GRADE 12 SEPTEMBER 2016 MATHEMATICAL LITERACY P1

NATIONAL SENIOR CERTIFICATE

GRADE 12

SEPTEMBER 2016

MATHEMATICAL LITERACY P1

MARKS: 150

TIME: 3 hours

This question paper consists of 15 pages and an addendum with annexures.

*MLITE1*

2 MATHEMATICAL LITERACY P1 (EC/SEPTEMBER 2016)

Copyright reserved Please turn over

INSTRUCTIONS AND INFORMATION 1. This question paper consists of FIVE questions. Answer ALL the

questions. 2. 2.1 Use addendum with ANNEXURES for the following questions:

ANNEXURE A for QUESTION 4.1 ANNEXURE B for QUESTION 5.1

2.2 ANSWER SHEET 1 for QUESTIONS 4.1.4 and 4.1.7.

Write your GRADE and YOUR NAME in the spaces provided on the ANSWER SHEET1 and hand in the ANSWER SHEET 1 with your ANSWER BOOK.

3. Number the questions correctly according to the numbering system used

in this question paper. 4. Diagrams are not necessarily drawn to scale. 5. Round off ALL the final answers according to the context used, unless

stated otherwise. 6. Indicate units of measurement, where applicable. 7. Start EACH question on a NEW page. 8. Show ALL calculations clearly. 9. Write neatly and legibly.

(EC/SEPTEMBER 2016) MATHEMATICAL LITERACY P1 3


QUESTION 1

1.1 Layla, a 43-year-old woman took a retirement annuity (RA) policy with an insurance company. The retirement annuity lump sum paid out to the policy holder is taxed by the SARS. In November 2015 she received a RA statement for this policy.

TABLE 1: Extract of retirement annuity statement as at 3 October

2015 for the financial year 2014–2015.

Policy number 7 011 567 723

Policy type Flexi Pension Pure (No cover)

Investment portfolio Smoothed Bonus Portfolio

Monthly contribution R631,94

Maturity value Minimum: R104 227,00 to Maximum: R506 474,00

Maturity date 1st AUGUST 2032

Death benefit R122 138,71

Premium increases (fixed)

10,00% per annum

Last instalment 1st July 2032

The next statement will be issued on the 3rd of October 2016 for the year 2015–2016.

Use information from TABLE 1 to answer the following questions: 1.1.1 Write the abbreviation SARS in full. (2) 1.1.2 Determine the period (in months) that the policy is to run from

1st November 2016 to the maturity date. (3)

(2) 1.1.3 Write the maximum maturity value in words. 1.1.4 Calculate the difference between the death benefit amount and

the minimum maturity value amount to be received at the maturity date. (3)

1.1.5 Write down the ratio of death benefit to the maximum maturity

value in the form 1 : ……. (3) 1.1.6 Write down the monthly contribution for the financial year

2014–2015. (2) 1.1.7 Calculate the total annual contribution for the financial period

2013–2014. (5)



1.2 Bonny designs, prints and posts birthday gift vouchers for different companies. Below is a promotion description advert for 500 vouchers and the cost involved.

TABLE 2: Promotion Description

Birthday Gift Vouchers

Redemption item Gift Voucher

Begin Date 1-April 2016

End Date 30 April 2016

Cost of Sales% 35%

No. of recipients 500

Meal Voucher Value $15,00

Expenses Vendor Cost Estimates (Dollars)

Printing Bet Printers $225

Postage Post Office $200

Graphics Design Premier Designs $175

Labour In house labour $50

Total Budget $650

[Source: www.restaurantowner.com] Currency: 1$(US dollar) = R15,409095 Use the information from TABLE 2 to answer the following. 1.2.1 Show how the total budget value of $650 was calculated. (2) 1.2.2 Express the graphics design expense as a percentage of the

total budget. Give your answer to the nearest percentage. (3) 1.2.3 Calculate the total cost (in dollars) of the meal vouchers issued

out during this month. (3) 1.2.4 Convert the total cost of meal vouchers issued into rands. (2) 1.2.5 Calculate the postage cost of ONE gift voucher in dollars. (2) 1.2.6 Write down the promotion period for the meal vouchers. (2) [34]



QUESTION 2 2.1 Nicky is a candle maker and sells the candles to people where she stays

and in church. PICTURE: Circular and rectangular candles

[Source: www:all-free-download.com]

(1 m3 = 1 000 000 cm3 and 1 litre = 1 000 cm3)

[Source: www:all-free-download.com] Study the picture of the respective candles above and answer the

following questions. 2.1.1 Calculate the volume (in cm3) of wax needed to make a cylindrical

candle.(Ignore the hole made for the wick) You may use the following formula: Volume of a cylindrical candle = 𝝅 × (radius)2 × height

where 𝝅 = 𝟑, 𝟏𝟒𝟐 (4) 2.1.2 Nicky melts five litres of wax a day and pours it into candle

moulds. Calculate the number of cylindrical candles she can make from five litres of wax. (3)

2.1.3 Calculate the weight of wax to make a cylindrical candle in grams.

(Give your answer to the nearest gram.) You may use the following formula: Candle weight (g) = paraffin wax density x volume of one candle,

Where the paraffin wax density = 0,93 g / cm3 (3)



2.1.4 Calculate the total surface area (TSA) of a rectangular candle made by Nicky.

You may use the following formula:

𝑻𝑺𝑨 = 2(𝑙 × 𝑤) + 2ℎ(𝑙 + 𝑤) (4) 2.1.5 Study the box below that Nicky will use to deliver the cylindrical

candles and answer the questions that follow.

Height of the box = 26 cm Width = 15 cm Length = 15 cm

Calculate the number of cylindrical candles that will be packed upright for the first layer at the bottom of the box. (4)

2.1.6 Nicky uses a thermometer to check the wax temperature when it is heated. Study the diagram supplied and answer the questions that follow.

[Source: Adapted from www.yms.co.za] (a) Write down the reading on the thermometer above. (2) (b) Convert the temperature reading on the thermometer to

degrees Celsius(℃). You may use the following formula:

℃ = (℉ − 𝟑𝟐°) ÷ 𝟏, 𝟖 (3)



2.2 Nicky bought chandelier lights at Lite City for her dining room. The area of her dining room ceiling is 12 m2. The rectangular light is 50 cm long and the height is 25 cm.

Study the diagram below that shows a side view of the dining room and

position of the light to answer the questions that follow.

2.2.1 Calculate the height from the floor to the bottom of the light. Give

your answer in metres. (3) 2.2.2 Calculate the width of the dining room if the length is 1,7 m more

than the height of the dining room. You may use the formula: Area of rectangle = length x width (3)

[29]



QUESTION 3 3.1 Grade 12 learners use stickers with their examination numbers that are

stuck on their desks. Study the classroom seating plan below for Grade 12 learners during their final examination in 2015 and answer the questions that follow.

3.1.1 Give the compass direction of a learner with examination number 008 from learner with examination number 005. (2)

3.1.2 Identify the scale of the map. (2) .

3.1.3 Calculate the actual dimensions of the bookshelf in metres. (3)

3.1.4 Acks, a learner with an examination number 015 arrived late. She was not allowed to walk in between the other desks. Draw the route she used to reach her desk. (2)

3.1.5 Determine the number of learners that started writing their examination on time for this session if all desks were occupied. (2)

3.1.6 Determine the probability that a learner randomly selected had an even examination number. (2)

Dustbin



3.2 Below is the map of Glensheiling Caravan Park in KwaZulu-Natal.

[Source: www.glensheiling.co.za]

Use the map of Glensheiling Caravan Park above to answer the following questions.

3.2.1 Determine the number of camping sites north of the playground. (2) 3.2.2 Leeckay is at reception and informed that 11b is allocated to him.

Write down the directions for him to get to his camping site. (3) 3.2.3 Determine the number of caravans/cabins shown on the layout. (2) 3.2.4 One camping site has trees and shrubs behind it and one tree

adjacent to it. Write down the number displayed on this camping site. (2)

3.2.5 Name ONE of the recreational facility close to the Trout Dam. (2) [24]



QUESTION 4

4.1 The South African rugby team (Springboks) played against New Zealand rugby team (All Blacks) during the World Cup. Study the sample of Springboks and All Blacks players’ test statistics provided in ANNEXURE A and answer the questions that follow.

4.1.1 Calculate the average weight for the Springbok team’s players. (3) 4.1.2 Identify the value of an outlier from the All Blacks players’ points. (2) 4.1.3 Determine the modal heights for both teams. (2) 4.1.4 Complete the frequency table for the number of matches played by

both the All Blacks and Springbok players in this sample. Use the table drawn in ANSWER SHEET 1 to answer this question.

Interval Tally Frequency

0 – 30

31 – 60

61 – 90

91 – 120

121 – 150 (5)

4.1.5 Explain the meaning of the term probability. (2) 4.1.6 Determine the probability of randomly selecting a player of this

sample of Springboks and All Black players with a name starting with J. Write your answer as a percentage. (2)

4.1.7 The heights of the first five Springbok players are plotted. Plot the

heights of the first five All Blacks players to form a double bar graph. Use the graph for QUESTION 4.1.7 that is provided on ANSWER SHEET 1. (5)



4.1.8 Use the graph that shows the tries scored by eight players from the All Blacks and Springboks teams below to answer the questions that follow.

(a) Calculate the median tries for All Blacks team. (3) (b) Determine the range of the tries for the Springboks team. (3) (c) Identify the type of graph displaying the players’ tries. (2)

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6 7 8 9

nu

mb

er

of

trie

s p

er

pla

yer

Eight players from each team

Tries made by eight players from the two teams

Springbok

All Blacks



4.2 South Africa is a nation of diversity, with a wide variety of cultures, languages and religious beliefs. Study the table below showing the census results for 2006 and 2011 to answer the questions that follow.

TABLE 3: SOUTH AFRICA’S POPULATION – CENSUS 2006 and 2011

2011 2006

Population group Number % of total Number % of total

1. African 41 000 938 79,2 37 662 900 79,5

2. White 4 586 838 B 4 365 300 9,2

3. Coloured 4 615 401 B 4 198 800 8,9

4. Indian/Asian 1 286 930 2,5 1 163 900 2,4

5. Other 280 454 0,5 -

TOTAL A 100% 100%

[Source: www.statssa.co.za] 4.2.1 Identify the median population group in South Africa in 2011. (2) 4.2.2 Calculate the value of A, the total population in South Africa in 2011. (2) 4.2.3 Identify population groups with the difference of 28 563 in numbers in

2011. (2) 4.2.4 Identify the population group that formed the minority in South Africa in

2006. (2) 4.2.5 Calculate the value of B, the percentage of the white population group. (3) [40]



QUESTION 5

5.1 Lindi received an account from a medical institution. People take out medical aid that deducts a certain amount from their salaries monthly and pays their medical bills. They become members of that medical aid. It does not pay everything and sometimes the patients are asked to pay a certain amount by the medical institution attended.

Study the statement in ANNEXURE B and answer the questions that

follow. 5.1.1 Name the institution that issued the statement. (2) 5.1.2 Determine the amount in arrears indicated on the statement. (2) 5.1.3 Determine the amount paid by the medical aid for elastocrepe. (2) 5.1.4 Identify the amount the patient is liable to pay for the consultation

on the 20 November 2015 (2) 5.1.5 Show how the total amount due was calculated. (2) 5.1.6 Give a reason why Lindi consulted the doctor on 20 November

2015. (2) 5.1.7 Calculate the price of the urine dipstick including Value Added Tax

(VAT). VAT = 14% (3) 5.1.8 Write down the number of months the outstanding amount was

due. (2) 5.2 Nonine fell sick and consulted a doctor. Use the table below that shows

the medication given to her to answer the questions that follow. Table: Certified copy of doctor’s script (some information is omitted)

Type of medication Volume

No. of days

Flusin DM: Take two medicine measures 10 mℓ three times a day

Syrup 100 mℓ

10

Ponstan 50 mg/5 mℓ: Take three medicine measures (15 mℓ) four times a day

200 mℓ 10

Augmentin ES 600: Take two medicine measures (10 mℓ) twice a day**complete course**

100 mℓ 5

5.2.1 Calculate the total number of millilitres of medicine measures that

Nonine has to take in the morning at breakfast and evening at supper. (2)



5.2.2 Calculate the remaining amount of Augmentin ES 600 if it is not taken at all on the last day. (2)

5.3 Springbok and All Blacks match statistics is displayed below: TABLE 4: Match statistics for All Blacks and Springbok teams

Match statistics

Teams Springbok All Blacks

Ball possession 40% 60%

Tackles 116 84

Express the percentage ball possession of the team that has the highest

percentage in a simplified common fraction. (2) [23] TOTAL: 150



GRADE:

NAME OF LEARNER:

ANSWER SHEET 1 QUESTION 4.1.4


0 – 30

31 – 60

61 – 90

91 – 120

121 – 150 (5)

QUESTION 4.1.7

(5)

170

175

180

185

190

195

200

205

210

1 2 3 4 5 6 7 8

Hei

ght

of

team

s(cm

)

First five players as displayed in the table

Heights for the first five team players

Springbok


GRADE 12

SEPTEMBER 2016

MATHEMATICAL LITERACY P1 ADDENDUM

MARKS: 150

This addendum consists of 3 pages of 2 annexures.


Copyright reserved Please turnover

ANNEXURE A

QUESTION 4.1 Some of the information is omitted. TABLE 5: South African (Springbok) rugby players test statistics

PLAYERS Height (cm)

Weight (kg)

Matches Points

1. Tendai Mtawarira 183 116 72 10

2. Bismack du Plessis 190 115 76 55

3. Eben Etzebeth 203 117 41 5

4. Lood de Jager 205 125 16 20

5. Schalk Burger 193 110 83 80

6. Duane Vermeulen 193 108 32 10

7. Handré Pollard 189 98 17 141

8. Bryan Habana 179 94 114 320

9. Jesse Kriel 186 96 8 15

10. JP Pietersen 191 102 63 110

11. Adriaan Strauss 184 112 51 30

12. Trevor Nyakane 178 120 20 5

13. Willem Alberts 192 120 35 35

14. Ruan Pienaar 186 92 87 135

TABLE 6: New Zealand (All Blacks) rugby players test statistics

PLAYERS Height (cm) Weight (kg) Matches Points

1. Joe Moody 188 112 9 5

2. Brodie Retallick 204 120 45 10

3. Richie McCaw 187 105 146 135

4. Daniel Carter 178 96 110 1 569

5. Conrad Smith 186 95 92 130

6. Keven Mealamu 181 109 130 60

7. Ben Franks 183 117 45 10

8. Sam Cane 189 105 29 50

9. Tawera Kerr-Barlow 187 117 45 10

10. Dane Coles 184 110 34 25

11. Samuel Whitelock 202 116 71 20

12. Kieran Read 193 110 82 100

13. Julian Savea 192 106 39 190

14. Ben Smith 186 94 46 95 [Adapted from the Daily Dispatch, 24 October 2015]



ANNEXURE B FOR QUESTION 5.1

STATEMENT PANADO MEDICAL CENTRE PO BOX 6667 East London, 5201 Tel: 043-123 6574,

Mrs Nomsa Lukho Box 2029 Greenfields 5208

Scale of benefits Balance due R499,68

Prac. no: 4515652222 Med Aid: Gems Med aid no:000154765

Account no.: Employer:

089338 Dept. of Education

Items or values marked with (*) are from a previous month.

Date 2015

Reference Patient Code Qty Original

M/A Portion

Member Liab

Balance

5/9 HBEdi*432075 003 Elastocrepe

Nomsa 0201 1 89,80 0,00 24,46* 24,46

20/11 HBEdi*New and established Patient: Consultation Pain Localised to other parts Of abdomen

Lindi 0190 1 309,70 309,70 0,00 334,16

20/11 HBEdi *For emergency consultation

Lindi 0146 1 147,40 108,49 38,91 481,56

20/11 HBEdi*Urine Dipstick, per dipstick

Lindi 4188 1 13,10 13,10 0,00 494,66

20/11 HBEdi* 831832002

Lindi 0201 1 5,02 5,02 0,00 499,68

Only unpaid values are reflected VAT of …………included REMITTANCE

Mrs Nomsa Lukho P.O. Box 2029 Greenfields 5208

Date: 20/11/2015 Dr J Namroo Banking details: Nedbank Corporate Branch Branch code: 195456 Acc. no.: 132 567 4359 Please fax proof of payment

180+ days: 0,00 150 days: 0,00 120 days: 0,00 90 days: 0,00 60 days: 24,46 30 days: 0,00 Current : 475,22 Total due: R499,68


GRADE 12

SEPTEMBER 2016

MATHEMATICAL LITERACY P1 MEMORANDUM

MARKS: 150

This memorandum consists of 8 pages.

Symbol Explanation

M Method

A Accuracy

CA Consistent accuracy

RT/RG/RM Reading from a table/Reading from a graph/Read from map

RP Reading from the plan

SF Substitution in a formula

S Simplifications

P Penalty (no units, incorrect rounding off etc.)

O Opinion

J Justification

R Rounding

NPR No Penalty for Rounding



QUESTION 1

Quest. Solution Explanation Marks

1.1.1 South African Revenue Services 2A (2)

1.1.2 15 years 9 months

= 15 x 12 + 9

= 189 months

1 A 15 years 9 months 1M Conversion to months 1 CA (3)

1.1.3 Five hundred and six thousand

Four hundred and seventy four rand 2A In words (2)

1.1.4 R122 138,71 – R104 227 = R17 911,71

1A Correct values 1M Subtraction: 1CA (3)

1.1.5 122 138,71 : 506 474

1 : 4,15

2M Ratio of Correct Values 1A (3)

1.1.6 R631,94 2RT (2)

1.1.7 6 3 1, 9 4

1 1 0 %

R

= R574,49 x 12 = R6 893,89 OR

R631,94 x 𝟏𝟎

𝟏𝟏𝟎

= R57,45 R631,94 – R57,45 = R574,49 x 12 = R6 893,89

OR 𝑹631,94

𝟏𝟏𝟎 x 100

= R574,49 x 12 = R6 893,89

1M Correct Values 1M dividing by 110% 1CA 1M x12 1CA (Accept 6893,88) 1M Multiplying by the fraction 1S 1M subtraction 1M Multiply by 12 1CA 1M Multiply 100 1M Denominator 1CA for R574,49 1M multiply by 12 1CA (5)



1.2.1 $225 + $200 + $175 + $50 = $650

2A Adding all the values (2)

1.2.2 $175 x 100 $650 = 26,9% = 27%

1M dividing by $650 and multiply by 100 1CA 1CA (3)

1.2.3 500 x $15,00 = $7 500

1M identifying 500 and $15,00 1A (2)

1.2.4 7500 x 15,409095 = R115 568,2125 = R115 568,21

1M multiplying by R15,409095 1S 1 CA (two decimal places) (3)

1.2.5 $200 500 = $0,4

1M for 200 1CA (2)

1.2.6 1 April 2016 – 30 April 2016 2 RT (2)

[34]



QUESTION 2


2.1.1 V = 𝜋𝑟2h = 3,142 x (2,5 cm)2 x 12,5 cm = 245,47 cm3

1A converting radius 1SF 1CA answer 1 unit NPR (4)

2.1.2 No. of candles =

5 000 𝑐𝑚3

245,47 𝑐𝑚3

= 20,4 = 20 candles

1M for 5 000 1M 1CA answer (3)

2.1.3 Candle weight = density x volume = 0,93g/cm-3 x 245,47 cm3 = 228,29 g

1SF 1M using 245,47 cm3 1CA answer NPR (3)

2.1.4 TSA = 2 x (2,6 x 2,8) + 2 x 6,1(2,6 + 2,8)

= 2(7,28) + 12,2 x (5,4) = 14,56 cm2 + 65,88 cm2

= 80,44 cm2

1SF 1S 1S 1CA answer

OR

𝑇𝑆𝐴 = 2𝑥(𝑙 x 𝑤) + 2(𝑙 x ℎ) + 2(𝑤 x ℎ) = 2(2,8 x 2,6) + 2(2,8 x 6,1) + 2(2,6 x 6,1) = 2(7,28) + 2(17,08) + 2(15,86) = 14,56 + 34,16 + 31,72 = 80,44 cm2

2 SF 1S 1CA answer

(4)

2.1.5 Diameter = 2,5 × 2 = 5 cm

No. of candles along the length = 15

5= 3

No. of candles along the width = 15

5= 3

Total number of candles for the first layer

= 3 × 3 = 9

1M diameter 1M length candles 1M width candles 1CA Check 2.1.1 for radius (4)

2.1.6

(a) 312℉ 2RD

(2)

(b) ℃ = (312° − 32°) ÷ 1,8

= 280° ÷ 1,8

= 155,6 ℃ Accept 155,56 ℃

1SF 1S

1A penalise if ℉ is written in the answer (3)



2.2.1 2,3 m – 0,25 m = 2,05 m

1M Conversion to metre 1M subtraction 1 CA answer (3)

2.2.2 𝐴 = 𝑙 𝑥 𝑤 12 m2 = (2,3m +1,7m) x w

12 m2 = 4 m x w 4 m 4 m 3 m = w

1M adding 1,7 1M dividing by 4 1A (3)

[29]

QUESTION 3

3.1.1 North east 2A (2)

3.1.2 1 : 75 2RP (2)

3.1.3 𝐿𝑒𝑛𝑔𝑡ℎ =9 𝑐𝑚 𝑥 75

100

= 6,75 m

Width = 1,3 x 75 ÷ 100 = 0,975 m = 1 m

1M 1A answer for length 1A answer for width

(3)

3.1.4

2M Drawing

(2)

3.1.5 15 2RP (2)

3.1.6 7 16

1M numerator 1M denominator (2)

3.2.1 4 2RD (2)

3.2.2 From the reception go straight along the orchard and turn right, then go down pass the playground and turn leftand go straight you will get 11b.

3RD

(3)

3.2.3 7 2RD (2)

3.2.4 9 2RD (2)

3.2.5 Table tennis OR Pool table 2RD any facility (2)

[24]



QUESTION 4


4.1.1 Av weight = 92+94+96+98+102+108+110+112+115+116+117+120×2+125

14

= 1 525

14

= 108,93 kg (Accept 108,929)

1M 1S 1CA

(3)

4.1.2 1 569 2A (2)

4.1.3 186 cm 2A (2)

4.1.4

1 Mark (both Tally and Frequency) x 5 = 5


0− 30 //// / 6

31−60 //// //// 10

61−90 //// // 7

91−120 /// 3

121−150 // 2

1 x 5 = 5

(5)

4.1.5 Probability is the chance or likelihood of an event happening.

2M Definition (2)

4.1.6 4 × 100 28

= 14,3%

1 M Fraction multiply by 100 1CA (2)

4.1.7

1 Mark per correctly plotted bar joined to an existing one



4.1.8 (a) 1 , 2 , 2 , 4 , 10 , 19 , 20 , 38 = 14

2 = 7

1M Correct values 1M 1CA (3)

(b) Range = 64 – 1 = 63

1Correct values 1M Subtracting 1A (3)

(c) Line graph 2A (2)

4.2.1 White 2A (2)

4.2.2 A = 41 000 938 +4 586 838 +4 615 401+1 286 930+280 454

= 51 770 561 1M Adding 1A (2)

4.2.3 Whites and Coloureds 2A (2)

4.2.4 Indian / Asian 2A (2)

4.2.5 B + B+ 79,2 + 2,5 + 0,5 = 100% = 100% – 82,2 2B = 17,8 B = 8,9%

OR OR 4 586 838

51 770 561 x 100%

4 615 5401

51 770 561 x 100%

= 8,859 = 8,915 = 8,9% = 8,9%

1M Adding to make 100 1S value of 2B 1A 1M fraction with correct Values 1M multiply by 100 1A (3)

[40]

QUESTION 5


5.1.1 Panado Medical Centre 2RT (2)

5.1.2 R24,46 2RT (2)

5.1.3 R89,80 – 24,46 = R65,34

1M Subtraction 1A (2)

5.1.4 R38,91 2RT (2)



5.1.5 R24,46 +R309,70 + R108,49 +R38,91 +R13,10 + R5,02 = R499,68

1M Adding 1A (2)

5.1.6 Pain located in other parts of the lower abdomen. 2 RT (2)

5.1.7 R13,10 x 14% = R1,83 + R13,10 = R14,93 OR R13,10 x 114% = R14,93

1M 1Adding 1A

(3)

5.1.8 60 days = 2 months

1M 1CA ( give a mark if answer is 30 days only) (2)

5.2.1 Morning + Evening (10 𝑚ℓ + 15 𝑚ℓ + 10 𝑚ℓ +10 𝑚ℓ + 15 𝑚ℓ + 10 𝑚ℓ)

= 70 𝑚ℓ

OR

(10 𝑚ℓ x 4) + (15 𝑚ℓ x 2) = 40 𝑚ℓ + 30 = 70 𝑚ℓ

1 M 1CA

(2)

5.2.2 10 𝑚ℓ + 10 𝑚ℓ = 20 𝑚ℓ

OR

10 𝑚ℓ x 2

= 20 𝑚ℓ OR

100 𝑚ℓ – (20 𝑚ℓ x 4) = 100 𝑚ℓ – 80 𝑚ℓ = 20 𝑚ℓ

OR

100 𝑚ℓ – (10 𝑚ℓ x 8) = 100 𝑚ℓ – 80 𝑚ℓ = 20 𝑚ℓ

1M 1A

(2)

5.3. 60

100 =

3

5 2A

(2)

[23]

TOTAL: 150

NASIONALE SENIOR SERTIFIKAAT

GRAAD 12

SEPTEMBER 2016

WISKUNDIGE GELETTERDHEID V1

PUNTE: 150

TYD: 3 uur

Hierdie vraestel bestaan uit 15 bladsye en ŉ addendum met bylaes.

*MLITA1*

2 WISKUNDIGE GELETTERDHEID V1 (EC/SEPTEMBER 2016)

Kopiereg voorbehou Blaai om asseblief

INSTRUKSIES EN INLIGTING 1. Hierdie vraestel bestaan uit VYF vrae. Beantwoord ALLE vrae. 2. 2.1 Gebruik addendum met BYLAE vir die volgende vrae:

BYLAAG A vir VRAAG 4.1 BYLAAG B vir VRAAG 5.1

2.2 ANTWOORDBLAD 1 vir VRAE 4.1.4 en 4.1.7

Skryf jou GRAAD en jou NAAM in die voorsiende spasies op die ANTWOORDBLAD en handig dit in saam met jou ANTWOORDEBOEK.

3. Nommer die vrae korrek volgens die nommeringstelsel wat hierdie

vraestel gebruik is. 4. Diagramme is nie noodwendig volgens skaal geteken nie. 5. Rond ALLE finale antwoorde toepaslik af volgens die konteks wat gebruik

is, tensy anders aangedui. 6. Dui meeteenhede aan waar van toepassing. 7. Begin ELKE vraag op ŉ NUWE bladsy. 8. ALLE berekeninge moet duidelik getoon word. 9. Skryf netjies en leesbaar.

(EC/SEPTEMBER 2016) WISKUNDIGE GELETTERDHEID V1 3


VRAAG 1

1.1 Layla, ŉ 43-jarige vrou het ŉ uittree-annuïteit (UA) polis uitgeneem met ŉ versekeringsmaatskappy. Die uittree-annuïteit uitkeerbedrag wat uitbetaal word aan die polishouer sal deur die SAID (SARS) belas word. In November 2015 het sy ŉ staat vir hierdie uittree-annuïteit polis ontvang.

TABEL 1: Uittreksel van uittree-annuïteit staat soos op 3 Oktober

2015 vir die finansiële jaar 2014–2015.

Polisnommer 7 011 567 723

Polistipe Flexi Pension Pure (Geen dekking)

Beleggingsportefeulje Stryk Bonus Portefeulje

Maandelikse bydrae R631,94

Uitkeerwaarde Minimum: R104 227,00 tot Maksimum: R506 474,00

Uitkeerdatum 1ste AUGUSTUS 2032

Sterftevoordeel R122 138,71

Premieverhoging (vaste)

10,00% per jaar

Laaste paaiement 1ste Julie 2032

Die volgende staat sal uitgereik word op die 3de Oktober 2016 vir die finansiële jaar 2015–2016.

Gebruik die inligting vanaf TABEL 1 om die volgende vrae te beantwoord: 1.1.1 Skryf die afkorting SAID (SARS) voluit. (2) 1.1.2 Bepaal die periode (in maande) dat hierdie polis is geldig vanaf

1ste November 2016 tot die uitkeerdatum. (3)

(2) 1.1.3 Skryf die maksimum uitkeerwaarde in woorde. 1.1.4 Bereken die verskil tussen die sterftevoordeelbedrag en die

minimum uitkeerwaarde wat teen die uitkeerdatum ontvang sal word. (3)

1.1.5 Skryf neer die verhouding van die sterftevoordeel tot die

maksimum uitkeerwaarde in die vorm 1 : … (3) 1.1.6 Skryf neer die maandelikse bydrae vir die 2014–2015 finansiële

jaar. (2) 1.1.7 Bereken die totale jaarlikse bydrae vir die 2013–2014 finansiële

periode. (5)



1.2 Bonny ontwerp, druk en pos verjaarsdagkoopbewyse aan verskillende maatskappye. Hieronder is ŉ promosie beskrywing advertensie vir 500 koopbewyse en die koste betrokke.

TABEL 2: Promosie Beskrywing

Verjaarsdag Geskenkbewyse

Verlossing item Geskenkbewys

Begindatum 1 April 2016

Einddatum 30 April 2016

Koste van verkope % 35%

Aantal ontvangers 500

Maaltyd Koopbewys Waarde $15,00

Uitgawes Verkoper Kosteberamings (Dollars)

Drukker Bet Drukkers $225

Posgeld Poskantoor $200

Grafiese Ontwerp Premier Ontwerpers

$175

Arbeid Binnehuisarbeid $50

Totale begroting $650

[Bron: www.restaurantowner.com] Wisselkoers: 1$(US dollar) = R15,409095 Gebruik die inligting in TABEL 2 om die volgende vrae te beantwoord: 1.2.1 Wys hoe die totale begroting van $650 bereken was. (2) 1.2.2 Druk die uitgawe vir die grafiese ontwerp uit as ŉ persentasie van

die totale begroting. Gee jou antwoord tot die naaste persentasie. (3)

1.2.3 Bereken die totale koste (in dollars) van die maaltyd koopbewyse

wat gedurende hierdie maand uitgereik was. (3) 1.2.4 Herlei die totale koste van die maaltyd koopbewyse wat uitgereik

was na Rand. (2) 1.2.5 Bereken die posgeld van EEN geskenkbewys in dollars. (2) 1.2.6 Skryf neer die promosie periode van die maaltyd koopbewyse. (2) [34]



VRAAG 2 2.1 Nicky is ŉ kersmaker en verkoop die kerse aan mense waar sy bly en ook

aan die kerk. PRENTE: Silindriese en reghoekige kerse

(1 m3 = 1 000 000 cm3 en 1 liter = 1 000 cm3)

[Bron: www:all-free-download.com] Bestudeer die prente van die verskillende kerse hierbo en beantwoord die

volgende vrae.

2.1.1 Bereken die volume (in cm3) van die was (wax) wat benodig word om ŉ silindriese kers te maak (Ignoreer die holte wat vir die pit gemaak is).

Jy mag die volgende formule gebruik: Volume van ŉ silindriese kers = 𝝅 × (radius)2 × hoogte

waar 𝝅 = 𝟑, 𝟏𝟒𝟐 (4)

2.1.2 Nicky smelt vyf liter was per dag en gooi dit in kersvorms. Bereken die aantal silindriese kerse wat sy van vyf liter was kan maak. (3)

2.1.3 Bereken die gewig van die was in gram om ŉ silindriese kers te

maak. (Gee jou antwoord tot die naaste gram.)

Jy mag die volgende formule gebruik: Kersgewig (g) = paraffienwas-digtheid x volume van een kers,

Waar die paraffienwas-digtheid = 0,93 g / cm3 (3)



2.1.4 Bereken die totale buite-oppervlak (TBO) van ŉ reghoekige kers wat deur Nicky gemaak word.

Jy mag die volgende formule gebruik:

𝑻𝑩𝑶 = 2(𝑙 × 𝑏) + 2ℎ(𝑙 + 𝑏) (4)

2.1.5 Bestudeer die boks hieronder wat Nicky sal gebruik om haar

sirkelvormige kerse af te lewer en beantwoord die vrae wat volg.

Hoogte van die boks = 26 cm

Breedte = 15 cm Lengte = 15 cm

Bereken die aantal silindriese kerse wat regop in die boks gepak sal word vir die eerste laag op die onderkant van die boks. (4)

2.1.6 Nicky gebruik ŉ termometer om die wastemperatuur na te gaan

wanneer dit verhit word. Bestudeer die diagram wat voorsien is en beantwoord die vrae wat volg.

[Bron: Aangepas vanaf www.yms.co.za]

(a) Skryf neer die temperatuurlesing van die termometer hierbo. (2) (b) Herlei die temperatuurlesing op die termometer na grade

Celsius (℃).

Jy mag die volgende formule gebruik: ℃ = (℉ − 𝟑𝟐°) ÷ 𝟏, 𝟖 (3)



2.2 Nicky koop kandelaarligte by Lite City vir haar eetkamer. Die oppervlak van haar eetkamer se plafon is 12 m2. Die reghoekige lig is 50 cm lank en die hoogte is 25 cm.

Bestudeer die diagram hieronder wat die syaansig van die eetkamer wys

en die ligging van die lig om die vrae wat volg te beantwoord.

2.2.1 Bereken die hoogte vanaf die vloer na die onderkant van die lig.

Gee jou antwoord in meter. (3) 2.2.2 Bereken die breedte van die eetkamer as die lengte 1,7 m meer

as die hoogte van die eetkamer is. Jy mag die volgende formule gebruik: Oppervlak van ŉ reghoek = lengte x breedte (3)

[29]



Vullisdrom

VRAAG 3 3.1 Graad 12 leerders gebruik plakkers met hul eksamennommers op wat

hulle op hul lessenaars vasplak. Bestudeer die sitplekplan van die Graad 12 leerders hieronder tydens hulle finale eksamen van 2015 en beantwoord die vrae wat volg.

3.1.1 Gee die kompasrigting van ŉ leerder met eksamennommer 008 vanaf ŉ leerder met eksamennommer 005. (2)

3.1.2 Identifiseer die skaal van die kaart. (2) .

3.1.3 Bereken die afmetings van die boekrak in meter. (3)

3.1.4 Acks, ŉ leerder met eksamennommer 015 het laat gekom. Sy was nie toegelaat om tussen die ander lessenaars deur te loop nie. Teken die roete wat sy gebruik om haar lessenaar te bereik. (2)

3.1.5 Bepaal die aantal leerders wat betyds hul eksamen begin skryf het indien al die lessenaars beset was. (2)

3.1.6 Bepaal die waarskynlikheid dat ŉ leerder lukraak gekies sal word wie se eksamennommer ŉ ewegetal is. (2)



3.2 Hieronder is ŉ kaart van Glensheiling karavaanpark in KwaZulu-Natal.

[Bron: www.glensheiling.co.za]

Gebruik die kaart van Glensheiling karavaanpark hierbo om die volgende vrae te beantwoord:

3.2.1 Bepaal die aantal kampeerterreine noord van die speelgrond. (2) 3.2.2 Leeckay is by ontvangs en word ingelig dat 11b aan hom

toegeken is. Skryf vir hom die rigtingaanwysings neer oor hoe hy by sy kampeerterrein sal uitkom. (3)

3.2.3 Bepaal die aantal karavane/kajuite wat in hierdie kaartuitleg

getoon word. (2) 3.2.4 Een kampeerterrein het bome en struike agter en een boom

langsaan. Skryf neer die nommer wat hierdie kampterrein aandui. (2) 3.2.5 Noem EEN ontspanningsfasiliteit naby die Foreldam. (2) [24]



VRAAG 4

4.1 Die Suid-Afrikaanse rugbyspan (Springbokke) het teen die Nieu-Seelandse rugbyspan (All Blacks) tydens die Wêreldbeker gespeel. Bestudeer die uittreksel van die Springbokke en All Blacks spelers se toets statistieke wat voorsien word in BYLAAG A en beantwoord die vrae wat volg.

4.1.1 Bereken die gemiddelde gewig van die Springbokspan se spelers. (3) 4.1.2 Identifiseer die waarde van ŉ uitskieter vanuit die All Black spelers se

punte. (2) 4.1.3 Bereken die modale hoogte vir beide spanne. (2) 4.1.4 Voltooi die frekwensietabel vir die aantal wedstryde wat deur beide

die All Black- en Springbokspelers gespeel was. Gebruik die tabel hieronder in ANTWOORDBLAD 1 om hierdie vraag te beantwoord:

Interval Telling Frekwensie

0 – 30

31 – 60

61 – 90

91 – 120

121 – 150 (5)

4.1.5 Verduidelik die betekenis van die term waarskynlikheid. (2) 4.1.6 Bepaal die waarskynlikheid om ŉ speler lukraak te kies vanuit die

Springbokke en All Blacks spelers wie se naam met ŉ J begin. Skryf jou antwoord as ŉ persentasie. (2)

4.1.7 Die lengte van die eerste vyf Springbokspelers is op die grafiek in

ANTWOORDBLAD 1 afgesteek. Herhaal dit vir lengte van die eerste vyf All Blackspelers om ŉ saamgestelde balkgrafiek te teken. Gebruik die grafiek wat vir VRAAG 4.1.7 in ANTWOORDBLAD 1 voorsien is. (5)



4.1.8 Gebruik die grafiek hieronder wat die drieë aangeteken toon deur agt spelers van die All Blacks en Springbokke om die vrae wat volg te beantwoord.

(a) Bereken die mediaan drieë vir die All Blackspan. (3) (b) Bepaal die omvang van die drieë vir die Springbokspan. (3) (c) Identifiseer die tipe grafiek wat deur die spelers se driee geïllustreer is. (2)



4.2 Suid-Afrika is ŉ nasie van diversiteit, met ŉ wye verskeidenheid kulture, tale en godsdienstige oortuigings. Bestudeer die tabel wat die sensusuitslae van 2006 en 2011 toon om die vrae wat volg te beantwoord.

TABEL 3: SUID-AFRIKAANSE BEVOLKING – SENSUS 2006 and 2011

2011 2006

Bevolkingsgroep Aantal % van tot Aantal % van totaal

1. Swart 41 000 938 79,2 37 662 900 79,5

2. Blankes 4 586 838 B 4 365 300 9,2

3. Kleurling 4 615 401 B 4 198 800 8,9

4. Indiër/Asiaat 1 286 930 2,5 1 163 900 2,4

5. Ander 280 454 0,5 -

TOTAAL A 100% 100%

[Bron: www.statssa.co.za] 4.2.1 Identifiseer die mediaan bevolkingsgroep in Suid-Afrika in 2011. (2) 4.2.2 Bereken die waarde van A; die totale bevolking in Suid-Afrika in 2011. (2) 4.2.3 Identifiseer die bevolkingsgroepe met ŉ verskil van 28 563 in getalle in

2011. (2) 4.2.4 Identifiseer die bevolkingsgroep wat die minderheid is in Suid-Afrika in

2006. (2) 4.2.5 Bereken die waarde van B, die persentasie van die blanke-

bevolkingsgroep. (3) [40]



VRAAG 5

5.1 Lindi ontvang ŉ rekeningstaat van ŉ mediese instelling. Mense sluit aan by ŉ mediese skema wat maandeliks ŉ sekere bedrag van hul salaris aftrek en betaal dan hul mediese rekeninge. Hulle word dan lidmate van daardie mediese skema. Hierdie mediese skema betaal nie vir alles nie; somtyds word pasiënte deur die mediese instelling gevra om ŉ sekere bedrag in te betaal.

Bestudeer die rekeningstaat in BYLAAG B en beantwoord die vrae wat volg. 5.1.1 Noem die instelling wat die rekeningstaat uitgereik het. (2) 5.1.2 Bepaal die agterstallige bedrag wat op die staat aangedui is. (2) 5.1.3 Bepaal die bedrag wat deur die mediese skema vir elastocrepe

betaal is. (2) 5.1.4 Identifiseer die bedrag waarvoor die pasiënt aanspreeklik gehou

word vir die doktersbesoek (konsultasie) op 20 November 2015. (2) 5.1.5 Wys hoe die totale bedrag verskuldig bereken was. (2) 5.1.6 Gee ŉ rede waarom Lindi die dokter op 20 November 2015 besoek

het. (2) 5.1.7 Bereken die prys van die urine maatstoklesing insluitende Belasting

op Toegevoegde waarde (BTW): BTW = 14% (3) 5.1.8 Skryf neer die aantal maande wat die uitstaande bedrag verskuldig

was. (2) 5.2 Nonine het siek geword en het ŉ dokter besoek. Gebruik die tabel hieronder

wat toon watter medikasie aan haar voorgeskryf is en beantwoord die vrae wat volg.

Tabel: Gesertifiseerde doktersvoorskrif (sommige inligting is

weggelaat)

Tipe medikasie Volume Aantal dae

Flusin DM: Neem twee medisynemaat 10 mℓ drie keer per dag

Stroop 100 mℓ

10

Ponstan 50 mg/5 mℓ: Neem drie medisynemaat 15 ml vier keer per dag

200 mℓ 10

Augmentin ES 600: Neem twee medisynemaat 10 mℓ twee keer per dag **voltooi die voorskrif**

100 mℓ 5

5.2.1 Bereken die aantal milliliter medisynemaat wat Nonine soggens met

ontbyt en saans met aandete moes neem. (2)



5.2.2 Bereken die oorblywende hoeveelheid Augmentin ES 600 as dit nie op die laaste dag geneem word nie. (2)

5.3 Die Springbokke en All Blacks wedstryd statistieke word hieronder aangedui: TABEL 4: Wedstryd statistieke vir die All Blacks en Springbok spanne

Wedstryd statistieke

Spanne Springbokke All Blacks

Balbesit 40% 60%

Duikslae 116 84

Druk die persentasie balbesit van die span met die hoogste persentasie uit

in ŉ vereenvoudigde gewone breuk. (2) [23] TOTAAL: 150



GRAAD 12:

NAAM VAN LEERDER:

ANTWOORDBLAD 1 VRAAG 4.1.4


0 – 30

31 – 60

61 – 90

91 – 120

121 – 150 (5)

VRAAG 4.1.7

(5)


GRAAD 12

SEPTEMBER 2016

WISKUNDIGE GELETTERDHEID P1 ADDENDUM

PUNTE: 150

Hierdie addendum bestaan uit 3 bladsye van 2 bylae.

2 WISKUNDIGE GELETTERDHEID V1 (OK/SEPTEMBER 2016)


BYLAAG A

VRAAG 4.1 Sommige van die inligting is weggelaat. TABEL 5: Suid-Afrikaanse (Springbok) rugbyspelers – toets statistieke

SPELERS Lengte (cm)

Gewig (kg)

Wedstryde Punte

1. Tendai Mtawarira 183 116 72 10

2. Bismack du Plessis 190 115 76 55

3. Eben Etzebeth 203 117 41 5

4. Lood de Jager 205 125 16 20

5. Schalk Burger 193 110 83 80

6. Duane Vermeulen 193 108 32 10

7. Handré Pollard 189 98 17 141

8. Bryan Habana 179 94 114 320

9. Jesse Kriel 186 96 8 15

10. JP Pietersen 191 102 63 110

11. Adriaan Strauss 184 112 51 30

12. Trevor Nyakane 178 120 20 5

13. Willem Alberts 192 120 35 35

14. Ruan Pienaar 186 92 87 135

TABEL 6: Nieu-Seeland (All Blacks) rugbyspelers – toets statistieke

SPELERS Lengte (cm)

Gewig (kg)

Wedstryde Punte

1. Joe Moody 188 112 9 5

2. Brodie Retallick 204 120 45 10

3. Richie McCaw 187 105 146 135

4. Daniel Carter 178 96 110 1 569

5. Conrad Smith 186 95 92 130

6. Keven Mealamu 181 109 130 60

7. Ben Franks 183 117 45 10

8. Sam Cane 189 105 29 50

9. Tawera Kerr-Barlow 187 117 45 10

10. Dane Coles 184 110 34 25

11. Samuel Whitelock 202 116 71 20

12. Kieran Read 193 110 82 100

13. Julian Savea 192 106 39 190

14. Ben Smith 186 94 46 95

[Aangepas vanaf die Daily Dispatch, 24 Oktober 2015]

(OK/SEPTEMBER 2016) WISKUNDIGE GELETTERDHEID V1 3


BYLAAG B VIR VRAAG 5.1

STAAT PANADO MEDICAL CENTRE POSBUS 6667 Oos-Londen, 5201 Tel: 043-123 6574,

Mev. Nomsa Lukho Posbus 2029 Greenfields 5208

Voordele skaal Balans verskuldig R499,68

Prak. nr.: 4515652222 Med Fonds: Gems Med Fonds nr.:000154765

Rekeningnr.: Werkgewer:

089338 Dept. van Onderwys

Items of waardes wat met (*) aangedui is, is vanaf ŉ vorige maand.

Datum 2015

Verwysing Pasiënt Kode Hoev. Oorspronklik

Med Fonds Gedeelte

Lid Verskuldig

Balans

5/9 HBEdi*432075 003 Elastocrepe

Nomsa 0201 1 89,80 0,00 24,46* 24,46

20/11

HBEdi* Nuwe en bestaande Pasiënt: Konsultasie Pyn tot ander dele van die laer buik

Lindi 0190 1 309,70 309,70 0,00 334,16

20/11 HBEdi* Vir Nood konsultasie

Lindi 0146 1 147,40 108,49 38,91 481,56

20/11 HBEdi* Urine Maatstoklesing, per maatstoklesing

Lindi 4188 1 13,10 13,10 0,00 494,66

20/11 HBEdi* 831832002

Lindi 0201 1 5,02 5,02 0,00 499,68

Slegs onbetaalde waarde word gereflekteer BTW van ………… ingesluit OORBETALING

Mev. Nomsa Lukho Posbus 2029 Greenfields 5208

Datum: 20/11/2015 Dr J Namroo Bankbesonderhede: Nedbank Corporate Branch Takkode: 195456 Rekeningnr.: 132 567 4359 Faks bewys van betaling asseblief

180+ dae: 0,00 150 dae: 0,00 120 dae: 0,00 90 dae: 0,00 60 dae: 24,46 30 dae: 0,00 Huidige : 475,22 Totaal verskuldig: R499,68


GRAAD 12

SEPTEMBER 2016

WISKUNDIGE GELETTERDHEID V1 MEMORANDUM

PUNTE: 150

Hierdie memorandum bestaan uit 8 bladsye.

Simbool Verduideliking

M Metode

A Akkuraatheid

CA Deurlopende akkuraatheid

RT/RG/RM Lees vanaf ŉ tabel/Lees vanaf ŉ grafiek/Lees vanaf ŉ kaart

RP Lees vanaf ŉ plan

SF Vervanging in ŉ formule

S Vereenvoudiging

P Penaliseer (geen eenhede, inkorrekte ronding, ens.)

O Opinie

J Regverdiging

R Ronding

NPR Geen penalisering vir afronding



VRAAG 1

Vraag Oplossing Verduideliking Punte

1.1.1 Suid-Afrikaanse Inkomstedienste 2A (2)

1.1.2 15 jaar 9 maande

= 15 x 12 + 9

= 189 maande

1A 15 jaar 9 maande 1M Omskakeling na maande 1CA (3)

1.1.3 Vyfhonderd en sesduisend

vierhonderd en vier en sewentig rand. 2A In woorde (2)

1.1.4 R122 138,71 – R104 227 = R17 911,71

1A Korrekte waardes 1M Aftrekking 1CA (3)

1.1.5 122 138,71 : 506 474

1 : 4,15

2M Verhouding van korrekte waardes 1A (3)

1.1.6 R631,94 2RT (2)

1.1.7 6 3 1, 9 4

1 1 0 %

R

= R574,49 x 12 = R6 893,89 OF

R631,94 x 𝟏𝟎

𝟏𝟏𝟎

= R57,45 R631,94 – R57,45 = R574,49 x 12 = R6 893,94

OF 𝑹631,94

𝟏𝟏𝟎 x 100

= R574,49 x 12 = R6 893,89

1M Korrekte waardes 1M Deel deur 110% 1CA 1M x12 1CA (Aanvaar 6893,88) 1M Vermenigvuldig met die breuk 1S 1M Aftrekking 1M Vermenigvuldig met 12 1CA 1M Vermenigvuldig met 100 1M Noemer 1CA vir R574,49 1M Vermenigvuldig met 12 1CA (5)



1.2.1 $225 + $200 + $175 + $50 = $650

2A Tel al die waardes op

(2)

1.2.2 $175 x 100 $650 = 26,9% = 27%

1M Deel deur $650 en vermenigvuldig met 100 1CA 1CA (3)

1.2.3 500 x $15,00 = $7 500

1M Identifiseer 500 en $15,00 1A

(2)

1.2.4 7500 x 15,409095 = R115 568,2125 = R115 568,21

1M Vermenigvuldig met R15,409095 1S 1 CA (twee desimale plekke)

(3)

1.2.5 $200 500 = $0,4

1M Vir 200 1CA

(2)

1.2.6 1 April 2016 – 30 April 2016 2 RT (2)

[34]



VRAAG 2


2.1.1 V = 𝜋𝑟2h = 3,142 x (2,5 cm)2 x 12,5 cm = 245,47 cm3

1A Herlei radius 1SF 1CA Antwoord 1 eenheid NPR (4)

2.1.2 Aantal kerse =

5 000 𝑐𝑚3

245,47 𝑐𝑚3

= 20,4 = 20 kerse

1M vir 5 000 1M 1CA Antwoord (3)

2.1.3 Kersgewig = digtheid x volume = 0,93g/cm-3 x 245,47 cm3 = 228,29 g

1SF 1M gebruik 245,47 cm3 1CA Antwoord NPR (3)

2.1.4 TBO = 2 x (2,6 x 2,8) + 2 x 6,1(2,6 + 2,8)

= 2(7,28) + 12,2 x (5,4) = 14,56 cm2 + 65,88 cm2

= 80,44 cm2

1SF 1S 1S 1CA Antwoord

OF

𝑇𝐵𝑂 = 2𝑥(𝑙 x 𝑤) + 2(𝑙 x ℎ) + 2(𝑤 x ℎ) = 2(2,8 x 2,6) + 2(2,8 x 6,1) + 2(2,6 x 6,1) = 2(7,28) + 2(17,08) + 2(15,86) = 14,56 + 34,16 + 31,72 = 80,44 cm2

2 SF 1S 1CA Antwoord

(4)

2.1.5 Deursnit =2,5 × 2 = 5cm

Aantal kerse oor die lengte = 15

5= 3

Aantal kers oor die breedte = 15

5= 3

Totale aantal kerse vir die eerste laag

= 3 × 3 = 9

1M Deursnit 1M Kerse oor die lengte 1M Kerse oor die breedte 1CA Verwys na 2.1.1 vir radius (4)

2.1.6 (a) 312 ℉ 2RD (2)

(b) ℃ = (312° − 32°) ÷ 1,8

= 280° ÷ 1,8

= 155,6 ℃ Aanvaar 155,56 ℃

1SF 1S

1A penaliseer as ℉ geskryf is in die antw. (3)



2.2.1 2,3 m – 0,25 m = 2,05 m

1C Herlei na m 1M Aftrekking 1 CA Antwoord (3)

2.2.2 𝑂𝑝𝑝𝑒𝑟𝑣𝑙𝑎𝑘 = 𝑙𝑒𝑛𝑔𝑡𝑒 𝑥 𝑏𝑟𝑒𝑒𝑑𝑡𝑒 12 m2 = (2,3 m +1,7 m) x b 12 m2 = 4 m x b 4 m 4 m 3 m = b

1M tel 1,7 by 1M deel deur 4 1A (3)

[29]

VRAAG 3

3.1.1 Noordoos 2A (2)

3.1.2 1 : 75 2RP (2)

3.1.3 𝐿𝑒𝑛𝑔𝑡𝑒 =9 𝑐𝑚 𝑥 75

100

= 6,75 m

Breedte = 1,3 x 75 ÷ 100 = 0,975 m = 1 m

1M 1A Antwoord vir lengte 1A Antwoord vir breedte (3)

3.1.4

2M Tekening

(2)

3.1.5 15 2RP (2)

3.1.6 7 16

1M teller 1M noemer (2)

3.2.1 4 2RD (2)

3.2.2 Vanaf ontvangs, gaan reguit langs die boord en draai regs, gaan dan verby die speelgrond en draai links ,gaan reguit aan en jy sal 11b aan jou linkerkant kry.

3RD

(3)

3.2.3 7 2RD (2)

3.2.4 9 2RD (2)

3.2.5 Tafeltennis OF Snoekertafel 2RD Enige ontspanning (2)

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VRAAG 4


4.1.1 Gemiddelde gewig = 92+94+96+98+102+108+110+112+115+116+117+120×2+125

14

= 1 525

14

= 108,93 kg (Aanvaar 108,929)

1M 1S 1CA

(3)

4.1.2 1 569 2A (2)

4.1.3 186 cm 2A (2)

4.1.4

(1 Punt vir beide telling en frekwensie) x 5 = 5


0− 30 //// / 6

31−60 //// //// 10

61−90 //// // 7

91−120 /// 3

121−150 // 2

1 x 5 = 5

(5)

4.1.5 Waarskynlikheid is die kans dat ŉ gebeurtenis sal plaasvind.

2M Definisie (2)

4.1.6 4 × 100 28

= 14,3%

1 M Breuk vermenig-vuldig met 100 1CA (2)

4.1.7

1 Punt vir elke kolom korrek afgesteek langs die bestaande een



4.1.8 (a) 1 , 2 , 2 , 4 , 10 , 19 , 20 , 38 = 14 2 = 7

1M Korrekte waardes 1M 1CA (3)

(b) Omvang = 64 – 1 = 63

1C Korrekte waardes 1M 1A (3)

(c) Lyngrafiek 2A (2)

4.2.1 Wit 2A (2)

4.2.2 A = 41 000 938 +4 586 838 +4 615 401+1 286 930+280 454

= 51 770 561 1M Optelling 1A (2)

4.2.3 Blankes en Kleurlinge 2A (2)

4.2.4 Indiërs / Asiate 2A (2)

4.2.5 B + B+ 79,2 + 2,5 + 0,5 = 100% = 100% – 82,2

2B = 17,8 B = 8,9%

OF OF 4 586 838

51 770 561 x 100%

4 615 5401

51 770 561 x 100%

= 8,859 = 8,915 = 8,9% = 8,9%

1M Tel by om 100 te maak 1S waarde van 2B 1A 1M Breuk met korrekte waardes 1M Vermenigvuldig met100 1A (3)

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VRAAG 5


5.1.1 Panado Medical Centre 2RT (2)

5.1.2 R24,46 2RT (2)

5.1.3 R89,80-24,46 = R65,34

1M Aftrekking 1A

(2)

5.1.4 R38,91 2RT (2)



5.1.5 R24,46 +R309,70 + R108,49 +R38,91 +R13,10 + R5,02 = R499,68

1M Optelling 1A (2)

5.1.6 Pyn tot ander dele van die laer buik. 2 RT (2)

5.1.7 R13,10 x 14% = R1,83 + R13,10 = R14,93 OF R13,10 x 114% = R14,93

1M 1Optelling 1A

(3)

5.1.8 60 dae = 2 maande

1M 1CA (gee 1 punt as die antw. slegs 30 dae) (2)

5.2.1 Soggens en Saans (10 𝑚ℓ + 15 𝑚ℓ + 10 𝑚ℓ +10 𝑚ℓ + 15 𝑚ℓ + 10 𝑚ℓ) =

70 𝑚ℓ OF

(10 𝑚ℓ x 4) + (15 𝑚ℓ x 2) = 40 𝑚ℓ + 30

= 70 𝑚ℓ

1M 1CA

(2)

5.2.2 10 𝑚ℓ + 10 𝑚ℓ = 20 𝑚ℓ

OF

10 𝑚ℓ x 2 = 20 𝑚ℓ

OF

100 𝑚ℓ – (20 𝑚ℓ x 4) = 100 𝑚ℓ – 80 𝑚ℓ

= 20 𝑚ℓ OF

100 𝑚ℓ – (10 𝑚ℓ x 8) = 100 𝑚ℓ – 80 𝑚ℓ = 20 𝑚ℓ

1M 1A

(2)

5.3. 60

100 =

3

5 2A

(2)

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TOTAAL: 150

GRADE 12 SEPTEMBER 2016 MATHEMATICAL LITERACY P1

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Transcript of GRADE 12 SEPTEMBER 2016 MATHEMATICAL LITERACY P1