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T2 W7 L2




(5th PERIOD)


FINAL EXAM: 25 MAY : 08h30




2.                 GATEWAYS

          1.1              2.1              3.1              4.1

          1.2              2.2              3.2              4.2


          TUT TEST 1          TEST 2        TEST 3

          TEST 4                   TEST 5        TEST 6

 4                   CLASS TESTS

            CLASS TEST 1      TEST 2        TEST 3        TEST 4

 5.                   TERM TEST 1

              TERM TEST 2

6        FINAL EXAMS  NOVEMBER 2009:

QUESTION 1 (12 marks)

Give examples of, and briefly point out the essential difference(s), if any, between each the following pairs of terms

1.1       An imaginary and an irrational number;

1.2       An integer and a whole number;

1.3       A base and an exponent in a power;

1.4       The gradient and the y-intercept of a linear function

1.5       A ratio and a rate;

1.6       A percentage and a decimal fraction.                                                                    (12)

QUESTION 2 (4 marks)

Starting from the 80th floor of a skyscraper in New York, a fireman climbs down ALL the stairs to the ground floor. He climbs down from the 80th floor to the 79th floor in 8 seconds. If the average time taken to climb down each consecutive floor, becomes  of a second more each time, calculate the total time in hours taken to reach the ground floor.  (4)

QUESTION 3  (7 marks)

A taxi-fleet owner of a number of similar 1600 cc four-door sedans, charges the following weekly rates for transport services:

·        R12 for every kilometer travelled; and

·        R20 basic fee per half an hour of travelling.

·        In addition to the above, the charge for waiting is R48 per hour.  Over weekends his fee is 25% more than his weekly rate.

3.1 Calculate his gross income for a 5-day week, if his fleet carried passengers a total of 2450 kilometers in 500 hours. The total waiting time during that week was 36 hours.

3.2 If petrol cost him R7.45 per liter, which allows him to travel 8 km on the average, how much petrol did he use during the week when he covered 2450 kilometers;

3.3 How much is his gross income for a weekend during which he conveyed passengers over 1450 km in 240 hours with a waiting time of 24 hours?

3.4 If his weekly fleet maintenance bill amounts to R2000, and the wages of the drivers total R 10 000, calculate his loss/profit for the week, using your answers in 3.1 and 3.2 above for the owner’s gross income and petrol costs.                                                                                                                        (7)

QUESTION 4  (8 marks)

A certain municipality levies the following rates:


Rate or Tariff









1.301 cents per rand

1.301 cents per rand

0.3035 rand per kwh; first 50 kwh free

R9.15 per kiloliters (kl)

R54.75 per bin removal

R15.39 per kiloliters (kl)

Determine the following:                       

4.1       The ratio of property rates payable for the site as compared to that for the building (improvements). The site is valued at R50 000 and the building at     R450 000.

4.2       The difference between two electricity charges of which the usages are 700 kwh and 675.12 kwh.

4.3       The charge for water consumption if the consumption is 34 050 liters and of    

            which the first 7.5 kl is free.

4.4       The monthly refuse charge if the refuse bin is removed twice weekly.

4.5       The sewerage collection charge for 14 681 liters of which the first 8 kl is free.                                                                                                                                      (8)     

QUESTION 5  (10 marks)                                                                                 

5.1       Simplify without calculator (Show ALL your calculations):       


            (a)        0.7 – 0.6 Χ 0.1  0.02 - 0.01      


            (c)        (–3)³ – 2Χ(–5)                                    

            (d)                                                     .

(e)        0.000 014 x 10                                                                               (10)                                                                                          

5.2      Simplify the following, and hence express your answer in scientific notation     correct to two decimal places:             


QUESTION 6 (5 marks)

Calculate  (where necessary, correct to 3 decimal places):

6.1       1.807 –  0.607 χ (6.07)              



QUESTION 7 (9 marks)

7.1      Simplify the following expression:                   

         – 1                                                                     (3)                   

7.2       Factorise completely:

     2p²(–q + 4) + 2(q – 4)                                                                                (4)

7.3       Determine i if    where p = 0.1378  and   q = 0.1325             (2)


QUESTION 8 (4 marks)                                                                                             

Solve simultaneously for x and y: –3x+ 4y = 18  and   5x + 8 y = 14                (4)                                                                                                                                                                                      

QUESTION 9 (7 marks)

Zastra intends to undertake a journey of 1 240 km by car.  She wants to know how much money she will need for petrol. Zastra knows that her petrol consumption is related to the speed at which she drives. At a speed of 120 km/h her car uses 1 liter every 9 km and at 60 km/h the 1 liter for every 12 km. At a speed of 90 km/h the car uses 1 liter every  10 km. Seven-eighths of the journey will be on highways,  of the journey will be in built-up areas where Zastra is only allowed to travel 60 km/h, and the remainder will be along roads where she can do 90 km/h.

9.1       How much money should Zastra have available for petrol, if petrol costs R7.45 per litre?

9.2       How many hours, correct to 1 decimal place, will Zastra take to complete the    journey, if she rests 15 minutes after every full 2 hours of traveling?


QUESTION 10 (4 marks)

A saleslady was paid R85.50 per working day, plus 4.5% commission on all sales. She worked for the period from 9 February 2009 up to, and including, 19 April 2009,  except for 9 days during this period for which she received no payment.  She sold items totaling R83 600 during this period.  How much did she earn for that period?                                                                                                                          (4)

QUESTION 11 (3 marks)

Four amounts in South African currency are:      2.05 million rands,  17 800 999 cents,  20 168.09 rands and 12 125 cents.    62% of a fifth amount equals 0.056 million cents. Calculate the total of these five amounts.                                                                   (3)

QUESTION 12 (5 marks)

A basic tax of R3000 is charged on an income of R30 000. For amounts more than      R30 000, this tax amount increases by R6.50 for every additional R200 income above (that is, the portion which is more than) R30 000. What does a person pay if he/she earns:

12.1          R40 000;

12.2          p rands where p is more than R30 000.                                                                                                                         

QUESTION 13 (7 marks)

13.1     A 2.0 liter motor car requires 65 liters petrol over a distance of 500 km.

            (1) How many kilometres are traveled (on the average) for every 1 liter of petrol                           


            (2) If the journey of 500 km takes 5.75 hours to complete, at what average rate                              

                will petrol used every hour?                                                                                (4)

13.2          At a family supermarket, 750 g of a particular type and brand of coffee is marked at   R49.99.  If 300 g of exactly the same type and brand of coffee is marked at R19.99, which is the better buy?                                                                                                                       (3)

QUESTION 14 (5 marks)

It costs a total of R138.90 to purchase 10 loaves of bread and 12 litres of cooldrinks in a store. If the store raises the price of bread by 20% and the price of cooldrinks by 10%, the total price of these items becomes R159.54. Find the original price of one loaf of bread.                                                                                                                                             (5)

QUESTION 15 (10 marks)

The Revenue function R(x) (Sales or Income function) of a particular product is 5x rands, while the Cost function C(x)  for the same product is  12.7 + 2x rands.

15.1     Express the profit P(x)  in the form of an equation where the Revenue function              

            equals the Cost function plus the Profit.   

15.2     Use the grid below to represent the profit function graphically.                              

15.3     What is the slope of a linear function which is perpendicular to the Revenue   Function .

15.4     Read off from your graph the profit, if x = 12.

14.5     Use your graph to find the selling price if the profit is R40.                                    (10)


                                                                                                     TOTAL MARKS:  100


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