NORTHERN CAPE DEPARTMENT OF EDUCATION AUTUMN CAMP 2020 MATHEMATICAL LITERACY TUTOR GUIDE
NORTHERN CAPE DEPARTMENT OF EDUCATION
AUTUMN CAMP 2020
MATHEMATICAL
LITERACY
TUTOR GUIDE
DEPARTMENT OF EDUCATION: PROVINCIAL OFFICE
MATHEMATICAL LITERACY
PROGRAMME FOR AUTUMN CAMP
23 - 29 March 2020
DAYS TOPIC SECTION IN LEARNER GUIDE
DA
Y 1
23-0
3-2
020
At the beginning of the period: Pre-test (30 min)
Finance
CLASSWORK:
Question 1 - 1h 20 min
Mark question 1
HOMEWORK - Question 1 no completed
DA
Y 2
24-0
3-2
02
0
Marking of homework.
Finance
CLASSWORK:
Question 2 - 30 min
Mark question 2
Question 3 - 45 min
Marking question 3
HOMEWORK - Question 4.1
DA
Y 3
25-0
3-2
020
Marking of homework.
Finance
CLASSWORK:
Question 4.2 - 20 min
Mark question 4.2
Question 5 - 1h 20 min
HOMEWORK - Work not finished in class
DA
Y 4
26-0
3-2
020
Marking of homework.
Finance
CLASSWORK:
Question 6 - 50 min
Mark question 6
HOMEWORK - Work not finished in class
DA
Y 5
27-0
3-2
020
Marking of homework.
Finance
CLASSWORK:
Work out the pre-test
Question 7 - 1h 20 min
Mark question 7
HOMEWORK - Work not finished in class
DA
Y 6
28-0
3-2
020
At the end of the period: Post-test (30 min)
Finance
Marking of homework.
CLASSWORK:
Question 8 - 35 min
Mark question 8
Question 9 - 30 min
DA
Y 7
29-0
3-2
020
Marking of homework.
Finance
CLASSWORK:
Mark question 9
Discussion on the post-test
1. Learners must do the classwork in class. Time that must be given is allocated.
2. Mark and discuss the questions in the class.
3. Homework must be given for the study session.
4. Homework must be marked and discussed the following morning, before new work is started.
5.** After the post-test has been written it must be submitted for marking (BY TUTOR).
After administration of the test the tutor must discuss the memo with the learners.
PLEASE NOTE:
These consolidation exercises must be used in conjunction with the learner notes received in
the beginning of the term.
Please ensure that learners thoroughly understand the exercise before moving to the next
exercise.
Assist learners in how to approach and answer questions especially level 3 and 4 questions.
QUESTION 1 (1H 20 MIN)
1.1.1 Interest refers to the amount that will be added to an account that is not settled yet /
Rente verwys na die bedrag wat by die agterstallige bedrag gevoeg word.
OR/OF
Extra amount is charged on the late payments /
Ekstra bedrag wat gehef word op laat betalings.
1.1.2 R14 819,50
1.1.3
1
100
50,81914
20,148 %
= 1,000033739329937
≈ 1%
1.1.4 APG 2039W Design & Theory Studio II
1.1.5 R14 967,70 – R8 650,00
= R6 317,70
1.1.6 Total amount / Totale bedrag
= R3 030 + R3 030 + R2 280 + R2 280 + R9 580 +
R4 530 + R29 460 + R2 087 + R395,95 +
R395,95
= R57 068,90
OR/OF
Total amount / Totale bedrag
= R62 594 – R6 317,70 + 2 × R395,95
= R57 068,90
OR/OF
Total amount / Totale bedrag
R40 386 + R23000 + R8650 – R14819,50 – R148,50 = R57 068,90
OR/OF
Total amount / Totale bedrag
R3 030 + R3 030 + R2 280 + R2 280 + R9 580 +
R4 530 + R29 460 + R395,95 + R395,95
= R54 981,90
1.1.7 Direct deposit / Direkte deposito
1.1.8 Monthly instalment / Maandelikse paaiement
R40 386,60 ÷ 5
= R8 077,32
OR/OF
Monthly instalment / Maandelikse paaiement
R8 077,32 × 5
= R40 386,60
OR/OF
Monthly instalment / Maandelikse paaiement
077,32R8
386,60R40
= 5
1.1.9
(a) R29 460 ×
104,62
100
= R30 821,052
R30 821,052 × 104,38
100
= R32 171,01408
R32 171,01408 × 105,17
100
= R33 834,26
1.1.9
(b)
𝑅395,95
𝑅39 594,70 x 100% OR/OF R39 594,70 ×
1
100
= 1% = R395,947
= R395,95
1.1.9
(c)
The amount due was still not payed on 30|09|17/ Die bedrag veskuldig was nogsteeds
nie betaal by 30|09|17 nie.
1.2.1 Inflation is a measure of rate at which the cost of goods is changing over a period of
time and is usually expressed as a percentage /
Inflasie is die meting van die koers waarteen die prys van goedere verander oor 'n
tydperk en word gewoonlik uitgedruk in persentasie.
OR/OF
The percentage increase of the food prices over the period 1970 – 2015 /
Die persentasietoename van kospryse oor die tydperk 1970 – 2015.
OR/OF
Percentage increase of price over a period of time /
Persentasie verhoging van prys oor 'n tydperk.
OR/OF
Inflation is the rising price of goods/items over time /
Inflasie is die stygende prys van goedere/dienste oor tyd.
1.2.2 R0,30 OR/OF 30c
1.2.3 R557,00 – R418,00
= R139,00
1.2.4 Percentage change / Presentasieverandering
1
100
R0,25
R0,25R75,00
%
= 29 900 %
OR/OF
Percentage change / Presentasieverandering
25,0
75 × 100% = 30 000%
Therefore % increase = 30 000% - 100%
= 29 900%
1.2.5 Cost price / Kosprys
1
104,90
117,5
100
= R89,28
OR/OF Cost price / Kosprys
117,5%
90,104
= R89,28
OR/OF
Cost price / Kosprys
175,1
90,104
= R89,28
OR/OF
Cost price / Kosprys
5,117
5,17× R104,90 = R15,62
R104,90 – R15,62
=R89,28
1.3.1 B OR/OF R241 600 000 000
1.3.2 Budget is the proposed way in which money will be spent on different items /
Begroting is die voorgestelde manier hoe die geld vir verskillende items gespandeer behoort
te word.
1.3.3 Skills development levy institutions /
Vaardigheidsontwikkelingheffingsinstellings
1.3.4
5,320
3,15× 100%
= 4,77%
OR/OF
Percentage of the total education budget /
Persentasie van die totale onderwysbegroting
1
100
000000500320
00000030015
R
R%
= 4,77%
1.3.5 Education Administration plus NSFAS amount
to 31,1 billion rand /
Onderwysadministrasie plus NSFAS bedrag
tot 31,1 miljard rand
9,7%
Accept any estimation from 9,5% but less than 9,86%
Aanvaar enige skatting vanaf 9,5% maar minder as 9,86%
OR/OF
15,8 + 15,3 = 31,1 billion / miljard
= 9,7%
Accept any estimation from 9,5% but less than 9,86%
Aanvaar enige skatting vanaf 9,5% maar minder as 9,86%
1.3.6 241,6 + 198,7 + 187,5 + 70,7 + 195,8 + 162,4 + 180 + 320,5 = R1557,20 Billion/Miljard 320,5
1557,2 × 100%
= 20,6%
1.3.7 R 1 557 200 000 000 × 2,6
100
= R40 487 200 000
R40 487 200 000 – R30 255 200 000
=R10 232 000 000
QUESTION 2 (30 MIN)
2.1 Vacancy = $2 224 560 – $2 046 595
= $177 965
2.2 The Break-even Occupancy Percentage
100%incomerentalPossible
repaymentloan Bankexpensestotal Projected
%1000001842$
1540531$580670$
= 78,92554945%
≈ 78,93%
2.3 Annual rent for bachelor flat in 2018 =
40
271 $318
= $7 956,775
Per month = 12
956,775 $7
= $663,06
2.4 Income from 2 bachelor flats = 2
40
454$321
= $16 072,70
General vacancy for one bedroom flats
= $138 483 – $16 072,70
= $122 410,30
Unit price for one bedroom flats = 60
884916$
= $ 15 281,40
Number of vacant one bedroom flats = 840,28115$
30,410122$
unoccupied bachelor flat : unoccupied one-bedroom flats
= 2 : 8
= 1 : 4
The prediction is correct
2.5.1
2.5.2 Both income and expenses increases every year
The income increases more per year than the expenses because the line of income goes up
more per year (steeper) than the expense.
OR
The trend is that the potential income growth rate increase at a much higher rate than the
total expenses rate.
60
70
80
90
100
110
120
130
140
150
160
2016 2017 2018 2019 2020
Am
ou
nt
in 1
0 t
ho
usa
nd
Do
lla
r
Year
Projected Net Operating Income and Expenses
Income
QUESTION 3 (45 MIN)
3.1.1 13% OR 0,13
3.1.2
(a)
𝑅9102,30
24
= R379,26
3.1.2
(b)
R8 999 + R400
= R9 399
3.1.2
(c)
15% × R8 499
OR
0,15 × R8 499
= R1 274,85
3.1.2
(d)
R403,70 × 30 months
= R12 111,00
Total Cost = R500 + R12 111,00
= R12 611
3.1.2
(e)
HP Laptop
R8 999 + R400
= R9 399
Lenovo Laptop
= R8 499
R9 399 – R8 499
= R900
3.1.2
(f)
The quality of the laptop/ Kwaliteit van die stootrekenaar.
OR/OF
The brand of the laptop/ Die maak van die stootrekenaar.
OR/OF
The features of the laptop/ Die funksies van die stootrekenaar.
3.2.1 R450
3.2.2 R550
3.3.3 R450 + [(number of hours – 1) × R400]
3.2.4
(a)
G = R450 + [ (3 – 1) × R400]
= R1 250
3.2.4
(b)
H = 550 ÷ 4400
= 8 hours
OR/OF
H = R3 250 – R 450
= 400 ÷ 2800
= 7 hours + 1 hour
= 8 hours
3.2.5 Two thousand and fifty rand
3.3 1st year = 20 000 × %
100
73,7
= R1 546
Amount = 20 000 + 1 546
= 21 546
2nd year = 21 546 × %100
98,7
= 1 719,37
Total amount = 21 546 + 1 719,37
= R23 265,37
OR
1st year amount = 20 000 × %100
73,107
= 21 546
2nd year amount = 21 546 × 100
%98,107
= 23 265,37
OR
R20 000 × 107,73% × 107,98% = R23 265,37
QUESTION 4 (40 MIN)
4.1.1 A + R103,3 + R500,4 = R1161,10
A + R 603,7 = R1161,1
A = R1161,1 – R603,7
A = R557,4
4.1.2 43,37% of Non-interest allocation = 82,6 billion
43,37% van Nierentedraende toewysing = 82,6 miljard
Non-interest allocation/Nierentedraende toewysing
= 82,6 billion/miljard ÷ 43,37%
= R190,89 billion/miljard
4.1.3 11,8 – 11,2 = 0,6 billion/miljard
= R600 000 000
4.1.4 % increase =
New old100%
old
% verhoging = -
100%Nuwe oue
oue
= 162,4 101,2
100%101,2
= 60,47%
4.1.5 This amount is a budget for an occasion where the country can encounter a natural
disaster./Hierdie bedrag word begroot vir 'n geleentheid wanneer die land 'n natruurramp
ondervind.
OR/OF
A budget for any unplanned occasion that the government has to take responsibility for./Dit
is 'n begroting vir 'n onbeplande uitgawe waarvoor die regering verantwoordelik is.
The country was experiencing draught the government had to help farmers with water for the
farms and food for the animals./Die land het 'n droogte ondervind en die regering moes die
boere help met water en voer vir die diere op die plase.
4.1.6 Equitable share %/Regmatige deel %
= 386,5÷ 471,4× 100%
= 81,99%
Correct .This is more than 80%
Korrek. Dit is meer as 80%
CA
4.2.1 R70 961 + R28 165 + B + R106 841 + R59 371 + R41 214 + R13 418 + R34 857 + R51 049
= R506 104
R405 876+B = R506 104
B = R506 104 –
B = R100 228
4.2.2 Total for 2015/16 ×107,2% = R410 699 million
Totaal vir 2015/16 ×107,2% = R410 699 miljoen
Total for 2015/15/Totaal vir 2015/16
= 410699
107,2%
= R383 144,73 million/miljoen
4.2.3 𝐻𝑖𝑔ℎ𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒−𝐿𝑜𝑤𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒
𝐿𝑜𝑤𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 x 100%
= 13 418−12 501
12 501 x 100%
= 7,3354%
= 7%
QUESTION 5 (1H 20 MIN)
5.1.1 January / Januarie
5.1.2 Samantha
5.1.3 R1 280,00 + R1 280,00
= R2 560,00
5.1.4 VAT – Value Added Tax /
BTW – Belasting op Toegevoegde Waarde
5.1.5
1,15
840,00R3
= R3 339,130435
= R3 339,13
5.1.6
61,380614,113,3339
13,333915,13840
61,3806100
11413,3339
13,3339115
1003840
RR
RR
OR
RR
RR
5.1.7
%877,0
100R3806,61
R3806,61-R3840
Mr Khumalo’s statement is incorrect/ Mr Khumalo se bewering is verkeerd.
5.2.1 Inflation is a measure of rate at which the cost of goods is changing over a period of time and
is usually expressed as a percentage /
Inflasie is die meting van die koers waarteen die prys van goedere verander oor 'n tydperk
en word gewoonlik uitgedruk in persentasie
5.2.2 Buying power / Koopkrag
Year / Jaar 1
R10 000,00 × 100
5,6
= R650,00
R10 000,00 – R650,00
=R9 350,00
Year / Jaar 2
R9 350,00 × 100
5,6
= R607,75
R9 350,00 – R607,75
=R8 742,25
5.2.3 The amount decreases over the 2 year period, which means the buying power decreased / Die
bedrag verminder oor die 2 jaar periode dus 'n aanduiding dat die koopkrag verminder.
5.3.1 . A =
0001
R150800
= 120
5.3.2 Total cost = R120,00n + R3 000,00
Total cost = R120,00 (920) + R3 000,00
= R113 400,00
Total cost = R120,00n + R3 000,00, where n = number of 64GB memory sticks
Calculate the total cost of 920 memory sticks.
5.3.3 Profit = income – total cost /
Wins = Inkomste – totale koste
R27 000,00 = (n × R150,00) – (n × R120,00 + R3 000,00)
R27 000,00 = 150n – (120n +3 000)
R27 000,00 = 30n - R3 000,00
R30 000,00 = 30n
n = 1 000
No, she is not correct.
Nee, sy is nie korrek nie.
OR/OF
Total Cost = (750 × R120,00 + R3 000,00)
= R93 000,00
Income/Inkomste = R150,00 × 750
= R112 500,00
Profit/Wins = R112 500,00 – R93 000,00
= R19 500,00
No, she is not correct.
Nee, sy is nie korrek nie
5.4.1 Interest: Amount earned on an investment. The money he will have earned on the R5
000,00 he invested after 5 years.
Interest rate: the percentage at which interest is calculated.
5.4.2 Interest =
100
512,1000,00R5
= R3 025,00
5.4.3 Interest =
100
712,1000,00R5
= R4 235,00
R4 235,00 – R3 025,00
=R1 210,00
No, he is not correct /
Nee hy is nie korrek nie.
5.4.4 Compound Interest Option/ Saamgestelde rente opsie
48,7043
)100
1,1221,6283(21,6283
21,6283
21,6785605
)100
1,125605(5605
5605
6055000
)100
1,125000(5000
R
RR
R
RR
RR
R
RR
RR
Simple Interest Option/ Enkelvoudige rente opsie
802530255000
30255605
605100
1,125000
RRR
RR
RR
Bertram's statement is incorrect/ Bertram se bewering is verkeerd.
QUESTION 6 (50 MIN)
6.1.1 Discount percentage/Persentasie afslag
= 100% 087,72 R160
140 R6
= 3,8353971 ≈ 3,8%
6.1.2 Sub Total/Subtotaal
= R160 087 – R6140 + (2 × R3 500 + R4 298,25 + R1 315,79)
= R166 561,76
6.1.3 Safety reason/as a safety feature.
Veiligheidsrede/as 'n veiligheidskenmerk
OR/OF
Protection from thieves and hijackers.
Beskerming teen diewe en kapers
OR/OF
Beautification of the car.
Verfraaiing van die motor
OR/OF
Longer lasting/Langdurend
6.1.4 27 months = 2 years and 3 months or 2
4
1years
27 maande = 2 jaar en 3 maande of 24
1jaar
1st year value/1ste jaar waarde
= R1 250 000 × 6% + R1 250 000 = R1 325 000
2nd year value/2de jaar waarde
= R1 325 000 × 6% + R1 325 000 = R1 404 500
Last 3 months/Laaste 3 maande
= R1 404 500 × 4
6%+ R1 404 500 = R1 425 567,50
Difference/Verskil
= R1 425 567,50 – R1 250 000 = R175 567,50
It is not enough/Dit is nie genoeg nie.
6.1.5 Mistake: calc. 14% on original price AND an extra 1% on accumulated price
Fout: bereken 14% op die oorspronklike EN tel 'n ekstra 1% by die totaal.
Correct calculation should be 15% on original price
Korrekte berekening sou wees om 15% by oorspronklike prys te tel
Amount/Bedrag = 1,15 × R160 087,72
= R184 100,88
OR/OF
The dealer added 1% on the VAT inclusive price of R182 500
Die handelaar het 1% by die BTW insluitende prys van R182 500 getel
He should have calculated the 15% directly on the original selling price excluding VAT.
Hy moet die 15% direk op die oorspronklike verkoopsprys sonder BTW tel
New selling price inl. VAT/ Verkoopsprys BTW ingesluit
= 115% × R160 087,72
= R184 100,88
6.2.1 Total cost = Base fare + 10 × cost per mile
Totale koste = Basisfooi + 10 × koste per myl
= $20,00 + 10 × $5,00 per mile
= $70,00
6.2.2 Maximum distance (in miles)/Maksimum afstand (in myl)
= $0,90
$4,65
= 5,166…
≈ 5
6.2.3 1 hour 9 minutes = 69 minutes
1 uur 9 minute = 69 minute
Post trip cost/Na-rit koste
= 29,73 mi × $3,55 /mi + 69 min × $0,45 / min
= $105,5415 + $31,05
= $136,59
Upfront cost/Vooruit koste = $8 + 29,73mi × $3,55/mi
= $113,54
The statement is valid/Die stelling is geldig
6.2.4 To cover cost for wasted time when a vehicle could have been used to assist someone when
you cancel the booking.
Om kostes te dek vir verlore tyd terwyl die voertuig gebruik kon word om iemand anders te
help wanneer jy die bespreking kanselleer.
OR/OF
Penalty for booking made if one do not finally use the vehicle (time wasting).
Boete vir 'n bespreking wat gemaak is as jy aan die einde nie die voertuig gebruik nie
(vermorsing van tyd)
OR/OF
Prevent hoax calls/ Verhoed fop oproepe
QUESTION 7 (1H 20 MIN)
7.1.1 Total amount = (22 × R250) + (22 × R400)
= R5 500 + R8 800
= R14 300
7.1.2 Total amount = R400 + (4,75% × R400)
= R400 + R19
= R419
7.1.3 Amount received per member
= Total bank balance – non-refundable initial fee
= R110 614,84 – (250 × 22)
= R110 614,84 – R 5 500,00
= R105 114,84 ÷ 22
= R4 777,95
7.2.1 A = R1 799,88 ÷ 12
= R149,99
7.2.2 Total goods value = R143 988 + R1 799,88
= R145 787,88
7.2.3 %100
787,88 R145
494,55 71R
= 12,00000302%
≈ 12%
7.2.4 VAT = R143 988 ×15% ÷115%
= R18 781,04347826
≈ R18 781,04
7.2.5 The amount of money that the lender charges for lending the money.
7.2.6 Interest = deferred amount × interest × 30 months p.a
= R143 597,33 × 11,23316% × 12
30
= R40 326,29
7.2.7 B = tot. cost of credit – all risks ins. – tot. deferred
= R195 540,52 – R2 049,90 – R183 923,62
= R9 567
7.2.8 Fitting charges, TV Licence fee, Service fee
7.2.9 Final instalment = R195 540,52 – (29 × R6 518,10)
= R195 540,52 – R189 024,90
= R6 515,62
7.2.10 No. The less discount shows R0,00/ Nee, die minus afslag bedrag wys R0,00.
7.3.1 Profit is when your income is greater than your expenses.
7.3.2
(a)
MTN R270 ÷ R15 = 18 vouchers
Profit on 18 vouchers = 18 × R0,51
= R9,18
Virgin Mobile R120 ÷ R15 = 8 vouchers
Profit on 8 vouchers = 8 × R0,81
= R6,48
Total profit for the day = R9,18 + R6,48
= R15,66
(b)
31,13
35,266,15
35,2100
1566,15
R
RR
RR
7.3.3 Number of weeks =
341,50
50,5122
= 15 days
= 3 school weeks
7.3.4 Total cost of machines = R1 539 × 52
= R80 028
Number of airtime vouchers = R80 028 ÷ R0,54
= 148 200
7.3.5 Total discount =
100
25,3× R14 760
= R479,70
QUESTION 8 (35 MIN)
8.1.1 SUBTOTAL
= R2 893,86 + R394,74 + R180 + R2 719,30 + R30,70
= R6 218,60
Calculating VAT
= R6 218,60 × 15% OR A = R6 218,60 × 1,15
= R932,79 = R7 151,39
A = R6 218,60 + R932,79
= R7 151,39
8.1.2 OPTION 2
Total cost = R3 499,00 + R499,00 + R189,00 + R235,00
+ (4 × R3,50) + 223,50R + 3350,00R + R349,00
= R5 882,00
Difference in price = R7 089,20 – R5 882,00
= R1 207,20
Mr Chan's estimation is NOT valid.
8.1.3 The brand of the gas stove.
OR
No time to shop around.
OR
The company will install the stove.
OR
Reputable dealer
OR
After sales service
OR
Any suitable answer
8.1.4 06/05/2015
OR
6 May 2015
8.2.1 Tax rebate reduces the tax payable
Medical aid credit reduces the amount of tax to be paid.
8.2.2 Taxable income = R742 000
Tax in 2015/2016
Tax payable = R208 587 + 41% of (R742 000 – R701 300) –
R13 257 – 12 × (2 × R270 + 3 × R181)
= R208 587 + 41% of (R40 700) – R13 257 – 12 × (R540 + R543)
= R208 587 + R16 687 – R13 257 – R12 996
= R199 021
Tax in 2014/2015
TI = R195 212 + 40% of (R742 000 – R673 100) – R12 726 – 12 ×
(2 × R257 + 3 × R172)
= R195 212 + 40% of (R68 900) – R12 726 – 12 × (R514 + R516)
= R195 212 + R27 560 – R12 726 – R12 360
= R197 686
The statement is NOT valid, the increase is R1 335,00/ Die bewering is nie geldig nie, dit
vermeerder met n R1335.
QUESTION 9 (30 MIN)
9.1 A = 201,86 × 108,1%
= 218,21 c/kWh
B = 198,89 × 105,2 %
= 209,23 c/kWh
C = 232,84 × 105,2%
= 244,95
9.2 Number of Units = 130 × 100 = 130 000
= 95,159
130000
= 81,27 Units of kWh
9.3 Block 1 = 100 units
Block 2= 300 units
Block 3 = 50 units
Total 450 units
Cost = 100 × 159,95 = 15995 c/kWh
= 300 × 183,99 = 55197 c/kWh
= 50 × 201,86 = 10093 c/kWh
Total = 812585 c/kWh
= 812585 ÷100 = R812,8 c
9.4 Block 1 = 100 × 159,95 = 15995 Block 2 = 300 × 183,99 = 55197
Block 3 = 250 × 201,86 = 50465
Block 4 = 20 × 215,40 = 4308
TOTAL COST = 15995+55197+50465+4308
= 125965 ÷ 100
= R1259,65