St Benedict School

Trials Paper 2 – 2009

Name : ______

ST BENEDICT SCHOOL

Grade 12

Mathematical Literacy

September 2009

Trials Exam

Paper 2

Time: 3 Hours

Total Marks: 150 Marks

Examiner: Mrs L. Foot

Moderator: Mr P Ramlall

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Please read the following carefully:

1. This paper consists of:
2. 8 questions on 15 pages
3. Annexure A - D are at the end of the paper
4. Answer ALL questions on this exam paper.
5. Please round all answers to 2 decimal places unless otherwise stated.
6. Calculators may be used in all questions – but please show workings, as marks have been allocated for working out.
7. Number the answers correctly according to the numbering system used in this question paper.
8. Write neatly and legibly.

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Summary of Marks

Question / Q1 / Q2 / Q3 / Q4 / Q5 / Q6 / Q7 / Q8 / Total
Possible Marks / 28 / 28 / 8 / 21 / 17 / 10 / 17 / 21 / 150
Marks Obtained
LOs / 1,2 / 1,2,3 / 3 / 1 / 4 / 4 / 3,4 / 1

“ I can do all things through Christ who strengthens me” Phil 4:13

Question 1 [28 Marks]

Mr Alec Rich started a new car dealership, AR Motors, in January 2009 in Cape Town. He bought the rights to market the new Wanday series. What makes this series so special is the unique Zets motor car. This sports car has very economical fuel consumption. The Zets was recently test driven by the Eastern Wheels car magazine.

The new Wanday Zets 1200CC

1.1 The Eastern Wheels’ team drove the Zets over a distance of 500 km at a constant speed of 100 km per hour. Their findings were as follow:

TABLE 1 : Fuel consumption of the Wanday Zets at a constant speed of 100km/h

1.1.1How much fuel did the car use to drive 50 km ? (2)

1.1.2 Use the given information to determine the missing values, A and B,

in TABLE 1.(4)

1.1.3 How far will the Zets be able to drive on 48 litres of fuel ? (3)

1.1.4 The distance from Ceres to Cape Town is 150 km. Calculate the cost

of a return trip with the Zets if the current petrol price is R 7,34 per

litre.(3)

1.2 Mr Rich buys the Zets at R55 000 per car. His fixed expenses, which

include rent, electricity, water and salaries, amount to R30 000 per month.

1.2.1TABLE 2 : Expenses per month

The formula which is used to calculate the total expenses, is :

Total expenses = fixed monthly expenses + (number of cars x cost per car)

Use the formula and the given information to determine the missing

values for C and D. (5)

1.2.2 Mr Rich draws two graphs to show his income and expenses for the

first four months. The graph showing his INCOME for the number of

cars sold, is drawn on ANNEXURE A.

Use the values in TABLE 2 to draw a second graph on ANNEXURE

A which shows the total expenditure. Label this graph “EXPENSES”.

(4)

1.2.3 Use the two graphs to answer the following questions:

(a) How many cars must AR Motors sell to break even?(2)

(b) What will AR Motors’ income be if they sell 4 cars?(2)

(c) What will their profit be if they sell 8 cars?(3)

Question 2 [ 28Marks]

2.1Steven decides to buy the following LCD T.V, so that he can watch the Springboks vs. British Lions Test based upon the advertisement below.

2.1.1Steven decides to buy the T.V. using the instalment option. Calculate the total cost of the T.V. Show all working. (6)

2.1.2Suppose Steven takes a loan from Standard Bank for the full cash price of the T.V. He is charged interest of 11% compounded monthly and agrees to repay the loan over 3 years in equal monthly instalments.

Use the formula:

Calculate the total amount to be paid back.(6)

2.1.3Which method of payment would you advise Steven to choose? Give a reason for your answer. (3)

2.2The T.V. comes packaged in the following box.

2.2.1Calculate the surface area of the box in m². 1m =1000mm(3)

2.2.2The cost of the cardboard to make of the box is R5 per 2m2. Calculate the cost of the cardboard? (3)

2.3Steven would like to buy a stand for his new T.V. The 2-dimensional top view picture below shows the design of the base of the stand. It is given that the length of AB = BC and the length of AC = 1200mm

2.3.1Use the Theorem of Pythagoras to calculate the length of the dotted line marked BC (width of stand).

Hint: Let the length of AB = BC= x(5)

Theorem of Pythagoras

2.3.2Steven has a T.V. cabinet that has a width of 0,9m. If the width of the T.V. stand (the base of the TV) is 848,52mm, show with the aid of calculations that the T.V. stand will be able to fit on his T.V. cabinet. (2)

Question 3[8 Marks]

Below is the front and side view of Steven’s TV cabinet.

3.1.1Using the dimensions from the diagram to calculate the volume of the whole wooden cabinet in m3.(Note: Ignore the shelves) (3)

3.1.2Now calculate the volume, in m3of the wood used to make this cabinet, if the depth of the shelf is 850mm. Show all working. (5)

(Note: all shelves are the same thickness)

Question 4[21 Marks]

Mel is very excited that her boyfriend John is driving down from Johannesburg to pick her up and take her to the Springbok rugby game in Durban.

4.1Use the map of Southern Africa and mileage table, provided in AnnexureB, to answer the following questions:

4.1.1How far is Johannesburg from Durban?(2)

4.1.2John’s car has an average petrol consumption rate of 10,5 litres/100km. If the current petrol price is R7,89 per litre, calculate how much John will have to budget for petrol to travel from Johannesburg to Durban and back. Round off your answer to the nearest Rand. (5)

4.2Before the trip John needs to exchange some British Pounds and buy some South African Rand so that he can buy the tickets for the game.

Rennies Foreign Exchange
Exchange Rate board (22/6/09)
WE BUY
(Rand per 1 unit of Currency) / WE SELL
(Rand per 1 unit of Currency)
British Pound (£) / 12,35 / 12,40
Euro (€) / 10,21 / 10,28
American Dollar ($) / 8,05 / 8,10
Terminology:
‘We Buy’ Rate:
The exchange rate at which Rennies will buy foreign currency from a customer.
‘We sell Rate’:
The exchange rate at which Rennies will sell foreign currency to a customer.
Commission Fees on Currency Exchange Transactions
Fee / Minimum Fee / Maximum Fee
1,7% of the Rand value being exchanged / R60 / None

4.2.1Using the exchange rate board, calculate how many Rands John will receive from £800. (2)

4.2.2A commission fee is also charged on the exchange. See above.

Calculate the commission on John’s transaction, if the rand value is R9880. (3)

4.2.3Show by calculations that John will only receive R9712.04 for his £800. (2)

4.3Mel has had an investment policy since 1998. The value of the investment at the end of year is shown in the graph below.

4.3.1This graph is an example of what kind of growth?(1)

4.3.2If the investment at the end of 1999 is R12000, calculate the rate of increase as a percentage between the end of 1998 and 1999. (3)

4.3.3During which year did the investment earn the most interest? Explain how you can see this on the graph. (3)

Question 5 [ 17Marks]

The following table summarises the number of spectators there were at the Springboks vs. the British Lions Test Match in Durban on the 20th of June 2009.

Age Category / Female / Female % of Total spectators / Male / Male % of Total Spectators / Total Spectators
1-10 / 500 / 0.8% / 1000 / 1.6% / 1500
11-20 / 5000 / 8% / 9500 / 15.2% / 14500
21-30 / 3500 / 5.6% / 5500 / 8.8% / 9000
31-40 / 4000 / 6.4% / 10500 / 16.8% / 14500
40-50 / 3000 / 4.8% / 20000 / 32% / 23000
Total / 16000 / 25.6% / 46500 / 74.4% / 62 500

5.1.1Show how the % for females from the age category 31-40 was calculated.

(2)

5.1.2Explain why it is better to use percentages to make a comparison between the male and females in each age category. (2)

5.1.3Use the grid on the Answer Sheet to draw a dual bar graph of males and females in each age category. (6)

5.2The following pie chart shows the results of all the games played between the Springboks and the Lions since 1891.

5.2.1What percentage of games where drawn overall?(1)

5.2.2What percentage of games where drawn in Durban?(2)

5.2.3If 44 tests have been played over the years, how many games have the Springboks won over the years? Show all working. (4)

Question 6 [10 Marks]

Zweli shows his family that he has been learning probability in maths.

6.1What is the probability that Zweli chooses a Jack of Hearts from the pack? (1)

6.2What is the probability that Zweli chooses a black six or a red two from the pack? (3)

6.3What is the probability that Zweli chooses a three or a nine?(2)

6.4Zweli’s dad says that he will take the family to the Wimpy if Zweli pulls out a Jack, then a Queen and then a King. The cards are not returned each time. What is the probability that this would happen. (4)

Question 7 [17 Marks]

Gerrie van Niekerk is a primary school learner who lives in Krugersdorp. He lives on the corner of Wishart Street and 5thStreet.Detach the map of part of Krugersdorp, Gauteng, on ANNEXURE D and use it to answer the following questions.

7.1Give a grid reference for the Jays Shopping Centre where Gerrie and his mother do their weekly grocery shopping. (1)

7.2Gerrie's grandmother lives with them and goes to the hospital for her medication once a month.

What is the relative position of Krugersdorp Central Hospital with respect to Gerrie's home? (1)

7.3Gerrie's father drives from Jays Shopping Centre to the petrol station to buy petrol for his car. Describe his route if the exit from Jays Shopping Centre is in 4thStreet. (Give compass direction) (1)

7.4There were complaints from parents of PaardekraalPrimary School that motorists were speeding in 3rd Street near the school. As a result of this they felt that stop signs should be installed at the intersection of 3rdStreet and Pretoria Street.

The speed limit is 60 km/h.

A parent, who is a traffic officer, recorded the speed of the 17 cars that passed the school between 14:15 and 15:00 on a particular Monday.

The speeds in kilometres per hour (km/h) are:

62;57; 55,5; 64; 70; 60

62; 60; 50; 97; 56; 71

61; 48; 59,5; 60; 61

7.4.1Determine the mean speed of the cars rounded off to the nearest whole number . (3)

7.4.2What is the modal speed? (1)

7.4.3Determine the median speed of the cars.(3)

7.4.4Do you think that the parents' request for stop signs to be installed at the intersection of 3rd Street and Pretoria Street is valid? Give reasons for your answer. (3)

7.4.5Could you suggest TWO other ways that would reduce the speed at which cars travel past the school? (2)

Question 8 [21 Marks]

In January 2005, Mr Radebe got a big promotion at work. His annual salary before tax was increased to R350 000.

8.1The tax table says that Mr Radebe will pay R78 070 plus 40% of the amount over R270 000 minus a rebate of R5 800. How much tax will Mr Radebe pay per year? (3)

8.2Mr Radebe wants to buy a house. A financial adviser suggests that he should spend a maximum of 30% of his monthly income after tax on paying back a home loan each month. According to this financial adviser, what is the highest monthly repayment Mr Radebe should have for his home loan? (2)

8.3Mr Radebe goes to his bank to find out how much he can take a loan for. The bank provides him with the following table that gives him the monthly repayment for each R1 000 borrowed (depending on the interest rate charged) for both a home loan over 20 years and a home loan over 30 years. The bank tells Mr Radebe that the current interest rate they are offering is 10%.

This table gives you the monthly repayments for each R1 000 borrowed.
Interest rate / Number of years loan is paid off over / Interest rate / Number of years loan is paid off over
20 years / 30 years / 20 years / 30 years
7% / R7,75 / R6,65 / 17% / R14,67 / R14,26
8% / R8,36 / R7,34 / 18% / R15,43 / R15,07
9% / R9,00 / R8,05 / 19% / R16,21 / R15,89
10% / R9,65 / R8,78 / 20% / R16,99 / R16,71
11% / R10,32 / R9,52 / 21% / R17,78 / R17,53
12% / R11,01 / R10,29 / 22% / R18,57 / R18,36
13% / R11,72 / R11,06 / 23% / R19,37 / R19,19
14% / R12,44 / R11,85 / 24% / R20,17 / R20,02
15% / R13,17 / R12,4 / 25% / R20,98 / R20,85
16% / R13,91 / R13,45 / 26% / R17,78 / R17,53

Give advice to Mr Radebe about the maximum home loan he can take if he pays off the loan over 20 years and the maximum home loan he can take if he pays off the loan over 30 years. Also advise him on the advantages and disadvantages of taking the loan over 30 years, the advantages and disadvantages of taking the loan over 20 years and the potential danger of borrowing the maximum amount that he can. (8)

8.4Mr Radebe decides to take a loan of R600 000 over 20 years. He is charged 10% annual interest. This graph shows how his loan is paid off over 20 years. The graph shows how much money he still owes at any one time during the 20-year period of the loan.

8.4.1Use the graph to determine how long it takes him to pay off the first half of the loan. Give your answer in years and months. (2)

8.4.2. Use the graph to determine how long it takes him to pay off the remaining half of the loan. Give your answer in years and months. (2)

8.4.3. Explain fully why it makes sense that your answers to 8.4.1. and 8.4.2. are different.(4)

Name/Examination Number: ______

ANNEXURE B

Question 4.1

Name/Examination Number: ______

ANNEXURE C

Question 5.1.3

Name/Examination Number: ______

ANNEXURE D

Question 7

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