste Vraestel) 10601/16 QUESTION 4 Formatted: Afrikaans 4.1 In 2015 a group of female friends decided to enter the Cape Argus Pick-n-Pay Cycle Tour as a team. They decided to call their team The Seasonal Fruits. Each member chose their favourite fruit and dressed in the bright colours of the fruit that each had chosen, on the day of the cycle tour. The team enjoyed the experience and decided to enter the cycle tour again in 2016. Table 2 below is a summary of the times in which each member of the team completed the tour in 2015 and 2016. Table 2: Time taken to complete the tour in 2015 and 2016 Formatted: Font: Bold, Afrikaans Formatted: Afrikaans Age in 2015 Time (2015) Age in 2016 Time (2016) 18 03:47:43 19 03:13:22 17 04:10:30 18 Injury 17 03:57:16 18 04:25:14 16 04:01:27 17 03:39:45 18 03:38:10 17 04:26:51 17 05:05:35 19 03:44:49 18 04:52:00 18 Injury 20 04:52:00 19 03:56:38 25 05:38:01 21 Injury 25 05:28:36 26 06:05:10 26 05:33:43 29 06:11:59 Use the information from the table above to answer the following questions. 4.1.1 Write down the total number of team members belonging to The Seasonal Formatted Table Fruits for 2016. (2) 4.1.2 Write down the maximum time that it took for a member of The Seasonal Fruits team to complete the tour in 2016. (2) 4.1.3 Determine the time range for members in 2015. (2) 4.1.4 Calculate the mean age of the team members that participated in the tour in 2015. (3) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 12 12 (Eerste Vraestel) 10601/16 4.2 Formatted: Afrikaans The 2015 and 2016 times for The Seasonal Fruits, rounded to the nearest minute, are shown below. 2015 306 292 250 228 338 329 281 237 251 292 2016 193 220 225 237 265 267 334 265 372 4.2.1 Write down the mode for the 2015 times. (1) 4.2.2 Calculate the mean time for 2016. Give your answer in hours and minutes. (3) 4.2.3 Determine the median time for 2015. (3) 4.2.4 Determine the range for 2016. (2) 4.3 4.3.1 Determine whether the following sample is representative or biased: “A researcher stands in front of the community library to ask whether the people passing through have read a book in the past month.” (2) 4.3.2 Explain the meanings of the following terms. a) Discrete data (2) Formatted: No bullets or numbering, Tab stops: 0.42", b) Continuous data (2) Formatted: No bullets or numbering, Tab stops: 0.42", Formatted: Afrikaans 4.4 Mrs Morake keeps a record of her sales of mats at her flea market stall for six days of trading. She sells the mats for R25,00 making a profit of R8,00 on each sale. She sold 26 mats during the six days. Below is a record of her sales. Day of the week Mon Tues Wed Thurs Fri Sat Amount obtained 50 100 75 100 150 175 4.4.1 Draw a line graph on ANSWER SHEET A to represent this information. (6) 4.4.2 Calculate the profit she made after trading for six days. (3) 4.4.3 Write down the days on which she received the same income. (2) [35] Formatted: Font: 1 pt, Afrikaans Formatted: Afrikaans Formatted: Afrikaans Formatted Table Formatted Table b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 13 13 (Eerste Vraestel) 10601/16 QUESTION 5 5.1 The South African Demographic and Health Survey was carried out in 1998. As a part of the survey, 5 671 men were surveyed about their alcohol drinking habits. Their respective blood pressure levels were measured and recorded. The results are summarized in Table 3, a contingency table. Table 3: Blood pressure of men who participated in The South African Demographic and Health Survey on alcohol drinking habits. Number of men High blood Blood pressure not Total Formatted: Centered pressure high Formatted Table Drink alcohol 688 1 864 2 552 Don’t drink alcohol 611 2 508 3 119 Total 1 299 4 372 5 671 Use the information above to answer the questions that follow. 5.1.1 Write down the total number of men with high blood pressure. (1) Formatted: Font: Sylfaen, Afrikaans Formatted: Afrikaans 5.1.2 Write down the number of men who do not drink alcohol and who do not have high blood pressure. (1) 5.1.3 Determine the ratio of men drinking alcohol who had high blood pressure. Formatted Table Round your answer off to the nearest whole number. (2) 5.1.4If you choose a male non-alcoholic drinker at random, what is the probability Formatted Table that he does not have high blood pressure? Give your answer as a common fraction in its simplest form. (2) INSTRUKSIES EN INLIGTING 1. Hierdie vraestel bestaan uit VYF vrae. Beantwoord AL die vrae. 2. Gebruik die ADDENDUM soos volg: - Gebruik BYLAAG A om Vraag 1 te beantwoord - Gebruik BYLAAG B om Vraag 1.1.3 te beantwoord - Gebruik BYLAAG C om Vraag 2.4 te beantwoord 3. Gebruik die ANTWOORDBLAD aan die einde van jou vraestel om Vraag 4.4.1 te beantwoord. 4. Nommer jou antwoorde korrek soos die nommeringstelsel wat in die vraestel gebruik is. 5. Begin elke vraag op ʼn NUWE bladsy. 6. Jy mag ʼn goedgekeurde sakrekenaar (nie-programmeerbaar en nie-grafies) gebruik, tensy anders aangedui. b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 14 14 (Eerste Vraestel) 10601/16 7. Toon ALLE berekeninge duidelik. 8. Rond ALLE finale antwoorde toepaslik af na aanleiding van die gegewe konteks, tensy anders aangedui. 9. Dui meeteenhede aan waar van toepassing. 10. Kaarte en diagramme is NIE noodwendig op skaal geteken nie, tensy anders aangedui. 11. Skryf netjies en leesbaar. Formatted: Space After: 0 pt b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 15 15 (Eerste Vraestel) 10601/16 VRAAG 1 1.1 Robert is die Menslike Hulpbron Beampte van Bettie’s Best Boutique en Mev. April is ʼn 48-jaar oue verkoopsbestuurder wat ʼn enkelouer met een kind is. Robert berei Mev. April se betaalstrokie vir Oktober 2015 voor. Die totale bydrae aan die Werkloosheidsversekeringsfonds (WVF) is 1% van die werknemer se Bruto Salaris en ʼn bypassende 1% vanaf die werkgewer. Bylaag A bevat Mev. April se betaalstrokie vir Oktober 2015 en Bylaag B bevat die belastingtabel vir individue vir die belastingjaar 2015/2016. Gebruik die inligting van Mev. April se betaalstrokie op BYLAAG A en die belastingtabel op BYLAAG B om die vrae wat volg te beantwoord. 1.1.1 Bereken die waarde van A. (2) 1.1.2 Bereken Mev. April se jaarlikse belasbare inkomste. Gebruik die formule: Belasbare inkomste = Jaarlikse inkomste – Jaarlikse Formatted: Left Pensioenfondsbydrae. (4) 1.1.3 (a) Mediese Belastingkrediet word van die jaarlikse belasting betaalbaar afgetrek om die belasting te bepaal wat sy moet betaal. Bereken die jaarlikse mediese belastingkrediet wat sy van haar jaarlikse belasting betaalbaar, kan aftrek. (2) (b) Gebruik die 2015/2016 belastingtabel wat op BYLAAG B voorsien Formatted: Indent: Left: 0", Hanging: 0.42" word om Mev. April se jaarlikse belasting betaalbaar, te bereken. Gebruik die formule: Jaarlikse belasting Betaalbaar = Jaarlikse Belasting – Korting – Mediese Belastingkrediet (2) (c) Bepaal die waarde van B op Mev. April se betaalstrokie Formatted: Left (BYLAAG A). (2) 1.1.4 (a) Bewys dat Mev. April se totale aftrekkings R3 803,45 is. (2) (b) Bepaal die waarde van C (BYLAAG A), Mev. April se netto Formatted: Left maandelikse inkomste. Gebruik die formule: Netto Inkomste = Bruto Inkomste – Totale Aftrekkings (2) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 16 16 (Eerste Vraestel) 10601/16 1.1.5 (a) Skryf die persentasie neer wat gebruik word om Mev. April se WVF (Werkloosheidversekeringsfonds-bydrae), te bereken. (2) (b) Bepaal die totale bedrag WVF wat deur Bettie’s Best Boutique aan die einde van Oktober aan SARS oorbetaal sal word. (2) 1.1.6 Mev. April gaan in Februarie 2016 trou. Sy beplan om haar toekomstige man as ʼn lid op haar mediese fonds skema, by te voeg. Bepaal haar jaarlikse belastingkrediet vir die 2015/16 belastingjaar. (2) 1.1.7 Mev. April se kind is in Graad 11 en beplan om vir verdere studies na matriek aansoek te doen. Om in staat te wees om haar kind vir die eerste studiejaar te registreer, het Mev. April besluit om R3 000 per maand, begin van November 2014 tot November 2015, te spaar. Die totale bedrag aan die einde van November 2015 was belê in ʼn 32-dag Daggeldrekening (“Call Account”) in ʼn bank wat 3,4% enkelvoudige rente per jaar bied. (a) Bepaal die totale bedrag wat na een jaar gespaar is. (1) (b) Vandaar, bereken die bedrag wat Mev. April aan die einde van Formatted: Indent: Left: 0", Hanging: 0.42" November 2016 in haar rekening sal hê. (2) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 17 17 (Eerste Vraestel) 10601/16 Formatted: Font: 1 pt 1.2 Gedurende die Desember vakansie was Mev. April in ʼn padongeluk oppad terug Johannesburg toe vanaf Port Elizabeth, betrokke. Die versekeringsmaatskappy het haar ingelig dat haar voertuig onherstelbaar beskadig is. Mev. April het besluit om die voertuig te vervang. Sy het die volgende advertensie in ʼn plaaslike koerant gesien. Geprys om te gaan! R104 995 Spaar R11 000 Mev. April was ʼn huurkoop-ooreenkoms van Brothers Bank aangebied. Sy is die volgende twee opsies aangebied: Opsie 1 Opsie 2 Deposito: R10 500 Geen Depostio nodig Tydperk: 5 jaar Tydperk: 5 jaar Rente: 10,5% halfjaarliks saamgestel Rente: 12% jaarliks saamgestel Admin fooi: R1 010 Admin fooi: R1 010 Registrasie/Lisensie: R788 Registrasie/Lisensie: R788 Gebruik die inligting hierbo om die vrae wat volg, te beantwoord. 1.2.1 Bereken die bedrag wat deur Mev. April gefinansier moet word indien sy besluit om Opsie 1 te kies. (3) 1.2.2 Bereken die bedrag wat Mev. April na twee jaar op Opsie 2 aan die bank sal skuld, sonder enige paaiemente wat aan die huurkoop rekening gemaak is. (5) 1.2.3 Bepaal die deposito as ʼn persentasie van die koopprys. (4) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 18 18 (Eerste Vraestel) 10601/16 1.3 Mev. April is bekommerd oor die impak wat die geprojekteerde inflasiekoers en die verhoging in munisipale tariewe en fooie op haar besteebare inkomste sal hê. Tabel 1 hieronder wys die verhoogde geprojekteerde tariewe. Tabel 1: Verhoging in tariewe vir 2017 Tariewe en dienste 2016 % verhoging 2017 gehef Vullisverwydering R140,00 A R157,50 Sanitasie R179,39 13% R202,71 Water verbruik R170,86 10,5% R188,80 Elektrisiteits- verbruik (nie- R584,79 14,3% R668,41 voorafbetaal) Erfbelasting R380,98 15% R438,13 Subtotaal BTW B R1 655,55 uitgesluit BTW op dienste R203,84 R231,78 Totaal R1 668,86 R1 887,33 Gebruik die inligting hierbo om die vrae wat volg te beantwoord. 1.3.1 Verduidelik die betekenis van rentekoers. (2) 1.3.2 Bepaal die waarde van A, die persentasie verhoging vir vullisverwydering. Gebruik die formule: Nuwe bedrag - Ou bedrag Persentasie verhoging = x 100 % Ou bedrag (3) 1.3.3 Bepaal die waarde van B. (2) 1.3.4 Deur berekeninge, toon aan hoe die BTW bedrag van R231,78 bereken was. (2) 1.3.5 Bereken die addisionele bedrag waarvoor Mev. April maandeliks moet begroot op haar munisipale rekening vir 2017. (2) [48] b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 19 19 (Eerste Vraestel) 10601/16 VRAAG 2 2.1 Ouers by Kings Primêre Skool is deel van die voedingskema by die skool. Hulle berei toebroodjies vir die minderbevoorregte leerders voor en deel die toebroodjies gedurende pouse uit. Die toebroodjies word verpak in plastiese driehoekige houers en daarna in pare op die skuinskant van die driehoekige houers in ʼn kartonboks verpak soos hieronder getoon. 12” Wydte 5 cm 10 cm 24” Lengte 10" Diepte 24" Lengte 12" Wydte 10 cm Afmetings: Afmetings: Lengte = 10 cm Lengte = 24 duim Wydte = 10 cm Wydte = 12 duim Verpakking Diepte = 5 cm Diepte = 10 duim soos van bo gesien 1 duim = 2,54 cm Volume = Lengte × Wydte × Diepte Gebruik die inligting hierbo om die vrae wat volg te beantwoord. 2.1.1 (a) Herlei die lengte, wydte en diepte van die kartonboks na cm. (4) Formatted: Tab stops: 0.42", Left + Not at 0.38" (b) Bereken die volume van die kartonboks in cm3. (2) Formatted: Tab stops: 0.42", Left 2.1.2 Bepaal hoeveel van die plastiekhouers in die ... (a) lengte van die kartonboks kan inpas. (3) Formatted: Tab stops: 0.42", Left (b) wydte van die kartonboks kan inpas. (2) Formatted: Tab stops: 0.42", Left 2.1.3 Indien ʼn totaal van 144 driehoekige plastiekhouers in een kartonboks kan inpas, bereken hoeveel bokse benodig sal word indien 1 500 leerders by die skool se voedingskema betrokke is. (2) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 20 20 (Eerste Vraestel) 10601/16 2.2 Wanneer die toebroodjies voorberei word, sit die ouers lukraak drie smere op die toebroodjies: Sandwich Spread, Kaassmeer en Marmite. ʼn Boks was lukraak gekies en die smere was in die volgende verhouding gevind: 5 Sandwich Spread, 59 Marmite en 80 Kaassmeer toebroodjies. 2.2.1 Skryf die verhouding van Kaassmeer toebroodjies tot Sandwich Spread toebroodjies in die eenvoudigste vorm neer. (2) 2.2.2 Skryf die waarskynlikheid (as ʼn persentasie) dat ʼn leerder ʼn Sandwich Spread Formatted Table toebroodjie sal ontvang, neer. (3) 2.3 Mev. Madiba, een van die ouers, moet die toebroodjies by Kings Primêre Skool aflewer. Die skool is 25,3 km vanaf Mev. Madiba se huis. Dit neem haar 45 minute om die skool te bereik. Hoe laat sal Mev. Madiba die skool bereik indien sy haar huis om 10:50 verlaat? (2) 2.4 Mev. Madiba is bekommerd oor haar dogter se algehele gesondheid en neem haar na die plaaslike kliniek om ondersoek te word. Haar dogter, Suzy, is 12 jaar oud, 150 cm lank en het ʼn liggaamsmassa-indeks van 27 kg/m2. Die verpleegster by die kliniek voorsien haar meet ʼn LMI (Liggaamsmassa-Indeks) kaart. (BYLAAG C). Gebruik die inligting hierbo en BYLAAG C om die vrae wat volg, te beantwoord. 2.4.1 Skryf die persentiel neer waarin Mev. Madiba se dogter val. (2) 2.4.2 Mev. Madiba het aan die verpleegster gesê dat sy bekommerd is dat haar dogter oorgewig is vir haar ouderdom en lengte. Staaf Mev. Madiba se opinie deur berekeninge. Massa (kg) Gebruik die formule: LMI = (5) (Lengte in m) 2 2.4.3 Suzy moet gewig verloor. Indien sy genoeg gewig verloor om op die 85ste persentiel te val, skryf haar nuwe LMI neer. (2) [29] b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 21 21 (Eerste Vraestel) 10601/16 VRAAG 3 3.1 Die Comrades-Marathon is ʼn ultra-marathon wat tussen Durban en Pietermaritzburg gehardloop word. Die wedloop begin om 05:30 en eindig om 17:30. Profiel van die Marathon tussen Pietermartizburg en Durban. HOOGSTE PUNT 11:30 AFSNY 900 750 Hoogte in meter 600 450 150 10 20 30 40 50 60 70 80 89 Afstand in km [Bron : www.crescentsofbrisbane.org] Formatted: Font: Not Bold Formatted: Default Paragraph Font, Font: Not Bold Gebruik die inligting hierbo om die vrae wat volg te beantwoord. Formatted: Font: Not Bold 3.1.1 Skryf die totale afstand van die Comrades-Marathon neer. (2) 3.1.2 ʼn Afsnypunt is ʼn spesifieke punt wat die hardlopers in ʼn voorgeskrewe tyd moet bereik sodat hulle hul deelname in die Comrades-Marathon mag bevestig. (a) Skryf die afsnypunt asook die tyd vir die marathon-hardlopers neer. (2) (b) Skryf die benaderde afstand vanaf die afsnypunt tot by die einde van die marathon neer. (1) 3.1.3 Skryf die twee punte waartussen die steilste afdraande helling lê, wanneer die marathon afdraande gehardloop sal word. (2) 3.1.4 Thebogo het in die Comrades-Marathon deelgeneem en met ʼn tyd van ses en ʼn half uur voltooi. Bereken Thebogo se gemiddelde spoed in km/h. Afstand Gebruik die formule: Gemiddelde Spoed = Tyd (2) 3.1.5 Beskryf in detail die marathon vanaf Drummond na Pinetown, soos op die kaart aangedui. Gebruik woorde soos opdraande, afdraande, helling en steil. (5) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 22 22 (Eerste Vraestel) 10601/16 3.2 Bestudeer die vloerplan van die huis hieronder en beantwoord die vrae wat volg. Skaal 1 : 500 Gebruik die vloerplan hierbo om die volgende vrae te beantwoord. 3.2.1 Identifiseer die skaal van die vloerplan. (2) 3.2.2 Verduidelik wat die skaal beteken in terme van die afmetings op die plan en die werklike afmetings. (2) 3.2.3 Meet die Suidwestelike muur van die huis. Gee jou antwoord in cm. (2) [20] b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 23 23 (Eerste Vraestel) 10601/16 VRAAG 4 4.1 In 2015 het ʼn groep vriendinne besluit om as ʼn span aan die Cape Argus Pick-n-Pay Fietstoer deel te neem. Hulle het besluit om hul span Die Seisoenale Vrugte te noem. Elke lid het hul gunsteling vrug gekies en in die helder kleure van die vrug wat hul gekies het, op die dag van die fietstoer, aangetrek. Die span het die ervaring geniet en besluit om weer in 2016 aan die fietstoer deel te neem. Tabel 2 hieronder is ʼn opsomming van die tye waarin elke lid van die span die toer in 2015 en 2016 voltooi het. Tabel 2: Tyd geneem om die toer in 2015 en 2016 te voltooi Ouderdom Tyd (2015) Ouderdom Tyd (2016) in 2015 in 2016 18 03:47:43 19 03:13:22 17 04:10:30 18 Besering 17 03:57:16 18 04:25:14 16 04:01:27 17 03:39:45 18 03:38:10 19 04:26:51 17 05:05:35 18 03:44:49 18 04:52:00 19 Besering 20 04:52:00 21 03:56:38 25 05:38:01 26 Besering 25 05:28:36 26 06:05:10 26 05:33:43 29 06:11:59 Gebruik die inligting in die tabel hierbo om die volgende vrae te beantwoord. 4.1.1 Skryf die totale aantal spanlede wat in 2016 aan Die Seisoenale Vrugte behoort het, neer. (2) 4.1.2 Skryf die maksimum tyd neer wat dit vir een van die lede van Die Seisoenale Vrugte geneem het om die toer in 2016 te voltooi. (2) 4.1.3 Bepaal die omvangstyd vir die lede in 2015. (2) 4.1.4 Bereken die gemiddelde ouderdom van die spanlede wat in 2015 aan die toer deelgeneem het. (3) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 24 24 (Eerste Vraestel) 10601/16 4.2 Die 2015 en 2016 tye vir Die Seisoenale Vrugte, afgerond tot die naaste minuut, word hieronder gegee. 2015 306 292 250 228 338 329 281 237 251 292 2016 193 220 225 237 265 267 334 265 372 4.2.1 Skryf die modale tyd vir 2015 neer. (1) 4.2.2 Bereken die gemiddelde tyd vir 2016. Gee jou antwoord in ure en minute. (3) 4.2.3 Bepaal die mediaantyd vir 2015. (3) 4.2.4 Bepaal die omvang vir 2016. (2) 4.3 4.3.1 Bepaal of die volgende voorbeeld verteenwoordigend of bevooroordeeld is: “ ʼn Navorser staan voor die gemeenskapsbiblioteek en vra of die mense wat deurkom ʼn boek in die afgelope maand gelees het.” (2) 4.3.2 Verduidelik die betekenis van die volgende terme. (a) Diskrete data (2) Formatted: No bullets or numbering, Tab stops: 0.42", Left + Not at 1.3" (b) Kontinue data (2) Formatted: No bullets or numbering, Tab stops: 0.42", Left + Not at 1.3" 4.4 Mev Morake hou ʼn rekord van haar mat-verkope by die vlooimark stalletjie vir ses dae se handel. Sy verkoop die matte vir R25,00 en maak ʼn wins van R8,00 op elkeen wat sy verkoop. Sy het 26 matte in die ses dae verkoop. Hieronder is ʼn rekord van die inkomste van haar verkope. Dag van die week Maan Dins Woens Don Vry Sat Formatted: Font: Bold Bedrag verdien 50 100 75 100 150 175 Formatted: Centered Formatted: Font: Bold Formatted: Font: Bold Formatted: Centered 4.4.1 Teken ʼn lyngrafiek op die ANTWOORDBLAD om die inligting voor te stel. (6) Formatted: Font: Not Bold 4.4.2 Bereken hoeveel wins sy na ses dae se handel gemaak het. (3) 4.4.3 Skryf die dae neer waar sy dieselfde hoeveelheid inkomste ontvang het. (2) [35] Formatted: Font: 1 pt b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 25 25 (Eerste Vraestel) 10601/16 VRAAG 5 5.1 Die Suid-Afrikaanse Demografiese en Gesondheidsopname is is 1998 gedoen. As deel van die opname was 5 671 mans se drinkgewoontes ondersoek. Hul onderskeidelike bloeddrukvlakke was geneem en aangeteken. Die resultate is in Tabel 3, ʼn gebeurlikheidstabel, opgesom. Tabel 3: Bloeddruk van mans wat in die Suid-Afrikaanse Demografiese en Gesondheidsopname oor alkoholiese drinkgewoontes deelgeneem het Aantal mans Hoë bloeddruk Bloeddruk nie hoog nie Totaal Drink alkohol 688 1 864 2 552 Drink nie alkohol nie 611 2 508 3 119 Totaal 1 299 4 372 5 671 Gebruik die inligting hierbo en beantwoord die vrae wat volg. 5.1.1 Skryf die totale aantal mans met hoë bloeddruk neer. (1) 5.1.2 Skryf die aantal mans wat nie alkohol drink en wat nie hoë bloeddruk het nie, neer. (1) 5.1.3 Bepaal die verhouding van mans wat alkohol drink en hoë bloeddruk het. Rond jou antwoord af tot die naaste heelgetal. (2) 5.1.4 Indien jy ʼn man lukraak kies wat nie alkohol drink nie, wat is die waarskynlikheid dat hy nie hoë bloeddruk sal hê nie? Gee jou antwoord as ʼn algemene breuk in sy eenvoudigste vorm. (2) b.o.

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 26 26 (Eerste Vraestel) 10601/16 5.2 Mnr L Mohapi is ʼn inwoner van Bergville. Hieronder is ʼn onvoltooide staat van sy munisipale rekening. Bestudeer die rekening en bygevoegde tarriefstruktuur en gebruik die inligting om sy rekeningstaat te voltooi. Bergville Munisipale Water en Riool Tariewe Rekening Detail soos teen 10/09/2015 Rek. Nr 43247876 Water (Tydperk 06/07/2015 tot 05/08/2015 – 31 Dae) (Werklike lesing) By 41 Burnside Road, Bergville/ERF0087983 Vorige lesing: (A)_____________ Huidige lesing : 125334kl Verbruik : 34.5kl Verbruikskoste (Huis 1) (B)R___________ Riool (Tydperk 06/07/2015 tot 05/08/2015 – 31 Dae) (Werklike lesing) By 41 Burnside Road, Bergville/ERF0087983 Verwyderingskoste (C)_______kl R181.60 BTW teen 14%: (D)R_________ LAASTE REKENING TOTAAL VERSKULDIG R519,50___________ WATER RIOOL Huishoudelik 1: Tarief Verwyderingskoste Volume Tarief (per kl) Volume Tarief (per kl) ≤6kl Gratis ≤4kl Gratis 6,1 – 15kl R8.60 4,1kl – 7kl R4.67 15,1 – 25kl R9.60 7,1kl – 15 R9.94 >25kl R10,60 >15kl R14.60 Gebruik die inligting hierbo om die vermiste waardes te bereken. 5.2.1 A (2) 5.2.2 B (3) 5.2.3 (a) Bereken die oorblywende bedrag van R181,60 vir verwyderingskoste Formatted: Indent: Left: 0", Hanging: 0.5" nadat 15 kl riool gebruik is. (3) (b) Bereken die totale aantal kiloliters riool wat verwyder is by die Formatted Table vermiste waarde C. (2) Formatted: Indent: Left: 0", Hanging: 0.5" 5.2.4 Indien die verbruikskoste R455,70 is, bereken die BTW wat op hierdie bedrag Formatted Table betaalbaar is. (2) [18] Formatted: Font: 6 pt TOTAAL: 150 EINDE

Downloaded from hlayiso.com 1 WISKUNDIGE GELETTERDHEID 2 2 (Eerste Vraestel) 10601/16 Formatted: Afrikaans b.o.

Downloaded from hlayiso.com 1 WISKUNDIGE GELETTERDHEID 3 3 (Eerste Vraestel) 10601/16 5.2 Mr L Mohapi is a resident of Bergville. Below is an incomplete statement of his municipal account. Study the account and accompanying tariff structure and use the information to complete the account statement. Bergville Municipality Water and Sewage Tariffs Account Detail as at 10/09/2015 A/c No 43247876 Water (Period 06/07/2015 to 05/08/2015 – 31 Days) (Actual reading) At 41 Burnside Road, Bergville/ERF0087983 Previous reading: (A)_____________ Current reading : 125334 Consumption : 34.5kl Consumption charge (Dom 1) (B)R___________ Sewage (Period 06/07/2015 to 05/08/2015 – 31 Days)(Actual reading) At 41 Burnside Road, Bergville/ERF0087983 Disposal charge (C)_______kl R181.60 VAT at 14%: (D)R_________ LATEST ACCOUNT TOTAL DUE R519,50___________ WATER SEWAGE Domestic 1: Tariff Disposal Charges Volume Tariff (per kl) Volume Tariff (per kl) ≤6kl Free ≤4kl Fre 6,1 – 5kl R8.60 4,1kl – 7kl R4.67 15,1 – 25kl R9.60 7,1kl – 15 R9.94 >25kl R10,60 >15kl R14.60 Use the information above to calculate the missing values. 5.2.1 A (2) 5.2.2 B (3) 5.2.3 a) Calculate the remaining amount of R181,60 for disposable charge after 15 kl of sewage has been used. (3) Formatted: Indent: Left: 0", Hanging: 0.5" b) Calculate the total number of kilolitres sewage used at missing value C. (2) Formatted Table Formatted: Indent: Left: 0", Hanging: 0.5" 5.2.4 If the consumption charge is R455,70, calculate the VAT payable on this Formatted Table amount. (2) [19] Formatted: Font: 1 pt, Afrikaans Formatted: Afrikaans TOTAL: 150 Formatted: Font: 10 pt, Afrikaans EINDE

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 1715 4 (Eerste Vraestel) 10601/16 Formatted: Afrikaans ANSWER SHEET A Question 4.4.1 Formatted: Afrikaans Formatted: Afrikaans Teken Mev. Morake se verkope vir ses dae op Formatted: Afrikaans Formatted: Font: Times New Roman Formatted: Font: Times New Roman, Bold, English (South Africa) Formatted: Font: Times New Roman, 10 pt, Bold Verkope in rand Formatted: Font: Times New Roman, 10 pt, Bold, English (South Africa) Maandag Dinsdag Woensdag Donderdag Vrydag Saterdag Formatted: Font: Times New Roman, 10 pt, Bold Formatted: Tab stops: 0.98", Left + 1.97", Left + 3.05", Dae van die week Left + 4.13", Left + 5.12", Left ANTWOORDBLAD Formatted: Font: Times New Roman, Bold Formatted: Centered, Tab stops: 0.98", Left + 1.97", Left Vraag 4.4.1 + 3.05", Left + 4.13", Left + 5.12", Left Formatted: Font: Times New Roman, 10 pt, Bold, English Rekord van Mev. Morake se inkomste van haar verkope vir ses dae (South Africa) Formatted: Centered Formatted: Font: Bold, English (South Africa)

Downloaded from hlayiso.com WISKUNDIGE GELETTERDHEID 1715 5 (Eerste Vraestel) 10601/16 MaandagMonday DinsdagTuesday WednesdayWoensdag ThursdayDonderdag FridayVrydag SaturdaySaterdag Formatted: Afrikaans