Grade 12 Mathematical Literacy Preliminary Exam Paper 2

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Transcript of Grade 12 Mathematical Literacy Preliminary Exam Paper 2

Time: 3 hours 150 marks
QUESTION 1
The Table Mountain Aerial Cableway Company has been providing visitors with a world-class experience since October 4, 1929. The company operates in a National Park and World Heritage Site.
The mountain’s magnetism has a way of drawing people in, compelling them to reach the summit. However, getting to the top was not always the effortless trip it is today.
The Table Mountain Aerial Cableway is a cable car transportation system offering visitors a five- minute ride to the top of Table Mountain in Cape Town, South Africa. It is one of Cape Town's most popular tourist attractions with approximately one million people a year using the Cableway. [Source: www.tablemountain.net/content/page/about-history]
1.1 The Cableway was completed in 1929 at a cost of GB£ 60,000 (equivalent to £ 11,4 million in
2011). It has been upgraded three times since then. [Source: en.wikipedia.org/wiki/Table_Mountain_Aerial_Cableway]
1.1.1 Determine the rate used to find the equivalent value for the GB£ in 2011 and write
your answer in the format GB£ 1 = £… in 2011. (3)
60 000 : 11 400 000 ma
11 400 000 ÷ 60 000m = 190
GB£ 1 = £ 190 in 2011 ca TL2 Fin
1.1.2 Approximately how many people used the Cableway from October 1929 until October
2018? (3)
1929 to 2018 = 89 years a 89 x 1 000 000m = 89 million peopleca TL2 Meas
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1.2 An American family of 5 visits Cape Town in May and decides to go up the Cableway. The family consists of 2 parents, 2 children of ages 11 and 14, and one grandparent aged 73. They find the following table of rates on the website:
Ticket type MORNING (08h30-13h00)
Return One way
Child 4-17 years of age R165 R90 Child
4-17 years of age R145 R90
SA Senior Citizen (7 days a week at Ticket Office)
R100 R50 SA Senior Citizen (7 days a week at Ticket Office)
R100 R50
1.2.1 Calculate the total cost for the entire family to go up the Cableway if they purchase
return tickets for the morning. (4)
R330 x 3ma + R165 x 2ma = R990 +m R330 = R1 320ca TL2 Fin [ if use Senior citizen rate = R660a + R100 + R330a = R1 090ca]
1.2.2 The son comments that he and his sister are “two for the price of one”. Use the return
rates to explain whether his comment is correct. (3)
His ticket is R165, his sister’s ticket is R165. The tickets for the 2 of them thus cost R330 which is the same price as 1 adult ticket. He is correct that their 2 Child tickets were the same price as one adult ticket. TL4 Fin
1.2.3 How much would they save if they waited and went up the Cableway after lunch
instead? Show all calculations. (5)
Afternoon: R290 x 3 + R145 x 2cm = 870 +m 290 = R1 160 R1 320 –m R1 160 = R160 They would save R160ca TL3 Fin
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1.2.4 The family is staying at the Belmond Mount Nelson Hotel. Consider the map on the
APPENDIX Page 1 and then answer the questions which follow.
a) Name TWO roads that they will travel on to get to the Table Mountain Cableway (2)
M62(Kloof Nek Road), M3, Tafelberg Road, Checkers Kloof Street, Hof Street (any 2) TL4 Maps
b) Should they prefer to take a bus to the Table Mountain Cableway, which busses are
available to transport them? (2)
Bus 106 or 107a and then 110.a TL4 Maps
1.3 The website states that “800 people can enjoy the trip every hour”. If each trip is only at three
quarters of its capacity, determine how many people will enjoy the trip in one morning (08h30
– 13h00). (5)
One morning (08h30 – 13h00) = 4,5 hoursa 800 x 4,5ma = 3 600 people maximumca 75%ma x 3 600 = 2 700 ca TL2 Meas
One morning 08h30 – 13h00 = 4,5 hoursa 800 × ¾ m = 600 a 600 × 4,5 hma = 2 700ca
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There is a 20% chance that there will be no
wind during thunderstorms, if it is raining
(precipitation) or when there is fog. On a
clear day there is a 40% chance of above
average wind speeds. [Source: http://weather.news24.com/sa/cape-town]
1.4.1 Study the information in table and use
it to complete the tree diagram below.
Give answers correct to two decimal places where necessary. (6)
(1 mark each) TL3 Prob
1.4.2 Determine the probability, as a percentage, that it is clear and there is below average
wind on the day that the American family plan to go up the Cableway. (4)
0,26ca x 0,6ca x 100ma = 15,6% ca TL3 Prob
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QUESTION 2
In Cape Town there are many Nature Reserves and so families that live there
often purchase annual access cards from SAN Parks. One of the options is given
below.
The Green Card:
The TMNP My Green Card is available exclusively to South African
residents of Cape Town, costs R157 and provides the holder with 12 free entries into any of the
Table Mountain National Park’s pay points: Cape of Good Hope (Cape Point); Boulders Penguin
Colony, Oudekraal and Silvermine, as well as to the braai and picnic areas at Tokai, Newlands
and Perdekloof. It offers fantastic value. [Source: www.sanparks.org/parks]
2.1 Tarren is going to study at UCT in 2020 and enjoys being in Nature. Could she purchase a
Green Card? Justify your answer. (2)
Yes. She will be a South African resident of Cape Town while she studies. (with valid justification) TL 4 Fin
2.2 Tarren discovers the attraction of being at Cape Point and decides that she will frequently go
there during the year. She considers buying a Green Card for R157.
2.2.1 Write down an equation that will represent the relationship between the number of visits she
makes to Cape Point and the cost per visit if she purchases a Green card. Let C be the
effective cost per visit and n the number of visits. (2)
C = 157a ÷ n a TL3 Fin
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2.2.2 The line on the graph paper below represents the cost of purchasing an individual
ticket each time Tarren visits Cape Point.
On the same graph paper, draw the graph that represents the cost per visit if she
purchases a Green card. (6)
TL3 Fin
2.2.3 Use the graph to determine the cost of an individual ticket to Cape Point. (2)
R76 aa(accept R75 – R78) TL2 Fin
2.2.4 Why does the graph stop after 12 visits? (2)
The Green Card is only for 12 entries.expl TL4 Fin
2.2.5 Do you think that Tarren should buy a Green card or not? Use calculations and/or
values from the graph to justify your answer. (2)
Yes. She only has to use the Green card 2 times (A on graph) [OR 2 x 76 = 152] in order to save money on the Cape Point tickets. Any visits she makes to the other parks will be “free” after that. TL4 Fin
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
160.00
180.00
Co st
p er
v isi
t ( R)
Green Card Individual Tickets
one other point
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2.3 Study the map below and then answer the questions which follow.
[Source: www.sanparks.org/images/parks/table_mountain/recreational_map.jpg]
2.3.1 Will Tarren be able to have a braai at Cape Point? Justify your answer. (2)
No.a There is no “Braai fires” symbol at Cape Point. expl TL4 Maps
2.3.2 Name TWO recreational activities that Tarren will be able to do at Cape Point. (2)
Walking/Hikinga or Photography/Viewinga TL4 Maps
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2.4 During the summer months on Sundays, some of the parks host open-air concerts. Below are graphs representing the ages of attendees at two different concerts: One concert features a pop singer and the other features a well-known jazz musician. Use the graphs to answer the questions which follow.
2.4.1 Which concert do you think is represented by the data from Graph A? Explain your
reasoning. (2)
The pop singer’s concert a because it is a much younger crowd.expl TL4 Data
2.4.2 Calculate the interquartile range of Concert A. (2)
37 – 20ma = 17 yearsca TL2 Data
2.4.3 If there were 5 000 people at Concert B, how many people were over the age of 33? (4)
Q1 = 33 .: 75% are over 33 75% x 5 000ma = 3 750 peopleca TL3 Data
2.4.4 Which concert appeals more to people of all ages? Explain your answer. (2)
Concert B a because the range of the age values is larger.expl TL4 Data
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2.4.5 Tarren looked at the graph and stated that the mean average age of the concert
attendees is 37. Do you agree or disagree with this statement? Explain your answer.
(2)
Agree, because 37,5 is the mean of the two mediansexpl OR Disagree, these graphs only show the medians of 2 of the concerts from the entire summer concert series.expl OR Disagree, there is not enough information to find the mean average age of the concert attendees.expl TL4 Data
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QUESTION 3
Kirstenbosch Botanical Garden, in Cape Town, is acclaimed as one of the great botanical gardens of the world. The garden is one of nine national botanical gardens in South Africa. It covers 528 hectares and has a cultivated garden area of 35 hectares, which displays a variety of South African plants. Kirstenbosch was founded in 1913 and was the first botanical garden in the world to be created to protect indigenous plants. [Source: en.wikipedia.org/wiki/Kirstenbosch_National_Botanical_Garden] 3.1 The table below lists the quantities and costs involved in running Kirstenbosch Botanical
Garden. Date 2004 2014 Number of staff employed 132 682 Staff Salaries R 9 891 000 R 246 780 058 Annual government grant allocation
R 3 656 000 R 264 254 000
Annual Income (including government grant)
R 13 555 000 R 324 422 259
Annual Costs (excluding salaries)
Percentage self-generated income
Visitors (per annum) 650 000 1 333 208 [Source: www.sanbi.org/wp-content/uploads/2018/04/sanbi-ar-2014-web.pdf]
3.1.1 Use the values from the table above to show whether Kirstenbosch Botanical Garden was running at a surplus or a loss in 2014. (4) R 324 422 259 – R 75 801 226a – R 246 780 058a = R 1 840 975ca Surplus in 2014ca TL4 Fin
3.1.2 Show how the “Percentage self-generated income” value for 2004 has been
calculated. (4)
Self-generated income: R13 555 000 – R3 656 000ma = R9 899 000a
× = 73% TL4 Fin
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3.1.3 Compare the average annual salary paid to staff in 2004 to the average annual salary paid
to staff in 2014. (6)
2004: R9 891 000 ÷ 132ma = R74 931,82 ca 2014: R246 780 058 ÷ 682ma = R361 847,59 ca The average salary in 2014 is more than 4 timesa the average in 2004.expl [The salaries have increased by 383%] TL4 Fin
3.2 A landscaper at Kirstenbosch
Botanical Gardens received an
000 in 2016/2017. He is 48
years old and does not
contribute any money to a
medical aid scheme. With the
use of the tax table given
below, show that more than
R10 000 in tax is deducted from
his salary for PAYE each month.
(5)
R520 000 annual taxable income 4th tax bracket a: Annual tax = 96 264 + 36% x (520000 – 406 400) – 13 500a(rebate) = 96 264 + 36% x 113 600ca – 13 500 = 96 264 + 40 896 – 13 500 = 137 160 – 13 500 = 123 660 ca
∴ Monthly tax = 123 660 ÷ 12 = R10 305ca , i.e more than R10 000 is deducted
monthly. TL4 Fin
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3.3 Elois decides to visit Kirstenbosch Garden and do a hike while she is in Cape Town. She
arrived and parked at Gate 1. Elois made her way to the Viewing Deck and then walked past
the Manor House and the Proteas. She saw the dam on her left and continued to follow the
path until she saw a sign indicating that the Yellowood Trail continued to the right. She
followed the Yellowood Trail back onto Smuts Track, through the Fragrance Garden and
along past the Vygies and Annuals until she got back to the Visitors centre.
3.3.1 Use the scale provided on the map on the Appendix to show that Elois walked more
than 2,5 km. Highlight the route she walked on the map. (7)
on map 4,2cma: 250m a 45 - 50cmca : 2 678 - 2 976mca ≈ 2,7km – 3km conv TL3 Maps
4,3 cm on map 44 – 52 cm = 2,55 – 3,02 km
4,2 cm on map 44 – 52 cm = 2,61 – 3,1 km
3.3.2 If she walked 2,9 km at a speed of approximately 5km/h and stopped at the Viewing
Deck for 30 minutes, how long would the hike take? Give your answer in hours and
minutes. (5)
5 km in 60 minutesconv 2,9 km in 34,8 minutesm 34,8 + 30m = 64,8 minutesca = 1 hour and 5 minutes.conv TL2 Meas
3.3.3 Elois is thirsty after her hike. Is there a convenient place for her to get a cooldrink and
a snack? Justify your answer. (3)
Yes. There are refreshments available near the parking – knife and fork symbolexpl TL4 Map
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3.4 To be environmentally friendly the garden store in Kirstenbosch sells
plants in recycled plastic bottles as shown alongside.
You may use the following information:
2,54 cm = 1 inch
1 cm3 = 1 m
Soil has a mass of approximately 600 – 900 kg per cubic metre
(depending on the type of soil)
Soil is sold in 10 kg bags
The dimensions of the bottle are:
4 inches in diameter by 12,25 inches, and the soil is filled to halfway up
the bottle.
3.4.1 The store manager has to order soil for 300 plants to be sold in the plastic bottles.
(a) Show that the volume of soil required for one of the plastic bottles is approximately
1200 cm3. (7)
Note: Do not calculate the neck of the bottle separately from the rest of the bottle,
but rather work with an estimated volume of the bottle.
4 inches is 2,54 x 4 = 10,16 cma .: radius = 10,16 ÷ 2 = 5,08 cm ca 12,25 inches is 2,54 x 12,25 = 31,115 cma Halfway up 31,115cm = 3,115÷ 2 ma = 15,558 ≈ 15cm Area of circle = π x (5,08)2 = 81,073 cm2 ca Volume of soil for 1 bottle = 81,073 x 15m = 1216 cm3 a≈ 1 200 cm3
TL3 Meas
(b) Calculate how many bags of soil the manager should order for the 300 plants. (5)
Volume of soil for 300 bottles = 1200 x 300ma = 360 000 cm3
1m3 x 1003 = 1 000 000 cm3 conv 1 000 000cm3 ≈ 750 kg .: 360 000 cm3 ≈ 270 kg ca 270 ÷ 10ma = 27 bags He should order 27 bags of soil.ca TL3 Meas
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3.4.2 One of the assistants suggests that the bottles be wrapped in blue or green paper so
that the “flower pots” look more appealing. The paper wrap is 70cm wide and costs
R17 for a roll that is 1m long. He is only going to cover up the soil part of the bottle and
leave the clear plastic showing.
(a) Use the circumference of the bottle to determine the dimensions of the paper he
will require to wrap one “flower pots”. (3)
Circumference of bottle = π x 10,16m = 31,9 cm Width of paper = 31,9cm.ca Length = 15cm (or 15,6cm) ca from 3.4.1(a) [Area required for 1 = 31,9 x 15cm = 478,5 cm2 ] TL3 Meas
(b) How much will the paper cost to cover the 300 containers? (6)
70cm wide .: he can cut 2 from the width.ca (31,9 x 2 = 63,8cm) 1 m = 100cm 100 ÷ 15 = 6,66… .: he can cut 6 lengths from one rollca 6 x 2 = 12 pieces per roll 300 ÷ 12 = 25 . He requires 25 rolls 25 x R17m = R425ca
[Area required for 1 = 31,9 x 15cm = 478,5 cm2 ca Area for 300 = 478,5 x 300m = 143 550 cm2 70 x 100 = 7 000cm2 per roll 143 550 ÷ 7 000 = 20,5 ≈ 21 rolls 21 x R17m = R357ca] Only 5 marks – not practical TL3 Meas
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3.5 Kirstenbosch grows indigenous South African plants, and a large number of these are
fynbos. Fynbos is a natural vegetation occurring in a small area in Africa and is known for its
exceptional degree of biodiversity. Fynbos forms part of the Cape floral kingdom, as one of
only six floral kingdoms in the world, and with 9 600 recorded plant species, 70% of them
found nowhere else on the planet, the region is a globally recognised biodiversity hotspot.
The Cape floral kingdom is the smallest and richest per area unit. The diversity of fynbos
plants is extremely high, and they have over 9000 species of fynbos plants, around 6 200 of
which are endemic. The primary fynbos plant families are proteas, ericas and restios. Of the
ericas, 600 occur in the fynbos kingdom and only 26 are found in the rest of the world.
Furthermore, although the fynbos kingdom comprises only 6% of the area of southern Africa,
it makes up half the species of the subcontinent. In fact, fynbos counts for almost 1 in 5 of all
plant species in Africa.
Kirstenbosch grows indigenous South African plants, and a large number of these are
fynbos. Fynbos is a natural vegetation occurring in a small area in Africa and is known for its
exceptional degree of biodiversity. Fynbos forms part of the Cape floral kingdom and 70% of
them are found nowhere else on the planet As one of only six floral kingdoms in the world,
the region is a globally recognised as a biodiversity hotspot. The Cape floral kingdom is the
smallest and richest per area unit. The diversity of fynbos plants is extremely high. There are
over 9 000 species of fynbos plants, around 6 200 of which are endemic (native and restricted
to a certain place). The primary fynbos plant families are proteas, ericas and restios. Of the
ericas, 600 occur in the fynbos kingdom and only 26 are found in the rest of the world.
Furthermore, although the fynbos kingdom comprises only 6% of the area of southern Africa,
it makes up half the species of the subcontinent. In fact, fynbos counts for almost 1 in 5 of all
plant species in Africa.
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One of the botanists (someone who studies plants) travelled to one small area in the
Cederberg and another in the Nelson Mandela Metropole to collect data on fynbos plants. He
recorded the data as shown in the tables below.
Cederberg Nelson Mandela Metropole
White 13 17 3 33 3 9 5 17
Pink or Red 21 23 11 55 6 4 11 21
Yellow 4 8 6 18 0 3 1 4
Other 10 5 9 24 10 13 15 38
Total 48 53 29 130 19 29 32 80
3.5.1 Represent the data collected on an appropriate graph to compare the plant families in
the two areas. (8)
appropriate graph (bar or broken line) even spaces + bars of same width heading key Horizontal labels Vertical label +…