Grade 12 NSC Math Lit P2 Preparatory 2018 Possible Answer hlayiso.com

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PREPARATORY EXAMINATION 2018 MARKING GUIDELINES MATHEMATICAL LITERACY PAPER 2 (10602) Symbol Explanation M Method MA Method with accuracy CA Consistent accuracy MCA Method with constant accuracy A Accuracy C Conversion S Simplification RT / RG / Reading from a table / graph / diagram RD SF Correct substitution in a formula O Opinion / Example / Definition / Explanation R Rounding off NPR No penalty rounding or omitting units AO Answer only, full marks J Justify KEY TO TOPIC SYMBOL: F = Finance; M = Measure ment; MP = Maps, Plans and other representations; DH = Data Handling; P = Probability 10 pages

Downloaded from hlayiso.com 10602/18 GAUTENG DEPARTMENT OF EDUCATION PREPARATORY EXAMINATION MATHEMATICAL LITERACY (Paper 2) MARKING GUIDELINES Q1 ANSWER EXPLANATION LEVEL 1.1.1 Monthly taxable income 1 SF substituting Monthly salary = R33 412,65 0,925 = R33 412,65 ÷ 0,925 1 A answer F3 1 MCA multiply by 12 [4] = R36 121,78 1 CA answer Annual salary = R36 121,78 x 12 = R433 461, 36 1.1.2 He is under 65 years old and earning an income of more 1 O explanation than R75 750; therefore, he qualifies to pay tax.  1 J justification F4 [2] 1.1.3 Taxable income before rebates 1 RT correct tax bracket = R61 910 + 31% (R400 951,80 – R296 540)  1 SF substituting = R94 277,66 R400 951,80 1 A answer Medical credit = R303 x 2 x 12 = R7272 1 M multiplying by 2 and 12 Payable tax = R94 277,66 – R7272 – R13500 1 CA answer = R73 505,66 1 M subtracting rebates Monthly tax = R73 505,66 ÷ 12 and medical credits F4 = R6 125,47 1 CA answer [10] 1 MCA dividing by 12 Therefore, his claim is invalid.  1 CA answer 1 J justification 2

Downloaded from hlayiso.com 10602/18 Q1 ANSWER EXPLANATION LEVEL 1.2.1 Cost of wages = 30% of R321 021,56 1 M multiplying by 30% F2 (a) = R96 306,47 1 A answer [2] (b) Cost of wages for each employee = R96 306,47 ÷ 4 1 MCA dividing by 4 F3 = R24 076,62 1 A answer [4] Monthly cost = R24 076,62 ÷ 3 1 M dividing by 3 = R8025,54 1 A answer OR 3 x 4 = 12 1 M multiplying 3 by 4 Cost of wages for each employee = R96 306,47 ÷ 12 1 A answer = R8025,54 1 MCA dividing by 12 1 A answer 1.2.2 Cost of materials (VAT exclusive) 1 M subtracting F4 = R321 021,56 – R96 306,47 1 A answer [6] = R224 715,09 Cost of materials (VAT inclusive) 2 M multiplying by 114% = R224 715,09 × 114% 1 A correct values = R256 175,20 1 J justification His claim is valid 1.2.3 Institution A: 10% ÷ 2 = 5% 1 A for 5% F4 1 M multiplying by 105% [10] Term 1: 105% of R210 050 = R220 552,50 1 A answer 1 CA answer Term 2: 105% of R220 552,50 = R231 580,13 Institution B: 8% ÷ 4 = 2% 1 A for 2% Term 1 : 102% of R210 050 = R214 251 1 A answer Term 2 : 102% of R214 251 = R218 536,02 1 CA answer Term 3: 102% of R218 536,02 = R222 906,74 1 CA answer Term 4: 102% of R222 906,74 = R227 364,88 1 CA answer True, he will repay less for a loan from institution B.  1 J opinion [38] 3

Downloaded from hlayiso.com 10602/18 Q2 ANSWER EXPLANATION LEVEL 2.1. Bedrooms 3 and 4 1 A correct answer MP2 Because they are on the northern side of the house.  2 J justification [3] 2.2 M2 Area = + 1 SF substitution of [4] = +  correct values = 21 + 12 1 A value of 3 = 33  1 A value of 4 1 CA answer OR Area = + 1 SF substitution of = +  correct values = 24 +9 1 A value of 4 = 33  1 A value of 3 1 CA answer OR Area = (7m × 6m) – (3m × 3m)  = 42 -9 = 33  2.3 Number of boxes = CA from 2.2 = 16,6 1 R answer F3 17 boxes 1 M for multiplication [5] 1 A answer Cost for tiling = R189,99 17 1 A answer for extra = R3 229,83 boxes 1 CA final answer Cost for two extra boxes of tiles =R189,99 × 2 = R379,98 Total cost = R3 229,83 + R379,98 1 R for number of boxes = R3 609,81 1 A for extra boxes 1 A answer OR 1 M for multiplication Number of boxes = 17 + 2 = 19 1 CA answer Cost = 19 × R189, 99 = R3 609,81 2.4 3days : 8,40 1 M for the proportion M3 x : 73  [4] 1 M for multiplying  correctly 1 CA answer 26,0714285 1 R for rounding  ≈ 4 weeks [16] 4

Downloaded from hlayiso.com 10602/18 Q3 ANSWER EXPLANATION LEVEL 3.1.1 Surface Area = 2(ℓ× h) + 2(w × h) + 2(ℓ × w) 1 C for 0,86 M2 = 2(1,1 × 2) + 2 (0,86 × 2) + 2 (1,1 × 0,86)  1 SF for correct [3] = 9,73m2  substitution 1 A answer 3.1.2 Radius = 0,65 1 A value of radius M4 2 Volume of a cylindrical geyser = πr h 1 SF for correct [6] = 3,142 (0,65)2 × 2 substitution = 2,65m3  1 A answer Volume of a rectangular cylinder = ℓ x w x h 1 SF correct =1,1 x 0,86 × 2 substitution = 1,89m3  1 A answer True, cylindrical geyser is bigger / has a greater capacity 1 J justification NPR 3.1.3 Radius = 65 cm and height = 200 cm 1 C both r and h M3 [6] Volume = 3,142 × (65 cm)2 × 200 cm 1 SF substitution of = 265 4990 cm3  correct values 1 A answer Therefore: 95% of 265 4990 cm3 = 252 2240,5 cm3  252 2240,5 cm3 ÷ 1000 = 2 522,2405ℓ 1 CA answer ≈ 2 522 ℓ 1 C conversion to litres 1 R rounding of litres 3.2.1 Cost for 39 kℓ without levy F3 1 A for every 2 correct [6] = (R0,00 × 6) + (R7,24 × 4) + (R11,84 × 5) + (R17,46 × 5) answers (3A) + (R23,34 × 10) + (R25,10 × 9) 1 CA answer = R0,00 + R28,98 + R59,20 + R87,30 + R233,40 + R225,90 = R634,78 1 CA answer Water levy = 10% of R634,78 = R63,48 1 CA answer Cost for 39 kℓ including levy = R634,78 + R63,48 = R698,26 3.2.2 2 ÷ 5 of R698,26= R279,30 1 A for correct F4 fraction / proportion [4] True, it is less than R300 1 M multiplying correct values 1 A answer 1 J justification 5

Downloaded from hlayiso.com 10602/18 Q3 ANSWER EXPLANATION LEVEL 3.2.3 1 A for each correct P3 B branch (3A) [7] B G B G B G B Children B G G B G G 2 A for outcomes Outcomes: 1 A probability 1 CA percentage BBB BBG BGB BGG GBB GBG GGB GGG The probability of having a boy as the first born and to have a girl and boy in any order is 2 = 25% 8 [32] 6

Downloaded from hlayiso.com 10602/18 Q4 ANSWER EXPLANATION LEVEL 4.1.1 Free standing house  1 A correct answer D4 The average price of building a free standing house in RSA 2 O opinion [3] is cheaper than building a townhouse.  4.1.2 Q 1 = (R4 698 + R4 609) ÷ 2 1 RG correct values D3 = R4 653,50 1 M adding values and [7] dividing by 2 Q 3 = (R6 136 + R6 102) ÷ 2 1 A correct answer = R6 119 1 A correct answer IQR = Q 3 – Q1  = R6 119 – R4 653,50 1 A correct formula = R1 465,50 1 SF correct values 1 CA answer 4.1.3  The type of landscape, dominated by rocky 1 O for reason / opinion MP4 lands.  1 O for reason / opinion [2]  Ocean, it is difficult to build in a sandy soil.   Tourist attraction.  More reinforcement is needed. Accept any valid answer 4.1.4 An average is calculated by adding all the real values 2 J for reason D2 divided by the total number of plans. [2] You cannot calculate an average by adding averages and dividing by the number of provinces. Accept any valid answer 7

Downloaded from hlayiso.com 10602/18 Q4 ANSWER EXPLANATION LEVEL 4.1.5 D2 1 A correct type [5] Cost versus the price of houses 1 A for FS and NW 1 A for MP, LP and EC FS 1 A for NC and GP 1 A for WC and KZN NW MP LP EC NC GP WC KZN 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 COST COSTFOR FORTOWN HOUSES TOWNHOUSES COST FOR FREE STANDING HOUSES 4.2.1 Number of full-time employees = 25% × 40 1 RT for 25% D2 = 10 employees 1 M for multiplying [3] by 40 1 A correct answer 4.2.2 Number of part-time employees = 75% x 120 1 RT for 75% D2 = 90 employees 1 M for multiplying [3] by 120 1 A correct answer 4.2.3 Median,  because it shows salary paid to half of the 1 A correct answer D4 employees.  2 J explanation [3] 4.2.4 Range = Max value – Min value 1 A correct formula D2 = R14 000 – R6 000 1 SF correct values [3] = R8 000 1 A answer 8

Downloaded from hlayiso.com 10602/18 Q4 ANSWER EXPLANATION LEVEL 4.2.5 It only focuses on outliers; few employees might fall in this 2 O explanation D2 category. [2] It is only based on the difference between the highest salary and the lowest salary.  4.2.6 50% of part time employees earn a salary of more than 2 A referring to D4 R11 000, whereas 50% of the full time employees earn a minimum, median or [4] salary of more than R10 000.  maximum 2 J conclusion Therefore, part time employees are paid better salaries.  OR The minimum and maximum salaries of full-time employees are higher than those of part-time employees  Therefore Pule is correct  4.2.7 Full time employment 1 A correct choice D4 The least paid employee earns R7 000,00 2 O Explanation [3] [40] 9

Downloaded from hlayiso.com 10602/18 Q5 ANSWER EXPLANATION LEVEL 5.1  Off-ramp to N12 and join N8 to Bloemfontein.  5 A for describing MP2  Off-ramp to N3 and join N5 after Harrismith, then join routes that pass [5] N1 to Bloemfontein.  through a national road from Johannesburg to Bloemfontein. 5.2 Measured distance: 4,3 cm 1 A for 4,3 cm MP3 Bar: 2,2 cm (Accept: 4,1 - 4,5 cm) [7] 1 A for 2,2 cm Actual distance = (4,3 cm ÷ 2,2 cm) × 300 km (Accept: 2,1 - 2,3 cm) = 586 km 1 MA for division Return distance = 586 km × 2 1 A for using 300 km = 1172 km 1 A for answer OR 1 MCA for multiplying by 2 2,2 cm : 300 km 1 CA answer 2,2 cm : 30 000 000 km 1 : 13 636 364 Note: measure on  4,3 cm × 13 636 364 = 58 636 365 cm final copy  58 636 365 cm ÷ 100 000 = 586 km 586 km × 2 = 1172 km 5.3 Time taken = 15h15 min - 10h45 1 M for subtraction M3 = 4 hours and 30 min 1 A for answer [6] = 4,5 hours 1 C for conversion 1 M Method  1 CA answer = 130,22 km / h  1 R correct rounding = 130 km / h  5.4 The general speed limits in terms of the South African 2 O Opinion MP2 National Road Traffic Act are: 60 km / h on a public road [2] within an urban area; 100 km / h on a public road outside an Accept any sensible urban area which is not a freeway; 120 km / h on freeways. explanation  5.5  It does not give enough detail.  4 O Opinion MP2  It does not have distances between cities and towns.  [4] Accept any sensible explanation [24] TOTAL 150 10