Monday, 07 June 2021 09:06

## GRADE 12 MATHEMATICAL LITERACY PAPER 2 MEMORANDUM - NSC PAST PAPERS AND MEMOS SEPTEMBER 2016

MATHEMATICAL LITERACY P2
MEMORANDUM
NATIONAL SENIOR CERTIFICATE
SEPTEMBER 2016

 Symbol Explanation M Method MA Method with Accuracy CA Consistent accuracy A Accuracy C Conversion SF Substitution in a formula F Choosing the correct formula RT/RG/RM Reading from a table/Reading from a graph/Reading from map S Simplifications J Justification P Penalty (no units, incorrect rounding off etc.) R Rounding

QUESTION 1 

 Ques Solution Explanation Level 1.1 Two bedroomed flats in 1 block = 2 × 3= 6Total no of flats in 8 blocks = 6 × 8= 48One bedroomed flats = 2 × 3= 6 ✓MTotal no of one bedroomed flats = 6 × 8= 48Total no of flats 48 + 48= 96 ✓CA 1M Calculating noof both flats1CA Total no offlat (2) L2 1.2 Income for 2 bedroomed flats=107,5 x 3200 M    100= 3440 ×48= R 165 120 ✓MIncome for 1 bedroomed flats= 2300 × 48= R110 400 ✓MTotal income =165 120 + 110 400= R275 520 ✓CA 1M Increasing by7,5%1M For 2bedroomed flats1M For 1 bedroomed flats1CA Total (4) L3 1.3 If 1 Ghanaian cedi = 3,77 South African Rand415 = 3,77 × 415 ✓M=R 1 564,55 ✓CAAmount outstanding = 2 300 – 1 564,55 ✓M= R735,45= R735  ✓CA 1C Using 3,771CA1M Difference1CA Answer (4) L2 1.4 If all occupied :48 × 3 440 = 165 120 ✓M93,75% × 48 = 4593,75% occupied = 45 × 3 440= 154 800 ✓CAMoney lost = 165 120 – 154 800= R 10 320OR93,75% × 165 120 ✓M= 154 800Money lost = 165 120 – 154 800 ✓M/A ✓M= R 10 320OR93,75% × 48 = 4548 – 45 = 3 × 3 440 ✓CA ✓M= R 10 320 ✓CAOR0,0625 × 48 = 3 M ✓CA3 × 3 440✓ M = R 10 320 ✓CAOR100 – 93,75% = 6,25% ✓M/A= 6,25% × 165 120 ✓M/A= R 10 320 ✓CA CA from 1.1.11M Total income1CA1M getting thedifference1CA1M Calculating93,75%1CA Answer1M Subtracting1CAMA For 451CA Difference1M Multiplying by34401CA Answer1M Calculating6,25%1CA1M Multiplying by34401CA1MA Differencebetween 100%and 93,75%2M1CA (4) L4 1.5 People in 8 blocks36 × 8 = 288 ✓M/A37,5 × 288100 ✓CA= 108Children = 288 – 108= 180 ✓CA ✓MAOR62,5 × 288 = 108 ✓M ✓MA100Children = 288 – 108 ✓M= 180 ✓CA 1MA Calculatingthe number ofpeople1CA1M Subtraction1CA Answer2M Using 62,5%1CA1M Subtraction1CA Answer (5) L2 1.6 Probability = 1  ✓A                    96 ✓A CA from 1.1.11A numerator1A denominator(2) L2

QUESTION 2 

 2.1 2.1.1 Range = max – min78 = 132 – A (min) ✓MA = 132 – 78 ✓M= 54  ✓CA 1M Concept of range1M Subtracting1CA (3) L2 2.1.2 Mean = sum of the numbers                           1490 =65+79+B+98+54+68+90+76+84+102+132+121+B+B                                             1490 × 14 =969 + 3B ✓S1260= 969 + 3B ✓M1260 – 969 = ✓3B291= ✓3B  3= BMode = 97 ✓ CA CA From 2.1.11MA Sum of values divided by 141S1M Multiplying and adding B’s1A (4) L4 2.1.3 54 65 68 76 79 84 90 97 97 97 98 102 121 132 ✓MAQ2 (median) = 90+97 ✓A                            2     ✓M= 93,5 ✓CAQ1 (lower Quartile) = 76 ✓CAQ3 (upper Quartile) = 98 ✓CA CA from 2.1.1 and 2.1.21MA Arranging in ascending order1M Adding the 2 values1M Dividing by 21CA Median1CA Q11CA Q2 (6) L3 2.1.4 In paper 2 the mean is lower than in paper 1 therefore paper 1 was performed better than 2✓ RORPaper 2 was more difficult ✓RORPaper 1 was more easier ✓ R 2R2R2R (2) L4 2.1.5 Probability = 3 A                    14 A CA from 2.1.1, 2.1.2 and 2.1.31A numerator1A denominator (2) L2 2.2 2.2.1 Costs for venue ✓A= R1 500+R1 200+(R150 × 66) ✓M= R12 600 ✓CACosts for venue B = R 1 000 + 220 × 66= R 15 520 ✓CADifference = 15 520 – 12 600= R 2 920 ✓CA 1M Multiply by 661CA Cost for venue A1CA Cost for venue B1CA Difference in cost (5) L3 2.2.2 Graph to show costs of venues A and BNo. of learners 1M Plotting 0 and 10001M For every 3 values plotted correctly1CA Joining points to form a line1CA Breakeven point(6) L3 2.2.3 Breakeven point is where the cost of Venue A is equal to the cost of venue B ✓O for the same number of learners ✓ONumber of learners = 20Cost = R5 700 ✓RG 1A Same cost1A Same number of learners1RG For reading the cost and the number of learners(3) L3

QUESTION 3 

 3.1 3.1.1 Annual income =368 450Tax bracket from table=284 101 – 393 200 ✓RTTax = 59 314 + 31% of the amount above= 284 100 ✓SF= 59 314 + 0,31(368 450 – 284 100)= 59 314 + 0,31 x 84 350= 59 314 + 26 148,50 – [(270 × 2) + 181 × 12] ✓M= 85 462,50 – 13 257 - 8652✓M =R63552,50         12         ✓M= R5 296,04 ✓MMonthly = 368 450 ÷ 12= R30 704,17% =5296,94 × 100      30704,17= 17,25% Accep17,3% ✓CA 1RT Correct tax bracket1SF1S1M Subtracting rebates1M Subtracting medical aid credits1M dividing by 121M Monthly Income1CA % (8) L4 3.1.2 Tax payable= 85 462,50 – (13 257 + 7 407 + 2 466) ✓M=85 462,50 – 23 130= 62 332,50 – 8 652 ✓M= 52 680,50= R 4 473,38Tax would be less  ✓J 1M Adding rebates1M subtracting rebates1J (3) L4 3.1.3 Option 1 = 30 704,17 × 6,9 × 3                                     100= 6 355,76 ✓M/AAmount = R 30 704,17 + 6 355,76 ✓M/A= R 37 059,93✓ CAOption 2:Year 1 = 106 × 30 704,17 ✓M              100= 32 546,42 ✓CAYear 2 = 106 × 32 546,42              100 = 34 499,20 ✓CAYear 3 = 106 × 34 499,20              100= R 36 569,16 ✓CAAdvise to use option 1 because there is more money in the investment at the end of the period  ✓O 1MA Multiply by 6,9% and 31MA addinginterest1CA1M Multiply by 10,6%1CA1CA Year 21CA Year 31O (8) L4 3.2 3.2.1 50 ℓ model:Surface area = (2 × π × r × l) + (π × r2 × 2) ✓SF= (2 × 3,142 × 225 × 610) + (3,142 × 225 × 225 × 2)= 862 479 + 318 127,5 S= 1 180 606,5 mm2 ✓CA100 ℓ model:Surface area = (2 × π × r × l) + (π × r2 × 2)=(2 × 3,142 × 275 × 840) + (3,142 × 275 × 275 × 2)= 1 451 604 + 475 227,5 S= 1 926 831,50 ✓CA1926831,50 ✓M          2= 963 415,75Not equal to the surface area of the 50 ml geyser ✓ O 2SF Substitution in the formula1S Simplification1CA Surface Area1S Simplification1CA Surface Area1M Dividing by 21O (8) L4 3.2.2 Length using a ruler = 50 mm ✓AActual length 840 mmScale is 50:840 ✓A=1:16,8 ✓CA 1A Measure 50 mm1A Scale1CAAccept 49 – 51 mm (answers will be1:17,1 – 1:16,5) (3) L3

QUESTION 4 

 4.1 4.1.1 Arrival 8:00Depart at = 8:00 + 3h 45min=11:45 ✓M/ATime taken at 90km per hourAverage Speed = distance travelled                                  time taken90 = 86              ✓ SF    time takenTime taken = 86                      90= 0,955555 × 60= 57,3 minutesArrival = 11:45 + 57,3 minutes ✓CA = 12:42 ✓CA ✓MWill be late by 12 minutes ✓ O 1MA Time1SF Substitution in the formula1CA Calculating minutes1CA Addition1A Time of arrival1O CA (6) L3 4.1.2 Costs:Hiring =R2 800Ferry = 70 × 2 (return)= 140 ✓M/A= 140 × 2 (for two days)= R280 ✓CAAccommodation = 543 × 2 × 3=R 3 258Total = 2 800 + 280 + 3 258= R6 338 ✓M/AAvailable = 700 × 14,391= R10 073,70 ✓CTherefore it will be enough 1MA Calculating return cost1CA Cost for 2 days1MA Calculate accommodation1MA Total1C Conversion1O (6) L3 4.1.3 No ferry rides because it can be swept away by heavy currents ✓OORCan cause ferry to capsize ✓CAORAccept any other relevant reason  ✓CA 2O Reason(2) L4 4.2 4.2.1 The % of aids related deaths is decreasing from 2007 to 2014 ✓AReasons – people more educated about HIV- People are taking medication✓ A- Practising safe sex ✓O(Accept any other TWO relevant reasons) 2A Explaining the trend2R 1Reason(4) L4 4.2.2 Total number of births= 1 125 755 + 1 132 500 + 1 141 468 +1 152 319 + 1 163 629 + 1 173 164 + 1 184867 + 1 196 395 + 1 207 711 ✓M= 10 477 808 ✓CATotal number of Aids related deaths= 343 194 + 297 659 + 257 504 + 228 051 + 213 864 + 211 839 + 203 293 + 189 376 +171 733= 2 116 513 ✓CADifference = 10 477 808 - 2 116 513= 8 361 295  ✓CA 1M Addition1CA Total (births)1CA Total (deaths)1CA Difference (4) L2 4.2.3 1207711 - 1196395 x 100 ✓M       1196395  ✓M= 0,95% ✓CAIncorrect ✓OAccept 0,9% 1M Difference1M Correct denominator1CA Finding %1O(4) L2 4.2.4 Bar graph to show percentage Aids related deaths over a period of years 5M1mark for eachcorrect bar(5) L2

QUESTION 5 

 5.1 5.1.1 To allow allowance for opening the doorsIf the doors are the same size, they will be too big and won’t fit. ✓O 2O(2) L4 5.1.2 Front doors = 2 700 ÷ 39,7= 6 doors ✓M= 1 830 ÷ 716= 2 doors ✓CANo. of doors = 6 × 2= 12 doors in 1 board ✓CADoors needed = 202 boards needed ✓ASides = 2700 ÷ 540= 5 ✓M1 830 ÷ 720 = 2No. of sides = 5 × 2 = 10Boards needed = 2 ✓CABack = 2 200 ÷ 720 = 31 200 ÷ 800 = 13 in 1 board ✓M ∴ For 10 backs = 4 boardsBottom = 2 700 ÷ 54= 51830 ÷ 716 = 25 × 2 = 10No. of boards = 2 ✓CATop = 3 400 ÷ 780 = 4For ten cupboards = 3 tops✓ M 1M Number of doors - length1M Number of doors - width1CA Total doors1A Number of boards1M Number of sides1CA Boards needed for sides1M Calculating the backs1CA Number of boards1CA Number of boards1M Number of tops(10) L3 5.1.3 Cost of material : 2 × cherry, 4 × melamine, × Masonite, 3 tops4 × 390 + 2 (390 + 90) + 4 x 90 + 800 × 3 ✓M✓ M= 1 560 + 960 + 360 + 2 400 ✓CA= 5 2805 280 × 114 ✓CA             100= R 6 019,20 ✓CA CA from 5.1.21M Using R901M Multiplying1M Addition1CA Total1M Using 14% VAT1CA Price including VAT (6) L3 5.1.4 Dimensions = 3m × 4m= 3 000mm × 4 000mm ✓CUsing 780mm by 600mm ✓A= 4000 x 3000    780      600= 5 × 5= 25 cupboards ✓M10 will fit ✓CA 1C Conversion tomm1A Using correctvalues1M Calculatingnumber ofcupboards1O Conclusion (4) L4 5.2 5.2.1 17+19+20+22+26+28+29+30+31+32+33+2(34)+ 5(35)+2(36)= 602No. of people= 1/3 × (602 – 2 wheelchairs)= 200 ✓M/A2Men + 3men = 2 : 3∴ Men = 200 x 2               80             =  5                80  ✓CA ORWomen = 3 x 200 ✓MA                 5= 120 ✓CAMen = 200 – 120= 80 ✓CA 1MA Number ofpeople in hall1M Using conceptof ratio1CA Number ofmen1M Concept of ratio1CA Number ofwomen1CA number ofmen (3) L3 5.2.2 Row A15Row B17 ✓ARow V33 1A First row1A Second row1A Third row (3) L3 5.2.3 32   ✓A602  ✓A= 0,053156146=0,053 ✓CA 1A numerator1A denominator1CA 3 decimalplaces (3) L3 5.2.4 Enter through door 4, turn right and go straight to the end of the seats. Turn left and go straight past 8 rows. On the 9th row turn left. The seats are in row M seat numbers 2 and 3 3A for cleardirections to theirseats(3) L4 5.2.5 Short-sighted person will be on D1 ✓AFarsighted person will be on T12 ✓AShort-sighted people can see things which are closer whereas longsighted people can see things which are far ✓A 1A Correct seatnumber1A Correct Seatnumber1O Reason (3) L4

TOTAL: 150