WELCOME TO THIS PAGE INTENDED FOR STUDENTS AT THE UNIVERSITY OF THE WESTERN CAPE REGISTERED IN 2010 FOR THE MODULE:
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 A real number and an imaginary number;
1.2 A fraction and a percentage;
1.3 A factor and a term in an algebraic expression;
1.4 The gradient of a linear function and that of a quadratic function;
1.5 A ratio and a fraction;
1.6 An equation and a proportion.
QUESTION 2 (7 marks)
A taxi-fleet owner of a number of similar 1600 cc four-door sedans, charges the following weekly rates for transport services:
· R15 for every kilometer traveled; and
· R22 basic fee per half an hour of traveling.
· In addition to the above, the charge for waiting is R54 per hour.
Over weekends his fee is 25% more than his weekly rate.
2.1 Calculate his gross income and average speed in km/h for a 5-day week, if his fleet carried passengers a total of 4450 kilometers in 300 hours. The total waiting time during that week was 36 hours.
2.2 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 4450 kilometers;
2.3 How much is his gross income for a weekend during which he conveyed passengers over 1450 km in 140 hours with a waiting time of 24 hours?
2.4 If his weekly fleet maintenance bill amounts to R10000, and the gross wages of the drivers total R 15 000, calculate his gross loss/profit for the week, using your answers in 2.1 and 2.2 above for the owner’s gross income and petrol costs.
QUESTION 3 (7 marks)
3.1 It takes 5 minutes on the average to ‘clean up’ one used brick salvaged from a demolished building and which were dumped free of charge on unused state property. Determine:
(a) How many bricks can be ‘cleaned up’ in a working day of hours, which includes a break of 30 minutes.
(b) If the labour wage for the day is R120 per person, calculate how much it costs to ‘clean up’ one brick. (2)
3.2 A small brick manufacturing business can manufacture 1000 similar sized bricks in one working day. In addition it costs them a daily wage total of R120 per day and a further R100 per day to rent the premises. The machinery and equipment cost a total of R220 to hire per day. Additional costs for fuel, raw material and sundry items, amount to R130 for the day.
(a) Calculate the total cost to manufacture 1000 bricks.
(b) Now calculate the cost to manufacture one brick.
(c) Compare your answer in 3.2 (b) to that in 3.1 (b) above. (3)
3.3 How many additional bricks need the worker to ‘cleaned up’ in 3.1 above in order to match the cost per brick calculated in 3.2. (2)
QUESTION 4 (7 marks)
A group of 22 employees of a manufacturing company decide to go on a weekend retreat for two days. Their expenses will be based on a return journey of 556 kilometres (to their destination and back), and the following:
· R1080 daily rental for a 20-seater bus, plus R2.25 per kilometer for each kilometer traveled;
· R10.47 per litre of petrol; (Note: Assume 1 litre of petrol covers 9.5 km)
· R425 per day to hire each of the required 4 bungalows.
· R516 daily rental plus R1.95 per kilometer for a double cab.
The staff members all agree to pay as follows:
· The total expense is divided equally amongst themselves; except for
· Two drivers, chosen from themselves, who each pay 7.5% less than the rest;
· Those who withdraw have to pay R300 EACH penalty fee.
Calculate the total amount each one has to pay, if three of them withdraw and decide not to join the weekend outing, and for which the company will carry 50% of the full costs (including for those who eventually withdrew).
QUESTION 5 (10 marks)
5.1 Simplify without calculator (Show all your calculations):
(a) 0.7 – 0.7× 0.01 0.02 - 0.01 (b)
(c) –– (–5) (d) …/Question 5.1(e)
(e) 0.000 160 3 × 10 (10)
5.2 Express the following in scientific notation correct to three decimal places:
QUESTION 6 (5 marks)
Use your calculator to calculate: (if necessary, correct to 3 decimal places):
QUESTION 7 (9 marks)
7.1 Simplify the following expression:
7.2 Factorise completely:
2m˛(–k + 4) + 2(k – 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
QUESTION 9 (5 marks)
A basic tax of R2000 is charged on an income of R20 000. For amounts more than R20 000, this tax amount increases by R22.50 for every additional R200 income which is more than ( or, that portion of his income which is above) R20 000. What does a person pay if he/she earns:
9.1 R60 000;
9.2 K rands where K is more than R30 000. (5)
QUESTION 10 (6 marks)
A small processing plant employs the following workers:
· Two supervisors at R10 500 in total per month;
· seven process operators at R 763.45 each per week; and
· three manual workers at R 295.78 each per week.
All the workers agree to go on a year-end outing and decide to pay as follows and based on their weekly salaries:
· The supervisors each pay a basic charge of R100 plus 9.8% of the portion of his/her weekly salary above R763.45;
· The process operators each pay a basic charge of R75 plus 7.25% of their the portion of their weekly salaries above R295.78;
· The manual workers only pay R55 each.
If ALL of them agree to make their contributions % of what originally had been agreed upon, calculate the total amount available for the outing of the workers. (6)
QUESTION 11 (7 marks)
Zinzi’s rectangular bathroom floor has 6 rows of tiles, each of which has 10 tiles. Each of these tiles are 33 cm by 33 cm
11.1 How wide and how long is Zinzi’s bathroom floor in metres?
11.2 Zinzi’s boyfriend Kosi, is prepared too tile her bathroom floor for free with new tiles which are times as wide, as well as times as long, as the old tiles. How many of the new tiles does Zinzi need to cover the floor?
11.3 Kosi warns her that the new tiles may not fit the room exactly, without having to cut the tiles smaller. Is he correct? (Give a reason.)
11.4 Zinzi and Kosi agree to buy new tiles at R49.99 per square meter, on which they receive a discount of 12.5%. How much did they pay for the tiles ? (7)
QUESTION 12 (3 marks)
At a family supermarket, 750 g of a particular type and brand of coffee is marked down by 10% and then sold for R44.99. Calculate the original price of that brand of coffee (that is, before the markdown).
QUESTION 13 (3 marks)
The average percentage of 102 students in a tutorial test which was marked out of 25, was 51.25%. If 47 students earned one extra mark for good class attendance, by how many percentage points did the class average increase?
QUESTION 14 (5 marks)
Zola receives twice as much pocket money as her little brother Tola, who receives 0.375×(3cd-5de) rands every week.
14.1 How much pocket money do they receive altogether in one year?
14.2 If they used their total yearly pocket money to buy a radio jointly, how much VAT did they pay on their radio? (Note: VAT = 14%)
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) is 12.7 + 2x rands.
15.1 Express the profit function P(x) in the form of an equation if the Revenue function equals the Cost function plus the Profit function.
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.
15.5 Use your graph to find the selling price (revenue or income) if the profit is R40. (10)
© DESMOND DESAI, DMD EDU-HOME, 2010
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