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Tutorial letter 101/0/2019

ACCESS TO MATHEMATICS

MAT0511

Year module

Department of Mathematical Sciences

IMPORTANT INFORMATION:

This tutorial letter contains important information about yourmodule.

MAT0511/101/0/2019

CONTENTS

Page

1 INTRODUCTION..................................................................................................................4

2 PURPOSE OF AND OUTCOMES .......................................................................................4

2.1 Purpose................................................................................................................................4

2.2 Outcomes .............................................................................................................................5

3 LECTURER(S) AND CONTACT DETAILS ..........................................................................7

3.1 Lecturer(s) ............................................................................................................................7

3.2 Department ..........................................................................................................................7

3.3 University..............................................................................................................................7

4 RESOURCES.......................................................................................................................8

4.1 Prescribed book(s) ...............................................................................................................8

4.2 Recommended book(s) ........................................................................................................8

4.3 Electronic reserves (e-reserves) ..........................................................................................8

4.4 Library services and resources ............................................................................................8

5 STUDENT SUPPORT SERVICES .......................................................................................9

6 STUDY PLAN.......................................................................................................................9

7 PRACTICAL WORK ............................................................................................................9

8 ASSESSMENT.....................................................................................................................9

8.1 Assessment criteria ..............................................................................................................9

8.2 Assessment plan ................................................................................................................10

8.3 Assignment numbers..........................................................................................................10

8.3.1 General assignment numbers ............................................................................................10

8.3.2 Unique assignment numbers..............................................................................................10

8.4 Assignment due dates........................................................................................................11

8.5 Submission of assignments................................................................................................11

8.6 The assignments ................................................................................................................11

8.7 Other assessment methods ...............................................................................................11

8.8 The examination .................................................................................................................12

9 FREQUENTLY ASKED QUESTIONS................................................................................12

10 SOURCES CONSULTED...................................................................................................12

2

MAT0511/101/0/2019

11 IN CLOSSING ....................................................................................................................12

12 ADDENDUM ......................................................................................................................13

12.1 ASSIGNMENT 01...............................................................................................................13

3

1 INTRODUCTION

Dear Student

We are pleased to welcome you to the MAT0511 module and hope that you will find it both inter-esting and rewarding. We shall do our best to make your study of this module successful. Youwill be well on your way to success if you start studying early in the year and resolve to do theassignments properly.You will receive a number of tutorial letters during the year. A tutorial letter is our way of communi-cating with you about teaching, learning and assessment.This tutorial letter, Tutorial Letter 101, which is your first tutorial letter for MAT0511, is particularlyimportant because it contains all the assignment questions, except for the last assignment. Italso contains important information about the scheme of work, resources and exam admissionprocedures, for this module. We urge you to read it carefully and to keep it at hand when workingthrough the study material, preparing the assignments, preparing for the examination and address-ing questions to your lecturers.We suggest you keep a separate file for all your MAT0511 tutorial letters, so that you will be able torefer to them easily, whenever necessary.The Department of Despatch will supply you with the following study matter for this module.

• Study Guides (4 books)

• this tutorial letter

Tutorial matter that is not available when you register will be posted to you as soon as possi-ble.

You can view the study guides and tutorial letters for the modules for which you are regis-tered on the University’s online campus, myUnisa, at http://my.unisa.ac.za. Note that youneed to register on myUnisa. Through myUnisa you can submit assignments, access libraryresources, download study material as well as communicate with the university, your lecturersand other students. Since UNISA is moving towards online delivery only, it is very importantto register on myUnisa and to access all your modules on myUnisa on a regular basis. Ad-ditional tutorial letters and the solutions to the assignments will be posted under AdditionalResouces on myUnisa.

2 PURPOSE OF AND OUTCOMES

2.1 Purpose

This module will be useful to students who have studied Mathematics at matriculation level but whodo not satisfy the minimum requirements for direct admission to tertiary-level study.Range statement for the moduleThe skills developed in this module are extended to the National Senior Certificate level 4. As faras possible the problems selected are applied in real contexts.

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MAT0511/101/0/2019

2.2 Outcomes

Specific outcome 1:Do operations on Real Numbers and use Basic Algebra ToolsAssessment criteria

1.1 Recognition and use of the different kinds of numbers, number sets and set notations.

1.2 Operate on real numbers and obeying the rules.

1.3 Solve problems which involve ratio, proportion and percentage.

1.4 Apply the definitions of integral exponents, scientific notation and roots.

1.5 Convert units and derived units in the metric system to other units in the metric system ornon-metric units to metric units and vice versa.

Specific outcome 2:Perform basic Algebraic operations by using Algebra toolsAssessment criteria

2.1 Perform basic Algebraic operations like adding, subtracting, multiplying and dividing of alge-braic expressions correctly, including working with Algebraic Fractions.

2.2 Solve Linear and Quadratic Equations and Inequalities, Equations containing Roots, andSystems of Equations in Two Unknowns, correctly.

2.3 Identify Arithmetic and Geometric Sequences and find specific terms of these sequences.

2.4 Solve Equations containing Exponents and Exponential Equations correctly, by applying theDefinitions and Exponential Rules.

2.5 Solve Logarithmic Equations by applying the various properties of logarithms correctly.

2.6 Solve problems by applying the Compound Interest formulas, Appreciation and Deprecia-tion formulas, Population Growth formula and Radio Active Decay and Half-Life Formulascorrectly.

Specific outcome 3:Plot Graphs and Interpret and Apply information on Given GraphsAssessment criteria

3.1 Draw a graph by plotting points or by using a given equation.

3.2 Apply Analytical Geometry formulas to find the coordinates of a point, distances betweenpoints, midpoints, and equations of circles.

3.3 Interpret information on a given graph to find the solutions of equations or inequalities.

3.4 Find the x– and y–intercepts if the equation of a graph is given; determine whether or not apoint lies on a given graph; find the x values for which y < 0, y = 0 or y > 0.

5

3.5 Identify the correspondence in a relation, whether the relation is a function, and the domainand range of a given relation.

3.6 Recognise whether or when two functions are equal.

3.7 Use functional notation correctly and determine function values by substitution of given do-main values.

3.8 Obtain new functions from existing functions by addition, subtraction, multiplication and divi-sion and the domains of these new functions.

3.9 Draw a straight line graph by using a table of values, two points or the point – slope method.Also draw vertical, horizontal, parallel and perpendicular lines,

3.10 Find the slope-intercept, point-slope, two-point or general equation of a line.

3.11 Find the intersection of two lines; or the vertical distance between two lines.

3.12 Apply knowledge of linear functions to problems involving linear cost- and income functions.

3.13 Sketch the graph of a linear inequality and the graph of the solution of a system of linearinequalities.

3.14 Recognise equations which show direct, indirect or joint proportionality amongst differentvariables.

3.15 Recognise the characteristics, sketch the graph, find the maxima or minima and find theequation (if three points on the parabola, or the vertex and another point on the parabola orthe x-intercepts and another point on the parabola are given) of a parabola defined by

y = ax2 + bx+ c and y = a (x− h)2 + k.

3.16 Use a rough sketch of a parabola to solve a quadratic inequality or rational inequality.

3.17 Recognise the characteristics of a hyperbola; sketch the graph of a hyperbola and find theequation of a hyperbola if a point on the hyperbola or the closest distance from the origin tothe hyperbola is given.

3.18 Interpret various combinations of graphs.

Specific outcome 4:Use Statistics to determine valuable information from collected data.

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MAT0511/101/0/2019

3 LECTURER(S) AND CONTACT DETAILS

3.1 Lecturer(s)

The lecturer responsible for this module is Dr Sunday Faleye. You can contact him at:

Dr Sunday FaleyeTel: (011) 670 9287Room no: C 6–49GJ Gerwel Buildinge-mail: [email protected]

A notice will be posted on myUnisa if there are any changes and/or an additional lecturer is ap-pointed to this module.

Please do not hesitate to consult your lecturer whenever you experience difficulties with your stud-ies. You may contact your lecturer by phone or through correspondence or by making a personalvisit to his/her office. Please arrange an appointment in advance (by telephone or by e-mail)to ensure that your lecturer will be available when you arrive.

If you should experience any problems with the exercises in the study guide, your lecturer willgladly help you with them, provided that you send in your bona fide attempts. When sending inany queries or problems, please do so separately from your assignments and address themdirectly to your lecturer.

3.2 Department

Department of Mathematical SciencesFax number: 011 670 9171 (RSA) +27 11 670 9171 (International)Departmental Secretary: 011 670 9147 (RSA) +27 11 670 9147 (International)e-mails: [email protected] or [email protected]

or the mail address

Department of Mathematical SciencesUniversity of South AfricaPO Box 392UNISA0003

3.3 University

Consult the brochure Study @ Unisa for information on how to contact the university. Always useyour student number when you contact the University.

7

4 RESOURCES

4.1 Prescribed book(s)

There is no prescribed textbook for this module. The study guides contain all the material thatyou need for exam purposes.

4.2 Recommended book(s)

We are working on a suitable book for this module which may be recommended for the module.When the book is finalesed, you will be contacted through myUnisa.

4.3 Electronic reserves (e-reserves)

There are no e-reserves for this module.

4.4 Library services and resources

The Unisa Library offers a range of information services and resources:

• for detailed Library information go to http://www.unisa.ac.za/sites/corporate/default/Library

• for research support and services (e.g. personal librarians and literature search services) goto

http://www.unisa.ac.za/sites/corporate/default/Library/Library-services/Research-support

The Library has created numerous Library guides:

http://libguides.unisa.ac.za

Recommended guides:

• Request and download recommended material:

http://libguides.unisa.ac.za/request/request

• Postgraduate information services:

http://libguides.unisa.ac.za/request/postgrad

• Finding and using library resources and tools:

http://libguides.unisa.ac.za/Research skills

• Frequently asked questions about the Library:

http://libguides.unisa.ac.za/ask

• Services to students living with disabilities:

http://libguides.unisa.ac.za/disability

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MAT0511/101/0/2019

5 STUDENT SUPPORT SERVICES

The Study @ Unisa brochure is available on myUnisa: www.unisa.ac.za/brochures/studiesThis brochure has all the tips and information you need to succeed at distance learning and, specif-ically, at Unisa.

6 STUDY PLAN

As adults you will make your own decisions about when you do your work. Those of you whoare employed or who have other responsibilities will have less time than those who are full-timestudents, but, as we mention in Book 1: Introduction, it is very important to set aside regular timeto study, and to try to stick to your schedule. The closing dates for the assignments already providethe outline of a schedule for you. Based on these dates, you should thus try to keep to the followingplan. You may progress through the material faster and submit assignments earlier. In this wayyou will be safer and provide for unforeseen circumstances which may occur.

Obviously the later you register, the less time you will have, but thefirst assignment is due in March.January – March Work through Book 1; submit Assignment 01.March – April Study Book 2 and submit Assignment 02.April – May Revise Books 1 and 2; submit Assignment 03.May – June Work through Book 3; submit Assignment 04.June Revise Book 3 and submit Assignment 05.July Work through Book 4; submit Assignment 06.July – August Revise the work in all the books. Submit Assignment 07.September and October Carefully go through all the printed solutions you will have

received and compare the solutions with your assignments.Also do the revision exercises.

See the brochure Study @ Unisa for general time management and planning skills.

7 PRACTICAL WORK

There are no practicals for this module.

8 ASSESSMENT

8.1 Assessment criteria

There are seven assignments and one examination.Examination admission.Please note that lecturers are not responsible for examination admission, and ALL enquiries aboutexamination admission should be directed by e-mail to [email protected]

You will be admitted to the examination if and only if Assignment 01 reachesthe Assignment Section by 5 April 2019.

9

8.2 Assessment plan

The assignments for MAT0511 serve different teaching purposes. In certain cases the assignmentquestions are a direct application of the work discussed in a single study unit, but often you willneed to bring together “bits” of knowledge, related to several different sections, in order to answerthe questions.

There are seven assignments for MAT0511. Six of these relate to the work dealt with in Books1 to 4. The final assignment is a revision assignment which consists of the October/November2018 exam paper.Each assignment has a specific (fixed) closing date. Please send in your assignments in goodtime, allowing for slow postage if you know you live in an area where there are sometimes postaldelays. You should post your assignment at least 7 days before the due date. After the closingdate, the assignments will be marked, and returned with our comments.We cannot give students extension for assignment submission, since all students will automati-cally receive solutions for the assignments after their respective closing dates. If you do not submitan assignment in time, please try to do it anyway, before looking at the solutions. You will learnmore in this way than from simply reading through the correct solutions we send you.The following table contains specific information for the specific assignments.

Assignment Closing date Type ofassignment

01 (Book 1) 05 April 2019 Multiple choice02 (Book 2) 18 April 2019 Multiple choice03 (Books 2 and 3) 10 May 2019 Written04 (Book 4) 21 June 2019 Multiple choice05 (Book 4) 12 July 2019 Written06 (Book 4) 02 August 2019 Multiple choice07 (Revision: 2007 exam) 16 August 2019 Written

8.3 Assignment numbers

8.3.1 General assignment numbers

The assignments are numbered as 01, 02, 03, 04, 05, 06, and 07.

8.3.2 Unique assignment numbers

Please note that each assignment has a unique assignment number which must be written on thecover of your assignment.

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MAT0511/101/0/2019

8.4 Assignment due dates

The closing dates for submission of the assignments are:

Assignment Closing date Unique number

01 05 April 2019 80400702 18 April 2019 86099203 10 May 2019 81851404 21 June 2019 75280605 12 July 2019 85346106 02 August 2019 74744707 16 August 2019 826825

8.5 Submission of assignments

You may submit your assignments either by post or electronically via myUnisa. Assignments maynot be submitted by fax or e–mail. For detailed information and requirements as far as assignmentssubmissions are concerned, see the brochure Study @ Unisa that you received with your studymaterial.Assignments should be addressed to:

The RegistrarP O Box 392UNISA0003

To submit an assignment via myUnisa:

• Go to myUnisa.• Log in with your student number and password.• Select the module.• Click on ”Assignments” in the menu on the left–hand side of the screen.• Click on the assignment number you wish to submit.• Follow the instructions.

8.6 The assignments

The assignment questions are contained in Addendum. Make sure that you do the correct assign-ments.Solutions will be available on myUnisa under Additional Resources before the examination date.

8.7 Other assessment methods

There are no other assessment methods for this module.

11

8.8 The examination

The examination for this module will be written on October/November 2019. If you are not suc-cessful in the October/November exam (i.e. if you have less than 50%) you may write the supple-mentary exam in January/February 2020 provided you qualify for that in the October/Novemberexam. Supplementary examination dates will be provided by the Examination Section.

Consult the brochure Study @ Unisa for general exam guidelines as well as advice on exam prepa-ration.You are not allowed to use a calculator in the exam.

9 FREQUENTLY ASKED QUESTIONS

The Study @ Unisa brochure contains an A-Z guide of the most relevant study information.

10 SOURCES CONSULTED

No other sources were consulted.

11 IN CLOSSING

Remember that there are no ”short cuts” to studying and understanding mathematics. You need tobe dedicated, work consistently and practise, practise and practise some more! We hope that youwill enjoy studying this module and we wish you success in your studies.

Your MAT0511 lecturer

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MAT0511/101/0/2019

12 ADDENDUM

12.1 ASSIGNMENT 01

ASSIGNMENT 01Study material: Book 2

Fixed closing date: 05 April 2019Unique Assignment Number: 804007

Important:

• This is a multiple choice assignment which must be answered on a MARK READINGSHEET.

• Please keep your rough work so that you can compare your solutions with those that will besent to you.

• 5 marks will be given for every correct answer.

Question 1Suppose

P = (−3, 4] and Q = {x ∈ R : −4 ≤ x < 0} .

Which of the following is/are true?

A. P ∪Q can be represented by the following number line.

4_ 4

B. P ∩Q ⊂ P ∪QC. −4 ∈ P ∩Q

1. Only A 2. Only B 3. Only C4. Only B and C 5. Only A and B

Question 2Which of the following is/are true?

A. 0, 3̇ = 0, 333........... =333

1 000B. −2

3< −3

4

C. 0, 3̇ > 0, 3

1. Only A 2. Only B 3. Only C4. Only A and C 5. A, B and C

13

Question 3The difference between −2

5and 1

5is

1. −35

2. 35

3. −15

4. 15

5. 1


A. 0 is a natural number.B. 1,13 < 1,103C. x < 0⇒ −x is a positive number

1. Only A 2. Only B 3. Only C4. A, B and C 5. None of them

Question 5Patricia bought the following items so that she could make a dress:

134

metres of material at R48,00 per metre2 reels of cotton at R7,99 per reel8 buttons at 79c per button.

She paid for these items with two fifty rand notes and one twenty rand note.Which of the following statements is/are true?(Try to do the calculations without a calculator.)

A. The total cost of the items bought for the dress was R106,30.B. The change Patricia received was R263,70.C. Patricia could have bought the material at another shop where the material was on sale, at a price of 12% less.

She would have saved R10,08.

1. Only A 2. Only B 3. Only C4. Only A and C 5. Only B and C

Question 6Suppose Sam and Japhta write a history test. Sam’s mark is x

40and Japhta’s mark is y

40. Which one

of the mathematical statements below represents the following?

“Japhta’s mark exceeds Sam’s mark by 20%.”

1. x− y = 20 2. y − x = 8 3. x− y = 8 4. y − x = 20 5. x = 20y

Question 7Suppose G = {x ∈ N : x ≥ 1} and H = {−3,−2,−1, 0, 1, 2}.Which of the following is/are true?A. G = [1,∞)B. G ∩H = {1, 2}C. H ⊆ Z

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MAT0511/101/0/2019

1. Only A 2. Only B 3. Only C4. Only B and C 5. A, B and C


A. The prime factors of 30 are 5 and 6.B. The HCF of 14 and 28 is 14.C. The LCM of 2, 3 and 7 is 84.

1. Only A 2. Only B 3. Only C4. Only B and C 5. None of them


A. 25

and 1025

are equivalent fractions.B. 2

3+ 3

4= 5

7

C. 1,256 ≈ 1,3 correct to the nearest tenth.


Question 10Consider the expression

3√

20−√

45 + 4√

125

2√

3.

If we simplify the expression and rationalise the denominator the answer will be

1.23√

15

62.

23√

5

2√

33.

√2 135

2√

34.

√6 405

65.

23√

5

2

Question 11A school had 1 200 learners in 2008. 60% of the learners took mathematics. There were four math-ematics teachers. In 2009 the enrolment will increase by 15%, but only 30 more learners (comparedto 2008) will take mathematics. The school will appoint one more mathematics teacher in 2009.

Which of the following is/are true?

A. In 2008 the ratio of the number of mathematics teachers to the number of mathematics learners was180 to 1.

B. In 2009 the school will have 1 380 learners.C. In 2009 the ratio of the number of mathematics learners to the number of mathematics teachers will

be 150 to 1.

1. Only A 2. Only B 3. Only C4. Only A and B 5. Only B and C

15

Question 12Suppose the price of a pair of shoes, including VAT (at a rate of 14% ), is R248. Then the VAT is

1. R(

14100× 248

)2. R

(10014× 248

)3. R

(14114× 248

)4. R

(11414× 248

)5. R

(100114× 248

)Question 13Which of the following is/are true?

A. If we simplify36 000 000× 25

100 000× 3 000 000

and write the answer is scientific notation we obtain 3× 10−3.B. The decimal number 42 can be represented in binary notation as 101010.C. The ratio of 33

4to 11

2is 5 : 2.

1. Only A 2. Only B 3. Only C4. Only A and C 5. All of them

Question 14Which of the following statements is/are true?

A.1

3−1=

(1

3

)−1

B.14

2=

1

2

C.30

3= 10

1. Only A 2. Only B 3. Only C4. Only A and B 5. Only A and C


A. 0,10301 can be written in scientific notation as 10,301 ×10−2.B.

√36 + 64 = 6 + 8

C. If the profit of a business was Rx, and the profit increases by 50%, the profit will then be R(x

2

).

1. Only A 2. Only B 3. Only C4. Only A and C 5. None of them

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MAT0511/101/0/2019

Question 16Assume n and m are integers and a and b are positive real numbers. Which of the following is/aretrue?

A.(ab

)−n=

(b

a

)nB. (a× b)m = am × bm

C.(an)m

(an)m+2 = a2n

1. Only A 2. Only B 3. Only C4. Only A and B 5. A, B and C

Question 1710kg/m2 is equivalent to

1. 10−3g/mm2 2. 10−2g/mm2 3. 103g/mm2 4. 102g/mm2 5. 10/mm2

Question 18Thabo paints a room twice as fast as Gerry does. Gerry takes 10 minutes longer than Pete to paintthe same room. If Thabo takes 3 hours to paint the room, then the time it takes Pete to paint theroom is

1. 1 hour and 20 minutes

2. 1 hour and 40 minutes

3. 5 hours and 50 minutes

4. 5,5 hours

5. 1,2 hours


A. If Susan earns R3 000 per month and her salary is 25% more than Isaac’s salary, then Isaac earnsR3 000 − (25% of R3 000).

B. A car and bus both leave Unisa at the same time. The car arrives at Ellis Park 15 minutes beforethe bus. Suppose the bus takes x minutes to travel from Unisa to Ellis Park. Then the car takes(x− 15) minutes to reach Ellis Park.

C. In 2009 I earn 50% more per month then I earned per month in 2008. In 2009 my monthlyexpenses decrease by 50%. Thus in 2009 I have double the amount of money left each monthcompared to 2008.


17

Question 20

The expression33 × 272 × 15

5−1 × 32can be simplified to

1. 38 × 52 2. 38 3. 1510

4. 38 × 5−2 5. 35 × 5−1

TOTAL: [100]

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MAT0511/101/0/2019

ASSIGNMENT 02Study material: Book 3

Fixed closing date: 18 April 2019Unique Assignment Number: 860992

Important:




In each of the following questions small letters of the alphabet (i.e. a, b, x, etc.) represent realnumbers.Question 1Which of the following is / are true?

A.a− bb− a

= −1.

B. If x = −2 and y = −3 then −x2 − 2y

x+ y2 = −4− 3 + 9 = 2.

C.

√x√

x+ 3is defined for x > −3.


Question 2Which of the following is / are true?

A.4s2 − 3st+ 5t2

3st− 4s2 − 5t2= 1

B. (3a+ 2b) (−3a− b) = −9a2 − 9ab− 2b2

C. 9y2 + 6xy − x2 = x2 − 6xy + 9y2


19

Question 3Which of the following is / are true?A. 3 (x− y)− 2x (y − x) = (x− y) (3 + 2x)

B. 16x4 y3 − 2x = 2x (4x2y2 + 2xy + 1) (2xy − 1)

C. 3x4 − x2y − 2y2 = (3x2 − 2y) (x2 + y)


Question 4By using the method of completing the square 1− 3x− 1

3x2 can be written as

1. −13

(x+ 9

2

)2+ 81

4

2. 13

(x+ 9

2

)2 − 314

3. −13

(x− 9

2

)2 − 314

4. −13

(x+ 9

2

)2 − 774

5. −13

(x+ 9

2

)2+ 31

4


A.x−2 − x−1 − 1

x− 1is a rational expression.

B.

(9 + x

9− x2− 1

3− x

)(x+ 3

3

)=

3

3− x

C.x2 + 5x+ 6

2x2 − x− 3÷ 2x2 + 10x+ 12

(3− 2x) (x+ 1)=

1

2

1. Only A 2. Only B 3. Only C4. Only B and C 5. None of them

Question 6The solution of

(x+ 1

2

)(2x− 1) ≥ 1 is

1. x ≥ ±√

32

2. x ≥√32

or x ≥ −√32

3. x ≥ 12

or x ≥ 1

4. x ≥√32

or x ≤ −√32

5. x ≤√32

or x ≥ −√32

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MAT0511/101/0/2019

Question 7

The solution of2x− 1

x− 1= 0 is

1. x = 12

or x = 1

2. x = 12

3. x = 1

4. x = 12

and x = 1

5. There is no solution

Question 8For what values of k will the equation x2 − 3x− kx = −61

4have two different real solutions?

1. k < −8 or k > 2

2. −8 < k < 2

3. k ≤ −8 or k ≥ 2

4. −8 ≤ k ≤ 2

5. No value of k

Question 9

The solution set of√

(x+ 3)2 + 4 = 0 is

1. {−7, 1}2. {−7}3. {1}4. R5. ∅

Question 10

Supposea

b=x+ y

y. Which of the following is / are true?

A.a

b= x B. a− b = x C.

a

b= x+ 1

1. Only A 2. Only B 3. Only C4. Only A and B 5. None of them

21

Question 11A man travels from Durban to Port Shepstone at a speed of 120 km/h and a woman travels fromDurban to Port Shepstone at a speed of 100 km/h. The man begins his journey 15 minutes after thewoman does. Suppose the man overtakes the woman x km from Durban. Which one of the followingequations can be used to find out how far they have travelled when he overtakes her?

1.x

120− x

100=

1

4

2.x

100− x

120= 15

3.x

100− x

120=

1

4

4.x

120− x

100= 15

5.x

120= 15− x

100

Question 12A tyre has two punctures leaking at a constant rate. The first puncture by itself would make thetyre flat in 15 minutes. The second by itself would make the tyre flat in x minutes. Both puncturestogether make the tyre flat in 10 minutes. Which one of the following equations can be used to solvefor x ?

1. x+ 15 = 10

2. 2 (x+ 15) = 3

3.3x

x+ 15= 2

4.x− 15

15x=

1

10

5. None of these equations

Question 13I have x red balls and y white balls in a box. I have 6 less white balls than red balls. If I take 3 whiteballs out of the box, the ratio of red balls to white balls will be 5 : 4. Which one of the followingsystems of equations can be used to solve for x and y ?

1.x− y = 6

4x− 5y = −15

}2.

y − x = 65x− 4y = −12

}

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MAT0511/101/0/2019

3.y − x = 6

4x− 5y = −3

}4.

x− y = 65x− 4y = −12

}5.

x− y = 65x− 4y = −3

}Question 14Which of the following is / are true?

A. −12, 12, 32, 52, . . . is an arithmetic sequence.

B. 0,1; 0,01; 0,001; 0,0001; . . . is neither an arithmetic nor a geometric sequence.

C. −1, 0, −2, 0, −3, 0, . . . is neither an arithmetic nor a geometric sequence.



A. 76 is the 20th term of the sequence 1, 5, 9, . . . .

B. If the nth term of a geometric sequence is given by tn =3

2n−1then the common ratio is 1

2.

C. The last term in the sequence 12, 1

4, 1

8, 1

16. . . will be 0.


Question 16In an arithmetic sequence the first term is a and the common difference is d. Suppose the third termis −12 and the fifth term is −27. Which one of the following systems of equations can be used to solvefor a and d ?

1.ad2 = −12ad4 = −27

}2.

ad3 = −12ad5 = −27

}3.

a+ 2d = −12a+ 4d = −27

}4.

a+ 3d = −12a+ 5d = −27

}5. None of these systems of equations

23


A.√

(−a)2 = −a for all values of a.

B. 3

√(−a)3 = −a for all values of a.

C. For all values of a and x, if −x = a then x2 = a2.



A. 813 = 2 B.

(18

)− 13 = 8

13 C. 2× 5−

23 = 10−

23


Question 19Suppose a ∈ R, a > 0 and a 6= 1. Which of the following is / are true?

A. If ax = −4 then 0 < a < 1.

B. Ifax

ay= az then x÷ y = z.

C. If ax − ay = az then x− y = z.



A. 2 (4x + 4−x) = 8x + 8−x

B.(2.3a − 4.3b

)2= 2

(3a − 2.3b

)2C. 9−4n = −38n


24

MAT0511/101/0/2019

Question 21The solution set of 3x+2 + 9 = 32x + 3x is

1. {0, 2}2. {2}3. {−2, 0}4. {−1, 2}5. ∅Question 22Suppose a ∈ R, a > 0 and a 6= 1. Which of the following is / are true?

A. loga (x+ y) = loga x+ loga yB. log x = log10 xC. loga x = − loga x if a < 0.


Question 23The solution set of log2 (x− 1)− log2 (x+ 1) = 2 is

1. ∅2. {1,−1}3.{

53

}4.{−5

3

}5.{−3

5

}Question 24An investment of R2 000 earns interest at an annual rate of 8% ; interest is compounded quarterly.After 3 years the total amount A of the investment, in rands, is given by

1. A = 2 000 e0,08×3

2. A = 2 000 (1,08)3

3. A = 2 000 (1,02)3

4. A = 2 000 (1,02)12

5. A = 2 000 (1,08)12

25

Question 25A population increases according to the formula

A = A0 ekt

where

A0 is the initial population (in millions)

A is the population (in millions) after t years; and

k is a constant.

Suppose this population doubles every 100 years. If there are 10 million people now, then the popu-lation A after 350 years is given by

1. A = 10 (2)3,5

2. A = 10 e(350) 2

3. A = 10 ln 74. A = 10 eln 7

5. A = 10 (2)350

TOTAL: [100]

26

MAT0511/101/0/2019

ASSIGNMENT 03Study material: Book 2 and 3

Fixed closing date: 10 May 2019Unique Assignment Number: 818514

Question 1Suppose

P = {x ∈ R : x < −1 or x ≥ 3} and Q = [0, 5).

(a) Write P ∩Q in interval notation. (2)

(b) Write P ∪Q in set builder notation. (2)

Question 2Write down the inequality represented on the number line below. Give it in both interval and setbuilder notation.

2_

1 (4)

Question 3

3.1 (a) Find 4, 1 + 25% of 25 + 10÷ 5 without using a calculator. (3)

(b) Give the answer correct to the nearest whole number. (1)

(c) Express the answer correct to one decimal place. (1)

3.2 (a) Find 34÷(23− 11

4

)without using a calculator. Write the answer as an improper fraction.

(4)

(b) Write down the reciprocal of the answer obtained in (a). (1)

(c) What is the only real number that does not have a reciprocal? Substantiate your answer.(2)

Question 4

4.1 A cleaning liquid contains three main ingredients A, B and C mixed in the ratio 12

: 114

:23, respectively. How many litres of each ingredient must be used to make 25 litres of the liquid?

Give the answer correct to one decimal place. (5)

4.2 Suppose 3 litres of Brand A milk cost R9,24 and 4 litres of Brand B mild cost R11,08.

(a) Which brand is cheaper? (3)

(b) How much will I spend if I buy 2 litres of Brand A and 3 litres of Brand B? (3)

Question 5Use percentages to find out which student performed better.Sarah obtained 16

25for her assignment and Pete obtained 36

45for his assignment. (5)

27

Question 6There are several units used for the measurement of electrical current. For example, amperes (abbre-viated by amps and denoted by means of A). We know that

1 kiloampere = 1 000 A

1 milliampere = 10−3A.

Express 0,625 kiloamperes in terms of milliamperes, in scientific notation. (3)

Question 7Using the method of completing the square, write

−1

3x2 + 2x+ 2

in the form a (x− h)2 + k. (4)

Question 8Find the solution set of

√2− x− x = 0. (8)

Question 9Working together, Tumelo and Jan can sand a floor in five–eighths of the time that it takes Jan tosand it by himself. Jan takes 6 hours to sand the floor alone. How long does it take Thumelo to sandthe floor by himself. (8)

Question 10Convert 1g/cm3 to kg/m3. (6)

Question 11Find all the values of x such that

(1− x) (x+ 3) ≥ 0. (6)

Question 12Solve 22x + 2x+1 = 23. (5)

Question 13Find the solution set of 34x − 6.32x − 27 = 0. (6)

Question 14Solve the following equation:

log2 (2x+ 1) + log2 (x− 1) = 1. (7)

Question 15Suppose Sipho earns 25% less than Susan does. How much does Susan earn if Sipho earns r rands?(3)

Question 16Determine whether the following sequences are arithmetic or geometric. Prove your answer.

16.1 log 3, log 33, log 39 (4)

16.2 log 2, log 4, log 8. (4)

TOTAL: [100]

28

MAT0511/101/0/2019

ASSIGNMENT 04Study material: Book 4 (Topics 1–6)Fixed closing date: 21 June 2019

Unique assignment number: 752806

Important:




Note: Small letters of the alphabet represent real numbers unless otherwise stated.

Question 1ABC is a right angle triangle with C = (3, 2) . M (0, 4) is the midpoint of AC.

AB

C

(0,4)M

(3,2)

Which of the following is / are correct?A. A = (−3, 6)B. B = (−3, 2)

C. d (A,C) = 2√

32 + (2− 4)2 units


Question 2The circle with the equation

x2 − 2x+ y2 + 6y = 6

has centre C and radius r, where

1. C = (1,−3) ; r = 42. C = (1,−3) ; r = 163. C = (−1, 3) ; r = 44. C = (−1, 3) ; r = 165. C = (0, 0) ; r =

√6

29

Question 3Suppose AB is the diameter of a circle, where A = (−1, 1) and B = (−4,−5) . The equation of thecircle is

1.(x+ 5

2

)2+ (y + 2)2 = 45

2. 4(x+ 5

2

)2+ 4 (y + 2)2 = 45

3.(x− 5

2

)2+ (y − 2)2 = 45

4. 4(x− 5

2

)2+ 4 (y − 2)2 = 45

5. 2(x+ 5

2

)2+ 2 (y + 2)2 =

√45

Question 4Which of the following relations is a function / are functions?

A. {(a, b) , (a, c) , (a, d) , (a, e)}B. {(b, a) , (c, a) , (d, a) , (e, a)}C.

{(1, 1) ,

(2,√

2),(3,√

3), (4, 2)

}1. Only A 2. Only B 3. Only C4. Only B and C 5. A, B and C

Question 5Which of the following defines a one–to–one function / define one–to–one functions in x ?

A. y = x2 B. x = y2 C. xy = 1


Question 6Suppose f, g and h are functions defined by

f (x) = 3x√

3 + x, g(x) =x+ 3

3x+ 2and h (x) =

√x− 1√x+ 1

.

Which of the following statements is / are true?

A. Df = {x ∈ R : x ≥ −3}B. Dg =

{x ∈ R : x 6= −2

3

}C. Dh = {x ∈ R : x > −1}


30

MAT0511/101/0/2019

Question 7Suppose the functions f and g are defined by

f(x) = x2 (x+ 1) (x− 2) and g (x) = x2.


A. f (−1) = 0

B. g (x+ 1) = x2 + 1

C.

(f

g

)(x) = (x+ 1) (x− 2) and D f

g= R.


Question 8Which of the following statements is / are true?

A. Every straight line is the graph of a linear function.B. The slope of a horizontal line is 0.C. The equation of a line parallel to the y–axis is y = c.


Question 9The slope–intercept form of the line through (1, 2) and (−3, 1) is

1. y = −14x+ 9

4

2. y = −14x+ 1

4

3. y = 14x+ 7

4

4. y = 4x− 2

5. y = −4x+ 6

Question 10The equation of line l1 is 2y−5x−1 = 0. Line l2 is perpendicular to l1 and passes through (5,−1) . Theequation of l2 is

1. 5y − 2x+ 15 = 02. 5y + 2x− 15 = 03. 5y + 2x− 5 = 04. 5y − 2x+ 5 = 05. 2y − 5x+ 27 = 0

31

Question 11

2_ 4 x

y

The equation of the line sketched above is

1. −4x+ 2y + 2 = 02. −4x+ 2y − 2 = 03. 2x− 4y − 2 = 04. 2x− 4y + 2 = 05. 2x− 4y + 8 = 0

Question 12A manufacturer produces T–shirts at a cost of R10 per T–shirt. Suppose we draw two graphs plottingproduction cost and income (in rands) against the number of T–shirts produced and sold. Supposethe break–even point is (50, 1 000) .Which of the following statements is / are true? (Assume that the cost and profit functions are linear.)

A. The manufacturer will make a profit if he sells 50 T–shirts.B. The fixed daily cost is R500.C. The manufacturer sells the T–shirts at R25 per T–shirt.


Question 13Which of the following statements is / are correct for the graph that represents the inequality x−2y >3 ?

A. The graph consists of all points above the line defined by x− 2y = 3.B. The graph consists of all points below the line defined by 2y − x = −3.C. The graph consists of all points below or on the line defined by y = 1

2x− 3

2.


32

MAT0511/101/0/2019

Question 14Consider the function defined by f =

{(x, y) : x ∈ R, y = 1

3(x+ 2)2 + 5

}. Which of the following

statements is/are correct?

A. The graph of f does not cut the x–axis.B. y ≥ 0 for all x ∈ Df .C. The y–intercept of the graph of f is 5.


Question 15The graph of y = 5 + 9x− 2x2

1. opens downwards and has vertex(214, 151

8

)2. opens upwards and has vertex

(214, −151

8

)3. opens downwards and has vertex

(−21

4, 151

8

)4. opens upwards and has vertex

(−21

4, −151

8

)5. opens downwards and has vertex

(−21

4, −151

8

)Question 16Which one of the following graphs is a rough sketch of the graph of y = −x2 + 2x− 3 ?1. 2.

(1, 2)_x

y

(1, 2)_

y

x

33

3. 4.

( 1, 4)_ _

y

x

( 1, 2)_ _

y

x

5.

( 1, 2)_ _

y

x

Question 17

The solutions of2x− 5

3− x≥ 0 are the values of x for which the graph of y = 2x2 − 11x+ 15

1. lies above the x–axis2. lies on or above the x–axis, excluding x = 33. lies below the x–axis4. lies on or below the x–axis, excluding x = 35. lies on or below the x–axis, excluding x = 3 and x = 5

2

34

MAT0511/101/0/2019

Question 18Suppose the function f is defined by

2xy − 25 = 0.


A. The graph of f is a hyperbola which lies in the first and third quadrants.B. The shortest distance from the origin to a point on the graph of f is 5 units.C. The line defined by y = x cuts the graph of f in two points.


Question 19Suppose that y = − 3

xand xy + 9 = 0 are equations that define two different hyperbolas. The line

defined by x+y = 0 cuts each of the hyperbolas twice, at the points A and B (for y = − 3x) and C and

D (for xy + 9 = 0). A and C are in the same quadrant; B and D are both in the quadrant oppositeA and C.Which of the following statements is/are true?

A. The hyperbolas have no points of intersection.B. The hyperbolas both lie in quadrants 2 and 4.

C. The ratio of the x–coordinate of A to the x–coordinate of C is√33.


Question 20If p is jointly proportional to q and r and inversely proportional to s, state (in words) the relationshipbetween q and the other variables.Which of the following statements is the correct one.

1. q is jointly proportional to p and r and inversely proportional to s.

2. q is directly proportional to s and inversely proportional to p and r.

3. q is jointly proportional to s and r and inversely proportional to p.

4. q is directly proportional to r and inversely proportional to p and s.

5. q is jointly proportional to p and s and inversely proportional to r.

35

Questions 21 to 25These questions are based on the following figure.

_ 5

0x

y

N

P

M

(1,0) (3,0)

f

h

g

The graph of f, which is a semi–circle with centre (3, 0) , meets the graph of g, which is a parabola, atthe points (1, 0) and P. The graph of h, which is a straight line, cuts the parabola at (0,−5) and atP. The points M and N are points on the parabola and straight line, respectively. They lie betweenthe two points of intersection of the graphs of h and g.MN is parallel to the y–axis.

Question 21 (use sketch above)The equation that defines f is

1. (x− 3)2 + y2 = 4

2. y =√−x2 + 6x− 5

3. y = −√−x2 + 6x− 5

4. y =√x2 − 6x+ 5

5. y = −√x2 − 6x+ 5

36

MAT0511/101/0/2019

Question 22 (use the same sketch above)The equation that defines g is

1. y = − (x− 1) (x− 5)2. y = (x− 1) (x− 5)3. y = − (x+ 1) (x+ 5)4. y = (x+ 1) (x+ 5)5. y = − (x− 3)2 + 4

Question 23 (use the same sketch above)The equation that defines h is

1. x+ y + 5 = 02. x− y + 5 = 03. x+ y − 5 = 04. x− y − 5 = 05. 5x− y − 1 = 0

Question 24 (use the same sketch above)All the values of x for which f (x)− h (x) < 0 are

1. 1 < x < 32. −∞ < x < 33. 3 < x < 54. 3 < x <∞5. 1 < x < 5

Question 25 (use the same sketch above)The maximum length of MN is the y–coordinate of the vertex of the parabola defined by

1. y = x2 − 5x2. y = −x2 + 5x3. y = −x2 + 5x− 104. y = x2 − 6x+ 55. y = −x2 + 6x− 5

TOTAL: [100]

37

ASSIGNMENT 05Study material: Book 4 (Topics 1–6)

Fixed closing date: 12 July 2019Unique Assignment Number: 853461

Question 1Suppose the functions f, g, h, r and ` are defined as follows:

f (x) = 3 log3 x+ log 13x

g (x) =

√(x− 2)2 − x

2

h (x) = 12x2 − 7x

r (x) = 42x+1 − 8

` (x) =√x

1.1 Write down Df and solve the equation f (x) = − log314. (6)

1.2 Write down Dg and solve the equation g (x) = 0. (6)

1.3 Write down Dh and solve the inequality 10 ≥ h (x) . (6)

1.4 Write down Dr and solve the equation r (x) = 0. (6)

1.5 Write down Dh·` without first calculating (h · `) (x) . (2)

1.6 Write down D fg

without first calculating fg. (4)

[30]

38

MAT0511/101/0/2019

Question 2

x

y

PS

T

Q

O R

y= x

y=_94x

The sketch shows the hyperbola defined by y = 49x

; the straight line defined by y = x; a circle withcentre at P, touching the x–axis and y–axis at R and S, respectively; and the straight line throughthe points T, S and R . The line joining T and Q is parallel to the y–axis.

2.1 Determine the coordinates of P and Q. (5)

2.2 Determine the coordinates of S and R. (2)

2.3 Find the radius of the circle, and write down the equation of the circle. (3)

2.4 Determine the equation of the line through T, S and R. (5)

2.5 Calculate the length of the line TQ. (5)

[20]

TOTAL: [50]

39

Assignment 06Study material: Topic 7 of Book 4, and Book 5

Fixed closing date: 02 August 2019Unique assignment number: 747447

For questions 1 to 5:A group of 60 university students wrote a test and obtained the following marks (percentages).

53 64 72 92 73 64 33 75 61 6084 65 58 76 53 63 74 56 71 5881 75 69 77 65 78 58 41 37 6179 40 74 31 39 68 75 67 89 5957 39 71 38 66 69 81 53 40 6762 60 35 37 75 49 36 58 62 46

These raw data are grouped into a frequency distribution with class width 5%; the lowest class limitis 30%.

Set up a frequency table and add columns when necessary to answer questions 1 to 5.


A. There is a maximum of 15 classes and a minimum of 13 classes.

B. The class with the highest frequency has class limits 60% and 64%.

C. If the class width is changed to 3% there will at be least 21 classes.


40

MAT0511/101/0/2019


A. The numbers 29, 5; 34, 5; . . . ; 94, 5 represent the class limits.

B. The numbers 32, 37, . . . , 92 represent the class midpoints.

C. The histogram representing the given data is given in the following sketch.

29,5 34,5 39,5 44,5 49,5 54,5 59,5 64,5 69,5 74,5 79,5 84,5 89,5

2

4

6

8

10

94,5

2

7

3

2

3

7

9

8 8

3

1 1

Percentages

Number of

students

6


41


A. The frequency polygon representing the data is given in the following sketch.

29,5 34,5 39,5 44,5 49,5 54,5 59,5 64,5 69,5 74,5 79,5 84,5 89,5

2

4

6

8

10

94,5

Percentages

Number of

students

B. The stem–and–leaf plot representing the data is given below.

3 3 7 1 9 9 8 5 7 64 1 0 0 9 65 3 8 3 6 8 8 9 7 3 86 4 4 1 0 5 3 9 5 1 8 7 6 9 7 2 0 27 2 3 5 6 4 1 5 7 8 9 4 5 1 58 4 1 9 19 2

C. From the correct stem–and–leaf plot representing the given data we see that twice as manystudents scored between 50% and 59% (including these marks) as the number of students whoscored between 40% and 49%, inclusive.


42

MAT0511/101/0/2019

Question 4Suppose 50% and over is a pass mark, and 75% and more is pass with distinction.Which of the following statements is/are true?

A. The pie graph below represents the given data (percentages are rounded to the nearest integerwhere necessary).

Fail

Pass

Pass(with distinction)

22% 23%

(without distinction)55%

B. The median of the marks classified as “pass without distinction” is 58%.

C. The mode of the “fail” marks is 39%.

1. Only A 2. Only B 3. Only C4. Only A and C 5. Only A and B


Use the grouped data in the first frequency table with class width 5%. Add columns if necessary.

A. The arithmetic mean of all the marks is 61% (to the nearest integer).

B. The mean deviation is 12% (to the nearest integer).

C. The arithmetic mean of all the “pass without distinction” marks is 60% (to the nearest integer).


43

For questions 6 and 7

23

4 1

An experiment consists of spinning a spinner (see above) 3 times in succession and recording thenumber of the triangle on which it comes to rest, i.e. the numbers 1, 2, 3 or 4. (For example, onepossible outcome could be (2,1,3).)


A. The sample space S is the set S = {1, 2, 3, 4} .

B. Consider the event E1 “obtain at least two numbers that are the same”. Then n (E1) = 16.

C. If P (E2) =n (E2)

n (S)and E2 is the event “obtain all three numbers the same”, then P (E2) =

1

16.



A. The probability that two numbers are the same is greater than the probability that all thenumbers are different.

B. The probability of not obtaining a 2 is the same as the probability of obtaining only the numbers1, 3 or 4.

C. The probability of scoring both 1 and 3 is 932.


44

MAT0511/101/0/2019


A.

A

B

C

D

Area of ∆CBD = AC × AB.

B. A right triangle cannot contain an obtuse angle

C. The sum of the angles in any quadrilateral is 360◦.


Question 9

o30

A B

CDE60 o

F

Which of the following statements is/are true?

A. Quadrilateral AECB is a trapezoid.

B. Area of quadrilateral AEFB = (AB + EF )× AD.

C. ∆AED ||| ∆FBC.


45


A. A sphere has radius 3a units. A right circular cylinder has height 4 times its radius, which is aunits.

The ratio of the volume of the cylinder to the sphere is 1 : 9.

B. Consider a circle with diameter d units and a square with diagonal d units. If a fly crawls roundthe circle once and an ant crawls round the square once, the fly travels further. (A calculatoris allowed.)

C. The volume of a right circular cone with height 15 cm is the same as the volume of a rightcircular cylinder with height 5 cm, if they both have the same radius.


Question 11If the radius of a circle is increased by 6% then its area is increased by

1. 0,36% 2. 3,6% 3. 6% 4. 12,36% 5. 36%

Question 12Consider the figure below.

A

B E C

D


A. If we draw CF so that F lies on AD and EA || CF, then ∆ABE ≡ ∆CDF.

B. In ∆BAE, AE = AB +BE.

C. If the area of ∆ABE = 7 cm2 and EC = 3BE then the area of ABCD is 42 cm2.


Question 13

c

ab cm

cm

cm

The container illustrated above is a rectangular box with a half–cylinder lid. If the lid is detachedand turned over so that it lies inside the box, how much liquid (in litres) can the box contain withthe lid in this position (excluding the lid)?

46

MAT0511/101/0/2019

1. 103(abc− πa2c

8

)2. 10−3

(abc− πa2c

2

)1. 10−3

(πa2c2− abc

)4. 10−3

(abc− πa2c

8

)5. 103

(πa2c8− abc

)

Question 14Consider the circle and square shown below for 1 to 5 below.

A B

r

CD

Which one of the following statements is NOT true?

1. The circle will fit inside the square if 2r < BC.

2. Suppose a rectangle PQRS has the same area as the square. The circle will fit inside therectangle ifπr2 < AB.DC.

3. If the area of ∆ADB is 10 mm2 and its base is AD then its altitude is 2√

5 mm. (Refer tosquare above.)

4. ∆ABD ||| ∆CDB.

5. ∆ABD ≡ ∆CDB.

Question 15A square piece of material with sides 150 cm is used to make a circular table cloth. The diameter ofthe completed cloth must be 1,2 m and 5 cm is provided for a hem. How much material is wasted?(Answer correct to 2 decimal places.)

1. 1,30 m2

2. 92,26 cm2

3. 0,92 m2

4. 129,97 cm2

47

5. 0,71 m2

Question 16

1,2 m

P

S R

Z

Q

h

2 mT

A theatrical company makes a pyramid for a stage production. The pyramid has a square base, withsides 1,2m. The top of the pyramid is 2 m above the base. How many litres of paint are neededto cover the outside of the pyramid, if 750 ml is used for every 2 m2, and if the base is not painted.(Answer correct to 2 decimal places.)

1. 3,34

2. 1,88

3. 18,79

4. 3,20

5. 6,68


A. Suppose a sphere has a diameter of 10 cm. Suppose the height of a closed right circular cylinderis double its radius, and that its radius is the same as the radius of the sphere. The ratio of thesurface area of the sphere to that of the cylinder is 2 : 3.

B. If the diameter and height of a right circular cone are equal then the lateral surface area of thecone is

√5πr2, where the radius is r. (Note: Lateral surface area of cone is the area of the sides

only.)

C. If the diagonals of a quadrilateral intersect at right angles the quadrilateral must be a square ora rhombus or a kite.


48

MAT0511/101/0/2019

Question 18Consider a photograph with dimensions 10 cm by 8 cm.Which of the following statements is/are true?

A. If the photograph is enlarged by a scale factor of 3 it will fit onto a piece of paper that measures30 cm by 20 cm.

B. If it is enlarged by a scale factor of 2,5 it will fit onto a 30 cm by 20 cm piece of paper with nospace left on the sides and 2,5 cm left at the top and at the bottom.

C. If it is reduced by a scale factor of 0, 75 then four such photographs will cover the page withdimensions 30 cm by 20 cm, exactly.


Question 19Suppose ABCD is an isosceles trapezoid with base DC and AB̂C = 120◦. Suppose AB || DC andAB = BC = 10 cm. Suppose the trapezoid is reflected downwards in the line DC.


A. The resulting figure, consisting of the two trapezoids, forms a regular hexagon.

B. The area of the resulting figure is 150√

3 cm2.

C. DC = 20 cm.


Question 20How deep must a circular swimming pool be if its volume is 64 000 litres and its diameter is 8 m? Ifthe depth is x m, then

1. x =4× 103

π2. x =

4× 102

π3. x =

4× 10

π

4. x =4

π5. x =

16

π

TOTAL: [100]

49

Assignment 07Study material: Books 2–5

Fixed closing date: 16 August 2019Unique Assignment Number: 826825

Note: This assignment consists of the October/November 2008 exam paper. The questions will besent to you in a separate tutorial letter.

Please look out for it!

TOTAL: [100]

50

mat0511 - hi-static.z-dn.net

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