Gr 12 Maths Lit Paper 1This page is teacher notes only – it is not for reproducing for the kids

Paper One– a basic knowing and routine applications paper that will consist of between five and eight shorter questions.

• The question paper should cover all four Learning Outcomes, with approximately 25% of the marks allocated to each Learning Outcome.

• Only Level 1 (Knowing) and Level 2 (Applying routine procedures in familiar contexts) questions should be set.

o Approximately 60% of the marks should be set at Level 1 and o 40% of the marks should be set at Level 2. (See Appendix 2 for explanations of the

Levels) • Question 1 could contain some basic calculations and simple short questions. Questions do

not necessarily need to be integrated between Learning Outcomes. • Question 2 could contain simple short context questions divided into sub-questions. Sub-

questions may not necessarily be integrated between Learning Outcomes. • For the rest of the paper:

There could be three to six further questions Each question should be set on a different context. Each context should contain questions from at least two different Learning Outcomes

LO's 1: Number and Operations in Context

o Finance Profit/ Loss

o Formulae into calculators o percentage, ratio, rate and proportion o Taxation

2:  Functional Relationships o Work out 'outputs' for given inputs o Break even points o Draw graphs

3: Space, Shape and Measurement o 2 & 3 D shapes

Cylinder Square , Right Triangle Pythag

o Unit Conversion o Scales o Maps & Directions

4: Data Handling o Collect data o + - Graphical Summaries

tallies; tables; pie charts; single and compound bar graphs; line and broken-line graphs

o + - Summarise data mean; median;  mode;  range  quartiles; (INTERPRETATION ONLY)

percentiles.(INTERPRETATION ONLY) o Probability

Predict outcomes 1

Tree diagrams

Notes on marking Any logically valid method of arriving at an answer must be marked correct. Continued accuracy marks should be awarded wherever applicable. Refer to the memo’s for the 2011 & 2012 papers for the details of mark allocations (method,

continued accuracy, etc)

When a correct answer is given with no working, full marks should be given Only remove marks for rounding or units were indicated in the memo

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Question Marks AS Cog Level1.1 2 1 11.2 2 1 11.3 2 1 11.4 2 1 11.5 2 1 11.6 2 1 11.7 3 4 11.8 2 3 11.9 3 1 21.10 3 1 21.11 2 3 22.1 1 4 12.2 1 2 12.3 2 4 12.4 2 1 12.5 2 4 23.1 1 2 13.2 2 2 13.3 3 3 13.4 3 3 13.5 3 2 13.6 2 2 13.7 2 4 13.8 2 4 13.9 3 4 13.10 3 4 23.11 4 1 24.1 8 1 14.2 2 1 14.3 2 1 14.4 3 1 14.5 2 3 14.6 2 3 14.7 2 3 14.8 1 3 14.9 3 3 14.10 3 4 24.11 2 4 14.12 2 4 14.13 2 4 25.1 1 2 15.2 2 2 25.3 3 2 25.4 3 2 25.5 2 3 15.6 3 3 15.7 3 3 25.8 2 1 25.9 2 3 25.10 1 3 26.1 2 2 26.2 3 2 26.3 9 2 26.4 2 2 26.5 1 2 26.6 3 2 27.1 3 3 17.2 2 3 27.3 5 3 2

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7.4 3 3 2

Marks: Question: 1 25Question: 2 8Question: 3 28Question: 4 34Question: 5 22Question: 6 20Question: 7 13Paper Total: 150

AS marks: AS: 1 41 27%AS: 2 38 25%AS: 3 44 29%AS: 4 27 18%

Cognitive Level marks: CL: 1 82 55%CL: 2 68 45%

Low Order (1-2): 150 100%High Order (3+): 0 0%

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Bergvliet High School

Gr 12 Maths Literacy - Paper 1Learner Name: ___________________________________ Register 12_____ Teacher: Gl / Hi

June 2013 MARKS: 150TIME:3 hrs

EXAMINER(S): G Hillebrand MODERATOR(S): R Gliddon, S van Rooyen, C Benson

__________________________________________________________________________________

INSTRUCTIONS

1. Answer all the questions clearly, leaving a 3cm right margin, and 3 lines between each question

2. Number the answers correctly according to the numbering system used in this question paper.

3. You may use an approved calculator (non-programmable and non-graphical), unless stated otherwise.

4. Show ALL the calculations clearly. 5. Round ALL the final answers off to TWO decimal places, unless stated otherwise. 6. Indicate units of measurement, where applicable. 7. Write neatly and legibly.8. Attach this sheet to the FRONT of your script and the ANNEXURE to the back.

Marks Achieved

Question: 1 25

Question: 2 8

Question: 3 28

Question: 4 34

Question: 5 22

Question: 6 20

Question: 7 13

Paper Total: 150

%

1

Question 11.1

Simplify: 2

1.2 Without rounding off, showing all digits convert 23,9 millimetres to metres. 2

1.3 How many bread-rolls is 4 dozen? 2

1.4 What is the time 3 hours and 23 minutes after 23:45? 2

1.5 Calculate two thirds of 5 323 2

1.6 What is the probability of rolling a 9 in one throw of an ordinary 6 sided die? 2

1.7 What is the median of the follow set of numbers:12 32 97 34 86 13 54 27

3

1.8 One South African Rand buys 40,62 Zimbabwean Dollars. 0

1.8.1 If a hotel room at Victoria Falls costs R1300 per night, what would you pay in Zimbabwean Dollars?

2

1.8.2 Taxi fare in Zimbabwe is quoted asTaxi Start Taxi 1km Taxi 1hour waiting

R26.87 R8.96 R35.82http://www.numbeo.com/taxi-fare/country_result.jsp?country=Zimbabwe&displayCurrency=ZAR

If you travel 22km from your hotel to a restaurant, and the taxi waits for 3 hours for you, and then takes you back to your hotel, how much do you have to pay the taxi driver for the whole journey?

Use the formulaCost = A + distance × B + waiting time × CWhere A is taxi start, B is distance in kilometres, and C is hours the taxi waits.

3

1.8.3 If the journey there (one way) takes 35 minutes, what is the average speed of the taxi in kilometres per hour?Use the formula

3

1.8.4 The taxi driver asks for a 100 Zimbabwean Dollar tip. How much is this worth in South African Rands?

2

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Question 2A school librarian tracks how many books are taken out of the library by Grade 12’s through a

term

0 1 2 3 4 50

5

10

15

20

25

30

35

40

12

34

26

18

6

1

Books taken out from the library in a term by Gr 12's

Number of Books

Num

ber o

f Gr1

2's

2.1 What is the most common number of books taken out in the term? 1

2.2 How many Grade 12’s took out 2 books? 1

2.3 How many Grade 12’s are there in this school? 2

2.4 What percentage of Grade 12’s did not take out any books in the term? 2

2.5 Why is a bar graph, rather than a histogram, the correct way to represent this data? 2

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Question 3Nutella is a popular hazelnut and chocolate spread.

The ingredients are listed on the side of the bottle as follows:NUTELLA

Ave Quantity per serving (20g)

Ave Quantity per 100g

Energy 435kJ 2175kJProtein 1.5g 7.3gFat, total 6.1g 30.3g- saturated 2.0g 10.0gCarbohydrate 10.9g 54.7g- sugars 10.9g 54.4gSodium 6.6mg 33mg

0

3.1 How much energy is there in an average serving of Nutella? 1

3.2 Which is the largest component of Nutella per 100g by mass? What is the gram-value of this component per 100g?

2

3.3 Clayton spreads a 2mm thick layer of Nutella on a square piece of bread 95mm on each side.What volume of Nutella does he put on the bread? Express your answer in cm3

Use the formulaVolume = height × length × breadth

3

3.4 The sheet lists a serving of Nutella as 20g.If the density of Nutella is 1.2g per ml, what is the volume (in ml’s) of 20g of Nutella?Use the formula

3

3.5 How much energy would 15g of Nutella contain? 3

3.6 The recommended daily energy intake for an adult it 8700kJExpress one 20g serving of Nutella as a percentage of an adult’s daily energy intake.

2

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3.7 Kelsey compares the monthly salaries of call-centre agents in Durban and Johannesburg.The following are the monthly salaries, in rand, earned by call-centre agents:

Durban 4 200 4 284 4 712 5 137 5 239 5 763 6 282 6 784 7 531

Johannes-burg 5 900 6 136 6 688 7 357 8 019 8 340 8 590 9 363 9 551

0

3.7.13.7.2 Calculate the range of the salaries earned at the Durban agency. 2

3.7.33.7.4 What is the median salary for the Johannesburg agents? 2

3.7.53.7.6 Calculate the mean salary of Durban call agents. 3

3.7.73.7.8 Calculate the percentage of the monthly salaries earned in Durban that are less than the minimum monthly salary earned in Johannesburg.

3

3.8 Kelsey wants to buy a computer, and finds one on a hire purchase agreement.The cost of the computer is R3500. The interest is 9% per annum, and the total amount to be paid is calculated using simple interest over two years.How much will the total cost of the computer be?Use the formula

A = P(1+i×n)Where A is the final amount,

P is the initial amount,i is the interest raten is interest rate

4

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Question 44.1 Zoey is a first year university student this year (2013). Her parents give her a monthly allowance

of R3 000 to cover her expenses which consist of the following:• Monthly cellphone payments• A total monthly instalment of R500,00 for two clothing stores, Teencraze and Fabfashion• Daily cost of R35,00 for food• R130,00 per weekend for entertainment• Transport costs of R175,00 per week

0

TABLE 1 below shows Zoey's budget for April:

TABLE 1: April 2013 budgetMonthly cellphone payments R180Teencraze account R260Fabfashion account AFood for the month BWeekend entertainment for four weeks CTransport for four weeks DTOTAL R2 950 0

4.1.14.1.2 Calculate the missing amounts A, B, C and D. 8

4.1.34.1.4 Calculate the difference between her allowance and her total expenses for the month. 2

4.1.54.1.6 Zoey needs R180 to go on a university excursion. Name ONE possible way in which she can reduce her monthly expenditure so that she will have enough money for the excursion.

2

4.1.74.1.8 Zoey will be a student at the university for four years. Analysts have predicted that transport costs will increase at a compound interest rate of 8% per annum.Calculate how much she will need to budget for her weekly transport in April 2016.Use the formula: A = P (1 + i)n, where A = final amount

P = initial amounti = interest raten = number of years

3

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4.2 The following seating plan was used for Zoey's first semester examination.Zoey's examination number was 211141103.

0

4.2.14.2.24.2.3 Identify the row and column in which Zoey sat. 2

4.2.44.2.54.2.6 How many students sat in the same row, as Zoey? 2

4.2.74.2.84.2.9 Determine the general direction of the emergency exit from where Zoey sat. 2

4.2.104.2.114.2.12 Is this the CLOSEST exit to Zoey? 1

4.2.134.2.144.2.15 Examination rules state that each candidate must occupy an area of at least 0,75 m2.Calculate the minimum total area that must be allocated to students in this examination venue.

3

4.2.164.2.174.2.18 If the seats were allocated entirely at random, what was the probability that she would get a front row seat?

3

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4.3 The exam paper had a multiple choice section, with 10 questions. Each questions had 4 options (A,B,C,D).Zoey had not studied, and decided to answer at random!

4.3.1 What is the probability that she got question 1 right? 2

4.3.2 What would her average percentage for the multiple choice section be? 2

4.3.3 What is the probability that she gets 100% for the multiple choice section? 2

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Question 55.1 Who’s winning the mobile platform wars, Apple’s iOS or Google’s

Android?

According to a survey, 133.7 million people in the U.S. owned smartphones.The following pie chart shows the split between Google’s Android phones, Apple’s iOS phones, and “Other phones’ – from Blackberry, Microsoft or Symbian.

Source: http://techland.time.com/2013/04/16/ios-vs-android/5.2 Which company produces iOS phones? 1

5.3 Which is the most popular platform by subscribers in the US? 2

5.4 How many Americans use iOS phones? 3

Some of the data for the ‘other’ category is made up of the percentages in Table 2:Table 2: Other Smartphone Platforms, Q1 2013:BlackBerry 5.4%Microsoft 3.2%Symbian 0.5% 0

5.5 If Blackberry were to be included in the pie chart, what would the angle of the sector (slice of pie) have to be?

3

5.6 An iPhone5 has a the following specifications:Height: 4.87 inchesWidth: 2.31 inchesDepth: 0.30 inchWeight: 3.95 ounces

0

5.6.1 What is the weight of an iPhone in grams, if one ounce is the same as 28.35grams? 2

5.6.2 What is the height, in millimetres, of an iPhone5?Use the formula

1 inch = 25,4 mm3

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5.6.3 The screen size of a cell phone is given as the diagonal measurement across the screen.If Mr Hillebrand’s cellphone has a screen measuring 65mm long and 45mm wide, what is its diagonal measurement in mm?Use the formula

35.7 The screen of his phone is 480 × 320 pixels. 0

5.7.1 Express this as a ratio in its simplest form. 25.7.2 How long and wide (in millimetres) is a single pixel on his phone? 25.7.3 Based on your answer to Question 5.7.2, is a pixel on Mr Hillebrand’s phone square or not? 1

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Option X

Option Y

2 points , correct line

0;200100;200400;950Correct line

Question 6Mr Siyo, who lives in Bloemfontein, wants to hire a car for a day to travel to Kimberley and back again. The distance from Bloemfontein to Kimberley is 180 km. He contacts a car-hire company and is given two options: Option X and Option Y.

Option X: The company charges a set fee of R450 per day plus 50 cents (R0,50) for every kilometre travelled.

TABLE 2: Cost of hiring a car using Option XDistance (km) 0 100 180 250 300 340 400Cost ( R ) 450 500 A 575 600 620 650

Option Y: The company charges a set fee of R200 per day for the first 100 km or part thereof. They charge R2.50 per kilometre for every additional kilometre travelled after the first 100 km.

TABLE 3: Cost of hiring a car using Option YDistance (km) 0 100 130 175 260 330 400Cost ( R ) 200 200 275 387.50 B 775 950

6.1 Calculate the value of A 2

6.2 Calculate the value of B 3

6.3 Use the grid provided on ANNEXURE A, showing the cost of hiring a car, and draw line graphs representing Option X and Option Y. Clearly label the two graphs.

9

6.4 Use the tables or the graphs to answer the following questions:After how many kilometres will the cost for Option X and for Option Y be the same?

2

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6.5 Write down the break-even cost. 1

6.6 Petrol costs R12,72 per litre. Mr Siyo paid R432,48 for the petrol he had used. How many litres of petrol did he use?

3

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Question 7Mr Schofield requires a cylindrical water tank to collect rainwater from his roof. This water will be used for irrigating his garden.

He wants to know how much rainwater the tank can hold. The inner radius of the tank is 0,980m and the inner height of the tank is 2,495 m.

7.1 Calculate the total volume, rounded off to THREE decimal places, of the water tank.Use the formula:

Volume of a cylinder = × (radius)2 × height,and using = 3,14

3

7.2 Determine the height, rounded off to THREE decimal places, of the water in the tank when it is 80% full.

2

7.3 The outside walls and roof of the rainwater tank need to be painted. The outer radius of the tank is 1 m and the outer height of the tank is 2,5 m.Calculate the surface area of the tank that will be painted using the formula:

Surface area of the tank = × radius × ( 2 × height + radius), andusing π = 3,14

5

7.4 Suppose the tank filled up at an average rate of 10 mm per minute.Calculate how long it took (in hours) for the water in the tank to reach a height of 2 100 mm, if the tank was initially empty.Use the formula:

3

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The first pie chart

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Learner: ________________________________ Reg:________ Teacher Gl / Hi

Annexure AQuestion 6.3

0 50 100 150 200 250 300 350 400 4500

100

200

300

400

500

600

700

800

900

1000

COST OF HIRING A CAR

Distance (in kilometres)

Cost

(In

Rand

)

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