**
WELCOME TO THIS PAGE INTENDED FOR STUDENTS AT THE UNIVERSITY OF THE WESTERN CAPE
REGISTERED FOR THE MODULE QSF 131:**

**T2 W7 L2**

YEAR MARKS

COURSE EVALUATION : FRIDAY 7 MAY 2010: DURING QSF LECTURE

(5^{th} PERIOD)

FINAL EXAM: 25 MAY : 08h30

RE-EVAL : WATCH NOTICE BOARDS

REVISION:

1. OVERVIEW OF COURSE: COURSE OUTLINE

**2.**
**
GATEWAYS**

1.1 2.1 3.1 4.1

**
1.2
2.2 3.2 4.2**

3. TUTORIAL TESTS

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 a**n 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 80^{th} floor of a
skyscraper in New York, a fireman climbs down ALL the stairs to the ground
floor. He climbs down from the 80^{th} floor to the 79^{th}
floor in 8 seconds. If the average time taken to climb down each
consecutive floor, becomes of a second ** more each** time, calculate the

__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 owners gross income
and petrol costs.
(7)

__QUESTION 4 (8
marks)__

A certain municipality levies the following rates:

SERVICE / ITEM |
Rate or Tariff |

PROPERTY RATES: Site Building ELECTRICITY WATER REFUSE SEWERAGE |
1.301 1.301 0.3035 rand per kwh;
R9.15 per R54.75 per bin removal R15.39 per |

Determine the following:

4.1 The ** ratio** of property
rates payable for the site

4.2 The ** difference** between
two electricity charges of which the usages are 700 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

(b)

(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:

(2)

__QUESTION 6 (5 marks)__

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

6.1 1.807 0.607 χ (6.07)

6.2

(5)

__QUESTION 7 (9 marks)__

7.1 Simplify the following expression:

1 (3)

7.2 Factorise completely:

2*p*²(*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*: 3*x*+ 4y = 18 and
5*x + *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?

(7)

__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?

__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

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

used?

(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 5*x* rands, while the
Cost function C(*x*) for the same product is 12.7 + 2*x* 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**

**© DESMOND DESAI,
DMD EDU-HOME, 2010**

All rights reserved. Designed and created by Desmond Desai, South Africa. This page is protected by Copyright. No part of this page may be reproduced, stored in a retrieval system, or transmitted in any form of by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright holder.