SENIOR CERTIFICATE EXAMINATIONS

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SENI CERTIICATE EXAMINATIONS MATHEMATICAL LITERACY P2 2017 MARKING GUIELINES MARKS: 150 Codes M MA CA A C J S R S O P R NP Explanation Method Method with Accuracy Consistent Accuracy Accuracy

1 SENI CERTIICATE EXAMINATIONS MATHEMATICAL LITERACY P MARKING GUIELINES MARKS: 150 Codes M MA CA A C J S R S O P R NP Explanation Method Method with Accuracy Consistent Accuracy Accuracy Conversion efine Justification/Reason/Explain Simplification Reading from a table a graph a diagram a map a plan Choosing the correct formula Substitution in a formula Opinion Penalty, e.g. for no units, incorrect rounding off, etc. Rounding Off No penalty for rounding omitting units These marking guidelines consist of 15 pages.

2 Mathematical Literacy/P2 2 BE/2017 KEY TO TOPIC SYMBOL: = inance; M = Measurement; MP = Maps, plans and other representations H = ata Handling; P = Probability. QUESTION 1 [39 Marks] (a) A 3 Probability = 15 A = 0,2 6 members scoring decreased: 6 out of 15 team members 6 A MA As a percentage = 100% 15 = 40% Arranging scores in ascending or descending order: 1A numerator 1A denominator 1CA simplification AO 1A no. decreased 1MA percentage with denominator 15 1CA simplification AO P 27; 28; 30; 32; 34; 38; 41; 42; 43; 43; 44; 46; 53; 56; 62 MA Median is 42. 1MA ordered data 2A median AO A (b) 43 2A mode (c) IQR = upper quartile lower quartile = Q3 Q1 RT = RT = 14 A The interquartile range of 1 st tournament is smaller than that of the 2 nd tournament (i.e. 14 compared to 50) Range of scores is smaller (i.e. 35) in the 1 st tournament compared to a range of 90 points scored in 2 nd tournament. Majority improved their scores. CA from 1.1.3(a) 1RT 46 1RT 32 1CA IQR value 2J comparison 2J comparison

3 Mathematical Literacy/P2 3 BE/2017 Highest score by a player in 1 st tournament is 38 points less than a player in 2 nd tournament. The interquartile range of 2 nd tournament is higher that of 1 st tournament (i.e. 50 points higher than 14 points). The lowest score of tournament 2 is 17 less than the lowest score in tournament 1. 2J comparison 2J comparison Players' performance in Tournament 1 were more consistent because the IQR is smaller and also the range is smaller. MA Points : 3 1 = = = 9 M Point scored = = 28 A 2J comparison 2J comparison (4) 1MA point in relation to position (multiply) 1M adding points 1A accumulated points Player 1CA player MA M A = 28 points Player 45 : 3,66 MA C 0,45 : 3,66 1MA balls multiply by points 1M adding 1A total points 1CA player AO (4) 1MAwriting in correct ratio 1C to cm to m M 15 : 122 1CA answer 45 : 3,36 45 : 366 MA C 1MAwriting in correct ratio 1C to m to cm 15 : 122 1CA answer

4 Mathematical Literacy/P2 4 BE/ Shaded Area = πr 2 (hoop) πr 2 (ball) A M = 3,142 (22,5cm) 2 A S 3,142 (12,4cm) = 1 590,6375 cm 2 483,11392 cm 2 = cm 2 Area of circle (hoop) = (radius) 2 A = 3,142 (22,5) 2 S 1A radius hoop 1A radius ball 1M subtracting 1S values 1CA area in cm 2 1CA area occupied by the ball 1CA answer 1A radius 1S correct values M = 1 590,6375cm 2 1CA area Area occupied by the ball = (radius) 2 A = 3,142 (12,4) 2 = 483,11392 cm 2 M Shaded area = 1 590, ,11392 cm 2 1A radius of a ball 1CA area occupied by the ball 1M difference 1.3 Proportional price money: = 1 107,52358 cm 2 1CA answer NPR (7) M 3 Y group share R8,1 mil = R2,7 mil 9 MA Each member of Y group will receive = O The player was correct. 2,7 million 5 M = R0,54 mil. C 0, = R MA getting 9 1M multiply by ratio 1CA price money to share 1M divide by 5 1CA each member share 1C to 1000s 1O conclusion based on calculation (7)

5 Mathematical Literacy/P2 5 BE/2017 Group Y receives 9 3 of the share Each member receives 5 1 A MA 2MA correct ratio 1A each member's share M A player from Y = 3 8,1 million 45 = 0,54 million = R C The statement is correct O 1M multiply with ratio 1CA simplification 1C conversion 1O conclusion (7) [39]

6 Mathematical Literacy/P2 6 BE/2017 QUESTION 2 (37) (a) RT Amount (106,18%) = R14,44 A K = R14,44 106,18 % or = R13,599 1RT correct values 1A dividing by 106,18% = R13,60 R RT (b) Q = [(11,50 10,88) 10,88] 100% = 5,7 1R value in rand 1RT correct values 1M subtracting values 1M percentage change 1CA value (c) RT 0, ,2 + 7,82 + 2,28 + 6,18 +5, ,07 +11,34 + Q = 6,00 x 10 Q = 60 54,32 = 5,68 1RT correct values 1M mean concept 1M subtracting values 1CA answer NPR A 0,99 17,32 15,07 5,99 9,42 8,16 4,46 9,04 10,27 15,64 E = A 10 A 96,36 = 10 = 9,64 Apr to Jan. 2016: both prices increased. 2J both increased (4) L 2 1MA adding values 1MA mean concept 10 1CA mean value Jan to Apr. 2016: J The price of the 600 g loaf of white bread remained the same (is constant). J The price of the 700 g loaf of white bread increased 1J 600 g constant 1J 700 g increased

7 Mathematical Literacy/P2 7 BE/ Per period per bread 600 g: Apr 2015 Jan 2016 : The price increased. J Jan 2016 Apr 2016: The price remained the same. J 700 g: Apr 2015 Jan 2016 : The price increased. Jan 2016 Apr 2016 The price increased. He will have to adjust his spending to cater for the increased price. That is money that he was saving to use for other things will be used for wheat products. Will experience financial difficulties (i.e. unable to afford bread any longer). If he buys the wheat products it will cost him more and he will have less money to spend on other stuff Can buy less and less Any other valid reason A 2.2 Increase in 2017 = 6,6% R6,72 = R0,44 A Increased price = R6,72 + R0,44 A = R7,16 J J 600g: 1J both increased 1J constant 700g 1J increased 1J increased 2J explanation 2J explanation 2J explanation 2J explanation 2J explanation (4) 1MA multiplying correct values 1A increase amount 1M adding 1CA increased price Increase in 2018 = R7,16 6% = R0,43 Increased price = R7,17 + R0,43 = R7,59 A A 2017: R6,18 1,066 = R A7, : R7,16 1,06 = R7,59 A A R6,72 1,066 1,06 A = R7,59 1CA increase % 1CA increased price (6)

8 Mathematical Literacy/P2 8 BE/ S V = 690 mm 445 mm 180 mm = mm Number of crates lengthwise 2 = 0,69 C Or = 2,89 2 crates Number of crates breadthwise 2 = = 4,4 0, ,89 1S correct values 2CA volume P if units is wrong 1C conversion 1M dividing 1CA number length wise M M 4 crates Now the remaining space is 0,62 m 2 m Turn crates: 1 more fit in 0,62 and two down 0,445 Total = (2 Lengthwise 4 breadth wise + 2) 9 on top of each other = 90 crates 1CA number 1M finding the total Number 1CA number of crates 80 will fit Layout: J 1J reason (7)

9 Mathematical Literacy/P2 9 BE/ R5 350 Cost price per bread = 80 8 = R8,36 A C Number of loaves to break even = SP CP S R1 720,70 = R11,50 R8,36 = 548 1M dividing 1A total number of loaves 1CA cost price 1S substitution 1CA number of loaves (5) [37]

10 Mathematical Literacy/P2 10 BE/2017 QUESTION 3 (38 marks) Total population = 41,1% RT 1RT correct values 1M dividing by % = ,75 1CA population (a) P(White female) = (b) R people MA 1 = 0,042 4,2% 24 Total males = RSA population emale population 1R number of people 1MA numerator and denominator 1CA simplification AO (4) P P = = P(male) = MA = 0, ,49 48,97% 1MA difference 1CA males total 1CA probability P(female) = = 0, ,51 or 51,03% 1A P(female) P(male) = 1 0, or 1 0,51 or 100% 51,03% 2016 = = 0, or 0,49 or 49,97% % A = 2, ,4% 1A subtracting from 1 1CA P(male) 1MA numerator and denominator 1M multiply by 100% 1CA percentage 2015 = or 2014 = MA % 100% MA numerator and denominator = 2,4% = 2,4% 1CA percentage

11 Mathematical Literacy/P2 11 BE/ Afri A 2014: 100% (80,2% + 8,9% + 8,5%)= 2,4% MA 2015: 100% (80,4% + 8,9% + 8,3%)= 2,4% 2016: 100% 80,6% 8,9% 8,1% = 2,4% Total distance of a space and a post = 100 mm + 40 mm Or 0,1 m + 0,04 m = 140 mm A = 0,14 m 1MA subtracting from 100% 1M adding other values 1CA percentage 1MA another year 1CA another year (5) 1A correct distance M istance between posts that must have a space and a post = mm 100 mm Or 3,460 m 0,14 m = 3 360mm = 3,360 m Convert to m 1M subtracting Number of small posts = 140 = 24 Total number of post = = 26 Or 3,360 0,140 = 24 irect sunlight coming into the rooms through the windows or doors for much longer. 1M adding lengths and dividing 1CA number of small post (4) 2J sun and time MP Sun spend most of the time on the north side of the house. It is the side on which the sun shines most of the time during the day. Open outward because they have short width O O esigned to store things, as such they will obstruct inward opening of the doors. O Storage space will be lost if doors open inwards 2J direction and time 2J sunshine 2O wideness 1O purpose 2O space MP O O Other rooms open inward. Their purpose is entrance into the room. 1O way of opening 1O purpose

12 Mathematical Literacy/P2 12 BE/ Carpeted floor = Area of a Passage + ining + Living rooms M R area = 3,3274 3,6576 S = 12, m 2 LR area = 4,5720 4,2672 = 19, m 2 Area of passage = 15% of (12, ,51) 1S finding area 1CA area of R 1CA area of LR 1M finding 15% = 15 % of 31,68 m = 4, m 2 1CA area of passage Total area = 12,17 m ,51 m 2 + 4,75 m 2 = 36,43 m 2 37 m 2 R Labour Cost: R R70 = R R2 590 = R4 190 A 1M adding 3/4 values 1CA total area 1R rounding [Max 6 marks if total area is calculated] (8) Area CA from above 1MA finding labour 1CA labour cost Number of boxes = 37 2,15 = 17, M dividing by 2,15 Cost for Boxes: 18 R299,90 = R5 398,20 1CA cost of boxes Number of underlay rolls: = 3,7 4 Underlayer: 4 R56,90 = R227,60 Total cost = R R5 398,20+ R227,60 = R9 815,80 A 1CA underlayer cost 1MA adding all 3 cost types 1CA total cost The budget is sufficient. O 1O conclusion (8) [38]

13 Mathematical Literacy/P2 13 BE/2017 QUESTION 4 [36 marks] RT RT RT Tax bracket 3, 4 and 5 Tax bracket 1 may be included due to typing error 1RT bracket3 1RT bracket 4 1RT bracket 5 $ $ $ $ $ and over. RT RT RT 1RT interval bracket 1RT interval bracket 1RT interval bracket $0 $1 200 Pay extra 2% on taxable income O 2O reason O The levy is an extra tax on their income. O Higher income earners are subjected to an extra tax in addition to usual income tax rates. 2O reason 2O reason

14 Mathematical Literacy/P2 14 BE/ Tax due 2016: RT A = $ % ( $ ,26 $ ) = $ % $ ,26 =$ $49 186,47 1MA correct values 1 RT correct values /4 =$ ,47 1CA tax due Medical levy = $ ,26 2% = $5 786,07 A Total due = $ ,47 + $5 786,07 = $ ,54 1MA levy value 1CA total due Tax due 2017: RT A = $ % ($ $ ) 1RT tax bracket 1MA correct values = $ % $ = $ $ ,45 = $ ,45 1CA tax due Medical levy = 2% $ = $6 220,02 Total for 2017: $ ,45 + $6 220,02 = $ ,47 Tax due difference: $ ,47 $ ,54 1CA total 1M finding difference = $9 882,93. 1CA simplification The statement is VALI. O 1O conclusion A A A Mary Rose restaurant; enmark hotel; Civic Centre 3A venues Accept hotel (12) MP

15 Mathematical Literacy/P2 15 BE/ O Because it runs over the river. 2O reason MP O Portions of a river not visible from above where the 2O reason highway crosses or passes the river. RT RT RT North west NW West of North 2RT direction Turn right walk along Walker Str A Turn right into Strickland Str A Pass South Coast Highway And turn left into Mount Shadforth Rd A Restaurant will be on his right Turn SW into Walker Street and proceed. A At the corner turn NW and continue. A Cross South Coast Highway Turn W into Mount Shadforth Rd. A The restaurant is on the northern side of the road. Measured distance between = 23 mm MA 1A route and turn 1A route and turn 1A turn and road 1A route and turn 1A route and turn 1A turn and road 2MA measuring MP MP MP Scale 23 mm is 100 m C How long it will take him = Time = 100m = 1,1m/s istance Speed A A 1C using scale 1A formula 1A speed = 90,91 seconds CA C CA In minutes 90, = 1,52 minutes. O No. He can walk in less than 2 minutes at that speed. 1CA calculating time 1C divide by 60 1CA minutes 1O conclusion C A 2 min = 120 sec A A istance = 1,1 m/s x 120 s = 132 m CA Measured distance = 23 mm Scale 23 mm = 100 m C MA He will be past the Indigo Cuisine restaurant [Accept measurements 23 mm to 25 mm] O 1C multiply by 60 1A time in seconds 1A speed 1A formula 1CA distance 2MA measurement 1C using scale 1O conclusion (9) [36] TOTAL: 150

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NATIONAL SENI CERTIFICATE GRADE 12 MATHEMATICAL LITERACY P2 FEBRUARY/MARCH 2009 MEMANDUM MARKS: 150 Symbol M MA CA A C S RT/RG F SF J P R Explanation Method Method with accuracy Consistent accuracy Accuracy