Tuesday, 14 September 2021 08:24

## MATHEMATICAL LITERACY PAPER 2 GRADE 12 MEMORANDUM - 2018 SEPTEMBER PREPARATORY EXAM PAPERS AND MEMOS

MATHEMATICAL LITERACY PAPER 2
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 

 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 301A Number of litres1CA Litres for tank water1CA Total litres for the month1MCA Total litres(5) L3 1.1.2 Litres used from tank = 24 450No. of kilolitres = 24 450 ÷ 1 000= 24,45 kℓ ✓First 6 = 6 × 07 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 1.1.11C Converting to kilolitres1MA 2nd Tariff1MA 3rd Tariff1MA 4th Tariff1MA 5th Tariff1CA Total amount1M Calculating VAT1CA VAT incl1O 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 litresStatement invalid. Cannot have enough water if it does not rain.✓ 1C mm to cm1SF Substitution1MA Finding the radius1S Simplification1C Convert to litres1R Nearest thousand1CA Rounded to nearest thousand1CA Total volume for two tanks1O Not valid (9) L3 1.2.1 Grade 10 : Grade 11 : Grade 12Ratio 5 : 3 : 2Grade 10 = 250 book packsTotal = 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 ✓OR5 = 2501 = 250 ÷ 5= 50 ✓3 = 50 × 3= 150 ✓2 = 50 × 2= 100 ✓Total = 250 + 150 + 100 ✓= 500 ✓ 1M Adding ratio1M Concept of ratio1M Changing subject of formula1M Dividing1CA Number of book packs1MA Unit ratio1MA Finding value of 31MA Finding value of 51M Addition1CA 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 1.2.11MCA Cost for book packs1M Dividing by 1,151CA Amount before VAT1M Subtraction1CA VAT amount1MCA Amount of 50 book packs1O Valid (7) L4 1.2.3 Probability = 150 + 100                      500    500= 250 ✓✓× 100     500✓= 50% ✓ CA from 1.2.11MCA Adding correct fractions1CA Numerator1CA Denominator1CA Percentage(4) L2

Question 2 

 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 Adding1M Dividing by 111CA 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 dividing1CA Mean1O Invalid (3) L4 2.1.2 201549,1; 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% ✓201651,5; 52,0; 65,3; 69,5; 70,5; 71,3; 73,7; 75,4; 76,5; 84,0,97,4Q1 (B) = 65,3% ✓IQR = 76,5 – 65,3= 11,2% ✓Statement valid ✓ 1M Ascending order1CA Q3 (A)1CA IQR1A Q1 (B)1CA IQR1O 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 income1RT Correct tax bracket1SF Substitution1S Simplification1M Subtract rebate1CA Monthly tax1MA Child grant for 101MA Old age grant for 21CA Total grants1O 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 ✓ORTotal annual income= 31 625 × 12 ✓= 379 500 ✓ × 1,058 ✓× 1,068 ✓= R428 813,75 ✓ 1M Multiplying by 5,8%1CA Value for 1st year1CA Value for 2nd year1M Multiplying by 121CA Annual salary1M Multiplying by 121CA Salary1CA Value for 1st year1CA Value for 2nd year1CA 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 KZN1CA Total1CA Total1CA 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 2018The number of the rest of the provinces ✓ decreases ✓ 1A Both FS & NW1A Remains the same1A Rest of provinces1A Decrease (4) L4 2.3.5 Both bars plotted correctly for1MA EC1MA KZN1MA NC1MA LP(4) L2

Question 3 

 Ques. Solution Explanation Level 3.1.1 Measured distance from Cape Town to Durban= 8,1 cm ✓✓ Accept 7,9 cm to 8,3 cmBar Scale3 cm ✓= 500 km Accept 2,9 cm to 3,1 cmActual Distance= 500 𝑥 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 𝑘𝑚                               11,5ℎ𝑟𝑠= 117,39 km/h ✓Time taken by second family= 21:00 – 8,50 – 1,5= 11 hrs ✓Speed of family = 1 350 𝑘𝑚                               11ℎ𝑟𝑠= 122,72 km/h ✓Statement is valid ✓ 2A Measure distance1A Measure bar scale1C Convert distance using bar scale1CA Distance1CA Time1CA Speed1CA Time1CA Speed1O ValidNPR (10) L4 3.1.2 Zambia ✓✓ 2A Country (2) L2 3.2.1 Unknown length (1) = 12 cm – 6 cm= 6 cmUnknown length (2) = 10 cm – 2 cm – 4 cm= 4 cmPerimeter = 10 + 4 + 4 + 2 + 12 + 6+ 6 + 2 + 6 + 4 ✓✓✓= 56cm ✓ 1M Finding 6 cm1M Finding 4 cm1M Adding all values1CA Perimeter(4) L2 3.2.2 Area = ℓ × bFigure 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 3.2.11MA Calculating area1MCA Area1MCA Area1CA Total area1CA Area of page1M Subtraction1CA 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 distance1RT Correct distance2 Explanation (4) L2 & L4 3.3.2 Punda to Mopani = 130 kmMopani to Paul Kruger = 220 km ✓Total = 130 km + 220 km= 350 km ✓Skukuza to Pafuri = 380 kmDifference = 380 km – 350 km= 30 km ✓Statement valid ✓ 1RT Correct values1MA Adding distances1CA Difference1O Valid (4) L2 & L4

QUESTION 4 

 Ques. Solution Explanation Level 4.1.1 Not offered at certain universities ✓✓ORNo students registered for the course ✓✓ 2A Reason(2) L4 4.1.2 Fees for Business at Bond = \$33 640Fees 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 correct1CA Total1C Convert to Rand1CA Amount in Rand (4) L3 4.1.3 Fees greater than \$15 000, but less than \$ 30000= 710 ✓✓= 0,7 ✓ 1A Numerator1A Denominator1CA Decimal(3) L2 4.2.1 % increase = 38 249−29 678✓✓ × 100 ✓                            29 678 = 28,88% ✓ 1RT Using correct values1SF Substitution1M Multiply by 1001CA PercentageNPR (4) L2 4.2.2 December ✓People get bonuses in December ✓✓ORPeople budget to spend in December ✓✓✓ 1A Month2R Reason(3) L2 & L4 4.2.3 August 2015 – 30 633August 2016 – 31 556 ✓Difference = 31 556 – 30 633= 923 ✓Amount = 923 × 550 000= R507 650 000 ✓14, 81 = 1 Euro507 650 000 = 1 × 507 650 000                                  14,81 ✓= 34 277 515,19 Euro ✓ 1RT Both values correct1MCA Difference1MCA Amount1C 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 hrsTotal number of hours = 5 + 120 + 8 hours= 133 hours ✓Level 2 = 133 hoursLevel 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 131CA Total number of hours1M Subtracting1CA Calculating hours for Level 11MCA Amount Level 31MCA Amount Level 21MCA Amount Level 11CA Total amount1O 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 4.3.11MA Return multiply by 141CA Total distance1MCA Transport cost1M Dividing values1CA Decimal1O Valid (6) L4

TOTAL: 150