Mathematical Literacy P1 Nov 2016 Memo Eng hlayiso.com

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICAL LITERACY P1 NOVEMBER 2016 FINAL MARKING GUIDELINE MARKS: 150 Symbol Explanation M Method MA Method with accuracy CA Consistent accuracy A Accuracy C Conversion S Simplification RT/RG Reading from a table/graph/diagram SF Correct substitution in a formula O Opinion/Example/Definition/Explanation P Penalty, e.g. for no units, incorrect rounding off, etc. R Rounding off NP No penalty rounding or omitting units This memorandum consists of 15 pages. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 2 DBE/November 2016 NSC – Memorandum Question 1 [43 Marks] Ques Solution Explanation Topic/L F 1.1.1 Booysen M 2A correct name L1 A (2) L1 1.1.2 July A 1A correct month 2026 A Accept 7th month 1A correct year Answer Only Full Marks (2) M/A L1 1.1.3 R1 185 627,28 – R466 000,00 1M/A subtracting correct =R719 627,28 CA values 1CA difference Answer Only Full Marks NP (2) RT M L1 1.1.4 Total Admin. fee = R5,70 × 12 × 20 1RT reading from table = R1 368 CA 1M multiplying correct total number of months 1CA total fee Answer Only Full Marks NP (3) M L1 1.1.5 7,25% + 0,5% = 7,75% A 1M adding correct % 1A sum Answer Only Full Marks (2) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 3 DBE/November 2016 NSC – Memorandum Ques Solution Explanation Topic/L L2 1.1.6 R 5,70 1MA dividing by 114% Amount without VAT = 114% MA = R5,00 M 1M subtracting ∴ VAT amount = R5,70 – R5,00 = R0,70 CA 1CA VAT amount OR OR 1M dividing by 114% A 1A multiply by 14% 14% VAT amount = × R5,70 1CA VAT amount 114% M = R0,70 CA Answer Only Full Marks (3) O L1 1.1.7 An amount advanced/borrowed 1O Amount borrowed to buy a house/flat/residential property 1O buying a O house/flat/residential property OR Money borrowed to buy a house (2) L1 1.1.8 B A 2A correct reason Accept C (2) MA L1 1.1.9 R383 159,13 – R383 158,37 1M/A subtracting correct (a) = R0,76 CA values 1CA simplification from balance column for October Answer Only Full Marks (2) L1 1.1.9 Credit A 2A correct column (b) (2) A L2 1.1.10 R 378 123,87 × 31 × 7,25% SF 1A 31 days Interest = 1SF correct balance and 365 = R2 328,31 CA % 1CA interest Answer Only Full Marks NP (3) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 4 DBE/November 2016 NSC – Memorandum Ques Solution Explanation Topic/L O L1 1.2.1 The cost that changes (not fixed/not constant/differs) 2O explanation depending on the number of persons. (2) A A L2 1.2.2 Total cost (in Rand) = 6 000 + 230 × 45 1A substituting 6 000 = 6 000 + 10 350 1A substituting 45 = 16 350 CA 1CA cost Answer Only Full Marks (3) L1 1.2.3 Avon RG 2RG reading from graph (a) (2) L1 1.2.3 200 RG 2RG reading from graph (b) Accept 160 (2) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 5 DBE/November 2016 NSC – Memorandum Ques Solution Explanation Topic/ L L2 1.2.4 TOTAL COST FOR EACH OF THE THREE VENUES (a) 30 000 A 25 000 CA 20 000 Amount in Rand A 15 000 10 000 AVON BEACH 5 000 CASTLE 0 A 0 50 100 150 200 250 300 Number of persons 1A starting point (0 ; 0) 1A end point of (200 ; 30 000) 1CA joining points 1A straight line (4) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 6 DBE/November 2016 NSC – Memorandum Ques Solution Explanation Topic/L L3 1.2.4 Cost for 250 persons = R11 000 + R25 × 250 SF 1SF substitution (b) = R17 250 CA 1CA cost Income from 194 tickets = R150 × 194 MA 1MA multiplication = R29 100 A 1A income Profit = R29 100 – R17 250 = R11 850 CA 1CA profit OR OR SF M 1SF substitution Profit = (R11 000 + R25 × 250) – (R150 × 194) 1M multiplication CA A 1CA cost = R29 100 – R17 250 1A income = R11 850 CA 1CA profit Note: If readings are taken from graphs then: Cost (accept range from 17 000 to 17 500) - 2 marks Income (accept range from 28 900 to 29 300) - 2 marks Full marks can only be given if the profit is exactly R11 850 NP (5) [43] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 7 DBE/November 2016 NSC – Memorandum QUESTION 2 [29 MARKS] Ques Solution Explanation Topic/L L1 2.1.1 d = 4,2 m – (1,2 m + 1,8 m) M 1M subtracting (a) = 1,2 m A 1A value = 1 200 mm C 1C conversion OR OR M C d = 4200 mm – (1 200 mm + 1800 mm) 1M subtracting = 1 200 mm A 1C conversion 1A value Answer Only Full Marks (3) MA L1 2.1.1 15m + 1,2 m + 1,2 m + 4,2 m + 1,2 m +1,2 m + 15 m 1M/A adding all (b) = 39 m CA values = 39 000mm C 1CA total length 1C conversion OR OR MA 15 m × 2 + 1,2 m × 4 + 4,2 m = 39 m CA 1M/A adding all = 39 000 mm C values 1CA total length 1C conversion Answer Only Full Marks (3) L2 SF 2.1.1 Total area = 1,8 m × 15 m + 1,2 m × 4,2 m 1SF substituting (c) = 27 m2 + 5,04 m2 S 1S simplification = 32,04 m2 A A 1A area 1A correct unit OR OR S SF 1SF substituting Total area = 2(1,2 × 1,2 ) m2 + [1,8 × (15 + 1,2)] m2 1S simplification = 2,88 m2 + 29,16 m2 1A area = 32,04 m2 A A 1A correct unit OR OR S SF 1SF substituting Total area = [2 (1,2 × 1,2 ) + (1,8 × 15) + (1,8 × 1,2)] m2 1S simplification = [2,88 + 27 + 2,16] m2 1A area = 32,04 m2 A A 1A correct unit OR OR Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 8 DBE/November 2016 NSC – Memorandum Ques Solution Explanation Topic/L SF Total area = 16,2 m × 4,2 m – 2 × (1,2 m × 15 m) 1SF substituting = 68,04 m2 – 36 m2 S 1S simplification = 32,04 m2 1A area A A 1A correct unit Max 2 out of 4 if only one area correctly calculated with unit (4) L1 2.1.1 1 3 of the length of the hall = 16,2 m A 1A length of runway (d) 1M multiply by 3 Length of hall = 16,2 m × 3 OR 16,2 m ÷ 13 M 1CA length of hall = 48,6 m CA Answer Only Full Marks (3) M L2 2.1.2 4,2 4,2 m = feet 1M dividing by 0,3048 conversion factor S = 13,7795.. feet ≈ 13,8 feet R 1S simplification 1R rounding Answer Only Full Marks (3) SF C L2 2.2.1 3 456 cm³ = A² × 24 cm 1SF substitute into A² = 3 456 cm³ ÷ 24 cm formula = 144 cm² CA 1C conversion to cm A = 144 cm 1CA simplification = 12 cm CA 1CA length of A SF OR OR 3 456 C 1SF substitute into A = � 24 CA formula 1C conversion to cm = 12 cm CA 1CA simplification 1CA length of A Answer Only Full Marks (4) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 9 DBE/November 2016 NSC – Memorandum Ques Solution Explanation Topic/L SF L2 2.2.2 Area of one label = (1 + 2 ×3,142 × 7) × 24 cm 1SF substitute into = 1 079,712 cm² A formula M 1A area of one label Total area of labels = 1 079,712 cm² × 76 1M multiply by 76 = 82 058,112 cm² ≈ 82 058 cm² R 1R rounding (accept 82 059) OR OR A SF M 1SF substitute into Total area of labels = [(1 + 2 ×3,142 × 7) × 24 cm] × 76 formula = 82 058,112 cm² 1A area of one label ≈ 82 058 cm² R 1M multiply by 76 1R rounding (accept 82 059) Penalise with one mark if π on calculator is used (4) L2 2.2.3 Volume of cylinder = 3,142 × 7² × 24 cm³ SF 1SF substitute into = 3 694,99 cm³ A formula MA 1A volume of Difference in volume = 3 694,99 cm³ – 3 456 cm³ cylinder = 238,99 cm³ 1M/A show how volume was obtained OR OR SF A MA Difference in volume = 3,142 × 7² × 24 cm³ – 3 456 cm³ 1SF substitute into = 238,99 cm³ formula 1A volume of cylinder 1M/A show how volume was obtained NP (3) L1 2.2.4 kilograms or kg or g A 2A unit (2) [29] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 10 DBE/November 2016 NSC – Memorandum QUESTION 3 [28 MARKS] Ques Solution Explanation Topic/L L1 3.1.1 Row A = 15 ; Row B = 16 ; Row C = 18 1A number in seats Row D = 19 ; Row E = 21 ; Row F = 22 A in row A – J Row G = 24 ; Row H = 25 ; Row J = 26 M 1M adding Total = 15 + 16 + 18 + 19 + 21 + 22 + 24 + 25 + 26 = 186 CA 1CA total OR OR Total = 432 – total left block – total right block M 1M subtracting = 432 – 121 – 125 A 1A totals for both = 186 CA blocks 1CA total OR OR Total A = (32 + 33 + 35 + 36 + 38 + 39 + 41 + 42 + 43) – (17 × 9) 1A number of seats = 339 – 153 M in right block = 186 CA 1M subtracting additional seats 1CA total Answer Only Full Marks 185 or 187 two marks (3) L1 3.1.2 North West/NW A 2A direction (2) L1 3.1.3 H30 A 3A if row AND seat OR are correct 8th row from the stage seat 30 2A if either row OR OR seat is correct second row from the back seat 30 (3) L2 3.1.4 Exit towards the left/ aisle A 1A Exit to left/ aisle Turn left in the aisle A 1A turn left in aisle Walk straight to entrance/exit 1. A A 1A walk towards At entrance/exit 1 the refreshment stand will be on the right. entrance/exit 1 1A location of refreshment stand (4) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 11 DBE/November 2016 NSC – Memorandum Ques Solution Explanation Topic/L P MA 3.1.5 87 12 % × 432 = 378 OR 0,875 × 432 = 378 1MA calculating % L2 1 A of 432 (CA from P= Q 3.1.1) 378 CA OR 0,26% OR 0,0026 1A numerator 1CA denominator Answer Only Full Marks (3) P 3.1.6 20% A 2A correct decimal L1 (2) L1 3.2.1 Unscrewed A 2A unscrewed (a) (2) L1 3.2.1 Anti-clockwise OR left OR counter-clockwise A 2A direction (b) (2) L2 3.2.2 3 A 2A 3 screws (2) M L1 3.2.3 3 A 2A correct diagram (2) L2 3.2.4 Actual length = 62 mm × 30 OR 6,2 cm × 30 1M multiply by = 1 860 mm A = 186 cm scale = 1,86 m C = 1,86 m 1A length in mm/cm 1C conversion OR OR C M 1C conversion Actual length = 0,062 m × 30 1M multiply by = 1, 860 m CA scale 1CA length in m Answer Only Full Marks (3) [28] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 12 DBE/November 2016 NSC – Memorandum QUESTION 4 [30 MARKS] Ques Solution Explanation Topic/L A M 1A identify correct highest and L1 4.1.1 322,15 – 180,29 mph lowest values = 141,86 mile per hour CA 1M subtraction 1CA difference Answer Only Full Marks NP (3) L1 4.1.2 14 RT 2RT correct number of riders (2) RT RT L1 4.1.3 1990 and 2006 1RT first year 16 years CA 1RT second year 1CA number of years Accept 17 years (3) L1 4.1.4 Ernest J HenneRT 2RT name of rider 6 times A 1A number of times (3) P A 4.1.5 5 1A number of years in 21st L3 × 100% century 25 A 1A total number of years = 20% CA 1CA probability as percentage Answer Only Full Marks (3) O L1 4.2.1 The number of children can only be whole numbers. 2O explanation OR O OR The number of children cannot be decimals/fractions 2O explanation (2) L1 4.2.2 16 to 18 RT 2RT identify correct age group (2) L1 4.2.3 2007 RT 1RT identify correct year (2) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 13 DBE/November 2016 NSC – Memorandum Ques Solution Explanation Topic/L RT L1 4.2.4 A = 209 309 + 539 177 1RT correct values = 748 486 A 1A value of A Answer Only Full Marks (2) L1 4.2.5 RT M 1RT correct values 194 901 B= × 100 1M multiply by 100 9 281 000 = 2,1 CA 1CA value of B (3) 4.2.6 L2 PERCENTAGES OF CHILDREN IN THE AGE GROUP 16 to 18 NOT ATTENDING ANY EDUCATIONAL INSTITUTION FROM 2002 TO 2009 20 19 A A 18 Percentage 17,5 17,3 17,8 17 A CA 16 15 14,8 14 A 13 12 11 10 2002 2003 2004 2005 2006 2007 2008 2009 Years 4A (1 for each two correctly plotted point) 1CA joining the points (5) [30] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 14 DBE/November 2016 NSC – Final Marking Guideline 4 November 2016 QUESTION 5 [20 MARKS] Ques Solution Explanation Topic/L D 5.1 United Kingdom OR Britain RT 2RT correct country L1 (2) F 5.2 1 South African rand = 0,070 US dollar L2 1,94 1M dividing by exchange ∴ $1,94 = R M rate 0,07 1A rand value = R27,71 A OR OR R95,57 ÷ $6,69 = 14,2855… M 1M dividing by price in $ 1,94 × 14,28855…. dollar = R27,71 A 1A rand value Answer Only Full Marks (2) F 5.3.1 113,96 1M dividing by exchange L2 A= euro M rate 16,28 = 7 euro A 1A euro value with unit Answer Only Full Marks (2) F 5.3.2 56,07 M 1M dividing by exchange L2 B= rate 267 = 0,21 A 1A rand value 1 Indian Rupee equals 0,21 South African rand Answer Only Full Marks (2) F 5.4 SGD $ 8,00 : SGD $ 2,50 A MA 1A identifying the correct L1 values = 16 : 5 CA 1MA ratio in correct order 1CA simplified ratio Answer Only Full Marks (3) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematical Literacy/P1 15 DBE/November 2016 NSC – Final Marking Guideline 4 November 2016 Ques Solution Explanation Topic/ L RT D 5.5 United States of America and Brazil RT 1RT United States of L1 America 1RT Brazil (2) O D 5.6 A median is the middle value of the 1O middle value L1 arranged/ordered/sorted data. O 1O arranged/ordered/ sorted (2) RT D 5.7.1 R118,75; R113,96; R99,30; R95,57; R95,22; R92,88; 1RT correct values L1 R84,21; R69,57; R62,40; R56,07; R50 A 1A correct order NP (2) D 5.7.2 Mean (in rand ) = M L2 50 + 56,07 + 62,40 + 69,57 + 84,21 + 92,88 + 95,22 + 95,57 + 99,30 + 113,96 + 118,75 11 A 937,93 1M adding values = 1A dividing by 11 11 ≈ 85,27 CA (check CA from Q 5.7.1) 1CA mean Answer Only Full Marks (3) [20] TOTAL 150 Copyright reserved