NATIONAL SENIOR CERTIFICATE GRADE 12

Transcription

1 NATIONAL SENI CERTIFICATE GRADE 1 MATHEMATICAL LITERACY P NOVEMBER 009 MEMANDUM MARKS: 150 SYMBOL A CA C J M MA P R RT/RG S SF O EXPLANATION Accuracy Consistent accuracy Conversion Justification (Reason/Opinion) Method Method with accuracy Penalty, e.g. for no units, incorrect rounding off, etc. Rounding off Reading from a table/reading from a graph Simplification Correct substitution in a formula Own opinion This memorandum consists of 3 pages. EXTERNAL MODERAT MR M.A. HENDRICKS INTERNAL MODERAT MRS J. SCHEIBER Please turn over

2 Mathematical Literacy/P DoE/14 November 009 QUESTION 1 [9] Penalise only once for rounding off Limpopo and Western Cape A Solution Difference = 30,1% 6,7% = 3,4% 1CA Solution If name provinces incorrectly but do the subtraction from the computer data correctly :1 mark 1.1. Did not use a computer = (100% 9,1%) of M Subtraction of % = 90,9% of = 88 06,6 1A Solution (or 88 07) 1CA Rounding up or rounding down 9,1 % of = 8 911,738 Did not use a computers 1A Number using computers (could round off here) = ,738 = 88 06, (or 88 07) 1M Subtraction 1CA Rounding up or rounding down

3 Mathematical Literacy/P 3 DoE/14 November A Difference in % Difference in % = 61,8% 13,% = 48,6% Difference in usage = 48,6% of M Calculating % = 18 61, CA Solution No. of cellphone users No. of computer users = 61,8% of ,% of = , ,38 = 18 61, M Calculating % and subtraction 1A Simplification 1CA Solution Total number of households surveyed = M Multiplying = A Total surveyed Number surveyed in Mpumalanga = ( ) 1M Subtraction of households 1M Addition of given values = = CA Solution x Mean = = M Calculating mean 1A Correct substitution x = x = x = M Calculations 1CA Multiplication 1CA Solution (5)

4 Mathematical Literacy/P 4 DoE/14 November O The provinces with high cellphone usage have a 4O Acceptable/relevant corresponding relatively high computer usage. opinion The provinces with a low cellphone usage have a corresponding relatively low computer usage. O Cellphone usage is more. O Give a valid reason or calculation O O Acceptable/relevant opinion O Valid reason or calculation O No trend in NC, MPU and LIM. O Any other justification 1..1 Increase for P500 = = 540 or Increase for Q600 = = 900 Q600 has the greatest increase in sales O No trend O Valid justification (4) 1A Range of P500 Range of Q600 A Highest range If give correct answer and no calculations : marks

5 Mathematical Literacy/P 5 DoE/14 November Width of screen on diagram = 18 mm to 0 mm 1A Width on diagram Length of screen on the diagram = 36mm to 38 mm 1A Length on diagram Scale is :5. This means that the actual width is 5 (or,5) times the given width. 5 Actual width of screen = 0 mm = 50 mm 5 Actual length of screen = 38 mm = 95 mm Scale drawing : width of screen : 5 = 0 : x x = 5 0 1M Using the given scale 1CA Actual width 1A Actual length 1M Using the given scale 1A Width on diagram 100 x = = 50 mm width of screen = 50 mm 1CA Actual width Scale drawing : length of screen : 5 = 38 : y 1A Length on diagram y = 38 5 = 95 length of screen = 95 mm NB: Width with 18 mm = 45 mm Width with 19 mm = 47,5 mm Length with 36 mm = 90 mm Length with 37 mm = 9,5 mm 1A Actual length ANSWERS ONLY FULL MARKS 4 marks if correct answer given in cm (5) 1..3 Graph B Q600 O The graph was drawn with the months reversed. A Identifying the graph 1O Support of statement 1.4.6

6 Mathematical Literacy/P 6 DoE/14 November 009 QUESTION [34] Penalise only once for rounding off.1.1 Percentage using other languages = 100% (64,4% + 11,9% + 9,1%) = 100% 85,4% = 14,6% Number speaking other languages 1A adding the given percentages 1CA Subtracting from 100% = 14,6% of = , M Calculating % of population 1CA Rounding Percentage speaking Sesotho = 64,4% of = ,4 Percentage speaking Afrikaans = 11,9% of = ,4 Percentage speaking isixhosa = 9,1% of = ,6 1A calculating number 1A calculating number 1A calculating number Number speaking Sesotho, Afrikaans and isixhosa = , , ,6 = 53 6,4 Number NOT speaking Sesotho, Afrikaans and isixhosa = ,4 = , CA Rounding (4) ANSWER ONLY FULL MARKS

7 Mathematical Literacy/P 7 DoE/14 November P(Afrikaans and isixhosa) = 1% P(not Afrikaans and isixhosa) 1A Identifying the percentage = 100% 1% 1M Subtraction = 79% (or 0,79 or or ) CA Solution Percentage speaking Afrikaans and isixhosa = 11,9% + 9,1% = 1% Percentage not speaking Afrikaans and isixhosa = 100% 1% = 79% P(not Afrikaans and IsiXhosa) = 79% Percentage speaking Afrikaans and isixhosa = 0,1 Percentage not speaking Afrikaans and isixhosa = 1 0,1 = 0,79 1A Identifying the percentage 1M Subtraction 1CA Solution 1A Identifying the percentage 1M Subtraction 1CA Solution Percentage not speaking Afrikaans and isixhosa = % speaking other languages + % speaking Sesotho = 14,6% + 64,4% = 79% 1A Identifying the percentage 1M Addition 1CA Solution

8 Mathematical Literacy/P 8 DoE/14 November (a) They are children / the elderly,/people who are sick/ill / don t have an identity document / may A Any two valid reasons for not speak the correct language for the area/lack them being unemployed of skills/ lack of qualifications Accept any other possible correct reasons. ().1.3(b) Workforce = 60% of = Unemployed = 6,4% of S = , Unemployed = 6,4% 60% = ,04 S M Calculating % 1A Workforce 1M Calculating % of unemployed 1S Simplifying 1CA Number unemployed (rounded up or down) 1M Calculating % 1A Workforce 1M Calculating % of unemployed 1S Simplifying 1CA Number unemployed (rounded up or down) If only work out 6,4% : marks (5) Gauteng has the highest economic activity in the country. It has many mines and most of the large factories, head offices of companies and banks, as well as the Stock Exchange are in Gauteng. J J Candidates valid reasons (1 mark per reason; must have sentences; do not accept single words) () 1.4.4

9 Mathematical Literacy/P 9 DoE/14 November (a) Total area of South Africa = ( ) km = km Land for farming = 80% of km = km 1M Addition 1A Total 1M Calculating 80% 1CA Total area for agriculture Free State = 10,6% of SA = M Calculating % SA = km 10,6% = ,434 km 80% of ,434 km = ,547 km 1A Area of South Africa 1M Calculating % km 1CA Total area for agriculture (4)

10 Mathematical Literacy/P 10 DoE/14 November 009..(b) Arable land = 11% of km 1M Calculating 11% = ,9 km ha = ,01 km = km C 1CA Arable land in the country 1C Conversion % arable land in the Free State 3000 km = 100% ,9 km = 9,88 % 9,83% R 1M Calculating % 1R Rounding off Continuing from nd solution in.. (a): Arable land = 11% of km = ,88 km = ,88 0,01 ha C 1M Calculating % 1CA Arable land in the country 1C Conversion = ha % arable land in the Free State = ha ha 100% 1 1M Calculating % 9,77% R 1R Rounding off (5)

11 Mathematical Literacy/P 11 DoE/14 November (a) The province with the smallest land surface is 1A Identifying Gauteng Gauteng Population density (GAU) people = km = 569,55... people/km 570 people/km 1M Substitution in formula 1CA Simplification Correct calculation without mentioning Gauteng full marks No rounding off penalty..3 (b) Tebogo s statement: The province with the smallest population is the Northern Cape 1A Identifying NC Population density (NC) people = km 1M Substitution = 3,046 people/km 3 people/km 1CA Simplification Tebogo is correct. 1A Identifying who is correct The population density of the Northern Cape is less than the population density of Gauteng. J Gauteng has a large population living on a small land surface area. J Northern Cape has a small population living on a large land surface area. J J Any other valid explanation. J Reason If get the province wrong but the rest of the answer is correct: 5 marks (6)

12 Mathematical Literacy/P 1 DoE/14 November 009 QUESTION 3 [34] Total Income = (number of Category 1 tickets) R (number of Category tickets) R (number of Category 3 tickets) R700 + (number of Category 4 tickets) R350 Total Income = (x 1 ) R (x ) R (x 3 ) R700 + (x 4 ) R350 1A Naming categories/using a variable 1A Prices of tickets 1A Summing all 4 categories Ignore the unit. Accept variables in the place of words Uses 1,, 3 and 4 instead of categories : marks Uses the same variable or word for all 4 categories : marks (a) Total Income = (1 45 R1 400) + (8 67 R1 050) + (4 546 R700) + (14 44 R350) 1A Correct number of tickets with corresponding price 1M Summing the products = R CA Total income ANSWER ONLY FULL MARKS Summing of tickets only no marks

13 Mathematical Literacy/P 13 DoE/14 November (b) Total expected number of tickets sold = Number of expected unsold tickets = = A Number of tickets sold 1CA Number of tickets not sold Average price = R = R55 48% of average price = 0,48 R55 = R5 1A Finding average price 1A Average price for Cat. 3 & 4 1CA 48% of average price Additional income = R CA Calculations = R CA Additional income Number of expected unsold tickets = = Average price = R = R55 Income from unsold tickets C C Number of unsold tickets A Average price = R55 = R CA Calculations Additional income after discount = 48% of R = R CA Additional income ANSWER ONLY FULL MARKS 48% of answer : 6 marks (7)

14 Mathematical Literacy/P 14 DoE/14 November Total cost = (5 R1 10) + (1 R1 400) = R A Cost for group matches 1A Cost for round 1 1CA Total cost ANSWER ONLY FULL MARKS Find the sum off all Category 1 tickets : 0 marks 3.. (a) i = 7% 1 = 0,5833 % 1A Divided by = 0,58% or 0,0058 or 0, CA Value of i () ANSWER ONLY FULL MARKS Disregard rounding off to decimal places. Relate answer to Quest.3.. (c) 3.. (b) 14 months 1A Number of monthly deposits (1) ANSWER ONLY FULL MARKS 3.. (c) x = R ,0058 [( 1+ 0,0058) 1] 14 SF SF Substituting = R481,4 1CA Simplification He must save R481,4 monthly. 1CA Rounding off (4) Substitute 3 values correct : SF marks Substitute values correct : 1 SF mark

15 Mathematical Literacy/P 15 DoE/14 November US dollars = 150 0,705 euros 1M Using conversion to euro = 108,0375 euros 1A Amount in euro 108,0375 euros = 108,0375 0, rouble = 4 690,7 rouble 1M Conversion to rouble 1CA Amount in rouble 150 US dollars = 150 0,705 0, rouble = 4 690,7 rouble 1M Multiplication 1M Division 1A Correct values 1CA Amount in rouble Conversion factor: 0,705 0, = 31, M calculating conversion factor 1A correct value 150 US dollars = , = 4 690,7 rouble 1M multiplying 1CA Amount in rouble Conversion factor : 0, ,705 1M calculating conversion factor = 0, A correct value 150 US dollars = 150 0, M Dividing = 4 690,8 roubles 1CA Amount in rouble (4) Penalise only once for rounding off

16 Mathematical Literacy/P 16 DoE/14 November 009 Quest Solution Explanation AS 3.4 PLAYERS' SHARE OF THE BONUS OF 3,6 MILLION DIRHAM A 18 players (x-intercept) 1A (y-intercept) 1A 40 players (x-intercept) Amount in thousands of dirham A (y-intercept) 1A Any other point calculated 1A Correct plotting of point 1A Joining the points (7) Number of players in the squad If join maximum and minimum point with a straight line : 5 marks Plot points and draw a curve : 6 marks Work out all the points and join the points with straight lines 7 marks Bar graph where vertical bars are drawn as straight lines for every value between 18 and 40 : 6 marks

17 Mathematical Literacy/P 17 DoE/14 November 009 QUESTION 4 [3] A Numerator P(boy in Grade 1) = 30 1A Denominator 30 () = ( 0,0 or 19,87%) 151 ANSWER ONLY FULL MARKS 4.1. Number of learners NOT in Grade 10 = = P(not in Grade 10) = 30 1A Number not in 10 1A Numerator 1A Denominator Grade ( 0,45 or 45,36%) P(not in Grade 10) = 1 = Number not in Grade 10 = Total number Number in Grade 10 = = P(not in Grade 10) = 30 1A Number not in Grade 10 1A Numerator 1A Denominator 1A Number not in Grade 10 1A Numerator 1A Denominator 4..1(a) The return distance = 45 km = 90 km 1M Correct distance 90 km is between 50 km and 100 km Cost = R800 1CA Cost for return distance between 50 km and 100 km () ANSWER ONLY FULL MARKS Write R600: 1 mark

18 Mathematical Literacy/P 18 DoE/14 November (b) Return distance = 100 km + 36 km Cost in rand = R R5 = R980 Cost in Rand = R800 + R5 ( ) = R800 + R180 = R Cost (in rand) = R800 + (return distance travelled 100 km) R5/km Cost in Rand = R800 + no. Of km over 100 ) R5 1M Adding 1A Distance above 100 km 1CA Cost ANSWER ONLY FULL MARKS 1A Basic cost up to 100 km 1A Return distance travelled 1A Rate per km Can use a variable in the formula Formula without Cost in rand : full marks SF 4..3 R1 650 = R800 + (return distance travelled 100) R = (return distance travelled 100) = distance travelled = distance travelled 1SF Substitution into own formula (from 4..) 1CA Dividing by 5 1CA Adding 100 km Distance travelled = 70 km 1CA Distance travelled Distance travelled = SF R R800 R5 km km = 70 km (4) ANSWER ONLY FULL MARKS If do not add 100 : 3 marks

19 Mathematical Literacy/P 19 DoE/14 November = 5 remainder 1A Division (a) The minimum number of minibuses needed is 6 1CA Solution () (b) Possible arrangement of passengers in the minibuses: 3 minibuses with 15 passengers each and with 10 O passengers and 1 with 1 passengers 5 minibuses with 13 passengers in each and 1 minibus with O 1 passengers ANSWER ONLY FULL MARKS Answer of 5 only 1 mark Answer of 5 with a good explanation : marks Explanation here must follow on from (a) O For combination of minibuses O For combination of minibuses 1..1 Accept any suitable combination as long as there are 10 or more passengers in a minibus, and a maximum of 15. O 4.3. One bus holds 50 passengers, so two buses are needed O For combination of minibuses 1A Number of buses () Cost of using buses = R600 = R1 00 1CA Cost of bus Cost of using minibuses = 77 R14 = R1 078 The minibus option is cheaper Cost of one bus with 50 learners = R600 Cost of minibus holding 7 learners = 7 R14 = R378 1A Multiplying no. of learners by cost 1CA Taxi cost 1CA Decision 1A cost for 1 bus 1CA number of learners 1CA cost for learners Total cost = R600 + R378 = R978 1 Bus + minibus taxis is the cheapest 1M adding 1CA Total cost (5)

20 Mathematical Literacy/P 0 DoE/14 November Radius of bus tyre = 60 cm Radius of minibus tyre = 60 cm 1 = 35 cm Circumference of minibus tyre 1A Radius of minibus tyre = 3,14 35 cm SF = 19,8 cm = 0,00198 km distance travelled 1 86 = 0,00198 km SF 1SF Radius = ½ diameter 1CA Circumference of minibus tyre in cm 1CA Converting to km 1SF Substitution into formula Distance travelled = ,00198 km = 4, km 1CA Distance travelled 7 Diameter of minibus tyre = 10 cm 1 = 70 cm 1A Diameter of minibus tyre Circumference of minibus tyre = 3,14 70cm = 19,8 cm SF = 0,00198 km distance travelled 1 86 = 0,00198 km Distance travelled = 1 86 SF 0,00198 km 1SF Substitution into formula 1A Circumference of minibus tyre in cm 1CA Converting to km 1SF Substitution into formula = 4, km 1CA Distance travelled

21 Mathematical Literacy/P 1 DoE/14 November 009 Radius of bus tyre = 60 cm 7 Radius of minibus tyre = 60 cm 1 = 35 cm Distance = Rotation Circumference = ,14 35 cm = ,6 cm C = 4,09646 km 4 km SF SF 1A Radius of minibus tyre 1SF Substitution into formula 1A Circumference of minibus tyre in cm 1CA Converting to km 1SF Substitution into formula 1CA Distance travelled (6)

22 Mathematical Literacy/P DoE/14 November 009 QUESTION 5 [1] No penalty for lack of units Volume of a round cake (Ronwyn) 1 F Identifying correct formula = π (radius) height F SF = 3,14 ( 50 cm) 15 cm 1SF Substitution 1A Correct radius = 9 437,5 cm 3 1CA Volume of round cake Answer using π Volume of a ring cake (Bronwyn) = π (R r ) height SF = 3,14 [(8 cm) (9 cm) ] 14 cm = ,88 cm 3 F = 9 45,43 cm 7 on the calculator 3 Answer using = 9 464,9 cm 3 1F Identifying correct formula 1A Correct R and r 1SF Substitution into formula π Answer using on the calculator 3 = ,55,7 cm 7 Answer using = cm 3 The ring cake as it is the cake with the largest volume 1CA Volume of ring cake CA Cake with bigger volume (10)

23 Mathematical Literacy/P 3 DoE/14 November Total outer surface area F 1F Identifying formula = π (radius) + π radius height SF = 3,14 (5 cm) + 3,14 5cm 15cm = 1 96,5 cm cm = 4 317,5 cm 1SF Substitution into formula 1A Value of radius 1A Value of height 1CA Surface area 1A Correct units (6) Answer using π on the calculator = 4 319,7 cm Answer using 7 = 4 31,4 cm 5. Cost for Option 1: Cost for 100 people 14 = 100 R10 + R A Multiplication/adding VAT 1.1. = R R1 680 = R Cost for 100 people = R = R Cost per head = R10 + R = R136,80 Cost for 100 people = R136, = R Cost for Option : Cost for 100 people = R R80 = R11 00 Option is the cheaper option O 1CA Simplification 1A Multiplication/adding VA 1CA Simplification 1A Multiplication/adding VAT 1CA Simplification 1M Addition/multiplication 1CA Simplification 1O Own opinion (5) TOTAL: 150