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MATHEMATICAL LITERACY PAPER 2 GRADE 12 MEMORANDUM - 2018 SEPTEMBER PREPARATORY EXAM PAPERS AND MEMOS
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GRADE 12
NATIONAL SENIOR CERTIFICATE
MEMORANDUM
SEPTEMBER 2018
| 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 |
QUESTION 1 [39]
| Ques. | Solution | Explanation | Level |
| 1.1.1 | Municipality = 87 × 5 × 30 ✓ = 13 050 litres ✓ Tank water = 250 – 87 = 163 litres ✓ Tanks = 163 × 5 × 30 = 24 450 litres ✓ Total for municipality and tanks = 13 050 litres + 24 450 litres = 37 500 litres ✓ | 1MA Multiply 5 and 30 1A Number of litres 1CA Litres for tank water 1CA Total litres for the month 1MCA Total litres (5) | L3 |
| 1.1.2 | Litres used from tank = 24 450 No. of kilolitres = 24 450 ÷ 1 000 = 24,45 kℓ ✓ First 6 = 6 × 0 7 to 10 kℓ next 4 = 4 × 7,14 = R28,56 ✓ 11 to 15 kℓ = 5 × 12,07 = R60,35 ✓ 16 to 20 kℓ = 5 × 17,65 = R88,25 ✓ 21 to 30 kℓ = 4,45 × 24,23 = R106,93 ✓ Total amount = R28,56 + R60,35 + R88,25 + R106,93 = R284,09 ✓ Amount with VAT = R284,09 x 1,14 ✓ = R323,86 ✓ Statement is valid ✓ | CA from 1.1.1 1C Converting to kilolitres 1MA 2nd Tariff 1MA 3rd Tariff 1MA 4th Tariff 1MA 5th Tariff 1CA Total amount 1M Calculating VAT 1CA VAT incl 1O Valid (9) | L3 and L4 |
| 1.1.3 | Tank 1: Volume = πr2h ✓✓ = 3.142 × (105)2 × 142✓ 2 = 1 229 739,525 ÷ 1 000 ✓ = 1 229,7 ✓ = 1 000 litres ✓ Tank 2: Volume = πr2h = 3,142 × (90)2 × 210 = 5 344 542 ÷ 1 000 = 5 344, 542 = 5 000 litres ✓ Total = 1 000 + 5 000 = 6 000 litres ✓ Water needed from tanks = 24 450 litres Statement invalid. Cannot have enough water if it does not rain.✓ | 1C mm to cm 1SF Substitution 1MA Finding the radius 1S Simplification 1C Convert to litres 1R Nearest thousand 1CA Rounded to nearest thousand 1CA Total volume for two tanks 1O Not valid (9) | L3 |
| 1.2.1 | Grade 10 : Grade 11 : Grade 12 Ratio 5 : 3 : 2 Grade 10 = 250 book packs Total = 5 + 3 + 2 = 10 ✓ 510 × total no. of book packs = 250 ✓ 0,5 × total number of book packs = 250 ✓ Total number of book packs = 250 0,5 ✓ = 500 book packs ✓ OR 5 = 250 1 = 250 ÷ 5 = 50 ✓ 3 = 50 × 3 = 150 ✓ 2 = 50 × 2 = 100 ✓ Total = 250 + 150 + 100 ✓ = 500 ✓ | 1M Adding ratio 1M Concept of ratio 1M Changing subject of formula 1M Dividing 1CA Number of book packs 1MA Unit ratio 1MA Finding value of 3 1MA Finding value of 5 1M Addition 1CA Total book packs (5) | L3 |
| 1.2.2 | Amount for books packs = R320 × 500 = R160 000 ✓ Amount without VAT = R160 000 1,15 ✓ = R139 130,43 ✓ VAT = R160 000 – R139 130,43 ✓ = R20 869,57 ✓ Amount for 50 = R3 20 × 50 = R16 000 ✓ Statement is valid ✓ | CA from 1.2.1 1MCA Cost for book packs 1M Dividing by 1,15 1CA Amount before VAT 1M Subtraction 1CA VAT amount 1MCA Amount of 50 book packs 1O Valid (7) | L4 |
| 1.2.3 | Probability = 150 + 100 500 500 = 250 ✓✓× 100 500✓ = 50% ✓ | CA from 1.2.1 1MCA Adding correct fractions 1CA Numerator 1CA Denominator 1CA Percentage (4) | L2 |
Question 2 [43]
| Ques. | Solution | Explanation | Level |
| 2.1.1 (a) | Mean 2015 = 59,6 + 76,9 + 75,7 + 68,2 + 97,1 + 77 + 84 + 70,4 +71,4 + 49,1 + 58,6 ✓ = 788 11 ✓ = 71,64 ✓ | 1M Adding 1M Dividing by 11 1CA Mean (3) | L2 |
| 2.1.1 (b) | Mean 2016 = 69,5 + 75,4 + 73,7 + 65,3 + 97,4 +76,5 + 84 + 70,5 + 71,3 + 57,1 + 52 = 786,7 = 786,7 11 ✓ = 71,52 ✓ Statement invalid ✓ | 1MA Adding and dividing 1CA Mean 1O Invalid (3) | L4 |
| 2.1.2 | 2015 49,1; 58,6; 59,6; 68,2; 70,4; 71,4; 75,7; 76,9; 77; 84; 97,1 ✓ Q3 (A) = 77% ✓ IQR = 77 – 59,6 = 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% ✓ IQR = 76,5 – 65,3 = 11,2% ✓ Statement valid ✓ | 1M Ascending order 1CA Q3 (A) 1CA IQR 1A Q1 (B) 1CA IQR 1O Valid (6) | L4 |
| 2.2.1 | Annual income = R31 625 × 12 = R379 500 ✓ Tax = 61 910 + 31% of taxable income above 296 540 ✓ = 61 910 + 0,31 × (379 500 – 296 540) ✓ = 61 910 + 0,31 × 82 960 ✓ = 61 910 + 25 717,6 = 87 627,6 – R13 635 ✓ = 73 992 ÷ 12 = 6 166,05 ✓ Grants for 10 children = 380 × 10 = 3 800 ✓ 2 old age people = 1 600 × 2 = 3 200 ✓ Total = 3 200 + 3 800 = R7 000 ✓ Statement invalid ✓ | 1MA Annual income 1RT Correct tax bracket 1SF Substitution 1S Simplification 1M Subtract rebate 1CA Monthly tax 1MA Child grant for 10 1MA Old age grant for 2 1CA Total grants 1O Invalid (10) | L3 and L4 |
| 2.2.2 | Amount after first year = R31 625 × 1,058 ✓ = R33 459, 25 ✓ Amount after second year = R33 459, 25 × 1,068 = R35 734,48 ✓ Annual salary = R35 734,48 × 12 ✓ = R428 813,75 ✓ OR Total annual income = 31 625 × 12 ✓ = 379 500 ✓ × 1,058 ✓× 1,068 ✓ = R428 813,75 ✓ | 1M Multiplying by 5,8% 1CA Value for 1st year 1CA Value for 2nd year 1M Multiplying by 12 1CA Annual salary 1M Multiplying by 12 1CA Salary 1CA Value for 1st year 1CA Value for 2nd year 1CA Annual salary (5) | L2 |
| 2.3.1 | KZN = OAG + CSG = 669 634 + 2 776 098 ✓ = 3 445 732 ✓ WC = OAG + CSG = 330 039 + 993 038 = 1 323 077 ✓ Difference = 3 445 732 – 1 323 077 = 2 122 655 ✓ | 1RT Correct values for KZN 1CA Total 1CA Total 1CA Difference(4) | L2 |
| 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 The number of the rest of the provinces ✓ decreases ✓ | 1A Both FS & NW 1A Remains the same 1A Rest of provinces 1A Decrease (4) | L4 |
| 2.3.5 |  | Both bars plotted correctly for 1MA EC 1MA KZN 1MA NC 1MA LP (4) | L2 |
Question 3 [31]
| Ques. | Solution | Explanation | Level |
| 3.1.1 | Measured distance from Cape Town to Durban = 8,1 cm ✓✓ Accept 7,9 cm to 8,3 cm Bar Scale 3 cm ✓= 500 km Accept 2,9 cm to 3,1 cm Actual Distance = 500 ? 8,1 3 ✓ = 1 350 km ✓ Time taken by first family = 21:00 – 8:00 – 1,5 = 11,5 hrs ✓ Speed of family = 1 350 ?? 11,5ℎ?? = 117,39 km/h ✓ Time taken by second family = 21:00 – 8,50 – 1,5 = 11 hrs ✓ Speed of family = 1 350 ?? 11ℎ?? = 122,72 km/h ✓ Statement is valid ✓ | 2A Measure distance 1A Measure bar scale 1C Convert distance using bar scale 1CA Distance 1CA Time 1CA Speed 1CA Time 1CA Speed 1O Valid NPR (10) | L4 |
| 3.1.2 | Zambia ✓✓ | 2A Country (2) | L2 |
| 3.2.1 | Unknown length (1) = 12 cm – 6 cm = 6 cm Unknown length (2) = 10 cm – 2 cm – 4 cm = 4 cm Perimeter = 10 + 4 + 4 + 2 + 12 + 6+ 6 + 2 + 6 + 4 ✓✓✓ = 56cm ✓ | 1M Finding 6 cm 1M Finding 4 cm 1M Adding all values 1CA Perimeter(4) | L2 |
| 3.2.2 | Area = ℓ × b Figure 1 = 10 cm × 4 cm = 40 cm2 ✓ Figure 2 = 4 cm × 6 cm = 24 cm2 ✓ Figure 3 = 6 cm × 6 cm = 36 cm2 ✓ Total area = 40 cm + 24 cm +36 cm = 100 cm2 ✓ Area of page = 28 cm × 20 cm = 560 cm2 ✓ Area of unshaded part = 560 – 100 ✓ = 460 cm2 ✓ | CA from 3.2.1 1MA Calculating area 1MCA Area 1MCA Area 1CA Total area 1CA Area of page 1M Subtraction 1CA Unshaded area (7) | L3 |
| 3.3.1 | Satara to Olifants = 54km ✓ N’wanetsi to Lower Sabi = 108km ✓ Distance is half; therefore, it can take them half the time to travel.✓✓ | 1RT Correct distance 1RT Correct distance 2 Explanation (4) | L2 & L4 |
| 3.3.2 | Punda to Mopani = 130 km Mopani to Paul Kruger = 220 km ✓ Total = 130 km + 220 km = 350 km ✓ Skukuza to Pafuri = 380 km Difference = 380 km – 350 km = 30 km ✓ Statement valid ✓ | 1RT Correct values 1MA Adding distances 1CA Difference 1O Valid (4) | L2 & L4 |
QUESTION 4 [37]
| Ques. | Solution | Explanation | Level |
| 4.1.1 | Not offered at certain universities ✓✓ OR No students registered for the course ✓✓ | 2A Reason(2) | L4 |
| 4.1.2 | Fees for Business at Bond = $33 640 Fees for Engineering at Edith Cowan = $ 25 760 ✓ Total = 33 640 + 25 760 = 59 400 ✓ $1 = R9,68 $59 400 = 9,68 × 59 400 ✓ = R 574 992 ✓ | 1RT Both values correct 1CA Total 1C Convert to Rand 1CA Amount in Rand (4) | L3 |
| 4.1.3 | Fees greater than $15 000, but less than $ 30000 = 710 ✓✓ = 0,7 ✓ | 1A Numerator 1A Denominator 1CA Decimal (3) | L2 |
| 4.2.1 | % increase = 38 249−29 678✓✓ × 100 ✓ 29 678 = 28,88% ✓ | 1RT Using correct values 1SF Substitution 1M Multiply by 100 1CA Percentage NPR (4) | L2 |
| 4.2.2 | December ✓ People get bonuses in December ✓✓ OR People budget to spend in December ✓✓✓ | 1A Month 2R Reason (3) | L2 & L4 |
| 4.2.3 | August 2015 – 30 633 August 2016 – 31 556 ✓ Difference = 31 556 – 30 633 = 923 ✓ Amount = 923 × 550 000 = R507 650 000 ✓ 14, 81 = 1 Euro 507 650 000 = 1 × 507 650 000 14,81 ✓ = 34 277 515,19 Euro ✓ | 1RT Both values correct 1MCA Difference 1MCA Amount 1C Convert to € 1CA Amount in € (5) | L3 |
| 4.3.1 | Hours worked: Level 3: Day 1 = 5 hours ✓ Day 2 to 13 = 10 hrs × 12 = 120 ✓ Day 14 = 8 hrs Total number of hours = 5 + 120 + 8 hours = 133 hours ✓ Level 2 = 133 hours Level 1 = 133 – 4 ✓ = 129 hours ✓ Amount for Level 3 = 248 × 133 × 2 = R65 968 ✓ Amount for Level 2 = 133 × 218,24 × 6 = R174 155,52 ✓ Amount for Level 1 = 129 × 163,68 × 32 = R675 671,04 ✓ Total Amount = 65 968 + 174 155,52 + 675 671,04 = R915 794,56 ✓ Statement invalid ✓ | 1A Hrs for Day 1 1MA Hrs for Day 2 to 13 1CA Total number of hours 1M Subtracting 1CA Calculating hours for Level 1 1MCA Amount Level 3 1MCA Amount Level 2 1MCA Amount Level 1 1CA Total amount 1O Invalid (10) | L4 |
| 4.3.2 | Distance for 14 days = 14 km × 2 × 14 days ✓ = 392 km ✓ Transport Cost for all employees = 392 km × 3,18 × 40 = R49 862,40 ✓ Amount as a fraction = 49 862,40 915 794,56 ✓ = 0,05 ✓ Statement is valid ✓ | CA from 4.3.1 1MA Return multiply by 14 1CA Total distance 1MCA Transport cost 1M Dividing values 1CA Decimal 1O Valid (6) | L4 |
TOTAL: 150
Published in Grade 12 September 2018 Preparatory Examinations