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About this Study Guide This Study Guide will prepare you very comprehensively for the exams that lie ahead. It focuses on the important material in your textbook and it will draw your attention to the words and concepts or issues that you must be able to explain or demonstrate during an exam. To keep the facts down to a minimum so that there is less to remember, mindmaps have been used to summarise the work. A mindmap is a technique for recording information in its simplest form. Each chapter has been summarised broadly and this is followed by mindmaps in more detail for each section of the chapter. Work through one chapter at a time and make sure that you understand every word and illustration that you come across. Normally mindmaps are presented in colour with words and illustrations in some cases in the place of words. Colour and illustrations are sometimes easier to remember than words. Colours can be used to signify a particular meaning and the illustrations can be as zany as you want them to be - as long as they are meaningful to you. In this Study Guide the mindmaps have been presented in black and white with very few illustrations. The reason for this is so that you can add as much colour as you like and as many illustrations as you want to. In some cases you will be required to insert an illustration or to answer a question. This is where you can have fun and use your imagination as you complete the questions and add colour to each page. Using highlighters and coloured pens, try to make each page in this Study Guide as colourful and as much fun as you can. There are no right or wrong ways to use colour and illustrations in a mindmap. Each mindmap is unique and it only has to be meaningful to you. When preparing a mindmap you start with your main topic in its own unique shape in the centre of the page. From this main topic you draw branches extending in different directions for each sub-topic, using a different colour for each branch. From each sub-topic, using the same colour as the branch, you extend branches in respect of each relevant fact regarding the sub-topic that you want to record. You can repeat this process for as many lower-level branches as you wish. Try to record keywords rather than sentences. At any stage of this process you can add illustrations in place of words. They are fun to draw and easier than words to recall.

Mindmaps can be prepared in many different shapes and formats. There is no hard and fast rule that says mindmaps should have a particular shape or sequence. They must make sense only to the person who created them. The mindmap illustrated here is in the simplest form. If you don’t like those in the book, have fun and create your own. You can be as creative as you want to be. Once you have prepared a mindmap you should practise re-creating it as quickly as you can until you can do so without looking at the original. Within 30 seconds re-draw each mindmap in black and white every day for a week and then once a week thereafter to keep the memory fresh in your mind for exam time. At the end of the Study Guide is a set of practice questions in the same formats that you will encounter in the examination. Working through these will prepare you for your examinations. Look up the answers in your textbook. Have fun as you work your way through this Study Guide and good luck with the exams. 1

GEOGRAPHY GRADE 12

CONTENTS ABOUT THIS STUDY GUIDE........................................................................................................................ 1

SECTION A: GEOGRAPHICAL SKILLS AND MAP TECHNIQUES………………………............................ 2 Unit 1 Map use and map skills ………………………………………………………….............................. 2 Unit 2 Map work and related fields ……………………………………………………............................... 7

SECTION B: CLIMATE AND WEATHER ……………………………………………………….......................... 11 Unit 1 Global air circulation …………………………………………………………….............................. 12 Unit 2 Synoptic weather maps and satellite image reading and interpretation and energy balance ………………………………………………………………........................... 13 Unit 3 Mid-latitude cyclones and associated weather patterns…….…………….................................. 16 Unit 4 Subtropical anticyclones and resultant weather over South Africa……..................................... 18 Unit 5 Tropical cyclones and associated weather …………………………………................................ 19 Unit 6 Climate at regional and local scale …………………………………………….............................. 21 Unit 7 Human-made climate – urban microclimate ………………………………….............................. 24 Unit 8 Climate hazards and human response to these ……………………………............................... 26

SECTION C: FLUVIAL PROCESSES AND LANDFORMS …………………………………........................... 27 Unit 1 Fluvial processes …………………………………………………………………............................. 27 Unit 2 Structural landforms ……………………………………………………………................................ 35

SECTION D: PEOPLE AND PLACES: RURAL AND URBAN SETTLEMENTS…………............................ 41 Unit 1 Processes and spatial patterns: Rural settlement ………………………….................................. 41 Unit 2 Processes and spatial patterns: Urban settlement …………………………................................ 46 Unit 3 Human environment: Interactions and sustainable strategies – rural......................................... 52 Unit 4 Human environment: Interactions and sustainable strategies – urban....................................... 57

SECTION E: PEOPLE AND THEIR NEEDS …………………………………………………............................ 62 Unit 1 Economic activities ……………………………………………………………….............................. 62 Unit 2 Water as a critical resource in South Africa …………………………………................................. 72

3. GEOGRAPHICAL INFORMATION SYSTEMS Complete the following mindmap and explain each of these concepts:

STEP 1 Capture data Where to get information from?

STEP 5 Product generation How is information communicated?

Types of input

STEPS WHEN FOLLOWING A GIS PROJECT STEP 2 Pre-processing What are the functions of pre-processing? STEP 3 Data management Two types: spatial

STEP 4 Data analysis Converts information

What is querying data?

attribute

Hints and tips: • • •

Field work can be asked in a map work paper. You could be asked how you would go about researching, for example, the effect that farming has on the pollution levels in the river, or the impact that a new industrial development will have on roads and traffic. You will have to think of how you would go about researching the issue.

Checklist – Can I…..? 1. List the different sources of data for GIS? 2. List the different types of data input methods? 3. Draw a flow chart illustrating the steps taken to produce a GIS project? 4. Explain how GIS helps to answer questions? 5. Explain the need for queries? 6. Explain how map overlays work in a GIS? 7. Design a research project based on an environmental or economic issue? 8. Compare and contrast the different types of map projections?

9

3. LAND-USE ZONES Complete the following mindmap by explaining each of these concepts: Rural-urban fringe Location:

Residential estate Location:

Characteristic:

Characteristic:

Railway

Low-income areas (LI)

River

MI

Township

High-income area (HI) Location:

HI

Location: Characteristic: Characteristic:

LI

CBD

Industrial areas Location:

MI

Greenbelt Location:

Characteristic:

Characteristic:

Zone of Transition Middle-income areas (MI) Location:

Location:

Characteristic:

Characteristic:

Informal settlements Location: On vacant land, along rivers and railway lines, in low-income areas, in the CBD and in the ruralurban fringe. Identify these areas using the symbol IS on the map.

Describe the characteristics:

48

HISTORY GRADE 12

CONTENTS

About this Study Guide ..............................................................................................

1

Chapter 1

Cold War ................................................................................................

2

Chapter 2

Uhuru .....................................................................................................

11

Chapter 3

Civil Protest ...........................................................................................

20

Chapter 4

Collapse of USSR ..................................................................................

31

Chapter 5

Democracy in South Africa ..................................................................

38

Chapter 6

Globalisation .........................................................................................

47

Chapter 7

Heritage ..................................................................................................

56

Write short notes on each of the following:

TIPS AND HINTS •

Make a timeline from 1945 to 1969 to assist you in understanding this section.

WEST 1945

1969

EAST •

Learn the different terminology and concepts to assist in understanding source-based questions.

•

Have an understanding of the role played by propaganda to promote different ideologies.

3

Civil protest in Eastern Europe during the 1980s: Case study: Lech Walesa and Poland.

TIPS AND HINTS Extended Writing. Use the visual of the Time Magazine ‘Shaking Up Communism’ as a stimulus and prepare a response. Extended writing requires evidence of: • Historical knowledge of the event • Historical context showing time and place • Historical significance such as cause and effect • Application of knowledge to the stimulus.

QUESTION TO CONSIDER: What role did Lech Walesa play in dismantling communism in Poland? Use the above mindmaps and the tips and hints to write a page on the above question.

30

LIFE SCIENCES GRADE 12

CONTENTS About this Study Guide ......................................................................................................................

SECTION 1

1

TISSUE, CELLS AND MOLECULAR STUDIES

Unit 1

DNA and protein synthesis .....................................................................................

2

Unit 2

Chromosomes, meiosis and the production of sex cells ....................................

6

Unit 3

Inheritance and genetic diseases ..........................................................................

10

SECTION 2

STRUCTURE, CONTROL AND PROCESSES IN BASIC LIFE SYSTEMS IN PLANTS AND HUMANS

Unit 4

Human reproductive system ..................................................................................

16

Unit 5

Fertilisation, implantation, pregnancy and birth ..................................................

22

Unit 6

Contraception, infertility, diseases and disorders ...............................................

27

Unit 7

Reproduction and food production in plants .......................................................

32

SECTION 3

ENVIRONMENTAL STUDIES

Unit 8

Local land issues .....................................................................................................

36

Unit 9

Local water issues ..................................................................................................

40

Unit 10

Local air issues ........................................................................................................

44

Unit 11

Management of biotic resources ............................................................................

48

SECTION 4

DIVERSITY, CHANGE AND CONTINUITY

Unit 12

Biological evidence for evolution ..........................................................................

51

Unit 13

Evolution theories, mutation and natural selection .............................................

55

Unit 14

Macro evolution, speciation and origins of humankind ......................................

59

Complete the following mindmap and be able to explain each of the concepts:

Word check – these are the important words and concepts in this section: Either of the alternative genes found at the same place on a chromosome Allelle When pollen from one flower lands on the stigma of a different flower Cross-pollinated Having two complete sets of chromosomes in the nucleus Diploid A characteristic found in the phenotype even though present on one chromosome Dominant The offspring of a deliberate breeding programme Filial generation A sex cell with a single set of chromosomes Gamete The unit of heredity found at a locus on a chromosome made of DNA Gene A science that studies inheritance of characteristics Genetics The genetic make-up of an organism, the alleles contained on its chromosomes Genotype The process in which characteristics are passed on from parents to children Heredity Having two different alleles at the same locus on homologous chromosomes Heterozygous

11

Tips and hints: This is a very large section because fossils have provided most of the early evidence for evolution. You should know examples of each type of fossil, how they help us explain evolution and give evidence of mass extinctions in the past. Also, you should know how they can be dated. Often the evidence for evolution is indirect, and depends on realizing that evolution is the simplest explanation for the facts. It is well established that the simplest scientific explanation for anything is most likely to be the correct one.

Complete the following mindmap and be able to explain each of the concepts: What ancient continent was made from S America, Africa, Australia, India?

What does the distribution of fossils tell us?

What evidence for evolution is there in the biodiversity of the southern continents? What caused the greater biodiversity of the southern continents?

Word Check – these are the important words and concepts in this section: Supercontinent made of the Southern Hemisphere land masses and India Gondwanaland

Tips and hints: The different pattern of biodiversity in the Northern and Southern Hemispheres is compelling evidence that animals and plants have evolved, rather than being created in their present homes. You should be aware of examples of living organisms and of fossil organisms that illustrate this. The distribution of fossils also gives us evidence that plate tectonics has caused continental drift, changing the position of continents relative to each other.

Complete the following mindmap and be able to explain each of the concepts:

53

MATHEMATICAL LITERACY GRADE 12 CONTENTS

ABOUT THIS STUDY GUIDE .................................................................................................................

1

CHAPTER 1

Numbers and Operations in Context ..........................................................................

2

Using numbers to calculate financial issues ...............................................................

3

Housing and finance....................................................................................................

4

Major household expenses ........................................................................................

5

Inflation, tax and currencies .......................................................................................

6

Typical exam questions ..............................................................................................

8

Functional Relationships..............................................................................................

9

Linear programming ...................................................................................................

11

Drawing graphs ..........................................................................................................

12

The impacts of compound change .............................................................................

14

Interpreting graphs and tables in the media ...............................................................

15

Typical exam questions ..............................................................................................

16

Space, Shape and Measurement ...............................................................................

17

2- and 3-Dimensional problems ................................................................................

19

Calculating areas and perimeters of 2-dimensional objects .......................................

20

Calculating the surface area of a cylinder....................................................................

21

Calculating the surface area of a sphere ....................................................................

22

Calculating the surface area of a cone .......................................................................

22

Typical exam questions .............................................................................................

23

Data Handling .............................................................................................................

24

Probability ...................................................................................................................

25

Tree diagrams ............................................................................................................

26

Measures of central tendency ....................................................................................

27

Typical exam questions...............................................................................................

28

CHAPTER 2

CHAPTER 3

CHAPTER 4

PREVIOUS EXAM PAPERS Paper 1, Section A ......................................................................................................

30

Paper 1, Section B .....................................................................................................

34

Paper 2 .......................................................................................................................

37

Inflation, tax and currencies Complete the following mindmap and be able to explain each of the concepts: Personal tax If annual income is between R80 000 and R130 000, personal tax is R14 400 plus 25% of the amount by which income exceeds R80 000. Monthly salary: R7 100 Overtime: R600 per month Monthly personal tax deduction: R695 Pension fund contributions: 7,5% of salary Tax rebate: R6 300 per annum What is the annual income?

Inflation Cost in 2000: R10 000 Cost in 2010: R22 265

How much is paid into the pension fund? By how much does the annual income exceed R80 000?

1. What is the percentage increase between 2000 and 2010?

How much tax is payable on this excess? 2. What is the average annual increase in cost?

How much tax is payable in total? How much tax must be paid in at the end of the tax year?

3. What do we call this average increase?

INFLATION, TAX AND CURRENCIES 4. Should annual salary increases be equal to Foreign currency

inflation? Explain your answer.

If the exchange rate (R/£) is R13,99, how many pounds will you get for R5 000? Value added tax How much commission in rands must be paid on this transaction if the commission due is 1,25%?

At 14%, how much VAT is payable on a purchase of R1 000?

How much VAT is included in a payment of R15,00?

Tips and hints Be aware that when working with the concept of inflation, at the end of the day what it means is that if we want our money to retain its buying power, we have to choose suitable ways of investing it.

Word check – these are the important words or concepts in this section the decreasing value of money; the increasing cost of goods Inflation a sum of money demanded by a government for its support or for specific facilities Tax or services, levied upon incomes, property, sales, etc. a fixed amount, other than wages, paid at regular intervals to a person or to the Pension person's surviving dependents in consideration of past services, age, merit, poverty, injury or loss sustained take off Deduct partial refund Rebate the amount of net income used in calculating income tax Taxable income pay as you earn – a system of withholding tax on a regular basis PAYE a unit of exchange, facilitating the transfer of goods and/or services. It is one form of Currency money, where money is anything that serves as a medium of exchange the amount of the difference in value between two or more currencies Exchange rate 6

[20]

SECTION B QUESTION 1 The table below is an extract from a letter from Sanlam to Mr Moloke. It shows the amounts that are available on an instant loan from Sanlam and the repayment involved. Dear Mr Moloke, As a valued Sanlam customer, we are pleased to be able to offer you a personal loan at the following rates: Loan amount 24 months 36 months 48 months 60 months R4 800 R229 R174 R147 R131 R8 000 R448 R338 R285 R253 R16 000 R864 R643 R534 R470 R25 000 R1 344 R1 000 R830 R730 FIXED REPAYMENTS!!!!! These loan repayments conveniently include a monthly premium of R3.95 per R1 000 of the loan and a monthly administration fee of R9.50 for your optional personal protection plan. 1.1

If Mr Moloke chooses to borrow R16 000 from Sanlam calculate how much he will finally repay if he takes the loan over: 1.1.1 24 months (2) 1.1.2 60-months (2) 1.1.3

In general do you advise him to borrow for a longer or shorter time? Give a reason for your answer.

(2)

1.2

If he chooses the 60-month option, calculate the interest that he will pay over the period.

1.3

The loan repayments include insurance premium and administration fees. If Mr Moloke borrows R16 000, how much of each month’s payment is the premium and how much is the administration fee? (4)

1.4

Mr Moloke has two other options for borrowing the money: 1.4.1 An uncle has offered to lend him the R16 000 for five years at 18% per annum simple interest. What will be the total cost for this option at the end of 5 years? (4) 1.4.2

1.5

The Standard Bank will lend him the R16 000 for five years at 16% per annum compound interest. Determine the cost of this option.

Hence recommend to Mr Moloke which of the three options would be best.

(3)

(5) (1) [23]

34

PHYSICAL SCIENCES GRADE 12

CONTENTS About this Study Guide....................................................................................................................................

1

Prior knowledge from Grade 11

Physics:

Relevant from Grade 11..................................................................................................

2



Chemistry:

Quantitative aspects of chemical change.......................................................................

2



Chemical equations

Intermolecular forces

SECTION 1

BASIC SKILLS NEEDED IN PHYSICAL SCIENCE............................................................

5



Unit 1:

The scientific method of investigation.....................................................................................

5



Unit 2:

Mathematical tools.....................................................................................................................

6

SECTION 2

MECHANICS..................................................................................................................

8



Unit 1:

Projectile motion in 1-D.............................................................................................................

8



Unit 2:

Relative velocity in 1-D..............................................................................................................

11



Unit 3:

Force, Momentum and Impulse......................................................................................

12



Unit 4:

Work, Energy and Power................................................................................................

13

SECTION 3

WAVES, SOUND AND LIGHT.................................................................................................

14



Unit 1:

Light and Colour.........................................................................................................................

14



Unit 2:

The Doppler Effect......................................................................................................................

15



Unit 3:

2-D and 3-D Wavefronts............................................................................................................

17

SECTION 4

ELECTRICITY AND MAGNETISM.........................................................................................

19



Unit 1:

Electrostatics..................................................................................................................

19



Unit 2:

Electric circuits............................................................................................................................

21



Unit 3:

Electrodynamics.........................................................................................................................

22



Unit 4:

Electromagnetic radiation...............................................................................................

23

MATTER AND MATERIALS...........................................................................................

25

SECTION 5:

Unit 1:

Optical phenomena and properties of materials....................................................................

25



Unit 2:

Organic molecules......................................................................................................................

28



Unit 3:

The mechanical properties of materials..........................................................................

31



Unit 4:

Organic macromolecules...........................................................................................................

31

CHEMICAL CHANGE...............................................................................................................

32

SECTION 6:

Unit 1:

Rate and extent of reaction.......................................................................................................

32



Unit 2:

Electrochemical reactions.........................................................................................................

34

SECTION 7:

CHEMICAL SYSTEMS..............................................................................................................

37



Unit 1:

The petrochemical industry . ....................................................................................................

37



Unit 2:

The chlor-alkali industry.............................................................................................................

37



Unit 3:

The fertilizer industry ................................................................................................................

38



Unit 4:

Batteries.......................................................................................................................................

39

EXAMPLES OF EXAM QUESTIONS WITH ANSWERS...................................................................................

41

PRIOR KNOWLEDGE FROM GRADE 11 PHYSICS The required PHYSICS information from Grade 11 has been included in the relevant sections of the Grade 12 material.

CHEMISTRY You need to be able to define and work with the following:

Some typical practice examples 1.

A student prepared an aqueous solution using 1.22g of sodium chloride in 250.0ml of water. a. Calculate the concentration of this solution in g/100ml b. What is the molar concentration of this solution? (moles/dm3)

2.

Calculate the molar concentrations of solutions that contain the following: a. 16.0g of KOH in 250.0ml water b. 12.5g of CaCl2 in 500.0ml water c. 18.0g HCl in 0.555dm3 water d. 22.3g H2SO4 in 0.100dm3 water e. 1.25mol HCl in 750ml water.

3. Iron (Fe) reacts with sulfur (S) to produce iron sulfide (FeS) a. Write the balanced chemical equation for this reaction. b. How many grams of iron are needed to combine with 45.7g of sulfur to form iron sulfide? 4. Energy is released from petrol when octane burns in oxygen according to the following equation: 2C8H18(l) + 25O2(g) → 16CO2(g) + 18H2O(g) a. What type of reaction is this? b. How many moles of O2 are needed to completely combust 17 moles of octane? c. What mass of CO2 would result from the reaction described in part b?

2

SECTION 6: CHEMICAL CHANGE This section covers:

Galvanic (Voltaic) cells Industrial preparation of ammonia Dynamic equilibrium Reversible reactions

Electrolytic cells

Open and closed systems Catalysts Collision theory Factors affecting rate of chemical reaction Measuring rate of chemical reaction Meaning of the term ‘rate’

UNIT 1: Rate and extent of reaction You must understand and be able to explain each of the following:

Word check – these are the important words or concepts in this section: A protein that acts as a catalyst in a biological reaction Enzyme The energy barrier that must be overcome in order for a reaction to proceed from Activation energy reactants to product The concept that when a reaction in equilibrium is disturbed, by changes in le Chatelier’s concentration, temperature or pressure, the system shifts the equilibrium in such a Principle way that it tends to counteract the change c d a b Equilibrium constant Kc = [C] [D] / [A] [B] for a reaction of the type aA + bB ↔ cC + dD at equilibrium (Kc) Reaction proceeds to products hardly at all Low values of Kc Reaction proceeds far towards products High values of Kc The point of equilibrium (closer or further from products), determined by such Position of factors as concentration of reactants and products, temperature and pressure equilibrium Reaction between nitrogen gas and hydrogen gas to form ammonia Haber Process 32

TOURISM GRADE 12

CONTENTS ABOUT THIS STUDY GUIDE CHAPTER 1

1

THE TOURISM INDUSTRY AS AN INTERRELATED SYSTEM ........... 2

Unit 1: What kind of an impact does service excellence have on economic growth and community development? ..................................................

4

Unit 2: How is government going about redressing the past imbalances in tourism participation? ............................................................................ 5 Unit 3: Working conditions in the tourism industry ........................................... CHAPTER 2

6

RESPONSIBLE AND SUSTAINABLE TOURISM IN ACTION! ............

10

Unit 1: What factors affect sustainable and responsible tourism development? .......................................................................................

12

Unit 2: What strategies are in place globally to protect the environment? .......

13

Unit 3: Marketing local tourism products or services that have the potential to develop into a unique tourism venture .................................................. 14 Unit 4: Using diversity and heritage to market and promote inbound and domestic tourism ................................................................................... 16 CHAPTER 3

TOURISM GEOGRAPHY, ATTRACTIONS AND TRAVEL TRENDS ....

20

Unit 1: Why are time zones and daylight saving important for the tourist or international traveller? ..........................................................................

22

Unit 2: Itinerary planning ..................................................................................

25

Unit 3: Travel advisories ................................................................................... 26 Unit 4: Money – the root of a successful holiday .............................................. 27 CHAPTER 4

MARKETING, EVENTS AND TOURISM TRENDS ............................... 32

Unit 1: What is SA Tourism doing? ................................................................... 34 Unit 2: How do current affairs and political situations affect tourism trends? ...

35

Unit 3: Can we meet our tourists’ needs? ........................................................

36

CHAPTER 5

PROVIDING QUALITY CUSTOMER CARE AND COMMUNICATION . 38

Unit 1: How do we know that our customers are satisfied? .............................. 40 Unit 2: Achieving service excellence, and maintaining quality service ............. 41 Unit 3: Tourism teamwork! ................................................................................ 42 Unit 4: Using the right technology to communicate effectively ......................... 43

UNIT 1:

WHAT KIND OF AN IMPACT DOES SERVICE EXCELLENCE HAVE ON ECONOMIC GROWTH AND COMMUNITY DEVELOPMENT?

Complete the following mindmap, providing explanations where needed.

What is it? What are the 5 components of service? How is it affected by service excellence?

Service excellence

Economic growth

What is GDP growth and why is it important?

Explain this term Explain this concept

The impact of service excellence on economic growth & community development

Community development

How can good service improve community development?

Service delivery Batho Pele Describe ways in which service delivery can be improved

What is it?

List the principles of Batho Pele

Hints and tips • • • •

When you are looking at the whole idea of service, it can be helpful to think of yourself as a customer by putting yourself in the customer’s shoes. Think of examples of good and bad service you yourself have experienced. How did you react? How did bad service make you feel? Use colour and illustrations to help you remember ways of improving service delivery. It is important that you understand the concepts of ‘economic growth’ and ‘community development’. Don’t forget! • In Grade 11 you learned about ways in which poor as well as excellent service impacts on the different sectors and sub-sectors of the tourism industry. Think back on this work – especially on how tourism can lead to economic growth and job creation. • Remember the multiplier effect? 4

Typical exam questions Here are some of the questions that you could expect for this chapter: 1.

Choose the correct answer to the following statements: (1 mark each)

1.1

The rate a bank will use when a foreign tourist exchanges his or her currency for the local South African currency: A B C D

1.2

The different lines of longitude used in the calculation of time are referred to as … A B C D

1.3

Greenwich Meridian equator international date line prime meridian.

The countries that advance their clocks one hour in relation to their local time will be practising… A B C D

1.6

eastward westward northward southward.

The 180° line of longitude is known as the … A B C D

1.5

daylight-saving time standard time time zones universal time.

If a traveller moves 15° left of GMT he or she would be travelling… A B C D

1.4

exchange rate bank selling rate bank buying rate foreign exchange rate.

universal time prime time Central African time daylight-saving time.

In drawing up an itinerary for ecotourists, the following information may not necessarily be important: A B C D

transport food accommodation man-made attractions.

2.

The city of Johannesburg determines its local time using the 30°E line of longitude, while the city of Beijing determines its local time using the 75°E line of longitude.

2.1

Calculate the time difference in hours between these two cities. (3 marks)

2.2

If South Africans are interested in watching the 2008 Beijing Olympics opening ceremony, starting at 14:00 Beijing local time, calculate the local time at which this ceremony will be screened for South African viewers. (3 marks)

30

MATHEMATICS GRADE 12

CONTENTS About this Study Guide ...............................................................................................

1

CHAPTER 1

Logarithms ......................................................................................

2

CHAPTER 2

Sequences and series ....................................................................

6

CHAPTER 3

Financial maths ..............................................................................

10

CHAPTER 4

Past algebra that can be asked ...................................................... 13

CHAPTER 5

Functions and inverses ..................................................................

CHAPTER 6

Calculus .......................................................................................... 21

CHAPTER 7

Linear programming .......................................................................

CHAPTER 8

Euclidean geometry ........................................................................ 29

CHAPTER 9

Co-ordinate geometry ..................................................................... 37

CHAPTER 10

Trigonometry ..............................................................................

42

CHAPTER 11

Transformations .............................................................................

49

CHAPTER 12

Data handling .................................................................................

56

CHAPTER 13

Probability ....................................................................................... 65

17

27

CHAPTER 3 This section covers:

FINANCIAL MATHS

n the Fill i lae u form

daily

Simple Interest monthly

From Grade 11

Compound interest

quarterly

6-monthly Linear annually

Depreciation

Reducing balance

WHAT YOU NEED TO KNOW ABOUT FINANCIAL MATHS Grade 12

Future value annuities & sinking fund

Loan repayments

Using time lines

Balance on a loan Finding n, using logs

Present value annuities

10

Complete the following mindmap: T T is the top of a tower and S is a point 50m closer to the ground. From E, a point on the ground, the angle of elevation of T is 24,5º and the angle of elevation of S, is 17,2º.

50m S

Find EC, the distance from the foot of the tower to point E. (Hint – First find ES, the link between the non right-angled triangles and the right-angled triangles.)

24,5˚ 17,2˚

C

E

Always look for a link between a right-angled triangle and a non-right angled triangle

TEST YOURSELF ON 2- AND 3DIMENSIONAL PROBLEMS

B

ABCD is a pyramid, with A, C and D in the ˆ D = 60º same horizontal plane. B A The angle of elevation of B from both C and A is 30˚. AC = 2 m. ABˆ D = 90°

A

30°

60°

2m

30°

i) Find AD D

ˆA =p ii) Now if BAˆ D = α, BAˆ C = BC and AC = d, prove that BD = d.tan α 2.cos p

Don’t forget to do the various examples from your textbook and past papers

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C

AGRICULTURAL SCIENCES GRADE 12

CONTENTS

About this Study Guide ..............................................................................................

1

Prior learning from Grade 11 .....................................................................................

2

Chapter 1

Agricultural safety ................................................................................

11

Chapter 2

Basic agricultural genetics ..................................................................

13

Chapter 3

Animal science ......................................................................................

17

Chapter 4

Management of the factors of production in agriculture ..................

24

Chapter 5

Marketing and entrepreneurship .........................................................

27

Important illustrations ................................................................................................

31

Exam questions ..........................................................................................................

38

Plant science This section covers:

Mineral nutrition

Plant nutrition

PLANT SCIENCE

Plant reproduction

Plant protection

Word check – these are the important words or concepts in this section: The process by which plants and some algae use the energy from sunlight to Photosynthesis produce sugar, i.e. converting light energy to chemical energy. The food producers of the cell. Chloroplasts The way in which fertilisation takes place in flowers by the transfer of pollen from Pollination the anthers of one flower to the stigma of the same flower or of another flower. A root-like stem of a plant which lies on or underneath the ground and usually Rhizome sends out roots below and leafy shoots above. A thin branch or a plant which lies on or underneath the ground, takes root at the Stolon tip and grows into a new plant. A type of grass used to make hay. Eragrostics An infectious organism that causes disease. Pathogen A microscopic agent of infection that is unable to grow or reproduce outside a host Virus cell. A chemical used to get rid of unwanted plant life. Herbicide

Mature flower

Stigma Style Filament

Connective Ovule Perianth Petal: Corolla Septal: Calyx Anther Microsporagium Floral axis Ovary

Articulation

Nectary

Stamen Pedicel

7

Complete the following mindmap and be able to explain each of the concepts:

What are three problems with selective breeding?

What are the benefits of bio-technology?

What are the benefits of indigenous genetic knowledge?

How can genetics help solve a food crisis?

What are the risks to indigenous genetic knowledge?

What are 4 criticisms of GM foods?

Word check – these are the important words and concepts in this section. Complete the missing explanation. The technology that allows for the manipulation of genetics. Bio-technology Removal of genes from one organism and inserting these into another. Genetic modification GM crops /super crops When a breeder chooses a male and a female because of certain Selective breeding characteristics. A gene recipient. Transgenic

Tips and hints Make sure that you are able to explain the positive aspects as well as the negative aspects of genetically modified agricultural products.

Checklist - Can I ….? Explain breeding and selection principles for effective plant, crop and animal production. Discuss selection and breeding principles. Explain how agriculturalists use genetics. Discuss the role of indigenous genetic knowledge in animal production. Explain the role of genetics in the development and improvement of agricultural commodities.

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