Mathematical Literacy Grade 12 IEB Paper 2 2016 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 2016 MATHEMATICAL LITERACY: PAPER II MARKING GUIDELINES Time: 3 hours 150 marks These marking guidelines are prepared for use by examiners and sub-examiners, all of whom are required to attend a standardisation meeting to ensure that the guidelines are consistently interpreted and applied in the marking of candidates' scripts. The IEB will not enter into any discussions or correspondence about any marking guidelines. It is acknowledged that there may be different views about some matters of emphasis or detail in the guidelines. It is also recognised that, without the benefit of attendance at a standardisation meeting, there may be different interpretations of the application of the marking guidelines. Key: a accuracy m method ca continuous accuracy r rounding ma method accuracy Topics F Finance MP Maps and Plans M Measurement P Probability DH Data Handling IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 2 of 11 QUESTION 1 1.1.1 Japan/JPY a country If only value (113,066) = 1 mark 2 OR If table read incorrectly then GBP = 2 marks. If only value (1,43214) = 1 mark 1.1.2 100 £750 × m 104,5 = £717,70 a £717,70 ÷ 0,69820 m dividing 5 a 0,69820 = $1 027,93 ca answer See attached pages for variations 1.2.1 R2 800 a 2 1.2.2 5 + 3 = 8 people on cruise R1 600 per person a R1 600 × 5 ma 3 = R8 000 a If |R2200×5 = R11000 – 1 mark only 1.2.3 6 people (R2 000 each) a 2 1.3.1 65 m2 ÷ 5,5 m a 65 m 2 m dividing = 11,82 m 3 Accept 11,8/11,9/12 (no rounding a penalised) Could use scale to determine length (11,6) 1.3.2 9 + 9 + 5,5 + 5,5 / 2(9 + 5,5) m Adding 4 values = 29 m a Accurate values a 4 Yes, it will be enough. ca No marks if calculated area 1.3.3 The breadth of the lower deck is 2,6 cm m measuring the plan but the breadth of the upper deck is comparing ruler 2,2 cm yet they both equal 5,5 m on the m measurement to actual plan. measurement m explanation makes sense OR 3 28 m = 12,7 cm is not proportional to m measuring the plan 9 m = 7,4 cm comparing ruler Could compare areas visually m measurement to actual measurement m explanation makes sense 1.3.4 The areas are not all calculated correctly. a description Saloon: 13 × 4,75 = 61,75 m2 a Upper deck: 9 × 5,5 = 49,5 m2 3 Could identify rounding as error a Accepted 4,75 instead of 5,5 as error IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 3 of 11 1.4 Needs: 1/2 cup = 16 servings 60 servings = 1,875 cups a 1,875 cups needed 1 cup = 226 grams 1,875 cups = 423,75 grams a 423,5 grams needed Frosting: 3 tablespoons = 16 servings 60 servings = 11,25 tablespoons ca 11,25 tablespoons 1 tablespoon = 14 grams 11,25 tablespoons = 157,5 g 157,5 grams needed for ca frosting Total needed = 423,75 g + 157,5 g m adding frosting = 581,25 grams Has: 2,5 blocks = 625 grams a 625 grams m 250×2,5 He has enough butter to make 60 brownies. ca OR 1 cup + 3 teaspoons 8 2 =113 g + (14 g × 3) = 113 g + 42 g = 155 g ÷ 16 × 60 = 581, 25 g needed 1 2 × 250 g 625 = g ca total butter needed 2 ∴ chef has enough Instead of calculating 2,5 blocks = 625 g, could convert 581,25 g to 2,325 blocks If only brownies or only frosting the max is 5/8 Accepted rounding 3,75 to 4 batches (total needed 620 g) Or 625 ÷ 155=4,03, which is more than 3,75 1.5 First year: no tax indication that there was a no tax paid in first year Second year: R1 650 + 2% × (R740 000 – R500 000) a correct tax bracket = R1 650 + 2% × R240 000 a R240 000 = R1 650 + R4 800 8 = R6 450 ca Total tax paid = R6 450 Total turnover = R1 015 000 a R1 015 000 – R6 450 = R1 008 550 ca turnover minus tax 1 008 550 ÷ 1 015 000 × 100 ma = 99,36% ca correct answer 1.6 R1 837,50 − R1 500 M Correct values × 100 R1 500 m X 100 = 22,5% increase a 6 m per cent divided by time 22,5% ÷ 1,5 years a 1,5 = 15% per annum IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 4 of 11 Or SI = P(1 + I x n) 337,5 = 1500 x I x 1,5 a 337,50 0,15 = i a Substitution 0,15 x 100 = i a 0,15 15% = i m 0,15 ca answer Or A = P(1 + i x n) 1837,50 = 1500(1 + i x 1,5) 1,225 = 1 + i x 1,5 0,225 = i x 1,5 0,15 = i 0,15 x 100 = i 15% = i Or 1837,5 – 1500 = 337,50 337,5 / 18 = 18,75 18,75 x 12 225 / 1500 x 100 = 15% 1.7.1 R13 500 ÷ R1 700 m = 7,9 a 3 = 7 full days car rounded down 1.7.2 R13 500 ÷ 10 = R1 350 per day a budget per day 60% × R1 350 m 3 = R810 for accommodation ca 55 QUESTION 2 2.1 24 m ÷ 91 steps m = 0,2637 m per step 0,2637 × 50 steps m = 13,19 m a 3 OR 50 ÷ 91 × 24 m = 13,19 m a OR 91 − 50 × 100 50 m = 45,05% = 24 m × 45% m = 24-10,8 m = 13,2 m a OR 91÷50 =1,82 =24÷1,82 =13,18 IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 5 of 11 OR 91÷24 = 3,79 50 ÷3,79 = 13,19 OR Pythagoras only OR Pythagoras and went on making calculations 2.2 Walking up the stairs: 91 × 0,17 calories m = 15,47 calories a Walking down the stairs: 91 ÷ 20 m = 4,55 calories a Total: 15,47 + 4,55 = 20,02 calories ca Drink: 100 ml/g = 38 calories 330 ml/g = 125,4 calories a 125,4 ÷ 20,02 m = 6,3 times up AND down/7 times ca OR 91 × 0,17 × 5 = 77,35 calories m × 0,17 a ×5 a 77,35 91 ÷ 20 × 5 = 22,75 calories m ÷ 20 8 a 22,75 77,35 + 22,75 = 100,1 calories ca 100,1 ∴ more than 5 times required ca 125,4 a 125,4 calories in drink OR 38 calories 0,17 cal : every step 38 calories : 𝑥𝑥 m 𝑥𝑥 = 224 steps a m 1 calorie : 20 steps down 38 calories : 𝑥𝑥 m 𝑥𝑥 = 760 steps down a = 760 – 224 steps ca = 536 steps ÷ 91 m = 5,89 and reason Must have reason for 2nd ca mark 2.3 Width of step = 1,3 cm/13 mm (12 mm) a plan measurement Scale: 4,5 cm = 30 m a scale measurement 3 cm = 20 m 4 1,5 cm = 10 m ∴ 1,3 ÷ 4,5 × 30 m = 8,7 m (8 m  8,9 m) ca answer OR 1,3 cm a 1 mm = 0,2 a ÷ 0,2 m IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 6 of 11 6,5 m ca OR 1,2 cm a 1 mm = 0,2 a ÷ 0,2 m 6m ca OR 1,2 cm a 2,9 cm a 4,4 cm m 7,9 m ca OR 7 mm represents 5 m a 1 mm = 0,714 m a Answer x 13 m =9,29 m ca OR 6 mm represents 5 m a 1 mm = 0,833 a Answer x 13 m =10,83 m ca ≈ 11 OR Measuring the base a 8,5 cm represents 55,3 m a 1 cm represents 6,5 m m = 8,45 m ca 2.4 North West OR WNW OR westerly/north a 2 westerly 2.5 Vcube = 20 cm × 20 cm × 20 cm m Vcube = 8 000 cm3 a Vpyramid = 8 000 cm3 ÷ 6 3 Vpyramid = 1 333,33 cm3 No penalty for not ca rounding Vpyramid ≈ 1 300 cm3 OR Vpyramid = 20 × 20 × 10 m Vpyramid = 4000 ÷ 3 3 a Vpyramid = 1333.33 ca 2.6.1 Distance Speed = m changing formula Time 193 = m 2 2 2 (2,03 hr) 2 60 3 60 =94,92 km/h a 2.6.2 15,5 km × 11 m =170,5 km a ∴ He will need to stop. ca OR 193 km ÷ 15,5 km 3 = 12,45 ℓ One tank = 11 ℓ ∴ he must stop. IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 7 of 11 OR 1 𝑘𝑘𝑘𝑘 = 0.66 𝑙𝑙 11 = 183.3 𝑘𝑘𝑘𝑘 𝑝𝑝𝑝𝑝𝑝𝑝 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 0.66 ∴ ℎ𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑢𝑢𝑢𝑢 2.6.3 Time at the airport = 5:05 a.m. to 2:45 p.m. = 9 hours 40 minutes a Time away from airport = 9 hours m 40 minutes – 1 hours 30 minutes = 8 hours 10 minutes a Travel time = 2 hours 20 minutes × 2 m 7 = 4 hours 40 minutes a ∴ Time at El Castillo = 8 hours 10 m minutes – 4 hours 40 minutes = 3 hours 30 minutes a (Variations in order accepted) 33 QUESTION 3 3.1 The cost of buying 60 ℓ (or full tank) of A mentioning it is the cost petrol on 3 July 2013 (or cost of R13,23) 2 A mentioning the date Or just a calculation of 60 ℓ × R13,23 = R793,80 3.2 The graph is not referring to the quantity explanation logical and of petrol, it is referring to the increasing A 2 correct cost of purchasing the 60 ℓ. 3.3 1 tube toothpaste = R9 A R127,80 ÷ 9 M 3 = 14,2 tubes OR 14 tubes (if round up to a 15 or down to 13 only get 2�3) 3.4 140 km A R151,20 or R150,77 (140 ÷ 13 × 14) no penalisation for A rounding 20 km A 5,4 or 5,38 A R21 or R21,54 (20 ÷ 13 × 14) A R473,80 or R473,91 or R473,37 or ca R474,34 6 13 IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 8 of 11 QUESTION 4 4.1 Bar graph A 2 4.2 44,1 + 42,3 + 41 + 40,6 + 39, 2 M adding 5 values 5 ma dividing by 5 207, 2 4 = A numerator 5 = 41,44 g ca ca only if divided by 5 4.3.1 31,7 g 33,7 g 35 g 36,3 g 36,4 g 37 g 39,2 g 40,6 g 41 g 42,3 g M 3 44,1 g A Median = 37 g A 4.3.2 No A 2 4.3.3 44,1 g – 31,7 g M A 3 = 12,4 g A 4.3.4 Mean A 3 There is no outlier. A 4.4 Play energy drink: 250 ml: 29,2 g Mark allocated for M division/ ratio 100 ml = 11,68 g A 11,68 g Lemon Twist: 330 ml: 39,2 g Mark allocated for M division/ ratio 100 ml = 11,88 g A 11,88 g Lemon Twist contains more sugar per According to learner's ca 100 ml answer 1250 330 = 3,79 tins in a bottle 5 3,79 × 44,1 = 167,14 𝑔𝑔 in bottle 167,14 × 100 = 13,4% 1250 ∴ 13,4%𝜖𝜖 > 13% thus yes. OR 29,2 ÷ 250 1:0,1168 100:11,6 39,2 ÷ 330 1: 0,1187 100: 11,88 4.5 44,1 g Dividing by 330 × 100 M Using two correct 330 ml values correctly = 13,36% A ∴1,25 ℓ bottle will also contain 13,36% 5 sugar as the amount of sugar per ml will be the same ratio. OR 1 250 ml : 167,05 g IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 9 of 11 167,05 g × 100 1 250 ml = 13, 4% ∴ Yes, it is correct to say so. OR 13% of 1250 = 162,6 g 1250 ÷ 330 = 3,78 44,1 × 3,78 = 167,05 g Or Correct calculations without units 5/5 Or Correct Calculations but units filled in 4/5 Or 13% × 330 = 42,9 44,1 > 13% ∴ 𝑌𝑌𝑌𝑌𝑌𝑌 4.6 Cream Soda = 36,4 g A value from graph 36,4 × 12 000 000 A 12 000 000 = 436 800 000 gram ca answer in gram 6 = 436,8 ton ca answer in ton 436,8 × R537 ma = R234 561,60 ca IEB Copyright © 2016 PLEASE TURN OVER

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 10 of 11 4.7 4 litres = 4 000 ml 4 000 ml × 4 weeks = 16 000 ml per month 16 000 ml/16 ℓ per A month 330 ml = 35 g = 7 teaspoons A 7 teaspoons per can 16 000 ÷ 330 M = 48,48 … cans A 7 × 48,48 … or 7 x 48 ma X 7 ≈ 340 teaspoons = 336 car rounding up to nearest car teaspoon OR 7 teaspoons per can A 4 000 ÷ 330 M = 12,12 … cans per week 12,12 … × 7 or 12 x 7 = 84 M = 84,84 … teaspoons per week 6 84,84 … × 4 A ×4 = 339,39 teaspoons 336 ca ≈ 340 teaspoons rounding up to nearest car teaspoon OR 330 g = 7 teaspoons A 7 teaspoons per can A 16 000 g 16 000 g = ? M = 339,39 teaspoons ca ≈ 340 teaspoons OR 35 rounding up to nearest 330 × 1000 = 106,06 car teaspoon 106,06 × 16 = 1696,97 1696,97 5 = 339,39 = 340 teaspoons 39 QUESTION 5 1 ma rk 5.1 A 6 𝟔𝟔 1 mark Bicyle 10 A Taxi (both) 3 2 A 2 Sunny day Taxi 7 10 A 1 𝟐𝟐 Father A 4 Getting to 10 school 6 𝟏𝟏 Bicycle 10 𝟒𝟒 5 a 4 Rainy day Taxi 7 10 𝟒𝟒 Father 10 IEB Copyright © 2016

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE: MATHEMATICAL LITERACY: PAPER II – MARKING GUIDELINES Page 11 of 11 5.2 3 2 3 × A fraction 7 10 7 6 3 fraction correct based on = or ca their tree diagram 70 35 4 OR 0,09 / 0,0857… Multiplying M Answer (based on their ca two fractions) 10 Total: 150 marks IEB Copyright © 2016