Mathematical Literacy Grade 12 P2 2018 Memo (Eng)

NATIONAL SENIOR CERTIFICATE GRADE 12 SEPTEMBER 2018 MATHEMATICAL LITERACY P2 MARKING GUIDELINE MARKS: 150 Symbol Explanation M Method M/A Method with Accuracy MCA Method with Consistent Accuracy CA Consistent Accuracy A Accuracy C Conversion S Simplification RT/RG/RM Reading from a table OR Reading from a graph OR 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 OR Reason AO Answer only NPR No penalty for rounding This marking guideline consists of 11 pages.

2 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2018) QUESTION 1 [39] Ques. Solution Explanation Level 1.1.1 Municipality = 87 × 5 × 30  1MA Multiply 5 L3 = 13 050 litres  and 30 1A Number of litres Tank water = 250 – 87 = 163 litres  1CA Litres for tank water Tanks = 163 × 5 × 30 1CA Total litres = 24 450 litres  for the month Total for municipality and tanks = 13 050 litres + 24 450 litres = 37 500 litres  1MCA Total litres (5) 1.1.2 Litres used from tank = 24 450 CA from 1.1.1 L3 No. of kilolitres = 24 450 ÷ 1 000 1C Converting to and = 24,45 kℓ  kilolitres L4 First 6 = 6 × 0 7 to 10 kℓ next 4 = 4 × 7,14 = R28,56  1MA 2nd Tariff 11 to 15 kℓ = 5 × 12,07 = R60,35  1MA 3rd Tariff 16 to 20 kℓ = 5 × 17,65 = R88,25  1MA 4th Tariff 21 to 30 kℓ = 4,45 × 24,23 = R106,93  1MA 5th Tariff Total amount = R28,56 + R60,35 + R88,25 + R106,93 = R284,09  1CA Total amount Amount with VAT = R284,09 x 1,14  1M Calculating = R323,86  VAT 1CA VAT incl Statement is valid  1O Valid (9) Copyright reserved Please turn over

(EC/NOVEMBER 2018) MATHEMATICAL LITERACY P2 3 1.1.3 Tank 1: Volume = πr2h  1C mm to cm L3 105 2 1SF Substitution = 3.142 × ( ) × 142  1MA Finding the 2 = 1 229 739,525 ÷ 1 000  radius = 1 229,7  1S Simplification = 1 000 litres  1C Convert to litres 1R Nearest thousand Tank 2: Volume = πr2h = 3,142 × (90)2 × 210 = 5 344 542 ÷ 1 000 = 5 344, 542 = 5 000 litres  1CA Rounded to nearest thousand Total = 1 000 + 5 000 = 6 000 litres  1CA Total volume for two tanks Water needed from tanks = 24 450 litres Statement invalid. Cannot have enough water if it does not rain.  1O Not valid (9) Copyright reserved Please turn over

4 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2018) 1.2.1 Grade 10 : Grade 11 : Grade 12 L3 Ratio 5 : 3 : 2 Grade 10 = 250 book packs Total = 5 + 3 + 2 1M Adding ratio = 10  1M Concept of 5 ratio × total no. of book packs = 250  1M Changing 10 0,5 × total number of book packs = 250  subject of formula 250 1M Dividing Total number of book packs =  1CA Number of 0,5 = 500 book packs  book packs OR 5 = 250 1 = 250 ÷ 5 1MA Unit ratio = 50  1MA Finding 3 = 50 × 3 value of 3 = 150  1MA Finding 2 = 50 × 2 value of 5 = 100  1M Addition Total = 250 + 150 + 100  1CA Total book = 500  packs (5) 1.2.2 Amount for books packs = R320 × 500 CA from 1.2.1 L4 = R160 000  1MCA Cost for book packs R160 000 1M Dividing by Amount without VAT =  1,15 1,15 = R139 130,43  1CA Amount before VAT VAT = R160 000 – R139 130,43  1M Subtraction = R20 869,57  1CA VAT amount Amount for 50 = R3 20 × 50 = R16 000  1MCA Amount of 50 book packs Statement is valid  1O Valid (7) 1.2.3 150 100 CA from 1.2.1 L2 Probability = + 1MCA Adding 500 500 correct fractions 250  1CA Numerator = × 100 1CA Denominator 500  1CA Percentage = 50%  (4) Copyright reserved Please turn over

(EC/NOVEMBER 2018) MATHEMATICAL LITERACY P2 5 Question 2 [43] Ques. Solution Explanation Level 2.1.1 (a) Mean 2015 L2 = 59,6 + 76,9 + 75,7 + 68,2 + 97,1 + 77 + 84 + 70,4 +71,4 + 49,1 + 58,6  1M Adding 788 1M Dividing by 11 =  11 1CA Mean = 71,64  (3) 2.1.1 (b) Mean 2016 L4 = 69,5 + 75,4 + 73,7 + 65,3 + 97,4 +76,5 + 84 + 70,5 + 71,3 + 57,1 + 52 = 786,7 1MA Adding and 786,7 dividing =  11 = 71,52  1CA Mean Statement invalid  1O Invalid (3) 2.1.2 2015 L4 49,1; 58,6; 59,6; 68,2; 70,4; 71,4; 75,7; 76,9; 77; 84; 1M Ascending 97,1  order Q3 (A) = 77%  1CA Q3 (A) IQR = 77 – 59,6 1CA IQR = 17,4%  2016 51,5; 52,0; 65,3; 69,5; 70,5; 71,3; 73,7; 75,4; 76,5; 84,0,97,4 Q1 (B) = 65,3%  1A Q1 (B) IQR = 76,5 – 65,3 = 11,2%  1CA IQR Statement valid  1O Valid (6) Copyright reserved Please turn over

6 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2018) 2.2.1 Annual income = R31 625 × 12 1MA Annual L3 = R379 500  income and L4 Tax = 61 910 + 31% of taxable income above 296 540  1RT Correct tax = 61 910 + 0,31 × (379 500 – 296 540)  bracket = 61 910 + 0,31 × 82 960  1SF Substitution = 61 910 + 25 717,6 1S Simplification = 87 627,6 – R13 635  1M Subtract = 73 992 ÷ 12 rebate = 6 166,05  1CA Monthly tax Grants for 10 children = 380 × 10 1MA Child grant = 3 800  for 10 2 old age people = 1 600 × 2 = 3 200  1MA Old age Total = 3 200 + 3 800 grant for 2 = R7 000  1CA Total grants Statement invalid  1O Invalid (10) 2.2.2 Amount after first year 1M Multiplying by L2 = R31 625 × 1,058  5,8% = R33 459, 25  1CA Value for 1st Amount after second year year = R33 459, 25 × 1,068 = R35 734,48  1CA Value for 2nd year Annual salary 1M Multiplying by = R35 734,48 × 12  12 = R428 813,75  1CA Annual salary OR Total annual income = 31 625 × 12  1M Multiplying by = 379 500  × 1,058 × 1,068  12 = R428 813,75  1CA Salary 1CA Value for 1st year 1CA Value for 2nd year 1CA Annual salary (5) Copyright reserved Please turn over

(EC/NOVEMBER 2018) MATHEMATICAL LITERACY P2 7 2.3.1 KZN = OAG + CSG 1RT Correct L2 = 669 634 + 2 776 098  values for KZN = 3 445 732  1CA Total WC = OAG + CSG = 330 039 + 993 038 1CA Total = 1 323 077  Difference = 3 445 732 – 1 323 077 = 2 122 655  1CA Difference(4) 2.3.2 Northern Cape  2RT Province (2) L2 2.3.3 Gauteng has a greater population  2A Reason (2) L4 2.3.4 FS and NW  remains the same  in 2017 and 2018 1A Both FS & NW L4 1A Remains the The number of the rest of the provinces  decreases  same 1A Rest of provinces 1A Decrease (4) 2.3.5 L2 War Veteran grant for the EC, KZN, NC and LP for 2017 and 2018 25 Both bars plotted 20 correctly for Number of WVG 15 1MA EC 1MA KZN 10 1MA NC 1MA LP 5 0 OK KZN NK LP Provinces (4) Copyright reserved Please turn over

8 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2018) Question 3 [31] Ques. Solution Explanation Level 3.1.1 Measured distance from Cape Town to Durban L4 = 8,1 cm  Accept 7,9 cm to 8,3 cm 2A Measure Bar Scale distance 3 cm = 500 km Accept 2,9 cm to 3,1 cm 1A Measure bar Actual Distance scale 500 𝑥 8,1 1C Convert =  3 distance using = 1 350 km  bar scale 1CA Distance Time taken by first family = 21:00 – 8:00 – 1,5 1CA Time = 11,5 hrs  1 350 𝑘𝑚 Speed of family = 11,5ℎ𝑟𝑠 = 117,39 km/h  1CA Speed Time taken by second family = 21:00 – 8,50 – 1,5 = 11 hrs  1CA Time 1 350 𝑘𝑚 Speed of family = 11ℎ𝑟𝑠 1CA Speed = 122,72 km/h  1O Valid Statement is valid  NPR (10) 3.1.2 Zambia  2A Country (2) L2 3.2.1 Unknown length (1) = 12 cm – 6 cm 1M Finding 6 cm L2 = 6 cm Unknown length (2) = 10 cm – 2 cm – 4 cm 1M Finding 4 cm = 4 cm 1M Adding all Perimeter = 10 + 4 + 4 + 2 + 12 + 6+ 6 + 2 + 6 + 4  values = 56cm  1CA Perimeter(4) 3.2.2 Area = ℓ × b CA from 3.2.1 L3 Figure 1 = 10 cm × 4 cm = 40 cm2  1MA Calculating Figure 2 = 4 cm × 6 cm area = 24 cm2  1MCA Area Figure 3 = 6 cm × 6 cm = 36 cm2  1MCA Area Total area = 40 cm + 24 cm +36 cm = 100 cm2  1CA Total area Area of page = 28 cm × 20 cm = 560 cm2  1CA Area of page Area of unshaded part = 560 – 100  1M Subtraction = 460 cm2  1CA Unshaded area (7) Copyright reserved Please turn over

(EC/NOVEMBER 2018) MATHEMATICAL LITERACY P2 9 3.3.1 Satara to Olifants = 54km  1RT Correct L2 & N’wanetsi to Lower Sabi = 108km  distance L4 1RT Correct Distance is half; therefore, it can take them half the time distance to travel.  2 Explanation (4) 3.3.2 Punda to Mopani = 130 km 1RT Correct L2 & Mopani to Paul Kruger = 220 km  values L4 Total = 130 km + 220 km 1MA Adding = 350 km  distances Skukuza to Pafuri = 380 km Difference = 380 km – 350 km = 30 km  1CA Difference Statement valid  1O Valid (4) Copyright reserved Please turn over

10 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2018) QUESTION 4 [37] Ques. Solution Explanation Level 4.1.1 Not offered at certain universities  2A Reason L4 OR No students registered for the course  (2) 4.1.2 Fees for Business at Bond = $33 640 1RT Both values L3 Fees for Engineering at Edith Cowan = $ 25 760  correct Total = 33 640 + 25 760 = 59 400  1CA Total $1 = R9,68 $59 400 = 9,68 × 59 400  1C Convert to = R 574 992  Rand 1CA Amount in Rand (4) 4.1.3 Fees greater than $15 000, but less than $ 30000 1A Numerator L2 7 1A Denominator =  10 1CA Decimal = 0,7  (3) 4.2.1 38 249−29 678 1RT Using L2 % increase = × 100  correct values 29 678 = 28,88%  1SF Substitution 1M Multiply by 100 1CA Percentage NPR (4) 4.2.2 December  1A Month L2 & People get bonuses in December  2R Reason L4 OR People budget to spend in December  (3) 4.2.3 August 2015 – 30 633 1RT Both values L3 August 2016 – 31 556  correct Difference = 31 556 – 30 633 1MCA Difference = 923  Amount = 923 × 550 000 1MCA Amount = R507 650 000  14, 81 = 1 Euro 507 650 000 1C Convert to € 507 650 000 = 1 × 1CA Amount in € 14,81  = 34 277 515,19 Euro  (5) Copyright reserved Please turn over

(EC/NOVEMBER 2018) MATHEMATICAL LITERACY P2 11 4.3.1 Hours worked: L4 Level 3: Day 1 = 5 hours  1A Hrs for Day 1 Day 2 to 13 = 10 hrs × 12 1MA Hrs for Day = 120  2 to 13 Day 14 = 8 hrs Total number of hours = 5 + 120 + 8 hours 1CA Total = 133 hours  number of hours Level 2 = 133 hours 1M Subtracting Level 1 = 133 – 4  1CA Calculating = 129 hours  hours for Level 1 Amount for Level 3 = 248 × 133 × 2 1MCA Amount = R65 968  Level 3 Amount for Level 2 = 133 × 218,24 × 6 1MCA Amount = R174 155,52  Level 2 Amount for Level 1 = 129 × 163,68 × 32 1MCA Amount = R675 671,04  Level 1 Total Amount = 65 968 + 174 155,52 + 675 671,04 1CA Total = R915 794,56  amount Statement invalid  1O Invalid (10) 4.3.2 Distance for 14 days = 14 km × 2 × 14 days  CA from 4.3.1 L4 = 392 km  1MA Return multiply by 14 1CA Total Transport Cost for all employees distance = 392 km × 3,18 × 40 = R49 862,40  1MCA Transport 49 862,40 cost Amount as a fraction =  1M Dividing 915 794,56 = 0,05  values Statement is valid  1CA Decimal 1O Valid (6) TOTAL: 150 Copyright reserved Please turn over