MATHEMATICAL LITERACY

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Basil Stafford
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1 MATHEMATICAL LITERACY PAPER GRADE 1 PRELIMINARY EXAMINATION 11 September :00 This memorandum consists of 11 pages.

2 MARKING GUIDELINES MATHEMATICAL LITERACY PAPER Symbol M M/A CA A C D J S RT/RG F SF O P R Explanation Method Method with accuracy Continuous accuracy Accuracy Conversion Define Justification/ Motivation/ supply a reason Simplification Reading from table OR graph OR diagram OR map OR plan Choosing of correct formula Substitution in formula Opinion/Example/Deduction/conclusion Penalise for example no units incorrect rounding etc. Rounding Page of 11

3 QUESTION R0 416, = R65 416, 71 (Gross annual income) - R14 700, 00 (Annual pension fund contribution) = R50 716, 71 (Annual taxable income) 1.1. Tax bracket = R (6 R60 836, ) = R R15 817, 54 = R49 995, 54 - R (primary rebate) = R36 360, 54 (tax per annum) Therefore: R36 360, 54 1 = R3 030, 05 (tax per month) R0 416, 67 (gross monthly salary) 1. R1 5, 00 (pension fund contribution) R3 030, 05 (tax: PAYE) = R16 161, 6 (Net monthly salary) , = = 4.66% 1 M multiply by 13 1 A 1 M subtraction 1 A pension fund A final answer (6) 1 RT correct tax bracket (CA) 1 S R M calculating 6% 1 A for R15 557, 54 1 S R49 735, 54 1 A minus rebate 1 A tax per annum 1 M divide by 1 1 A tax per month (9) 1 M subtract pension fund 1M subtract tax per month 1 CA final answer (3) 1 MA adding correct values 1 MA divide by 10 1 A (3) F 3 F 4 F DH Page 3 of 11

4 , 66% Inflation + real increase = 4, 66 % + 5% = 9, 66% Therefore the teachers claim is INVALID 9, 66% 1, 5% Time travelled = 07:00 06:4 = 18 minutes Distance = speed time = 18 = 0, 3 hours km = speed 0, 3 hours Speed = 16 km 0, 3 hours = 53, 33 km/h 1 MA calculating inflation 1 A for 4, 66% 1 MA adding 5% 1 A J invalid conclusion (6) 1 A time in minutes 1 C Conversion 1 SF 1 M divide 1 A correct answer (5) F 4 M (a) 1 litre = 0, 19 gallons gallons = gallons 1 litre/0,19 gallons = 9, 13 litres C Conversion to litres 1 C Convert 60 miles to km 1 M divide km by litres 1 mile = 1, 609 km 60 miles = 60 1, 609 km = 96, 54 km Consumption rate km/litre = 96,54 km 9,13 l = 10, 57 km/l 1 A final answer (5) M 4 (b) Total km travelled = 16 km 5 = 160 km 1 MA multiply by 1 MA multiply by 5 Amount of fuel use = 160 km 10,57 km/l = 15, 14 litres 1 M divide 160 km by consumption rate 1 CA final answer (4) M 3 Page 4 of 11

5 miles/h = 60 1, 609 km/h = 96, 54 km/h 96, 54 km/h 60 km/h = 36, 54 km/h She was over-speeding 1 C Converting speed to km/h 1 CA answer 1 M use 60 km/h 1 J conclusion/deduction (4) M 4 [45] Page 5 of 11

6 QUESTION m = 4 m V = π r h = 3, 14 (4m) 0, 8 m = 40, m 3 1 MA divide by 1 A answer for radius 1 F correct formula 1 SF 1 M divide by 1 CA answer (6) M 3 Therefore: 40, = 0, 11 m 3.1. Area = π r = 3, 14 (4m) = 50, 7 m Therefore: 50,7.1.3 Volume = l b d = 5, 14 m 136 m 3 = 10 m 8 m h 136 m 3 = 80 m h 136 m 3 80 m = h 1, 7 m = h 1 SF Substitution 1 A for area of swimming pool 1 A for area of semicircular part (3) 1 SF substitute into formula 1 S Simplification 1 M dividing by the area 1 CA Answer (4) M M m 3 + 0, 11 m 3 = 156, 11 m 3 156, 11 m 3 = 156, 11 kl 156 kl 1 MA using the given volume of the rectangular part 1 M adding 1 M using the volume for semi-circular pool 1 CA answer in m 3 1 C for correct rounded off conversion to kilolitres Note: CA from.1.1 (5) F Page 6 of 11

7 .1.5 Number of kilolitres used Cost kilolitre per Total Cost 6 kl Free R0, 00 9 kl R7, 85 R70, kl R11, 9 R169,35 15 kl R13, 05 R195, R14, 00 R1 750 Total exclusive) (VAT R185,75 1 A for 6 free kl 1 A for 15 kl 1 A for R169, 35 1A for R195, 75 1 A for R CA for R 185, 75 CA for R306, 01 1 CA for R 491, 76 O conclusion F 4 VAT (14%) R306, 01 Total inclusive) (VAT R491,76 Therefore: Her statement is INCORRECT. She was overcharged. (11) [9] Page 7 of 11

8 QUESTION North-Westerly direction RG reading from map 3.1. No She will be travelling in the wrong direction to the Northern Cape Take the N and continue west You will pass the following places: Mosselbay, Knysna, Port Elizabeth, East London, Umtata and then Port Shepstone cm : 3 km 3 cm : cm 1 : This means that 1 unit on the map represent units in reality , 4 cm 100 = 1 40 km OR 1: , 4 : Therefore: 1 40 km Time = Distance Speed Time = km 110 km/h = 13, 45 hours Therefore: her statement was INCORRECT. It will take her less than 15 hours. 1 A answer () M & S J Justification () M & S 1 M referring to National road N 1 M referring to direction 1 M referring to at least 3 place (3) 1 RT reading from map 1 C conversion to same unit 1 CA number scale J explanation (5) 1 M measuring correct distance 1 M multiply by scale 1 CA Answer 1 A correct unit (4) 1 M manipulating of formula 1 SF substitution 1 A answer O conclusion M & S M & S 3 M & S 3 (5) M & S 4 Page 8 of 11

9 $350 13, 0 = R MA multiplication F () 3.. R ,14 = R3 997, 37 Therefore: R4 557 R3 997, 37 = R559, 63 1 MA divide by 1, 14 1 M subtraction 1 CA Answer F 3 (4) R = R Therefore: R = R318, 99 Therefore: R R318, 99 = R 3 17, 99 1 M multiply by 7 1 CA Answer 1 M calculating 1% city tax 1 CA answer 1 M Adding 1 CA Answer F 3 (6) [33] Page 9 of 11

10 QUESTION Contestant : A BMI = = mass (in kg) height (in m) 44 (1,55 m) 1 SF Substitution into Formula 1 J Reason = 18, 3 A = Underweight (U) Contestant 7: B BMI = 30 = (1,55) 1 mass (in kg) height (in m) B (1,55) 30 = B = 7, 08 kg B (1,55) (1,55) 1 1 SF Substitution into Formula 1 S Simplification 1 Rounding off DH 4 7 kg (7) 4.1. Contestant is underweight Contestant 7 is overweight Therefore: Her claim is VALID 1 M identifying correct contestant 1 M classification of contestant 1 M identifying correct contestant DH 4 1 classification of contestant 7 1 O conclusion (5) Min: 44 Q1: 55 Q: 59 Q3: 6 Max: 7 IQR = 6 55 = 7 1 A minimum 1 M calculating Q1 M calculating Q 1 M Calculating Q3 1 A maximum M calculating IQR (8) DH 3 Page 10 of 11

11 , 8 m 1, 55 m 1, 55 m = 1, 7 Therefore: 1,7 8 = 1, 59 m Unhealthy lifestyle Wrong eating habits No exercise (Any relevant answer) Eat more fruit and vegetables Exercise Healthy diet 4. (Any relevant answer) 4..1 Raisons = 8 Caramel = 8 Biscuits = 15 1 MA sum total 1 M excluding the two contestants who do not qualify 1 CA sum total 1 M dividing by 8 1 CA Answer (5) for each correct answer for each correct answer = 10% 1 A correct probability concept 1 M calculating percentage 1 CA Answer A numerator A denominator (4) (4) (3) (3) (4) DH 4 DH DH P P P 3 [43] GRAND TOTAL [150] Page 11 of 11

MATHEMATICAL LITERACY

MATHEMATICAL LITERACY PAPER GRADE 2 PRELIMINARY EXAMINATION 04 September 207 09:00 This memorandum consists of 0 pages. MARKING GUIDELINES MATHEMATICAL LITERACY PAPER Symbol M M/A CA A C D J S RT/RG F