Gr12 MLIT P2 S16 MEMO Eng hlayiso.com

NATIONAL SENIOR CERTIFICATE GRADE 12 SEPTEMBER 2016 MATHEMATICAL LITERACY P2 MEMORANDUM MARKS: 150 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 etc. R Rounding /Reason This memorandum consists of 10 pages.

2 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2016) QUESTION 1 [21] Ques Solution Explanation Level 1.1 Two bedroomed flats in 1 block =2×3 L2 =6 Total no of flats in 8 blocks =6×8 = 48 One bedroomed flats =2×3 1M Calculating no =6 M of both flats Total no of one bedroomed flats = 6 × 8 = 48 Total no of flats 48 + 48 = 96 CA 1CA Total no of flat (2) 1.2 Income for 2 bedroomed flats L3 M 1M Increasing by = 7,5% = 3440 ×48 1M For 2 = R 165 120 M bedroomed flats Income for 1 bedroomed flats= 2300 × 48 1M For 1 = R110 400 M bedroomed flats Total income =165 120 + 110 400 1CA Total (4) = R275 520 CA 1.3 If 1 Ghanaian cedi = 3,77 South African Rand L2 M 415 = 3,77 × 415 1C Using 3,77 =R 1 564,55 CA 1CA Amount outstanding = 2 300 – 1 564,55 M 1M Difference = R735,45 = R735 CA 1CA Answer (4) Copyright reserved Please turn over

(EC/SEPTEMBER 2016) MATHEMATICAL LITERACY P2 3 1.4 If all occupied : CA from 1.1.1 L4 48 × 3 440 = 165 120 M 1M Total income 93,75% × 48 = 45 93,75% occupied = 45 × 3 440 1CA = 154 800 CA 1M getting the Money lost = 165 120 – 154 800 M difference = R 10 320 CA 1CA M OR 1M Calculating 93,75% × 165 120 93,75% = 154 800 1CA Answer M/A 1M Subtracting Money lost = 165 120 – 154 800 M 1CA = R 10 320 CA OR M MA For 45 93,75% × 48 = 45 M/A 1CA Difference CA 1M Multiplying by 48 – 45 = 3 × 3 440 M 3440 1CA Answer = R 10 320 CA M OR 1M Calculating 0,0625 × 48 = 3 CA 6,25% 3 × 3 440 M 1CA = R 10 320 CA 1M Multiplying by 3440 OR 1CA 100 – 93,75% = 6,25% M/A 1MA Difference between 100% = 6,25% × 165 120 M/A and 93,75% = R 10 320 CA 2M 1CA (4) 1.5 People in 8 blocks L2 36 × 8 = 288 M/A 1MA Calculating × 288 the number of people = 108 CA 1CA Children = 288 – 108 1M Subtraction = 180 CA MA 1CA Answer M OR 2M Using 62,5% × 288 = 108 MA 1CA 1M Subtraction M 1CA Answer (5) Children = 288 – 108 = 180 CA 1.6 A CA from 1.1.1 L2 Probability = A 1A numerator 1A denominator (2) Copyright reserved Please turn over

4 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2016) QUESTION 2 [29] 2.1 2.1.1 Range = max – min 1M Concept of L2 78 = 132 – A (min) M range A = 132 – 78 M 1M Subtracting = 54 CA 1CA (3) 2.1.2 CA From 2.1.1 L4 Mean = MA 1MA Sum of values 90 = divided by 14 90 × 14 =969 + 3B S 1260= 969 + 3B M 1S 1260 – 969 = 3B 1M Multiplying and 291= 3B adding B’s =B Mode = 97 CA 1A (4) 2.1.3 MA CA from 2.1.1 and L3 54 65 68 76 79 84 90 97 97 97 98 102 121 132 2.1.2 1MA Arranging in A ascending order Q2 (median) = M 1M Adding the 2 values = 93,5 CA 1M Dividing by 2 Q1 (lower Quartile) = 76 CA 1CA Median Q3 (upper Quartile) = 98 CA 1CA Q1 1CA Q2 (6) 2.1.4 In paper 2 the mean is lower than in paper 1 R L4 therefore paper 1 was performed better than 2 2R OR Paper 2 was more difficult R 2R OR Paper 1 was more easier R 2R (2) 2.1.5 A CA from 2.1.1, L2 Probability = A 2.1.2 and 2.1.3 1A numerator 1A denominator (2) 2.2 2.2.1 Costs for venue A M 1M Multiply by 66 L3 = R1 500+R1 200+(R150 × 66) 1CA Cost for venue = R12 600 CA A Costs for venue B = R 1 000 + 220 × 66 1CA Cost for venue = R 15 520 CA B Difference = 15 520 – 12 600 1CA Difference in = R 2 920 CA cost (5) Copyright reserved Please turn over

(EC/SEPTEMBER 2016) MATHEMATICAL LITERACY P2 5 2.2.2 Graph to show costs of venues A and B L3 14000 CA 1M Plotting 0 and 12000 1000 10000 M 1M For every 3 costs in rands values plotted 8000 M correctly Venue B 6000 Venue A CA 1CA Joining points 4000 M to form a line 2000 M 1CA Breakeven 0 0 20 40 60 point No. of learners (6) 2.2.3 Breakeven point is where the cost of Venue A is L3 equal to the cost of venue B O for the same 1A Same cost number of learners O 1A Same number of learners Number of learners = 20 RG 1RG For reading Cost = R5 700 the cost and the number of learners (3) QUESTION 3 [30] 3.1 3.1.1 Annual income =368 450 L4 Tax bracket from table=284 101 – 393 200 RT 1RT Correct tax bracket Tax = 59 314 + 31% of the amount above = 284 100 SF 1SF = 59 314 + 0,31(368 450 – 284 100) = 59 314 + 0,31 x 84 350 S M 1S = 59 314 + 26 148,50 – [(270 × 2) + 181 × 12] 1M Subtracting = 85 462,50 – 13 257 - 8652 M rebates 1M Subtracting = medical aid credits M = R5 296,04 M 1M dividing by 12 Monthly = 368 450 ÷ 12 1M Monthly Income = R30 704,17 %= × 100 = 17,25% CA Accep17,3% 1CA % (8) 3.1.2 Tax payable M 1M Adding rebates L4 = 85 462,50 – (13 257 + 7 407 + 2 466) =85 462,50 – 23 130 = 62 332,50 – 8 652 M 1M subtracting = 52 680,50 rebates = R 4 473,38 Tax would be less J 1J (3) Copyright reserved Please turn over

6 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2016) 3.1.3 L4 Option 1 = 30 704,17 × ×3 1MA Multiply by = 6 355,76 M/A 6,9% and 3 Amount = R 30 704,17 + 6 355,76 M/A 1MA adding interest = R 37 059,93 CA 1CA Option 2: 1M Multiply by Year 1 = × 30 704,17 M 10,6% = 32 546,42 CA 1CA Year 2 = × 32 546,42 CA 1CA Year 2 = 34 499,20 Year 3 = × 34 499,20 1CA Year 3 = R 36 569,16 CA Advise to use option 1 because there is more O money in the investment at the end of the period 1O (8) 3.2 3.2.1 50 ℓ model: L4 Surface area = (2 × π × r × l) + (π × r2 × 2) SF 2SF Substitution in = (2 × 3,142 × 225 × 610) + (3,142 × 225 × 225 × 2) the formula = 862 479 + 318 127,5 S 1S Simplification = 1 180 606,5 mm2 CA 1CA Surface Area 100 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 1S Simplification = 1 926 831,50 CA 1CA Surface Area 1M Dividing by 2 M = 963 415,75 O 1O (8) Not equal to the surface area of the 50 ml geyser 3.2.2 Length using a ruler = 50 mm A 1A Measure 50 mm L3 Actual length 840 mm 1A Scale Scale is 50:840 A 1CA =1:16,8 CA Accept 49 – 51 mm (answers will be 1:17,1 – 1:16,5) (3) Copyright reserved Please turn over

(EC/SEPTEMBER 2016) MATHEMATICAL LITERACY P2 7 QUESTION 4 [31] 4.1 4.1.1 Arrival 8:00 L3 Depart at = 8:00 + 3h 45min =11:45 M/A 1MA Time Time taken at 90km per hour Average Speed = 90 = SF 1SF Substitution in the formula Time taken = = 0,955555 × 60 = 57,3 minutes CA 1CA Calculating Arrival = 11:45 + 57,3 minutes minutes = 12:42 CA M 1CA Addition Will be late by 12 minutes O 1A Time of arrival 1O CA (6) 4.1.2 Costs: L3 Hiring =R2 800 Ferry = 70 × 2 (return) 1MA Calculating = 140 M/A return cost = 140 × 2 (for two days) 1CA Cost for 2 = R280 CA days Accommodation = 543 × 2 × 3 =R 3 258 M/A 1MA Calculate Total = 2 800 + 280 + 3 258 accommodation = R6 338 M/A 1MA Total Available = 700 × 14,391 = R10 073,70 C 1C Conversion Therefore it will be enough 1O (6) 4.1.3 No ferry rides because it can be swept away by 2O Reason L4 heavy currents O OR Can cause ferry to capsize CA OR Accept any other relevant reason CA (2) 4.2 4.2.1 The % of aids related deaths is decreasing from 2A Explaining the L4 2007 to 2014 A trend Reasons – people more educated about HIV - People are taking medication A - Practising safe sex O 2R 1Reason (Accept any other TWO relevant reasons) (4) Copyright reserved Please turn over

8 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2016) 4.2.2 Total number of births L2 = 1 125 755 + 1 132 500 + 1 141 468 + 1 152 319 + 1 163 629 + 1 173 164 + 1 184 867 + 1 196 395 + 1 207 711 M 1M Addition = 10 477 808 CA 1CA Total (births) Total 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 CA 1CA Total (deaths) Difference = 10 477 808 - 2 116 513 = 8 361 295 CA 1CA Difference (4) 4.2.3 M L2 1M Difference x 100 1M Correct M denominator = 0,95% CA 1CA Finding % Incorrect O 1O Accept 0,9% (4) 4.2.4 Bar graph to show percentage Aids related L2 deaths over a period of years 60 55 Percentage Aids related deaths M 50 M 45 M 5M 40 M 1mark for each 35 correct bar M 30 25 20 15 10 5 0 2002 2005 2007 2009 2014 Years (5) Copyright reserved Please turn over

(EC/SEPTEMBER 2016) MATHEMATICAL LITERACY P2 9 QUESTION 5 [37] 5.1 5.1.1 To allow allowance for opening the doors 2O L4 If the doors are the same size, they will be too big and won’t fit. O (2) 5.1.2 Front doors = 2 700 ÷ 39,7 L3 = 6 doors M 1M Number of = 1 830 ÷ 716 doors - length = 2 doors CA 1M Number of No. of doors = 6 × 2 doors - width = 12 doors in 1 board CA 1CA Total doors Doors needed = 20 2 boards needed A 1A Number of boards Sides = 2700 ÷ 540 1M Number of =5 M sides 1 830 ÷ 720 = 2 No. of sides = 5 × 2 = 10 1CA Boards Boards needed = 2 CA needed for sides Back = 2 200 ÷ 720 = 3 1 200 ÷ 800 = 1 3 in 1 board M 1M Calculating the backs For 10 backs = 4 boards CA 1CA Number of boards Bottom = 2 700 ÷ 54 =5 1830 ÷ 716 = 2 5 × 2 = 10 No. of boards = 2 CA 1CA Number of boards Top = 3 400 ÷ 780 = 4 For ten cupboards = 3 tops M 1M Number of tops (10) 5.1.3 Cost of material : 2 × cherry, 4 × melamine, × CA from 5.1.2 L3 Masonite, 3 tops M M 4 × 390 + 2 (390 + 90) + 4 x 90 + 800 × 3 1M Using R90 1M Multiplying = 1 560 + 960 + 360 + 2 400 CA 1M Addition = 5 280 CA 1CA Total CA 5 280 × 1M Using 14% VAT = R 6 019,20 CA 1CA Price including VAT (6) Copyright reserved Please turn over

10 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2016) 5.1.4 Dimensions = 3m × 4m L4 = 3 000mm × 4 000mm C 1C Conversion to mm Using 780mm by 600mm A 1A Using correct values = × =5×5 = 25 cupboards M 1M Calculating number of 10 will fit CA cupboards 1O Conclusion (4) 5.2 5.2.1 17+19+20+22+26+28+29+30+31+32+33+2(34)+ L3 5(35)+2(36) = 602 No. of people= 1/3 × (602 – 2 wheelchairs) 1MA Number of = 200 M/A people in hall 2Men + 3men = 2 : 3 CA 1M Using concept of ratio Men = ×2 = 80 CA 1CA Number of OR men 3 Women = × 200 MA 1M Concept of ratio 5 1CA Number of = 120 CA women Men = 200 – 120 1CA number of = 80 CA men (3) 5.2.2 Row A15 1A First row L3 Row B17 A 1A Second row Row V33 1A Third row (3) 5.2.3 36 A 1A numerator L3 A 1A denominator = 0,053156146 1CA 3 decimal =0,053 CA places (3) 5.2.4 Enter through door 4, turn right and go straight to 3A for clear L4 the end of the seats. Turn left and go straight directions to their past 8 rows. On the 9th row turn left. The seats seats are in row M seat numbers 2 and 3 (3) 5.2.5 Short-sighted person will be on D1 A 1A Correct seat L4 Farsighted person will be on T12 A number Short-sighted people can see things which are 1A Correct Seat closer whereas longsighted people can see number things which are far A 1O Reason (3) TOTAL: 150 Copyright reserved Please turn over