Mathematical Literacy Grade 11 P1 2020 Memo (Eng)

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 11 NOVEMBER 2020 MATHEMATICAL LITERACY P1 EXEMPLAR MARKS: 100 TIME: 2 hours *Imlit1* This question paper consists of 9 pages, including an answer sheet.

Downloaded from hlayiso.com 2 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2020) INSTRUCTIONS AND INFORMATION 1. This question paper consists of FOUR questions. Answer ALL the questions. 2. 2.1 Use the ANSWER SHEET for QUESTION 4.3.2. 2.2 Write your NAME and GRADE in the spaces provided on the ANSWER SHEET for QUESTION 4.3.2. Hand in the ANSWER SHEET with your ANSWER BOOK. 3. Number the answers correctly according to the numbering system used in this question paper. 4. Maps and diagrams are not necessarily drawn to scale, unless stated otherwise. 5. Round off ALL final answers according to the context used, unless stated otherwise. 6. Indicate units of measurement, where applicable. 7. Start EACH question on a NEW page. 8. You may use an approved calculator (non-programmable and non-geographical), unless stated otherwise. 9. Show ALL calculations clearly. 10. Write neatly and legibly. Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICAL LITERACY P1 3 QUESTION 1 1.1 Moses earns a gross salary of R10 500 per month. The basic monthly expenses used from the income are as follows: Housing expense 21%; Food 36%, Transport 10%; Cellphone bills 1,9%. The rest is for savings. Use the above information to answer the following questions. 1.1.1 Calculate the total gross salary per annum. (2) 1.1.2 Determine the amount of the monthly food expense. (2) 1.1.3 Write down the ratio of the housing percentage to the food percentage in the simplest form. (2) 1.1.4 Calculate Moses’s percentage for savings from his salary. (3) 1.2 Thando, a Mathematical Literacy teacher, collected and analysed test results of his class. The test was marked out of a total mark of 50. The results of the learners are indicated below: 38 21 12 18 41 28 24 34 10 35 Use the above information to answer the questions that follow. 1.2.1 Is the above data primary or secondary? (2) 1.2.2 Write down the highest mark obtained in the test. (2) 1.2.3 Explain the meaning of the term ‘median’. (2) 1.2.4 Write down the mark out of 50 for a learner who achieved 70% in the test. (2) 1.2.5 Write down the number of learners who failed the test, if the pass mark is 20 out of 50. (2) 1.3 A shopkeeper bought a dress for R750 and sold it, making a loss of R50. 1.3.1 Explain the meaning of the term ‘loss’ in this context. (2) 1.3.2 Calculate the percentage loss made on the sale. (2) [23] Copyright reserved Please turn over

Downloaded from hlayiso.com 4 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2020) QUESTION 2 2.1 Mrs Rogue invested money monthly from 2016 to 2020 at Company A. She terminated her investment and received the statement below from Old Mutual: Contract number Contracting Name of Start date Last party Investment plan of contract premium due date Smart MAX 17801249 R. Rogue Focused 01/07/2016 30/06/2031 Education Plan/1 Fund value as at 23 March 2020 Investment fund Unit price (cents) Number of Fund value units Allan Gray Balanced Fund C Class 8 266,470 A R8 038,07 Total R8 038,07 Difference between fund value and termination value Fund value R8 038,07 Reduction fees and transaction charges B Termination value R6 995,25 Withdrawals up to 23 March 2020 R765,57 Expected premium details as at 23 March 2020 Current Annual Next New premium Investment Premium premium Increase premium fund(s) Split rate increase Allan Gray R332,75 … 01/07/2020 R366,02 Balanced Fund 100% monthly C Class Total contributions since contract start date Total premiums paid R12 924,75 2.1.1 Write down the name of the investment plan that Mrs Rogue has. (2) 2.1.2 Calculate the value of A, the number of units earned from the given fund value. (4) 2.1.3 Show by means of calculations that Mrs Rogue lost 45,88% of the total premiums she contributed towards the fund by terminating her investment before the last premium. (4) 2.1.4 Calculate the value (in Rands) of B, the reduction fees and transaction charges. (2) 2.1.5 Write down the withdrawal value as at 23 March 2020. (2) Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICAL LITERACY P1 5 2.1.6 Calculate the percentage increase on the monthly premium. Give your final answer to the nearest percentage. You may use the following formula: ࢔ࢋ࢝ ࢖࢘ࢋ࢓࢏࢛࢓ ି ࢉ࢛࢘࢘ࢋ࢔࢚ ࢖࢘ࢋ࢓࢏࢛࢓ Percentage increase = × ૚૙૙% ࢉ࢛࢘࢘ࢋ࢔࢚ ࢖࢘ࢋ࢓࢏࢛࢓ (4) 2.2 Alice sells food from a kiosk that she rents in a township. The expenses associated with ingredients and labour for a plate amount to R30. The formula for expenses: Expenses = R500 + R30 × Number of plates She sells food per plate. The graph below shows her expenses and income for a month. ALICE’S EXPENSES AND INCOME FROM SALES 1800 1600 1400 Amount in Rands(R) 1200 1000 800 Expenses 600 Income 400 200 0 0 5 10 15 20 25 30 35 Number of plates Use the above information and the graph to answer the questions that follow. 2.2.1 Write down the independent variable in the above context. (2) 2.2.2 Determine the amount Alice pays as fixed expenses. (2) 2.2.3 Write down the formula for the income if a plate is sold at R50, in the form of: Income = … (2) 2.2.4 Determine the profit at the break-even point. (2) 2.2.5 Determine the loss when 8 plates are sold. (4) [30] Copyright reserved Please turn over

Downloaded from hlayiso.com 6 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2020) QUESTION 3 The Global Wellness Institute did research about the amount of spa revenue generated in different regions of the world in 2017. TABLE 1: NUMBER OF SPAS, REGIONS AND THE REVENUE GENERATED Regions Names of Regions Number of Revenue in Spas Billion dollars ($b) P North America 30 394 22,9 Q Latin America-Caribbean 13 856 6,6 R Sub-Saharan Africa 3 984 … S Middle East – North Africa 6 057 2,8 T Europe 46 282 33,3 V Asia – Pacific 48 679 26,5 TOTAL … … [Source: globalwellnessinstitute.org] Use the information above to answer the questions that follow. 3.1 Calculate the total number of spas used for the research in 2017. (2) 3.2 Calculate the mean number of spas used. Give your final answer to the nearest whole number. (2) 3.3 Express the number of spas in Europe as a percentage of the total number of spas. (2) 3.4 Determine the number of regions that lies above the range number of spas. (2) 3.5 Write down the unit ratio of spas in regions P and V. (3) 3.6 Calculate the total revenue in billion dollars for the spas if sub-Saharan Africa’s revenue is $5,0 billion less than Latin America-Caribbean’s revenue. (4) 3.7 Calculate the median revenue of the regions. (3) 3.8 Determine the probability (as a percentage) of randomly selecting a region with more than 40 000 spas. (3) [21] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICAL LITERACY P1 7 QUESTION 4 4.1 GOOD BOYS CAR WASHING BAY is in an area where water is charged according to the water tariffs structure shown in TABLE 2 below. TABLE 2: WATER TARIFF STRUCTURE Block Usage in Normal Charge per kilolitre kilolitre (kƐ) (kƐ) (Excluding VAT) 1 0–6 R0,00 2 +6 – 15 R9,35 3 +15 – 30 R11,16 4 +30 – 45 R12,53 5 +45 – 60 R13,98 6 60+ R15,34 NOTE: VAT is Value Added Tax. The VAT rate is 15%. Use TABLE 2 above to answer the question that follow. Calculate how much GOOD BOYS CAR WASHING BAY pays a month including VAT when they use 25 kƐ of water and give a reason why a step up (increasing block rate) system of water tariffs is used to charge water consumption other than a flat single rate. (6) 4.2 Andile received a donation from his brother who works in Rwanda. The donation was 745 614,04 Rwanda Francs (RWF). The bank deducted 10% for bank charges. Andile states that he will receive R12 750. Verify the statement with the necessary calculations. Use the exchange rate R 0,019 = 1 RWF (6) 4.3 Ibanda High School recorded absentees in the Grade 11 Mathematical Literacy class during the first week when schools reopened after the COVID-19 pandemic break. The data is shown in the table below. Monday Tuesday Wednesday Thursday Friday Girls 4 6 8 7 10 Boys 5 3 8 9 7 Use the above information to answer the questions that follow. 4.3.1 Determine the probability that a learner chosen at random was absent on Wednesday. (3) 4.3.2 Complete the double bar graph on the ANSWER SHEET provided by plotting the missing bars for the number of boys and girls absent. (5) Copyright reserved Please turn over

Downloaded from hlayiso.com 8 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2020) 4.4 A Grade 11 Mathematical Literacy class at Ibanda High wrote an examination marked out of 100 marks. The results arranged in ascending order are shown below. 23 41 42 50 50 51 54 55 56 57 60 61 65 66 66 67 68 69 70 70 70 72 C 74 76 79 82 85 86 88 Use the above information to answer the questions that follow. 4.4.1 The mean of the above data is equal to 64,2. A learner calculated that the value of C in the above data is 74. Verify, with the necessary calculations, whether the answer is valid. (4) 4.4.2 The frequency table of the above data is shown below. Class interval Frequency 20–29 1 30–39 D 40–49 2 50–59 7 60–69 8 70–80 8 80–89 4 Determine the value of D and give a reason for your answer. (2) [26] TOTAL: 100 Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICAL LITERACY P1 9 ANSWER SHEET QUESTION 4.3.2 NAME OF LEARNER: GRADE 11: Number of absent learners during the week 12 10 8 Number of absent learners 6 4 2 0 Monday Tuesday Wednesday Thursday Friday Days of the week Girls Boys Copyright reserved Please turn over

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Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 11 NOVEMBER 2020 MATHEMATICAL LITERACY P1 MARKING GUIDELINE EXEMPLAR MARKS: 100 Symbol Explanation M Method MA Method with accuracy CA Consistent accuracy A Accuracy C Conversion S Simplification RT/RG/RM Reading from a table/Reading from a graph/Read from map F Choosing the correct formula SF Substitution in a formula J Justification P Penalty, e.g. for no units, incorrect rounding off etc. R Rounding Off/Reason AO Answer only NPR No penalty for rounding This marking guideline consists of 8 pages.

Downloaded from hlayiso.com 2 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2020) MARKING GUIDELINES NOTE: x If a candidate answers a question TWICE, only mark the FIRST attempt. x If a candidate has crossed out (cancelled) an attempt to a question and NOT redone the solution, mark the crossed out (cancelled version) x Consistent accuracy (CA) applies in ALL aspects of the marking guidelines, however it stops at the second calculation error. x If the candidate presents any extra solution when reading from a graph, table, layout plan and map, then penalise for every extra incorrect item presented. LET WEL: x As ƌ kandidaat ƌ vraag TWEE keer beantwoord, merk slegs die EERSTE poging. x As ƌ kandidaat ƌ antwoord van ƌ vraag doodtrek (kanselleer) en nie oordoen nie, merk die doodgetrekte (gekanselleerde) poging. x Volgehoue akkuraatheid (CA) word in ALLE aspekte van die nasienriglyn toegepas, maar dit hou by die tweede berekeningsfout op. x Wanneer ƌ kandidaat aflesings vanaf ƌ grafiek, tabel, uitlegplan en kaart geneem en ekstra antwoorde gee, penaliseer vir elke ekstra verkeerde item. Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICAL LITERACY P1 3 QUESTION 1 [23 marks] Ques. Solution Explanation T&L 1.1.1 Annual gross salary = R10 500 × 12 9 M 1M Multiply by 12 F = R126 000 9A 1A Gross per annum (2) L1 1.1.2 Monthly food expense = R10 500 × 36% 9M 1M % Calculation F = R3 780 9CA 1CA Amount (2) L1 1.1.3 Housing % : Food % F = 21% : 36% 9M 1M Correct values and order L1 = 7 : 12 9CA 1CA Simplest form (2) 9M 1.1.4 Savings % = 100% – (21% +36% +10% + 1,9%) 1M Adding correct values F = 100% – 68,9%9M 1M Subtracting from 100 L1 = 31,1% 9CA 1CA Percentage (3) 1.2.1 Primary data 99A 2A Correct data type D (2) L1 1.2.2 41 99 RT 2RT Highest mark D (2) L1 1.2.3 Median is the middle value of a set of data which is arranged 2A Explanation D from small to big. 99A (2) L1 1.2.4 35 99 A 2A Correct mark D (2) L1 1.2.5 3 99 RT 2RT No. of learners failed D (2) L1 1.3.1 Loss is when the cost is more than the income. 99 A 2A Correct explanation F OR L1 Loss incurred when selling price is less than cost price of an item. 99 A (2) 1.3.2 % loss = ହ଴ × 100% 9M 1M Fraction multiplied by F ଻ହ଴ 100% L1 = 6,67% 9 CA 1CA Percentage NPR (2) [23] Copyright reserved Please turn over

Downloaded from hlayiso.com 4 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2020) QUESTION 2: FINANCE [30 marks] Ques. Solution Explanation Topic /Level 2.1.1 SmartMAXFocussed Education Plan 1 99 RT 2A Correct investment plan F (2) L1 2.1.2 8266 ,470 1C Converted to Rands F Number of units = 9C 1CA Value L2 100 = R82,6647 9 CA 8038 ,07 1M Division = 9M 82 ,6647 1CA No. of units = 97,23703104 9 CA (4) 2.1.3 % loss = 12 924,75 – 6 995,25 9 M 1M Subtraction of values F = R5 929,50 9 S 1S Simplification L3 5929 ,50 9 M 1M Dividing correct values = u 100 9 M 1M Multiply by 100% 12924 ,75 = 45,88% OR OR 6995 ,25 9 M Percentage loss = u 100 9 M 1M Dividing correct values 12924,75 1M Multiply by 100% = 54,12% 9S 1S Simplification = 100% – 54,12% 9M 1M Subtraction of % = 45,88% (4) 2.1.4 B = R8 038,07 – R6 995,25 9 MA 1MA Subtraction F = R1 042,82 9C A 1CA Correct answer (2) L2 2.1.5 R765,57 99RT 2RT Correct value F (2) L2 9RT 2.1.6 366 ,02  332 ,75 1RT Correct values F % increase = u 100 9 SF 1SF Substitution 332 ,75 L2 = 9,998% 9 S 1S Simplification = 10% 9 R 1R Nearest % (4) 2.2.1 Number of plates 99 RT 2RT Number of plates F (2) L2 2.2.2 Fixed expenses = R500 99 RT 2RT Fixed expenses F (2) L2 2.2.3 Income = R50 × Number of plates sold 9 M 9 A 1M Multiplication with R50 F 1A Correct formula (2) L2 2.2.4 R0 OR (No Profit) 99 RT 2RT No profit F (2) L2 Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICAL LITERACY P1 5 2.2.5 Loss for 8 plates = Expenses – Income 1RT R740 F 9RT 9 RT 1RT R400 L3 = 740 – 400 9M 1M Subtraction = R340 9A 1A Loss OR (From graph allow 340±10) OR Expenses = 500 + 8 × 30 = R740 9M IM for R740 Income = 50 × 8 = R400 9M 1M for R400 Loss = 740 – 400 = R340 9A 1M subtraction 1A for R340 exact answer (4) [30] Copyright reserved Please turn over

Downloaded from hlayiso.com 6 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2020) QUESTION 3: DATA HANDLING (18 marks) AND PROBABILITY (3 marks) Ques. Solution Explanation T/L 3.1 Total number of spas = 30 394 + 13 856 + 3 984 + 6 057 + 46 282 + 48 679 1M Adding correct values D =149 252 9M 9A 1A Total (2) L1 3.2 Mean = ଵସଽ ଶହଶ 9M CA from 3.1 D ଺ 1M Division L2 = 24 875,33 1R Whole number = 24 875 9 R (2) 3.3 European spas as a % = ସ଺ ଶ଼ଶ ×100 9M 1M Fraction with correct D ଵସଽ ଶହଶ values and L2 = 31% 9CA multiplication by 100 1CA Percentage (2) 3.4 Range = 48 679 – 3 984 D = 44 695 9S 1S Calculate range L3 Number of regions above range = 2 CA9 1CA Number of regions (2) 3.5 ସ଼ ଺଻ଽ 30 394 : 48 679 = 1 : ଷ଴ ଷଽସ 9M 9M 1M Ratio D 1M Fraction L3 1CA Unit ratio =1 : 1,60 9 CA NPR (3) 3.6 Revenue in sub-saharan Africa = 6,6 – 5,0 9M 1M Subtraction D = 1,6 9S 1S Simplification L3 Total revenue for spas 1M Addition = 22,9 + 6,6 + 1,6 + 2,8 + 33,3 + 26,5 9M 1CA Total revenue = $93,7 billion 9CA Penalise 1 mark if not in billions (4) 3.7 1,6; 2,8; 6,6; 22,9; 26,5; 33,3 9M CA the value $1,6 from 3.6 D included in the data L3 Median revenue = ଺,଺ ା ଶଶ,ଽ 9M 1M Arranging in order of ଶ descending or ascending = $14,75 billion 9CA 1M Concept of median 1CA Answer in billions (3) 3.8 P (Regions with more than 40 000 spas) 1RT Correct numerator and P 9RT denominator L2 ଶ = × 100 9M 1M Multiplication by 100 ଺ 1CA Percentage = 33,33% 9CA NPR (3) [21] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICAL LITERACY P1 7 QUESTION 4: FINANCE (12 marks), DATA HANDLING (11 marks) AND PROBABILITY (3 marks) Ques. Solution Explanation T/L 4.1 Cost = Kilolitre Cost 6 6 × 0 = 0 9M 1M Cost of first 6 kƐ F L4 9 9 × 9,35 = R84,15 1M Cost for both 9 and 10 9M kilolitres 10 10 × 11,16 = R111,6 1CA Total cost Total = 25 litres 84,15 + 111,60 = R195,75 9M 9M 1M Multiply by 15% R195 ×115% = R225,11 9CA 1CA Cost including VAT OR 9M 9M Cost = (6 × 0) + (9 × 9,35) + (10 × 11,16) = R84,15 + R111,60 = R195,75 9CA Including VAT = R195,75 × 15% 9M = R29,3625 = R195,75 + R29,3625 = R225,119CA Increased block rate tariffs to encourage saving of water 9A OR 1A Reason Also assist small businesses or families with free water 9A Accept any other sound reason. (6) 4.2 R0,019 = 1 RWF 1M Concept of ratio F R? = 745 614,04 RWF 9M L4 R? = 0,019 × 745 614,04 9M 1M Multiplication = R14 166,66676 9S 1S Simplification value in R Bank charges = 14166,66676× ଵ଴ 9M 1M Multiplication of 10% ଵ଴଴ 1A Value of 10% = R1 416,666676 9A 1M Subtraction Andile received = R14 166,66676 – 1 416,66676 9 M = R12 750 1A Valid Statement is valid. 9A OR OR ଵ଴ 1M Multiplication of 10% Bank charges = × 745 614,04 RWF 9M 1A Value of 10% ଵ଴଴ = 74 561,404 9A 1M Subtraction Andile received in RWF = 745 614,04 – 74 561,404 9M 1S Simplification value = 671 052,636 9S In Rands: R0,019 = 1 RWF 1M Concept of ratio R? = 671 052,636 RWF 9M 1M Multiplication Andile received = R0,019 × 671 052,636 9M = R12 750 Statement is valid 9CA 1CA Valid (6) Copyright reserved Please turn over

Downloaded from hlayiso.com 8 MATHEMATICAL LITERACY P1 (EC/NOVEMBER 2020) 4.3.1 Total absentees = 67 9 M 1M Addition to 67 P Absentees on Wednesday =16 9A 1A Absentees on Wed L2 P(absent on Wed) = ଵ଺ 9CA 1CA Fraction ଺଻ (3) 4.3.2 1A for Monday boys at 5 D Number of absent learners during the week 1A for Tuesday girls at 6 L2 12 1A for Thurs for girls at 7 1A for Thurs for boys at 9 10 1A for Fri for boys at 7 Number of absent learners 9A 8 9A 9A 6 9A 9A 4 2 0 Monday Tuesday Wednesday Thursday Friday Days of the week Girls Boys (5) 4.4.1 Value of C: D 64,2 = 9M ஼ ା ଵ ଼ହଷ 1M Addition (1 853) and L4 ଷ଴ division by 30 64,2 × 30 = C + 1 853 1M Subtraction C = 1 926 – 1 853 9M 1CA Value of C = 73 9CA Answer invalid 9O 1A Invalid (4) 4.4.2 D = 0 9A 1A Value of D D No learners scored 30 – 39 marks 9A 1A Explanation L4 (CA value of D from 4.4.1 included in the data) (2) [26] TOTAL: 100 Copyright reserved Please turn over

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