SEPTEMBER 2019 MATHEMATICAL LITERACY P2intervention.roodie.co.za/assets/files/W2Gr12MathsLit.pdfNATIONAL SENIOR CERTIFICATE GRADE 12 SEPTEMBER 2019 MATHEMATICAL LITERACY P2 MARKS:

TIME: 3 hours
This question paper consists of 11 pages; a 6-pages addendum and a 1-page answer sheet.
*MLITE2*
Copyright reserved Please turn over
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This question paper consists of FOUR questions. Answer ALL the questions.
2. Use the ADDENDUM with ANNEXURES for the following questions:
ANNEXURE A for QUESTION 1.1
ANNEXURE B for QUESTION 1.3
ANNEXURE C for QUESTION 2.1
ANNEXURE D for QUESTION 4.1
ANNEXURE E for QUESTION 4.2
Write your NAME and GRADE in space provided on the ANSWER SHEET for
QUESTION 3.2.5. Hand your ANSWER SHEET in with your ANSWER BOOK.
3. Number the questions correctly according to the numbering system used in this
question paper.
4. You may use an approved calculator (non-programmable and non-graphical), unless
stated otherwise.
5. Show ALL calculations clearly.
6. Maps and diagrams are NOT drawn to scale, unless otherwise stated.
7. Indicate units of measurement, where applicable.
8. Round off ALL final answers appropriately accordingly to the given context, unless
stated otherwise.
10. Write neatly and legibly.
(EC/SEPTEMBER 2019) MATHEMATICAL LITERACY P2 3
QUESTION 1
1.1 Ayryn bought a house in 2018. She decided to draw up a loan model for the duration
of the loan period as shown in ANNEXURE A (some information has been omitted).
Use the information in ANNEXURE A (TABLE 1) to answer the questions below.
1.1.1 Show, with calculations, how the interest amount of R6 088,06 for month 3
was calculated. (3)
1.1.2 The bank uses the following Home Loan Factor Table to calculate the
monthly repayments on home loans:
TABLE 2: Home Loan Factor Table 2018
Years
Interest
% Factor
[Adapted from http://capetownproperty.blaauwberg.net]
Use TABLE 2 above with TABLE 1 in ANNEXURE A and show how the
monthly repayment was calculated.
Monthly repayments are calculated by dividing the home loan amount
by 1 000 and multiplying by the factor.
The factor used depends on the number of years and the interest rate. (3)
1.1.3 Calculate the closing balance of month 3. (2)
1.1.4 Ayryn stated if she had chosen a shorter period, her monthly repayment would
have been less. Refer to the loan factor table and briefly explain, without
calculations, whether Ayryn’s statement is valid or not. (3)
1.1.5 A friend told Ayryn that after 119 repayments, she will already have paid
R15 000 more than the original home loan amount. Verify, with the necessary
calculations, whether this statement is valid or not. (5)
1.1.6 What effect will an increased monthly repayment have on the total interest she
has to pay on her home loan? (2)
1.2 Ayryn wants to extend one of her rooms. The extension will be 2 metres by 2 metres.
The builder must lay the concrete floor before the building can start. The builder will
use the chart as shown below as a guideline.
[Source: http://pinterest.com]
The height of the concrete floor is 300 mm.
1.2.1 Calculate the volume of the concrete floor in cubic metres (m3) that must be
filled with concrete.
You may use the formula:
Volume = Length × Breadth × Height (3)
1.2.2 Determine how many bags of cement should be used for the volume
calculated in QUESTION 1.2.1. (4)
1.2.3 After the building of the room was completed, Ayryn needed to paint the
inside walls. The painter indicated that two coats will be needed.
The surface area of the room to be painted is 15 m2.
8% more paint will be needed.
The spread rate is 5 m2 per litre.
Calculate how many 5-litre tins must be bought. (4)
1.3 The graph shown in ANNEXURE B shows the prediction of the South African
average house prices forecast to 2020.
Use the graph (ANNEXURE B) to answer the following questions.
1.3.1 It is predicted that the price of an average house in South Africa increased by
5% in 2015 and by 4% thereafter to 2020.
Based on the above prediction determine the price of an average house for
2016. (4)
1.3.2 Calculate the percentage change in the price of an average house in South
Africa for the period illustrated in the graph. Give your final answer to the
nearest percentage. (4)
QUESTION 2
2.1 Gustav, a 52-year-old employee, married with 2 children, aged 10 and 16 years
respectively, earns a gross annual salary of R401 137,75. He contributes 7,5% (non-
taxable) of his annual salary to a pension fund. He also contributed to a medical aid
scheme for the whole family.
Use the Tax Table for the 2018–2019 financial year in ANNEXURE C to answer the
following questions.
2.1.1 Calculate Gustav’s taxable income for the 2018–2019 financial year. (3)
2.1.2 For 11 months Gustav pays R2 500 per month for his 10-year-old and R3 200
per month for his 16-year-old in school fees.
He claims that with the tax he is paying for the year, he could have paid his
children’s school fees. Show, with the necessary calculations, whether his
statement is valid or not. (9)
2.2 Sipho is teaching Social Sciences to Grade 9 learners at his school. He uses the pie
charts below to show how the population percentages in South Africa changed
according to the different race groups. The pie charts represent 1911 and 2004
respectively. Study the pie charts below to answer the questions below.
[Source: http://reddit.com]
2.2.1 Determine the probability of randomly choosing a person other than African
from the 2004 population. (2)
2.2.2 Calculate the difference in the total number of the African population group
between 1911 and 2004 in South Africa. (7)
6 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2019)
2.2.3 The percentage of the Coloured population in 1911 and 2004 is the same.
Show, with the necessary calculations, whether the number of Coloured
populations in these two years are the same. (3)
2.2.4 Comment on the trend and the percentages of African and Indian race groups
over the period. (2)
2.3 The Grade 12 class for 2019 has a farewell function to organise. Each learner must
contribute R300,00. There are 25 couples and 17 singles.
The organisers got two quotes as follow:
Option 1: R1 500 for the hall and R250 per person for the meal
Option 2: R270 per person for the singles and 4% less for couples per person
2.3.1 Determine the total number of people that will attend the farewell. (2)
2.3.2 The organisers claim that if they choose Option 1 instead of Option 2, they can
have more money left to spend on photos. Verify, with the necessary
calculations, whether the statement is valid or not. (8)
[36]
QUESTION 3
3.1 Below is an extract of a map that show the location of two airports in Germany,
Frankfurt-Hahn and Frankfurt airports. Study the map and answer the questions that
follow.
[Adapted]
3.1.1 In which general direction is Neuwied from Mainz? (2)
3.1.2 Calculate the actual distance in miles between the two airports. Give your final
answer to THREE decimal places. (4)
3.1.3 Write the scale of the map as a unit ratio (1: …) to the nearest million.
You may use the following conversion:
1 mile = 1,609 kilometres (4)
3.1.4 Give ONE possible reason why airports in general are located away from
residential areas. (2)
3.1.5 On which road on the western side will you travel from Worms to Koblenz? (2)
3.1.6 The travelling distance from Worms to Koblenz is 78 miles.
Judith claims that if she leaves Koblenz at 07:20 and travels at an average speed
of 40 miles per hour, she will be on time for her interview at 09:15 in Worms.
Show, with the necessary calculations, whether her claim is valid or not.
You may use the formula:
Distance = Speed × Time (7)
3.2 Kenneth plan to visit Judith in Frankfurt. Judith sent him the annual average
minimum and maximum temperatures for Frankfurt as shown below.
[Adapted from http://lh-travelguide.com]
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Minimum
Study the information above and answer the questions below.
3.2.1 The range of the data for the minimum temperature is 15 °C. Determine the
lowest temperature indicated by A. (3)
3.2.2 Judith made two mistakes when calculating the median of the maximum
temperatures. The following is her calculation:
Median = 22 + 24
(b) Calculate the median. (2)
3.2.3 Kenneth says he hates getting cold. Advise him with a reason which months
he must visit Judith. (3)
3.2.4 Determine the probability that the minimum temperature will be greater than
minus 1 °C, but less and equal to 9 °C. Give your final answer as a decimal
fraction to THREE decimal places. (3)
3.2.5 The line graph for the maximum temperatures has been drawn in ANSWER
SHEET 1. Use the same set of axes to draw the line graph for the minimum
temperatures. (5)
QUESTION 4
4.1 Jona wants to build his own hot air balloon. He follows the illustrations as shown in
ANNEXURE D.
4.1.1 Diagram R is only a part of Diagram Q. Determine the total area of the
material that the hot air balloon is made of.
You may use the following formulae:
Area of rectangle = Length × Width
Area of triangle =
× base × height (8)
4.1.2 Give a reason why there must be an overlap of 3 mm on the sides as
illustrated in Diagram T.
(2)
4.1.3 Briefly explain what Jona has to do with the hot air balloon in Diagram T and
Diagram U.
(2)
4.1.4 Write down the function of the hair dryer in Diagram V. (2)
4.2 Jona wants to have a ride in a hot air balloon. He did some research and came across
an illustration shown in ANNEXURE E. It shows how hot air balloons are lifted
depending on the temperature.
4.2.1 Use ANNEXURE E to describe the relationship between the temperature of
the hot air balloon and the lift of the hot air balloon.
(4)
4.2.2 The table below shows the density of air at sea level for various temperatures
of the hot air balloon.
Air Density Table Temperature in °C Air density kg/m3
0 1,293
10 1,247
20 1,204
30 1,165
40 1,128
80 1,000
90 0,972
100 0,946
[Source: http://buoyancy.png]
With reference to the table above and ANNEXURE E to answer the following
question.
You may use the following formula:
Lift = (Air density outside the hot water balloon – Air density inside hot
air balloon) × Volume of the hot air balloon (7)
4.2.3 The instructor has hot air balloons with a variety of colours. Thirty-three
green, eight orange, nineteen pink, twenty-one red and twelve blue. Determine
the probability that Jona will choose either a green or a blue hot air balloon to
ride in. Give your final answer as a common fraction in its simplest form. (3)
4.3 Jona and three friends wants to visit Cappadocia, a historical region in Central Anatolia
in Turkey where they will also go for the hot air balloon rides. They investigated the
cost of their accommodation and the cost of the hot air balloon rides to get an idea of
the costs.
Accommodation: R1 030 per person per night
Hot air balloon rides: R750 per person per ride
NOTE:
They are checking in on Monday (15 April 2019) and checking out on Friday (19
April 2019).
Group bookings for the hot air balloon rides for 4 persons will be charged at a
discount of 15% per person.
Use the information above to calculate how much Jona and his friends will pay in total
for the accommodation and one hot air balloon ride, if they go as a group. Give your
final answer in Turkish Lira.
Exchange rates as at 08 February 2019:
1$ (American Dollar) = 5,25 Turkish Lira
1$ (American Dollar) = 13,63 ZAR (South African Rand) [Source: http://ferates.com] (10)
[38]
ANSWER SHEET 1: QUESTION 3.2.5
NAME and SURNAME: ………………………………………………………………….
-5
0
5
10
15
20
25
30
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
T em
p er
Copyright reserved
*MLADE2*
2
0 0
In te
re st
0 0
9 3 ,7
5 1 ,2
5 1 ,2
4 2 ,1
9 9 ,6
9 9 ,3
3 3 ,4
9 9 ,9
5 7 ,4
9 4 ,0
7 7 ,5
3 5 ,0
2 4 ,5
5 1 ,7
0 9 ,2
ANNEXURE C: QUESTION 2.1
Taxable Income (R) Rates of tax (R)
0–195 850 18% of taxable income
195 851–305 850 35 253 + 26% of taxable income above 195 850
708 311–1 500 000 207 448 + 41% of taxable income above 708 310
Tax Rebate 2018/2019
Tax Thresholds
Person 2018/2019
Medical aid credits 2018/2019 year of assessment
(1 March 2018–28 February 2019)
R310 per month for the taxpayer who paid the medical scheme contributions
R310 per month for the first dependant
R209 per month for each additional dependant(s)
[Source: http://sars.co.za]
n g
Symbol Explanation
M Method
CA Consistent accuracy
A Accuracy
C Conversion
S Simplification
RT/RG/RM Reading from a table OR Reading from a graph OR Read from map
F Choosing the correct formula
SF Substitution in a formula
J Justification
P Penalty, e.g. for no units, incorrect rounding off etc.
R Rounding Off OR Reason
AO Answer only
2 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2019)
MARKING GUIDELINES
NOTE:
If a candidate answers a question TWICE, only mark the FIRST attempt.
If a candidate has crossed out (cancelled) an attempt to a question and NOT redone
the solution, mark the crossed out (cancelled version)
Consistent accuracy (CA) applies in ALL aspects of the marking guidelines,
however it stops at the second calculation error.
If the candidate presents any extra solution when reading from a graph, table,
layout plan and map, then penalise for every extra incorrect item presented.
LET WEL:
As kandidaat vraag TWEE keer beantwoord, merk slegs die EERSTE poging.
As kandidaat antwoord van vraag doodtrek (kanselleer) en nie oordoen nie,
merk die doodgetrekte (gekanselleerde) poging.
Volgehoue akkuraatheid (CA) word in ALLE aspekte van die nasienriglyn
toegepas, maar dit hou by die tweede berekeningsfout op.
Wanneer kandidaat aflesings vanaf grafiek, tabel, uitlegplan en kaart geneem
en ekstra antwoorde gee, penaliseer vir elke ekstra verkeerde item.
(EC/SEPTEMBER 2019) MATHEMATICAL LITERACY P2 3
QUESTION 1 [37]
100
= R6 088,06
= 6 442 500
= R748 944,95
The shorter the loan period, the higher the monthly repayment
OR
The shorter the loan period, the higher the loan factor
OR
No
Accept any other relevant response
1A Not valid
1R Shorter period
1R Higher MRP
= R766 657,50
= R16 657,50
Statement valid
1MA Multiplying
correct values
1CA Amount
1M Subtraction
1CA Difference
Accept any other relevant response
2A Explanation
= 1,2 m3
1SF Substitution
1CA Answer in m3
1.2.2 Bags of cement =
= 16, 2 m2
= 6,48
OR
= 16,2 m2
5
(4)
M
L3
1.3.1 Price for 2015 = 1 251 158,39 + (1 251 158,39 × 0,05) MA
= 1 251 158,39 + 62 557,9195
= R1 313 716,31
Price for 2016 = 1 313 716,31 + (1 313 716,31 × 0,04)
= 1 313 716,31 + 52 548,65238
= R1 366 264,96
= R1 366 264,96
1 029 331 × 100%
QUESTION 2 [36]
= 401 137,75 – (0,075 × 401 137,75)
= 401 137,75 – 30 085,33
= 63 853 + 0,31 × (371 052,42 – 305 850)
= 63 853 + 0,31 × 65 202,42
= 63 853 + 20 212,75
= 84 065,75 – 13 635
= 70 430,75 – 12 456
= 27 500 + 35 200
= 20,7%
OR
= 20,7%
= 79,3%
= 37, 001 380 million
OR 37 001 380
= 401 9665,46
= 32 981 714, 54
millions
= 477 820,56
= 3 732 800
1MA % for 1911
Percentage of the Indian race group decreased
1A African increase
1A Indian decrease
2.3.1 Number of people = (25 × 2) + 17
= 50 + 17
= 67 people
= 1 500 + 16 750
= R12 950
= R4 590
= R 17 550
QUESTION 3 [39]
(2)
Distance = 8,6 cm
Actual distance = 20
(4)
Convert miles to kilometres = 20 miles × 1,609
= 32,18 km
= 3 218 000 cm
= 1 cm : 848 842,1053
≈ 1 : 1 000 000
1MA Convert km to cm
1S Simplification
ratio
(4)
M
L3
2R Reason
3.1.6 Distance = Speed × Time
Time = 78
Arrival time = 07:20 + 1:57
= 1h 55 minutes
1SF Substitution
formula
1M Adding times
1CA Arrival time
formula
1M Travel time
1O Not valid
3.2.1 Range = Highest – Lowest
= -2°C
1A Mistake 1
1A Mistake 2
3.2.2 (b) Correction:
3 ; 4 ; 6 ; 7 ; 10 ; 13 ; 14 ; 19 ; 19 ; 22 ; 24 ; 24
Median = 13 + 14
Minimum temperatures are high
Maximum temperatures are high
(5)
D
L2
[39]
-5
0
5
10
15
20
25
30
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Te m
p er
at u
A
A
A
A
A
QUESTION 4 [38]
= Area of rectangle – Area of 1 – Area of 2
= (Length × Width) – ( 1
2 × base × height) – (
2 × base × height)
= (130 cm × 25 cm) – (0,5 × 50 cm × 25 cm) – (0,5 × 50 cm × 15 cm)
= 3 250 cm2 – 625 cm2 – 375 cm2
= 2 250 cm2 × 5
OR
Area of 5 panels = 130 cm × 25 cm
= 32 500 cm2 × 5
2 × base × height
= 3 125 cm2
2 × base × height
= 1 875 cm2
Total Area = 16 250 cm2 – 3 125 cm2 – 1 875 cm2
= 11 250 cm2
1SF Correct values
OR
(2)
M
L4
4.1.3 Diagram T – A ring should be attached to the wide side of the
hot air balloon
Diagram U – A paper clip to be attached to the ring
1A Explain
Diagram T
1A Explain
(2)
L4
4.2.1
When the temperature increases, the lift of the hot air balloon is
higher.
OR
When the temperature decreases, the lift of the hot air balloon is
lower.
4.2.2 Air Density of Hot air balloon B = 0,972+0,946
2
= 1,918
2
= 0,959 kg/m3
Lift = (Air density outside of the hot air balloon – Air density
inside hot air balloon) × Volume of the hot air balloon
Lift = (1,204 kg/m3 – 0,959 kg/m3) × 2 400 m3
= 0,245 kg/m3 × 2 400 m3
= 588 kg
= R16 480
= 750 – 112,50
= R2 550
= R19 030
13,63
= 7 329,97 Turkish Lira
1A 4 nights × 4
TYD: 3 uur
Hierdie vraestel bestaan uit 11 bladsye; insluitend 6-bladsy addendum en 1 bladsy
antwoordblad.
Kopiereg voorbehou Blaai om asseblief
INSTRUKSIES EN INLIGTING
Lees die volgende instruksies noukeurig deur voordat die vrae beantwoord word.
1. Hierdie vraestel bestaan uit VIER vrae. Beantwoord AL die vrae.
2. Gebruik die ADDENDUM met BYLAE vir die volgende vrae:
BYLAE A vir VRAAG 1.1
BYLAE B vir VRAAG 1.3
BYLAE C vir VRAAG 2.1
BYLAE D vir VRAAG 4.1
BYLAE E vir VRAAG 4.2
Skryf jou NAAM en GRAAD in die voorsiende spasie op die ANTWOORDBLAD vir
VRAAG 3.2.5. Handig jou ANTWOORDBLAD saam met jou ANTWOORDEBOEK
in.
3. Nommer die vrae korrek volgens die nommeringstelsel wat in hierdie vraestel gebruik
word.
4. Jy mag goedgekeurde sakrekenaar (nieprogrammeerbare en niegrafies) gebruik,
tensy anders aangedui.
5. ALLE berekeninge moet duidelik getoon word.
6. Kaarte en diagramme is NIE volgens skaal geteken NIE, tensy anders aangedui.
7. Dui meeteenhede aan, waar van toepassing.
8. Rond ALLE finale antwoorde toepaslike volgens die gegewe konteks af, tensy anders
aangedui.
10. Skryf netjies en leesbaar.
(EC/SEPTEMBER 2019) WISKUNDIGE GELETTERDHEID V2 3
VRAAG 1
1.1 Ayryn het in 2018 huis gekoop. Sy het besluit om leningsmodel vir die duur van die
leningsperiode op te trek soos in BYLAE A getoon (sommige inligting is weggelaat).
Gebruik die inligting in BYLAE A (TABEL 1) om die onderstaande vrae te beantwoord.
1.1.1 Toon, met berekeninge, hoe die rente bedrag van R6 088,06 vir maand 3 bereken
was. (3)
1.1.2 Die bank gebruik die volgende Huislening Faktortabel om die maandelikse
terugbetalings op huislenings te bereken:
TABEL 2: Huislening Faktortabel 2018
Jare
Rente % Faktor
[Aangepas vanaf http://capetownproperty.blaauwberg.net]
Gebruik TABEL 2 hierbo saam met TABEL 1 in BYLAE A en toon hoe die
maandelikse terugbetaling bereken was.
Maandelikse terugbetalings word bereken deur die huisleningsbedrag
deur 1 000 te deel en met die faktor te vermenigvuldig.
Die faktor wat gebruik word hang af van die aantal jare en die
rentekoers. (3)
1.1.3 Bereken die eindsaldo vir maand 3. (2)
1.1.4 Ayryn beweer dat as sy korter leningsperiode gekies het, sou haar maandelikse
terugbetaling minder gewees het. Verwys na die leningsfaktortabel en verduidelik
kortliks, sonder berekeninge, of Ayrun se bewering geldig is of nie. (3)
1.1.5 Vriend vertel vir Ayryn dat na 119 maande se terugbetalings, dan sal sy alreeds
R15 000 meer as die oorspronklike huislening afbetaal het. Verifieer, met die
nodige berekeninge, of die bewering geldig is of nie. (5)
1.1.6 Watter effek sal verhoogde maandelikse terugbetaling op die totale rente wat sy
aan haar huislening moet betaal, hê? (2)
1.2 Ayryn wil een van haar kamers uitbrei (groter maak). Die uitbreiding sal 2 meter by
2 meter wees. Die bouer moet die betonvloer lê voordat die bouery kan begin. Die
bouer sal die aanwysings hieronder as riglyn gebruik.
[Bron: http://pinterest.com]
Die hoogte van die betonvloer is 300 mm.
1.2.1 Bereken die volume van die betonvloer in kubieke meter (m3) wat met
betonmengsel gevul moet word.
Jy mag die formule gebruik:
Volume = Lengte × Breedte × Hoogte (3)
1.2.2 Bepaal hoeveel sakke sement gebruik moet word vir die volume wat in
VRAAG 1.2.1 bereken is. (4)
1.2.3 Nadat die bouery van die kamer klaar was, moet Ayryn die binnemure laat
verf. Die verwer het aangedui dat twee lae verf benodig sal word.
Die buite-oppervlakte van die kamer wat geverf moet word, is 15 m2.
8% meer verf word benodig.
Die spreidingskoers is 5 m2 per liter.
Bereken hoeveel 5-liter blikke verf gekoop moet word. (4)
1.3 Die grafiek in BYLAE B toon die voorspelling van die Suid-Afrikaanse gemiddelde
huispryse se vooruitskatting tot 2020.
Gebruik die grafiek (BYLAE B) om die volgende vrae te beantwoord.
1.3.1 Dit word voorspel dat die prys van gemiddelde huis in Suid-Afrika met 5%
in 2015 en met 4% daarna tot 2020 gestyg het.
Gebaseer op die bogenoemde voorspelling, bereken die prys van gemiddelde
huis vir 2016. (4)
1.3.2 Bereken die persentasie verandering in die prys van gemiddelde huis in Suid-
Afrika vir die periode soos aangedui in die grafiek. Gee jou finale antwoord tot
die naaste persentasie. (4)
VRAAG 2
2.1 Gustav, 52-jaar oue werknemer, getroud met 2 kinders, ouderdomme 10 en 16 jaar
onderskeidelik verdien bruto jaarlikse salaris van R401 137,75. Hy dra 7,5% (nie-
belasbaar) van sy jaarlikse salaris aan pensioenfonds by. Hy dra ook by tot
mediese fonds skema vir die hele familie.
Gebruik die Belastingtabel vir die 2018–2019 finansiële jaar in BYLAE C om die vrae
wat volg te beantwoord.
2.1.1 Bereken Gustav se belasbare inkomste vir die 2018–2019 finansiële jaar. (3)
2.1.2 Vir 11 maande betaal Gustav R2 500 per maand vir sy 10-jarige en R3 200 per
maand vir sy 16-jarige aan skoolfooie.
Hy beweer dat met die belasting wat hy vir die jaar betaal, kon hy sy kinders se
skoolfooie betaal het. Toon, met die nodige berekeninge, of sy bewering geldig
is of nie. (9)
2.2 Sipho onderrig Sosiale Wetenskappe aan graad 9 leerders by sy skool. Hy gebruik die
onderstaande sirkeldiagramme om te wys hoe die bevolkingspersentasies in
Suid-Afrika volgens die verskillende rassegroepe verander het. Die sirkeldiagramme
stel 1911 en 2004 onderskeidelik voor. Bestudeer die sirkeldiagramme hieronder om
die onderstaande vrae te beantwoord.
[Bron: http://reddit.com]
2.2.1 Bepaal die waarskynlikheid dat persoon, ander as Swart, willekeurig vanaf
die 2004 bevolking gekies word. (2)
2.2.2 Bereken die verskil in die totale Swart bevolking tussen 1911 en 2004 in
Suid-Afrika. (7)
2.2.3 Die persentasie Kleurling bevolking is dieselfde in 1911 en 2004. Toon, met
die nodige berekeninge, of die aantal Kleurling bevolking dieselfde in die
twee jare is. (3)
2.2.4 Lewer kommentaar oor die tendens tussen die Swart- en Indiër-
bevolkingsgroepe oor hierdie periode. (2)
2.3 Die graad 12 klas van 2019 het afskeidsfunksie om te reël. Elke leerder moet R300
bydra. Daar is 25 paartjies en 17 enkellopers.
Die organiseerders het twee kwotasies soos volg gekry:
Opsie 1: R1 500 vir die saal en R250 per persoon vir die maaltyd
Opsie 2: R270 per persoon vir die enkeles en 4% minder vir paartjies per persoon
2.3.1 Bepaal die aantal persone wat die afskeid sal bywoon. (2)
2.3.2 Die organiseerders beweer dat indien hulle Opsie 1 in plaas van Opsie 2 kies,
sal hulle meer geld oor het om op foto’s te spandeer. Verifieer, met die nodige
berekeninge, of die bewering geldig is of nie. (8)
[36]
VRAAG 3
3.1 Hieronder is uittreksel van kaart wat die ligging van twee lughawens in
Duitsland, Frankfurt-Hahn en Frankfurt lughawens aandui. Bestudeer die kaart en
beantwoord die vrae wat volg.
[Aangepas]
3.1.1 In watter algemene rigting is Neuwied vanaf Mainz? (2)
3.1.2 Bereken die werklike afstand in myl tussen die twee lughawens. Gee jou finale
antwoord tot DRIE desimale plekke. (4)
3.1.3 Skryf die skaal van die kaart as eenheidsverhouding (1: …) tot die naaste
miljoen.
1 myl = 1,609 kilometer (4)
3.1.4 Gee EEN moontlike rede waarom lughawens oor die algemene weg van
residensiële gebiede geleë is. (2)
3.1.5 Op watter pad, aan die westelike kant, sal jy reis vanaf Worms na Koblenz? (2)
3.1.6 Die reisafstand vanaf Worms na Koblenz is 78 myl.
Judith beweer dat indien sy Koblenz om 7:20 verlaat en teen gemiddelde
spoed van 40 myl per uur reis, sal sy betyds vir haar onderhoud om 09:15 in
Worms wees. Toon, met die nodige berekeninge, of haar bewering geldig is of
nie
Afstand = Spoed × Tyd (7)
3.2 Kenneth beplan om Judith in Frankfurt te besoek. Judith stuur hom die gemiddelde
jaarlikse minimum en maksimum temperature vir Frankfurt soos hieronder getoon.
[Aangepas vanaf http://lh-travelguide.com]
Maand Jan Feb Mar Apr Mei Jun Jul Aug Sep Okt Nov Des
Minimum
Bestudeer die inligting hierbo en beantwoord die vrae hieronder.
3.2.1 Die omvang van die data vir die minimum temperature is 15 °C. Bepaal die
laagste waarde wat deur A aangedui word. (3)
3.2.2 Judith het twee foute gemaak om die mediaan van die maksimum
temperature te bereken. Die volgende is haar berekening:
Mediaan = 22 + 24
(b) Bereken die mediaan. (2)
3.2.3 Kenneth noem dat hy koue haat. Adviseer hom met rede watter maande
hy Judith moet besoek. (3)
3.2.4 Bepaal die waarskynlikheid dat die minimum temperatuur groter as minus
1 °C, maar kleiner en gelyk aan 9 °C sal wees. Gee jou finale antwoord as
desimale breuk tot DRIE desimale plekke. (3)
3.2.5 Die lyngrafiek vir die maksimum temperature is op ANTWOORDBLAD 1
geteken. Gebruik dieselfde assestelsel om die lyngrafiek vir die minimum
temperature te teken. (5)
VRAAG 4
4.1 Jona wil sy eie warmlugballon bou. Hy volg die illustrasies soos in BYLAE D
aangedui.
4.1.1 Diagram R is slegs gedeelte van Diagram Q. Bepaal die totale oppervlakte
van die materiaal waarvan die warmlugballon gemaak is.
Jy mag die volgende formules gebruik:
Oppervlakte van reghoek = Lengte × Breedte
Oppervlakte van driehoek =
× basis × hoogte (8)
4.1.2 Gee rede waarom daar oorvleueling van 3 mm aan die kante soos
geïllustreer in Diagram T moet wees. (2)
4.1.3 Verduidelik kortliks wat Jona met die warmlugballon in Diagram T en
Diagram U moet doen. (2)
4.1.4 Skryf die funksie van die haardroër in Diagram V neer. (2)
4.2 Jona wil rit in warmlugballon hê. Hy het navorsing gedoen en op illustrasie soos
aangetoon in BYLAE E afgekom. Dit toon hoe warmlugballonne afhangende van die
temperatuur styg.
4.2.1 Gebruik BYLAAG E om die verwantskap tussen temperatuur van
warmlugballon en die styging van die warmlugballon te beskryf. (4)
4.2.2 Die tabel hieronder toon die digtheid van lug by seevlak vir verskillende
temperature van die warmlugballon.
0 1,293
10 1,247
20 1,204
30 1,165
40 1,128
80 1,000
90 0,972
100 0,946
[Bron: http://buoyancy.png]
Met verwysing na die tabel hierbo en BYLAAG E om die volgende vraag te
beantwoord.
Styging = (Lugdigtheid buite die warmlugballon – Lugdigtheid binne die
warmlugballon) × Volume van die warmlugballon (7)
4.2.3 Die instrukteur het warmlugballonne met verskillende kleure. Drie-en-dertig
groen, agt oranje, negentien pienk, een-en-twintig rooi en twaalf blou. Bepaal
die waarskynlikheid dat Jona willekeurig warmlugballon sal kies wat óf
groen óf blou vir sy rit sal wees. Gee jou finale antwoord as gewone breuk in
die eenvoudigste vorm. (3)
4.3 Jona en drie vriende wil Cappadocia, historiese gebied in Sentraal-Anatolia in
Turkye, besoek waar hulle ook in warmlugballonne sal reis. Hulle het die koste vir
hulle akkommodasie en die koste vir die warmlugballonritte ondersoek, om idee van
die koste te kry.
Akkommodasie: R1 030 per persoon per nag
Warmlugballonritte: R750 per persoon per rit
LET WEL:
Hulle teken in op Maandag (15 April 2019) en teken uit op Vrydag (19 April 2019).
Groepbesprekings vir die warmlugballonritte vir 4 persone sal teen afslag van 15%
per persoon gevra word.
Gebruik die inligting hierbo om te bereken hoeveel Jona en sy vriende in totaal vir
akkommodasie en een warmlugballonrit sal betaal, indien hulle as groep bespreek.
Gee jou finale antwoord in Turkse Lira.
Wisselkoerse soos op 08 Februarie 2019:
1$ (Amerikaanse Dollar) = 5,25 Turkse Lira
1$ (Amerikaanse Dollar) = 13,63 ZAR (Suid-Afrikaanse Rand) [Bron: http://ferates.com] (10)
[38]
ANTWOORDBLAD 1: VRAAG 3.2.5
Gemiddelde Minimum en Maksimum temperature in Frankfurt
Jan Feb Mrt Apr Mei Jun Jul Aug Sept Okt Nov Des
NASIONALE
*MLADA2*
2
0 0
R en
te k
o er
s (p
er j
a a
0 0
9 3 ,7
5 1 ,2
5 1 ,2
4 2 ,1
9 9 ,6
9 9 ,3
3 3 ,4
9 9 ,9
5 7 ,4
9 4 ,0
7 7 ,5
3 5 ,0
2 4 ,5
5 1 ,7
0 9 ,2
BYLAE C: VRAAG 2.1
0–195 850 18% van belasbare inkomste
195 851–305 850 35 253 + 26% van belasbare inkomste bo 195 850
708 311–1 500 000 207 448 + 41% van belasbare inkomste bo 708 310
Belastingkorting 2018/2019
Belastingdrempels
Mediese fonds krediete 2018/2019 jaar van assessering
(1 Maart 2018–28 Februarie 2019)
R310 per maand vir die belastingbetaler wie die mediese skema bydrae betaal
R310 per maand vir die eerste afhanklike
R209 per maand vir elke addisionele afhanklike(s)
[Bron: http://sars.co.za]
n g
Simbool Verduideliking
M Metode
CA Deurlopende akkuraatheid
A Akkuraatheid
C Omskakeling
S Vereenvoudig
RT/RG/RM Lees vanaf tabel OF Lees vanaf grafiek OF Lees vanaf kaart
F Kies korrekte formule
SF Vervanging in formule
R Afronding OF Rede
2 WISKUNDIGE GELETTERDHEID V2 (EC/SEPTEMBER 2019)
MARKING GUIDELINES
NOTE:
If a candidate answers a question TWICE, only mark the FIRST attempt.
If a candidate has crossed out (cancelled) an attempt to a question and NOT redone
the solution, mark the crossed out (cancelled version)
Consistent accuracy (CA) applies in ALL aspects of the marking guidelines,
however it stops at the second calculation error.
If the candidate presents any extra solution when reading from a graph, table, layout
plan and map, then penalise for every extra incorrect item presented.
LET WEL:
As kandidaat vraag TWEE keer beantwoord, merk slegs die EERSTE poging.
As kandidaat antwoord van vraag doodtrek (kanselleer) en nie oordoen nie,
merk die doodgetrekte (gekanselleerde) poging.
Volgehoue akkuraatheid (CA) word in ALLE aspekte van die nasienriglyn toegepas,
maar dit hou by die tweede berekeningsfout op.
Wanneer kandidaat aflesings vanaf grafiek, tabel, uitlegplan en kaart geneem
en ekstra antwoorde gee, penaliseer vir elke ekstra verkeerde item.
(EC/SEPTEMBER 2019) WISKUNDIGE GELETTERDHEID V2 3
VRAAG 1 [37]
100
= R6 088,06
1RT Korrekte
= 6 442 500
1RT Korrekte faktor
(3)
V2
F
= R749 299,39 + R6 088,06 – R6 442,50
= R748 944,95
1A Eindsaldo
terugbetaling
OF
OF
Nee
Aanvaar enige ander relevante antwoord
1A Nie geldig
1R Korter periode
1R Hoër MTB
= R766 657,50
= R16 657,50
Bewering geldig
1MA Vermenigvuldig
korrekte waardes
1CA Bedrag
1M Aftrekking
1CA Verskil
Aanvaar enige ander relevante antwoord
2A Verduideliking
= 1,2 m3
1SF Vervanging
M
V2
1.2.2 Sakke sement =
= 16, 2 m2
= 6,48
OF
= 16,2 m2
blikke
(4)
M
V3
1.3.1 Prys vir 2015 = 1 251 158,39 + (1 251 158,39 × 0,05)
= 1 251 158,39 + 62 557,9195
= R1 313 716,31
Prys vir 2016 = 1 313 716,31 + (1 313 716,31 × 0,04)
= 1 313 716,31 + 52 548,65238
= R1 366 264,96
= R1 366 264,96
1 029 331 × 100%
VRAAG 2 [36]
= 401 137,75 – (0,075 × 401 137,75)
= 401 137,75 – 30 085,33
= 63 853 + 0,31 × (371 052,42 – 305 850)
= 63 853 + 0,31 × 65 202,42
= 63 853 + 20 212,75
= 84 065,75 – 13 635
= 70 430,75 – 12 456
= 27 500 + 35 200
= 20,7%
OF
= 20,7%
1CA Waarskynlikheid
= 79,3%
= 37, 001 380 miljoen
OF 37 001 380
= 401 9665,46
= 32 981 714, 54
= 477 820,56
= 3 732 800
1MA % vir 1911
Persentasie Indiër-bevolking neem af
1A Swart neem af
1A Indiër neem toe
2.3.1 Aantal persone = (25 × 2) + 17
= 50 + 17
= 67 persone
= 1 500 + 16 750
= R12 950
= R 17 550
VRAAG 3 [39]
en
OW
3.1.1 Noordwes OF Wes van noord 2A Rigting (2) M&P
V2
3.1.2
Afstand = 8,6 cm
Werklike afstand = 20
(4)
Herlei myl na kilometer = 20 myl × 1,609
= 32,18 km
= 3 218 000 cm
= 1 cm : 848 842,1053
≈ 1 : 1 000 000
1S Vereenvoudig
(2)
Tyd = 78
Aankoms tyd = 07:20 + 1:57
1SF Vervanging
1M Tel tye op
1M Reistyd
3.2.1 Omvang = Hoogste – Laagste
= -2 °C
reël
3.2.2 (b) Regstelling:
3 ; 4 ; 6 ; 7 ; 10 ; 13 ; 14 ; 19 ; 19 ; 22 ; 24 ; 24
Mediaan = 13 + 14
Minimum temperature hoog
Maksimum temperature hoog
1A Korrekte maande
1R Min hoog
P
V2
3.2.5
A
Jan Feb Mrt Apr Mei Jun Jul Aug Sep Okt Nov Des
CA
VRAAG 4 [38]
= Opp van reghoek – Opp van 1 – Opp van 2
= (Lengte × Breedte) – ( 1
2 × basis × hoogte) – (
2 × basis × hoogte)
= (130 cm × 25 cm) – (0,5 × 50 cm × 25 cm) – (0,5 × 50 cm × 15 cm)
= 3 250 cm2 – 625 cm2 – 375 cm2
= 2 250 cm2 × 5
OF
Oppervlakte van 5 panele = 130 cm × 25 cm
= 3 250 cm2 × 5
2 × basis × hoogte
= 3 125 cm2
2 × basis × hoogte
= 1 875 cm2
Totale Opp = 16 250 cm2 – 3 125 cm2 – 1 875 cm2
= 11 250 cm2
1SF Korrekte waardes
OF
2R Rede
(2)
M
V4
4.1.3 Diagram T – Ring moet aan die breë kant van die
warmlugballon geheg word
Diagram U – Skuifspeld moet aan die ring geheg word
1A Verduidelik
Diagram T
1A Verduidelik
V2
4.1.4 Om warm lug in die warmlugballon te blaas 2R Rede
(2)
Wanneer die temperatuur styg, dan is die styg van die
warmlugballon hoër.
laer.
4.2.2 Lugdigtheid van warmlugballon B = 0,972+0,946
2
= 1,918
2
Lugdigtheid binne die warmlugballon) × Volume van die
warmlugballon
= 0,245 kg/m3 × 2 400 m3
= 588 kg
= R16 480
= R19 030
13,63
= 7 329,97 Turkse Lira
1A 4 nagte × 4
c326075ae37fccf96f73a06311fdba7ee697aa935517fadbe95daa6e73c70e87.pdf
c326075ae37fccf96f73a06311fdba7ee697aa935517fadbe95daa6e73c70e87.pdf
ab0bf2ee0ea04f0e3dd4135b21a9395a509c5741acfe5e79d4d3211c773b39ae.pdf

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