Grade 12 NSC Mathemetical Literacy Preperatory 2016 Possible Answers hlayiso.com

Downloaded from hlayiso.com PREPARATORY EXAMINATION 2016 MEMORANDUM MATHEMATICAL LITERACY P1 (10601) Codes Explanation M Method MA Method with Accuracy CA Consistent Accuracy A Accuracy C Conversion D Define J Justification / Reason / Explain S Simplification Reading from a table OR a graph OR a diagram OR a map RT / RD / RG OR a plan F Choosing the correct formula SF Substitution in a formula O Opinion P Penalty, e.g. for no units, incorrect rounding-off, etc. R Rounding off NP No penalty for rounding-off OR omitting units 14 pages

Downloaded from hlayiso.com 10601/16 GAUTENG DEPARTMENT OF EDUCATION PREPARATORY EXAMINATION – 2016 MATHEMATICAL LITERACY (First Paper) MEMORANDUM KEY TO TOPIC SYMBOL: F = Finance; M = Measurement; MP = Maps, Plans and other representations DH = Data Handling; P = Probability QUESTION 1 [47] Ques Solution Explanation Level 1.1.1 Gross monthly income 1M Method 1A Answer L1 = R14 872 + R780 M F Answer only full marks = R15 652 A (2) 1.1.2 Annual income = R15 652 x 12 1MA Calculating annual income = R187 824 MA 1M Subtraction 1MA Multiplication by Taxable income = Annual income ‒ Annual 12 Pension 1A Answer L3 M MA F = R187 824 – (R1 112,03 x 12) = R187 824 – R13 344,30 = R174 479,70 A (4) OR R15 652 – R1 112,03 MA 1MA Deduct / Minus 1A Answer = R14 539,97 A 1MA Multiplication by 12 1A Answer Annual = R14 537,97 x 12 MA = R174 479,70 A (4) 2

Downloaded from hlayiso.com 10601/16 Ques Solution Explanation Level 1.1.3a Medical Tax Credits = (Tax Credit of Main 1MA Addition and Multiplication member + Tax Credits of dependants) x 12 by 12 1A Answer = (R257 + R257) x 12 MA = R6 168 A L2 F OR (R257 x 2) x 12 MA = R6 168 A (2) 1.1.3b Tax payable = Annual tax ‒ Rebate ‒ Medical 1RT Reading correct value credits 1MA Multiply by 2 and 12 RT MA 1S Simplification both = (18% × R174 479,70) ‒ R12 726 ‒ (R257 × 2 × 12) brackets L2 1CA Answer F = R31 406,35 ‒ R12 726 ‒ R6 168 S CA from Q1.1.2 = R12 512,35 CA (3) 1.1.3c Monthly PAYE = R12 512,35 ÷ 12 1CA Answer 1R Rounding = R1 042,695833 L1 CA from Q1.1.3a F ≈ R1 042,70 CA (2) 1.1.4a Total deductions 1MA Addition = R1 042,70 + R1 112,03 + R1 500 + 1A Answer R148,72 MA L1 Answer only ful arks F = 3 803,45 A (2) 1.1.4b Nett monthly income = R15 652 – R3 803,45 1MA Subtraction MA 1A Answer TL1 F = R11 848,55 A Answer only full marks (2) 1.1.5a 1% A 2A Answer TL1 (2) F 1.1.5b Total amount for the month paid over for UIF 1MA Knowing to double the amount = R148,72 x 2 OR R148,72 + R148,72 1A Answer TL1 MA F Answer only full marks = R297,44 A (2) 3

Downloaded from hlayiso.com 10601/16 1.1.6 Annual medical tax credit 1MA Adding R172 and Multiply by 12 = [(R257 x 2) + R172] × 12 MA 1A Answer TL2 = R686 x 12 Answer only full marks F (2) = R8 232 A 1.1.7a Annual amount saved 1A Answer = Monthly amount saved x 12 Answer only full marks L1 = R3 000 x 12 F = R36 000 A (1) 1.1.7b Simple interest 1A Answer = Amount saved x interest rate x term 1CA Answer = R36 000 × = R1 224 A Amount saved = R36 000 + R1 224 = R37 224 CA OR L1 F R36 000 x M 1M Multiply by 103,4 % 1CA Answer = R37 224 CA OR R36 000 + (R36 000 x ) M 1M Addition 3,4% 1CA Answer = R37 224 CA (2) 1.2.1 Amount to be financed 1MA Subtract deposit = Purchase Price ‒ (Deposit + Admin Fee + 1MA Adding correct Registration/Licence Fee) values L2 MA MA 1A Answer F = R104 995 ‒ (R10 500 + R1 010 + R788) (3) = R96 293,00 A 4

Downloaded from hlayiso.com 10601/16 Ques Solution Explanation Level 1.2.2 Amount to be financed 1MA Adding correct = Purchase Price + Admin Fee + amounts Registration/Licence Fee 1A Answer 1MA Addition and = R104 995 + R1 010 + R788 MA multiplication 1CA Answer year 1 = R106 793 A 1CA Answer year 2 Year 1: R106 793 + ( ) MA L2 F = R106 793 + R12 815,16 = R119 608,16 CA Year 2: = R119 608,16 + ( ) = R119 608,16 + R14 352,9792 = R133 961,14 CA (5) 1.2.3 Percentage Deposit 1MA Correct values in MA fraction = M 1M Multiply by 100% 1A Answer L1 1R Rounding F = 10,0004… % A (4) = 10% R 1.3.1 Interest rate: 2O Definition A percentage of a sum of money charged by the bank for lending money to a person. O L1 OR F Any similar definition (2) 1.3.2 Percentage increase 2SF Substitution = 1S Simplification 1CA Answer = SF L2 F S (3) = 12,5% CA 5

Downloaded from hlayiso.com 10601/16 Ques Solution Explanation Level 1.3.3 Value B 1MA Addition = R140,00 + R179,39 + R170,86 + R584,79 + 1A Answer L1 R380,98 MA F Answer only full marks = R1 465,02 A (2) 1.3.4 Vat 2017 = R1 655,55 × MA 1MA Correct value 1MA Multiply by 14% L1 (2) F = R231,78 1.3.5 Additional amount to budget 1M Calculating 12% = R1 887,33 ‒ R1668,86 MA 1A Answer L1 F = R218,47 A Answer only full marks (2) [47] 6

Downloaded from hlayiso.com 10601/16 QUESTION 2 [29] Ques Solution Explanation Level 2.1.1(a) Length = 24 inches x 2,54 C 1C Conversion = 60,96 cm A 1A Answer length 1A Answer breadth Width = 12 inches x 2,54 1A Answer height = 30,48 cm A Depth = 10 inches x 2,54 L2 = 25,4 cm A (4) M 2.1.1(b) Volume = L × B × H 1SF Substitution SF 1CA Answer = 60,96 cm × 30,48 cm × 25,4 cm = 47 194,74432 cm3 L2 = 47 194,74 cm3 CA M (2) 2.1.2a Triangular containers to fit in length 1MA Division with correct MA values = (60,96 cm ÷ 10 cm) × 2 MA 1MA Multiply by 2 L2 1AR Answer M = 12,192 (3) ≈ 12 A 2.1.2b Triangular containers to fit in width 1MA Division and multiply with correct values = (30,48 cm ÷ 10 cm) × 2 MA 1A Answer 1R Rounding L2 = 6,096 M ≈6 A R (2) 2.1.3 Number of cardboard boxes 1MA Division 1AR Answer correctly = rounded Answer only full marks = MA L1 M = 10,4166 … boxes ≈ 10,5 boxes OR 10½ boxes AR (2) 2.2.1 80 : 5 MA 1MA Correct ratio L1 1S Simplification M 16 : 1 S (2) 7

Downloaded from hlayiso.com 10601/16 Ques Solution Explanation Level 2.2.2 P(Sandwich Spread) = × 100% M 1M Multiply by 100% 1MA Correct values in MA fraction 1A Answer L1 = 3,472 …% L ≈ 3,47% A NP for rounding (2) 2.3 The time that it will take Mrs. Madiba to reach 1MA Addition the school. 1A Answer L1 = 10:50 + 45 min MA M = 11:35 A (2) 2.4.1 97th Percentile RG 2RG Read from graph L1 (2) M 2.4.2 150 cm ÷ 100 = 1,5 m C 1C Conversion 1SF Substitution 1M Manipulating formula 1CA Answer 2J Justification 27 kg/m2 = SF L2 M 27 kg/m2 × 2,25 m2 = Mass (in kg) M 60,75 kg = Mass CA Yes J Mrs. Madiba’s opinion is correct. J (6) 2.4.3 Suzy’s new BMI = 21,8 kg/m2 RG 2RG Reading from the L1 graph M (2) [29] 8

Downloaded from hlayiso.com 10601/16 QUESTION 3 [20] Ques Solution Explanation Level 3.1.1 Total distance = 89 km RM 2RM Reading from map L1 (2) MP 3.1.2a Drummond RM 2RM Reading from map L1 MP 11:30 OR Half past 11 RM (2) 3.1.2b Approximately 45 km RM 1RM Reading form map L1 (1) MP 3.1.3 Between Botha’s Hill and Pinetown RM 2RM Reading from map L1 OR MP Botha’s Hill to Winston Park RM (2) 3.1.4 Average Speed = 1SF Substitution 1CA Answer 89 km NP for rounding = SF L1 6,5 h MP = 13,6923 … km/h ≈ 13,69 km/h CA (2) 3.1.5 Just after Drummond is an uphill 5A One mark per Slight uphill on Botha’s hill A description Small downhill down Botha’s hill A L2 Steepest sloping uphill A MP Steepest sloping downhill A Long downhill run A (5) 3.2.1 1 : 500  RM 2RP Reading from plan L1 (2) MP 3.2.2 Every 1 unit on the plan represents 500 units 2RP Reading from plan in actual dimensionsRP No units of L1 measurements necessary MP e.g. cm, mm, m. (2) 3.2.3 South Western Wall = 9,8 cm RP 2RP Reading from plan L1 (2) MP [20] 9

Downloaded from hlayiso.com 10601/16 QUESTION 4 [35] Ques Solution Explanation Level 4.1.1 12 MA 2MA Adding the number of ages L1 (2) D 4.1.2 6 hours 11 minutes 59 sec  RT 2RT Reading from table OR L1 06:11:59 (2) D 4.1.3 Time range = 5h 38m 01s ‒ 3h 38m 10s 1MA Subtracting correct MA values 1A Answer = 1h 59m 51s A L1 Answer only full marks D (2) 4.1.4 Mean age = 1MA Concept of mean 1M Denominator MA 1A Answer = M L2 D = 19,1 ≈ 19 years A (3) 4.2.1 Mode = 292 minutes A 1A Correct Mode L1 (1) D 4.2.2 Mean = 193 + 220 +…+ 372 1A Mean 9 1MA Mean time 1C Conversion 2 478 = 9 = 275,33 minutes A L3 D 275,33 Mean time = MA 60 = 4,5888 … hours (3) = 4 hours 35 minutes C 10

Downloaded from hlayiso.com 10601/16 Ques Solution Explanation Level 4.2.3 228; 237; 250; 251; 281; 292; 292; 306; 329; 338 1MA Ascending order MA 1MA Concept of median 1A Answer Median = 281 + 292 MA L2 2 D = 286,5 minutes A (3) 4.2.4 Range = Highest ‒ Lowest 1MA Concept of range 1A Answer = 372 ‒ 193 MA L1 Answer only full marks D = 179 minutes A (2) 4.3.1 Baised AA 2RG Reading from graph L1 (2) D 4.3.2 (a) Only a definite number of values is possible. The data takes only certain 2J Justification L1 values. E.g. the number of learners in a D class. (One cannot have ‘half a learner’.) (2) (b) Information can be measured continuously. An infinite number of 2J Justification L1 steps. (2) D 11

Downloaded from hlayiso.com 10601/16 4.4.1 L2 D 1A 50 1A 100 6A for the 6 points correctly plotted 1A 100 1A 150 1A 75 1A 175 (6) 4.4.2 Profit = R8,00 x 26  M 1M x 26 = R208,00  AA 2A Answer Answer only full L1 marks D (3) 4.4.3 Tuesday  and Thursday  RT 2RG Reading from table L1 (2) D [35] 12

Downloaded from hlayiso.com 10601/16 Question 5 [19] Ques Solution Explanation Level 5.1.1 1 299 men RT 1RT Reading from table (1) L1 D 5.1.2 2 508 men  RT 1RT Reading from table L1 (1) D 5.1.3 Drinkers : High Blood Pressure 1MA Ratio with correct values 2552 : 688 MA 1AR Answer and rounding L1 3.709 :1 D 4 :1 AR (2) 5.1.4 P(No High Blood Pressure) = 2 508 1MA Numerator L2 3 119 MA 1A Denominator D (2) 5.2.1 P = Current reading ‒ Consumption 1MA Subtraction 1A Answer = 125 334 kℓ ‒ 34,5 kℓ MA L1 Answer only full marks M =125 299,5 A (2) 5.2.2 ≤6kl free 1M First 2 charges 9 × R8,60 = R77,40 1M Multiply by 9,5 10 × R9,60 = R96.00 M 1CA Answer L1 9,5 × R10,60 =R100,70 MA F Total (Q) = R274.10 CA (3) 5.2.3a 1M Calculation of first three ≤4kl free tariffs 3 × R4,67 = R14.01 1MA Dividing amount 8 × R9,94 = R79,52 remaining by R14,60 R93,53 1CA Answer L3 FM Remaining amount = R181,60 ‒ R93,53 = R88,07 M (3) 5.2.3b Remaining kℓ = 1MA Calculate remaining kl used 1CA Answer = 6,03 kℓ MA L3 R = 4kℓ + 3kℓ + 8kℓ + 6,03kℓ FM = 21.03 kℓ CA (2) 13

Downloaded from hlayiso.com 10601/16 Ques Solution Explanation Level 5.2.3c S = 14% of (R181,60+ R274,10) MA 1MA 14% of correct amounts 1S Simplification of S= × R455,70 S bracket 1A Answer L1 M S = R63,798 (3) S = R63,80 A 5.2.4 T = R63,80 + R 455,70 M 1M Addition 1CA Answer L1 T = R519,50 CA M Answer only full marks (2) [19] TOTAL: 150 14