Mathematical Literacy FINANCE

MATHEMATICAL LITERACY Grade 12 SELF STUDY GUIDE BOOKLET 1A FINANCE TABLE OF CONTENTS 1

Page 1. Introduction ( to be provided, generic for all study guides) 3 2. How to use this self-study guide 4 3. Topic: Finance 6 3.1 Key concepts 6 3.1.1 Tariffs 8 3.1.2 Tax 17 3.1.3 Interest and Hire-purchase 37 3.1.4 Income and expenses; Profit and loss 48 3.1.5 Cost and selling price, Break even analysis 55 3.2 Solutions to practice questions 3.2.1 Tariffs 70 3.2.2 Tax 73 3.2.3 Interest and Hire-purchase 78 3.2.4 Income and expenses; Profit and loss 82 3.2.5 Cost and selling price, Break even analysis 84 4. Examination guidance (Subject specific) 89 5. Study and Examination Tips ( Subject Specific) 91 6. Reference 92 7. Acknowledgements 93 2

1. Introduction The declaration of COVID-19 as a global pandemic by the World Health Organisation led to the disruption of effective teaching and learning in many schools in South Africa. The majority of learners in various grades spent less time in class due to the phased-in approach and rotational/ alternate attendance system that was implemented by various provinces. Consequently, the majority of schools were not able to complete all the relevant content designed for specific grades in accordance with the Curriculum and Assessment Policy Statements in most subjects. As part of mitigating against the impact of COVID-19 on the current Grade 12, the Department of Basic Education (DBE) worked in collaboration with subject specialists from various Provincial Education Departments (PEDs) developed this Self-Study Guide. The Study Guide covers those topics, skills and concepts that are located in Grade 12, that are critical to lay the foundation for Grade 12. The main aim is to close the pre-existing content gaps in order to strengthen the mastery of subject knowledge in Grade 12. More importantly, the Study Guide will engender the attitudes in the learners to learning independently while mastering the core cross-cutting concepts. 3

2. How to use this Self-Study Guide. • This study guide covers selected sections of Finance which form part of paper 1. • The topic is drawn from the CAPS Grade 10 – 12 Curriculum. Selected sections are presented in the following way: o What you should know at the end of the section. o Explanation of key concepts. o Summary/Notes. o Worked examples. o Practice questions. o Solutions to practice questions. • Mathematical Literacy is a highly contextualised subject. Whilst every effort has been taken to ensure that skills and concepts you will be examined on are covered in this study guide, it is in fact the context used in the examination that will determine how these skills and concepts are assessed. • This study guide covers all the cognitive levels. • Go through the worked examples on your own. • Do practice examples on your own. Then check your answers. • Read symbols and explanation table below to understand how marks are allocated. Symbol Explanation M Method M/A Method with accuracy MCA Method with consistent accuracy CA Consistent accuracy A Accuracy C Conversion S Simplification RT/RG/RD Reading from a table/graph/diagram SF Correct substitution in a formula O Opinion/Example/Definition/Explanation P Penalty, e.g. for no units, incorrect rounding off, etc R Rounding off NPR No penalty for rounding NPU No penalty for the units AO Answer only, if correct, full marks • Reward yourself for things you get right. • If any of your answers are incorrect, make sure that you understand where you went wrong, before moving on to the next section. • The study guide covers both generic and subject specific examination tips. You are expected to read and understand the tips, so that you are able to study more effectively. 4

3. TOPIC: FINANCE 3.1 Notes/Summaries/Key Concepts TERMINOLOGY MEANING Account A record of income and expenditure relating to a particular period or purpose. Balance This is the difference between debits and credits. Bank statement The details of all the transactions made from one bank account in a given time period. Break-even point Break-even point is where the business is at an activity level (doing business) at which total cost = total sales, i.e. you have made enough income to cover the costs. At the break-even point, you are making neither a profit nor a loss; from that point on you will be making a profit with each sale (until new costs are incurred). Budget A plan of how to spend money. An estimate of income and expenditure. Bursary A sum of money given to you by an organisation to cover the cost of your formal studies. Capital Money that is owned by someone and used for the purpose of investing or lending. Commission The sum of money paid to an agent (usually a salesperson) that is a percentage of the total value of goods sold by the agent. Compound interest Interest charged on an amount due, but including interest charges to date. Consumption rate The rate at which a commodity, such as water, electricity or fuel, is consumed. Cost-effective Best value for money. Cost price This is the amount that it costs per unit to either manufacture or purchase an item or to prepare for a service that will be delivered. This amount is pure cost, no mark-up or profit has been added yet. Cost rate The price of a product per mass, volume, length or time unit. Credit This is an entry in an account that shows a payment made into the account. Credit balance The amount in the account is your own. Credit card A credit card is a service bank product that allows you to buy goods and pay for them at the end of the month. Credit limit The maximum amount you can spend on your credit card. Debit Money deducted or money flowing out of an account. An entry in an account showing a payment made from the account. Debit balance The amount owed to a lender or seller. Debit order It is an arrangement whereby you give permission to a third party to withdraw money from bank account on a regular basis. Deposit A payment made into a bank account. Disposable income Income that is left over after all payments have been made. Exchange rate The value of one currency relative to the value of another currency. Expenditure An amount of money that is spent on something. Fine print The legal terms and conditions printed on a contract applicable to a transaction or account. Fixed deposit A single deposit invested for a fixed period at a fixed interest rate. Fixed expenses These are amounts that must be paid every month and stays the same for a period of time, like rent, school fees and transport costs. Fund A source of money. Gross income The total amount of all an individual’s income before deductions. Hire purchase Goods and products such as furniture can be purchased using a long- term lease or hire agreement. Inflation An increase in the price of a basket of goods or services that is representative of the economy as a whole. Interest Money paid regularly at a particular rate for the use or loan of money. It can be paid to you by a finance organisation or bank (in case of savings); or it may be payable by you to a finance organisation on money you borrowed from the organisation. Interest rate value This is the % rate of interest that will be charged on your loan amount, i.e. a percentage value of the original loan amount. 5

Interest value This is the actual rand amount of interest that will be added to your loan. Investment To put money into an organisation or bank (e.g. by buying shares), so as to gain interest on the amount at a higher rate. Investment Something in which you have invested money. Money invested for a period of time. Invoice A comprehensive document that details all the work done or items sold, and what costs are due. Lay-bye It is a form of credit where the buyer pays a deposit and pays the balance in instalments while the shop keeps the item(s) until it has been paid off. Loan A loan is an agreed sum of money that is lent by a bank or moneylender (e.g. personal loan or home loan). Luxury item or service An item or service that is not essential for daily life, but which makes life easier or more convenient. Net pay The amount an employee “takes home” after income tax has been deducted. Overdraft An overdraft is an arrangement you make with the bank that allows you to draw more money than there is in your account. PAYE (abbr.) Pay as you earn: tax taken off your earnings by your employer and sent to the South African Revenue Service before you are paid (the balance). Remittance slip A piece of paper that accompanies a payment and contains the most important details of the transaction. Salary An amount of money paid for the work you do. (This is normally paid monthly.) Selling price This is the price at which something is offered for sale. Simple interest Interest charged on the original amount due only, resulting in the same fee every time. Statement A summary of transactions (debits and credits, or payments and receipts) made on an account. Tariff The rate charged for a service rendered, e.g. import duties, water consumption cost, etc. Tax A compulsory levy imposed on citizen’s earnings or purchases to fund the activities of government. Taxable A service, purchase, income, item or earning that will have tax charged to it. Tax invoice Printed record of what was bought, what it cost, what was taxable, the tax amount, method of payment, amount tendered, and change due, if any. Trillion One-million-million (one followed by twelve zeros). UIF (abbr.) Unemployment Insurance Fund: A government-run insurance fund which employers and employees contribute to, so that when employees are retrenched they can collect some earnings (a portion). Variable expenses Expenses that change over time or from one week/month to the next. These are things that you usually pay or buy each month, but the amount changes e.g. telephone and electricity costs. VAT Value Added Tax (VAT) is a tax that is levied at 15% (currently in South Africa) on most goods and services, as well as on the importation of goods and services into South Africa. VAT exclusive price The price before VAT is added. VAT inclusive price The price after VAT is added. Wages Withdrawal Money taken out of a bank account. Zero rated VAT items These are goods that are exempted from VAT. Groceries that are basic foodstuffs are zero-rated in South Africa, e.g. brown bread, milk, mielie meal, samp, rice, etc.. 6

3.1.1 Tariffs Objectives By the end of this section, learners must be able to: 1. Work with the following tariff systems: 1.1 Municipal tariffs (e.g electricity, water, sewage) 1.2 Telephone tariffs (e.g cell phone, fixed line) 1.3 Transport tariffs (e.g bus, taxi, train) 1.4 Banking Charges (not included in this manual) 2. Calculate cost using given tariffs and/or formulae. 3. Draw and interpret graphs of various tariff systems 4. Compare TWO or MORE different options for a tariff system to determine the most appropriate/cost effective option for individuals with particular needs. 5. Draw graphs to represent the different options and interpret the point(s) of intersection. Summary A tariff is the charge in rands per measuring unit for a specific service. Tariffs are not always constant; they change from time to time. The formulae for calculating the total cost is: Total cost = number of units ⨉ tariff (cost per unit) In this section we are going to deal with the following tariffs: Municipal eg electricity, water, sewage Tariffs Transport Telephone e.g bus, tax, train, parking e.g cell phone, landline 7

Electricity tariffs Ø Electricity usage is measured in kilowatt per hour (KWh). Ø The amount of electricity that a person will pay each month depends on the number of Kwh of electricity used during the month. Ø Electricity billing options include Prepaid (i.e. pay as you use) or a fixed billing system (i.e. using electricity and paying at the end of the month) Ø Electricity is charged at a sliding scale. This means that the more electricity you use, the higher the rate at which you are charged for electricity. The table below indicates the example of sliding scales for electricity tariffs Household (all tariffs are VAT exclusive) VAT to be charged at 15% Block 1 0 - 50 KWh R0,8375 per KWh Block 2 51 - 350 KWh R0,9440 per KWh Block 3 351 - 600 KWh R1,2629 per KWh Block 4 Over 600KWh R1,5156 per KWH Worked example 1 Use the table above to answer the questions that follow: 1.1 Write down the tariff per kWh charged in block 2. 1.2 Determine the amount to be paid for 250 kWh of electricity. Solutions 1.1 R0,9440 1.2 Using the table, we can see that the 250kWh is made up of the following: First 50 kWh = 50 × R0,8375 = R41,875 (no rounding at this stage) ∴ 250kWh – 50kWh = 200kWh Then 200 = 200 × R0,9440 = R188,80 Total amount = R41,875 + R188,80 = R230,675 (no rounding at this stage) 15 Amount of VAT = × R230,675 100 = R34,60125 (no rounding at this stage) Total amount to be paid = R230,675 + R34,60125 = R265,27625 » R265,28 8

Water tariffs Water tariff, just like electricity tariffs also varies from one place to the other. Ø Water consumption is measured in kilolitres (kℓ) Note: 1 kℓ = 1000ℓ Ø The amount payable for water also depends on the number of kl of water used during the month. Ø Water is charged at a sliding scale. The more water you use, the higher the rate at which you are charged. The table below indicates the example of sliding scales for water tariffs Residential (all tariffs are VAT exclusive) VAT to be charged at 15% Up - 6 kℓ First 6 kℓ Free > 6 kℓ - 10 kℓ Next 4 kℓ R5,21 per kilolitre > 10 kℓ - 15 kℓ Next 5 kℓ R7,87 per kilolitre > 15 kℓ - 20 kℓ Next 5 kℓ R10,52 per kilolitre > 20 kℓ - 30 kℓ Next 10 kℓ R13,38 per kilolitre > 30 kℓ – 40 kℓ Next 10 kℓ R13,97 per kilolitre > 40 kℓ Over 40 kℓ R16,96 per kilolitre Worked example 2 Use the table above to answer the questions that follow: 2.1 Give a possible reason why the first 6 kℓ would be free. 2.2 Calculate the total cost for 21 kℓ. 9

Solution 2.1 To accommodate households with low or no income. 2.2 Using the table, we can see that the 21 kℓ is made up of the following: 6 + 4 + 5 + 5 + 1 = 21 kℓ The first 6 kℓ @ R0,00 = R0,00 The next 4 kℓ @ R5,21/ kℓ = R20,84 The next 5 kℓ @ R7,87/ kℓ = R39,35 The next 5 kℓ @ R10,52/ kℓ = R52,60 The last 1 kℓ @ R13,38/ kℓ = R13,38 Total 21 kℓ = R126,17 15 Amount of VAT = × R126,17 100 = R18,9255 Total amount = R126,17 + R18,9255 = R145,0955 » R145,10 Telephone tariffs Cell phone tariffs Cell phone networks uses either prepaid or contract billing structures. Different networks charge different tariffs. The most common networks in South Africa are: Ø Vodacom Ø MTN Ø Cell C Ø Telkom Prepaid tariff system The general formula for the prepaid tariff system is: Prepaid cost = total number of units ⨉ tariff Note: Units can be in minutes or seconds In a prepaid tariff system, if no calls are made, there are no costs. 10

Contract tariff system A cell phone contract for a specific period is taken out from a service provider. The cost per month includes: Ø Subscription fee Ø Cost for the calls The general formula for the contract tariff system is: Contract cost = subscription fee + (total number of minutes – number of free minutes) ⨉ tariff Worked example 3 Tshepo came across the following option as he was shopping for a new cell phone. • Monthly subscription = R279,00 • Free 50 minutes • Calls cost R0,99 per minute Solution Total amount = subscription fee + (Total minutes – free minutes) × tariff Calculate the total amount Tshepo will pay if he used 75 minutes on a particular month. = R279,00 + (75 – 50) × R0,99 = R279,00 + (25 × R0,99) = R279,00 + R24,75 = R303,75 11

Practice Questions Question 1 The table below shows the rates for domestic prepaid electricity: TARIFF BLOCK RATES PER KWH Block 1 (0 – 50) kWh R0,76 Block 2 (51 – 350) kWh R0,97 Block 3 (351 – 600) kWh R1,16 Block 4 (> 600) kWh R1,39 Use the table above to answer the questions that follow. 1.1 The George family used 250 kWh of electricity for the month of December. Calculate (3) the amount they need to pay. 1.2 In January they used 351 kWh. Determine the difference between the December and (5) January payments. Question 2 The table below indicates the Mangaung local Residential water tariffs for 2016/2017 and 2017/2018. These tariffs are applicable for both the prepaid and billed accounts. All tariffs are VAT exclusive. Mangaung local municipality water tariffs (Residential) Step tariffs 2016/2017 % increase 2017/2018 Prices (R) per kℓ Prices (R) per kℓ 0 – 6 kℓ 6, 91 8% 7,46 7 – 15 kℓ 15, 95 9% 17,39 16 – 30 kℓ 17, 00 11% 18, 87 31 – 60 kℓ 19, 04 11, 5% 21,23 Above 61 kℓ 21, 58 12, 5% 24, 28 Basic charge per month 22, 00 12% 24, 64 Use the table above to answer the questions that follow. 2.1 Define the concept basic charge in the given context. (2) 2.2 Show how the tariff of R18, 87 during the 2017/2018 period was calculated. (2) 2.3 A certain household has received a bill of R205, 24 at the end of August 2018. Use the tariffs table above to calculate the number of kilolitres of water the household consumed. (5) 2.4 Mangaung local municipality has introduced a prepaid system of paying water. On the 01/09/2018, Mrs Mnisi loaded 133kℓ of water and on the 15/09/2018 when she checked the meter readings, only 53,7kℓ of water was remaining. Determine the amount of water she has used thus far. (2) 12

Question 3 The Department of Correctional Services became aware of a problem that Metro High School was experiencing with violent incidents at the school. They invited the school to visit one of their prisons on condition that one teacher had to accompany every group of 10 learners or fewer. Mr Palm, the principal, must hire a bus to take the learners and teachers to visit the prison. Graphs representing the total cost of hiring buses from two different companies are drawn below. 13

3.1 The total cost for hiring a bus from Company P is calculated by using the following formula: Total cost (in rand) = number of passengers x 35 Use the graphs above and write down a formula for calculating the total cost (in rands) for Company Q in the form: Total cost (in rands) = … (2) 3.2 Mr Palm has budgeted R900,00 for the total cost of the bus transport. Use the graphs above or the formulas in QUESTION 4.1 to determine the following: 3.2.1 The maximum number of passengers that can be transported using Company (4) Q. 3.2.2 The ratio of learners to teachers, if the maximum number of passengers is (4) transported according to the condition set out by Correctional Services regarding the number of teachers. Question 4 MaNdlovu has a landline telephone. A service provider has offered her a choice of two different call packages CALL PACKAGE 1 CALL PACKAGE 2 • Monthly rental of R150 • Monthly rental of R300 • First 100 minutes are free • First 500 minutes are free • Calls cost R0,50 per minute • Calls cost R0,50 per minute 4.1 Write down a formula that can be used to calculate the total cost (in rands) for CALL PACKAGE 2, in the form: Total cost (in rands) = … (2) 4.2 Using the formula in 3.2, calculate the total cost (in rands) if MaNdlovu made calls for (4) a total duration of 510 minutes. 4.3 Determine, with calculations, the call package that will be cost effective for (6) MaNdlovu if she makes only 300 minutes of calls per month. 14

Question 5 The parking ticket of Ntsiki’s mother at Bram Fischer International airport showed the following information: ACSA parking ticket Date of entry: 06 January 2015 Time: 07:30 Date of exit: 10 January 2015 Time: 09:15 Table 1: Bram Fischer International parking tariffs. Shaded Parking Open Parking Duration Rand ( R ) Rand ( R ) 0 – 5 min Free Free 5 min – 1 hour 17 12 1 – 2 hours 23 14 2 – 4 hours 31 17 4 – 12 hours 45 31 12 – 24 hours 100 67 After 24 hours 100× d + R44 for part 67× d + R29 for part thereof thereof Number of days (full days) = d Drop and Go (R) Lock-Up Garages 0 – 15min Free 12 hours or less R100 15 – 30 min 24 30 min – 1 hour 58 1 – 2 hours 117 Full day R150 2 – 24 hours 244 Tariffs increase for every additional hour or part thereof with R55 Lost ticket (If there is no proof of travel) R500 5.1 Determine the amount that Ntsiki’s mother must expect to pay for using the airport’s shaded (3) parking. 5.2 Explain each of the following: 5.2.1 The circumstances under which a person will feel disadvantaged if the parking ticket is (2) lost. 5.2.2 The length of time for both the shaded and open parking, that a lost parking ticket (4) would be an advantage. 5.3 What measures are taken to discourage car owners, who must wait for the passengers, to use the (2) drop and go parking? 15

Tax Objectives By the end of this section, learners must be able to: 1. Define the difference between VAT inclusive and VAT exclusive. 2. Show the original value once VAT has been added or calculate the final value once VAT has been added. 3. Calculate UIF and understand why UIF is deducted. 4. Explain the meaning of Personal Income Tax. 5. Interpret a salary slip, tax tables and personal income tax forms in order to do personal tax calculations. 6. Calculate the Taxable Income and Non-Taxable Income. 7. Use the Tax table to calculate the Tax payable. 8. Work with rebates and medical credits. 9. Calculate the nett pay of an individual. 10. Investigate how an increase in salary can influence a person’s tax bracket. What is meant by tax? It is a compulsory contribution to government revenue, levied on the workers' income and business profits, or added to the cost of some goods, services, and transactions. Why do we pay tax? To provide funds for government programmes, e.g to provide public goods and services like healthcare; schools; roads etc. Who pays tax? VAT is paid by everyone who buys goods or pays for services rendered, however some goods are exempted from tax e.g. Fresh fruit; brown bread etc. Personal income tax is only paid by individuals who earn above a certain amount of money (as determined by the government from one year to the next). 16

In this booklet we are going to deal with the following taxes: VAT TAX INCOME TAX VAT (Value added Tax) All goods and services are subjected to VAT, unless it is zero rated at 0% or exempted from tax. VAT is currently calculated at 15% of the value of the goods/services. VAT inclusive means that VAT has already been added to the prices of the goods/services. VAT exclusive means that VAT must still be added to the price of the goods/services. INCOME TAX Income Tax is defined as a compulsory payment to the state, which is deducted from person or business’ earnings for the state to provide services to its citizens. This amount is paid to the South African Revenue Services (SARS) and can be deducted from taxpayer’s salary every month (PAYE) 17

VAT VAT – Value Added Tax VAT is currently levied at the standard rate of 15%. You need to calculate VAT when: • You are selling something and have to add VAT to the price. • You want to check an invoice and make sure that the correct amount of VAT is included. • VAT- inclusive amount: means that 15% VAT has already been added to the amount. • We calculate the original amount using the following principle: !"#$%& (%)*$+(%, -!. Original amount = /,/1 • VAT- exclusive amount : means that 15% VAT must still be added. • Thus, Original amount + amount of VAT = amount including VAT VAT VAT inclusive exclusive VAT inclusive VAT exclusive The item costs R529,99. The item costs R460,86 excluding It includes 15% VAT. 15% VAT. This means VAT was added to the This means VAT must be added to original price. the original price Thus, Original price = R529,99 ÷ 1,15 1,15 x R460,86 = R529,989 = R460,8608696. Round off answer (2 dec): R460,86 Round off answer (2 dec): R529,99 The original price was R460,86 VAT amount: VAT amount: R529,99 – R460,86 = R529,99 –R460,86 R69,13 = R69,13 OR OR 233 R529,99 x 224 = $460,86 15 × $460,86 = $69,13 100 Now, R460,86 + R60,13 = R529,99 Now: R529,99 –R460,86 = R69,13 18

NB! COMMON MISTAKE MADE!!! The item costs R529,99 (VAT inclusive). Calculate the original price. VAT inclusive means that VAT was added to the original price. VAT = R529,99 X 0,15 = R79,50 VAT amount: R529,99 – R79,50 = R450,49 which is incorrect (This is incorrect as the VAT was not calculated on the final price, but on the original price) Correct calculation 233 R529 × 224 = R460,00 VAT Exemption: Some products or services may not be taxed. This means that there is no VAT charge for them otherwise referred to as VAT exempted. Below is a list of some VAT exempted products and services. v Passenger service by rail or road. v Supply of donated goods by a charitable organisation. v Rentals on residential property. v The sale or rental of land outside SA. v Educational services. v Union membership fees v Caring services for children by a crèche or an after-school care centre. v Some basic food items e.g Fresh fruit; brown bread etc. 19

Working with an invoice E.g. Below is a Municipality Tax Invoice for Chester Williams. Sixole Municipality VAT No: 29810784 P. O. Box 5200 The Hage 2443 Account number: 400200321 Date: 04 April 2017 Chester Williams Account for March 20 Marion Place 2017 Carrod Road Invoice No. 5537774 The Hage ITEM UNITS VAT COST Electricity 435 26,19 187,05 Electricity Grant -45,99 -2,77 -19,78 Water Services 11 3,57 25,53 Assessment Domestic 195,59 Rates Sewer 1 14,08 100,55 Refuse removal 1 6,21 44,34 Subtotal 47,28 533,28 VAT 47,28 TOTAL DUE: 580,56 1. Why is there no VAT charge for the assessment rates? Assessment rates are charges for owning residential property. This is a VAT exempted item on the invoice. 2. Why is there a negative charge on the invoice? The municipalities allow each household a certain amount of free electricity. The electricity grant is the amount that one does not have to pay for, so it is subtracted from the amount used for that month. Please note the VAT for that amount of electricity is also subtracted. 3. Are the water and electricity costs VAT inclusive or exclusive? They are VAT exclusive and thus VAT is calculated separately and added to the total at the end. 4. Why is the account dated in April but is says account for March? The statement was calculated for the month of March but was only issued in April. 20

Worked example 1 Below find a till slip for Sasha ‘s groceries. Study the till slip ans answer the questions that follow: SHANEY STORES 11TH STR, DOODELVILLE TEL: 031 454 5765 TAX INVOICE: VAT No. 44223377556644 Milk Tart R17,99 Apple Crumble R29.99 Carrier bag R0,40 Carrier bag R0,40 Marshmallow R9,99 Dairy Custard R17,99 Hot dog rolls R6,65 Lemon Biscuits R7,99 ENT. Bacon/egg 0,458kg R22,90 @ R49,99/kg Sunflower Oil 250ml R14,99* Popcorn R7,99 Chicken Mayo Roll R23,99 Brown Bread R10,99* Pumpkin Seed R6,99* Sauce Peri Peri R13,99 Balance before VAT R193,24 EFT credit card payment R217,28 Tax Code Taxable Tax Value Zero VAT R32,97 R0,00 VAT R160,27 R23,73 Total Tax R23,73 1.1 Why are some of the items marked with an asterisk (*) ? (2) 1.2 Determine the total cost of the items that are VAT inclusive. (2) 1.3 Show, by means of calculations whether you believe the VAT calculations are correct or (4) not. Solutions 1.1 They are exempted from VAT/zero rated items 1.2 R 193,24 – (R6,99+ 10,99 +14,99) = R160,27 OR R 193,24 – R32,97 = R160,27 1.3 R160,27 × 15% = R24,04 Calculations are incorrect as VAT is supposed to be R24,04 and not R23,73 21

Worked example 2 The cricket coach of a school would like to buy cricket equipments for the school cricket team. The piece list is shown below ITEM COST Helmet R350 each Gloves R95,50 a pair Box of 4 cricket balls R170 a box Cricket pads R135 a pair Cricket bats size 3 R550 each Cricket bats size 5 R750 each Use the information above to answer the questions that follow. 2.1 If the coach needs 16 balls, how many boxes of cricket balls woulld he need? (2) 2.2 If the coach orders, 4 helmets; 3 pairs of gloves; 8 of balls; 3 pairs of cricket pads; 2 size 3 (3) bats and 2 size 5 bats, what will the total cost of the items be? 2.3 Determine the amount of VAT at 15% that will be charged on the order. (2) 2.4 If a handling fee of R100 is charged on the goods bought. How much (incl. VAT) will the (2) school have to pay in total for this order? 2.5 The annual budget for cricket is R10 800, what percentage of the budget was spent on equipment for this season? (3) Solutions 2.1 4 boxes 2.2 4× $350 + 3 × $95,50 + 2 × $170 + 3 × $135 + 2 × $550 + 2 × $750 = R5 031,50 2.3 VAT = Value added tax: 15% × R5 031,50 = R754,73 2.4 R5 031,50 + R754,73 + R100 = R5 886,23 2.5 4 556,78 × 100 23 533 = 54,5 % 22

Practice Questions Question 1 The price of a pair of sandals is R79,99 excluding VAT. VAT is charged at 15% 1.1 calculate the amount of VAT charged on the sandals. (2) 1.2 Determine the VAT-inclusive price of the sandals. (2) Question 2 An advert quotes the i-phone (cellphone) at R13 950 (VAT inclusive). VAT is charged at 15% Calculate the original price of the cellphone. (3) Question 3 The Easter Show is an annual event held in Cape Town. The Elie family, consisting of two adults aged 45 and 48, three children aged 5, 6 and 16 and a grandmother aged 75, planned to visit the Rand Show. TABLE 1 below shows the duration and ticket prices of the 2017 Easter Show. TICKET PRICING DURATION VISITORS PRICES INCLUSIVE OF AGE CATEGORY 15% VAT Adults (aged 17 to 64) R150 Friday 14 April Pensioners (65 years and older) R50 Teens (aged 13 to 16) R50 to Children (aged 6 to 12) R20 Children (under 6) free 18 April to 20 April Adults and pensioners receive a 50% discount Sunday 23 April 09:00 – 19:00 3.1 Calculate the amount of VAT payable on a teen’s ticket. (3) 3.2 If the family visited the Easter Show on 20 April instead of 23 April, they would have saved (10) more than a quarter on the total cost of the tickets. Verify, showing all calculations, whether the statement is valid. 3.3 Provide a reason why pensioners are often offered discounts. (2) INCOME TAX Income Tax is defined as a compulsory payment to the state, which is deducted from person or business’ earnings for the state to provide services to its citizens. 23

This amount is paid to the South African Revenue Services (SARS) and can be deducted from taxpayer’s salary every month (PAYE). The process of calculating personal income tax can be illustrated as follows: 24

GROSS INCOME The sum of all earnings before any deductions have been made. TAX DEDUCTIBLE INCOME PENSION FUND •Government Employees have GEPF while Private Sector has a Provident Fund. •7,5% of your basic salary is contributed towards a pension fund and is tax-deductible. •It should be multiplied by 12 to give the annual contribution. DONATIONS * A gift to a person who usually is registered with the authorities under Section 18A. * The maximum amount allowed for tax deduction is R100 000. u TAX THRESHOLD • Persons earning more than the tax threshold are liable to pay tax. • The income level at which someone needs to pay tax. • Anyone who earns less than this amount does not have to pay tax. • This amount is determined by the government every year. TAX THRESHOLD 2020/2021 Below age 65 R83 100 Age 65 to below 75 R128 650 Age 75 and older R143 850 Example: A person who is 60 years old and earns less than R83 100 does not have to pay tax. 25

INCOME TAX TABLE SARS (South African Revenue Services) issues tables to be used when determining tax to be paid by individuals. Taxable income = Gross income – Tax deductible expenses. Tax deductible expenses include contributions to a pension/provident funds and donations. Rates of tax for individuals 2021 tax year (1 March 2020 - 28 February 2021) Taxable income (R) Rates of tax (R) 1 – 205 900 18% of taxable income 205 901 – 321 600 37 062 + 26% of taxable income above 205 900 321 601 – 445 100 67 144 + 31% of taxable income above 321 600 445 101 – 584 200 105 429 + 36% of taxable income above 445 100 584 201 – 744 800 155 505 + 39% of taxable income above 584 200 744 801 – 1 577 300 218 139 + 41% of taxable income above 744 800 1 577 301 and above 559 464 + 45% of taxable income above 1 577 300 Tax Rebates Tax Rebate Tax Year 2021 2020 2019 2018 2017 2016 2015 Primary R14 958 R14 220 R14 067 R13 635 R13 500 R13 257 R12 726 Secondary (65 and older) R8 199 R7 794 R7 713 R7 479 R7 407 R7 407 R7 110 Tertiary (75 and older) R2 736 R2 601 R2 574 R2 493 R2 466 R2 466 R2 367 Tax Thresholds Age Tax Year 2021 2020 2019 2018 2017 2016 2015 Under 65 R83 100 R79 000 R78 150 R75 750 R75 000 R73 650 R70 700 65 an older R128 650 R122 300 R121 000 R117 300 R116 150 R114 800 R110 200 75 and R143 850 R136 750 R135 300 R131 150 R129 850 R128 500 R123 350 older Monthly medical tax credits Main Member R319 First dependent R319 Each additional member R 215 https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals 26

For persons earning above the tax threshold REBATES It is the relief individuals who pay tax get according to their age § Rebates are fixed amounts deducted (taken off) from your annual tax payable. § Everyone qualifies for the PRIMARY rebate. § People 65 and over qualify for the PRIMARY and SECONDARY rebates. § People 75 and over qualify for the PRIMARY, SECONDARY and TERTIARY rebates. § Rebates are subtracted AFTER you have calculated the annual tax payable. MEDICAL TAX CREDITS § Medical tax rebates are received by the main member (The person who pays the medical aid). § This rebate gets deducted AFTER the annual tax payable has been calculated. § The medical tax credit allocated for the first dependent equals that of the main member, every member thereafter has the same different medical tax credit. 27

STEPS TO CALCULATE INCOME TAX STEP 1: Determine the annual income Multiply the monthly income by 12 STEP 2: Determine the tax deductible income. STEP 3: Subtract the tax-deductible items e.g. Pension and donations Taxable income= Annual Income – tax deductible income STEP 4: Check if the person qualifies to pay tax by using tax threshold table. Those earning less than the threshold do NOT have to pay tax. STEP 5: Identify the correct tax bracket and write it down. Substitute the taxable income into the given formula. Use BODMAS to find the tax for the year. STEP 6: Calculate and subtract the rebates Remember: check the age of the individual to see which rebate(s) they qualify for STEP 7: Calculate and subtract the medical tax credits, remember to check the number of how of dependents. This value is to be multiplied by 12 for the annual amount. STEP 8: To determine the monthly income tax, divide the answer by 12. ANSWER 28

Worked example 1 Consult the Tax Table for indiividuals for 2020/2021 tax year to answer the questions that follow: (See Annexure) 1.1 Into which bracket does a person who earns a taxable income of R454 563 fall? Answer: Bracket 4: 105 429 + 36% of taxable income above 445 100 1.2 Which rebate would a 52 year old person receive? Answer: Primary rebate 1.3 Expain whether a 65 yr old earning 120 000 should pay tax or not. Answer: No, they earn below the tax threshold. Worked example 2 Casy is 25 years old and earns a monthly income of R25 000. Using the table below, calculate the amount of tax payable without considering the rebates. Solution 29

Worked example 3 Bongani is a 35 year old man who earns an annual taxable income of R236 700. 2019 tax year (1 March 2018 – 28 February 2019) Taxable income (R) Rates of tax (R) 1 – 195 850 18% of taxable income 195 851 – 305 850 35 253 + 26% of taxable income above 195 850 305 851 – 423 300 63 853 + 31% of taxable income above 305 850 423 301 – 555 600 100 263 + 36% of taxable income above 423 300 555 601 – 708 310 147 891 + 39% of taxable income above 555 600 708 311 – 1 500 000 207 448 + 41% of taxable income above 708 310 1 500 001 and above 532 041 + 45% of taxable income above 1 500 000 Age Threshhold 2018/2019 Under ager 65 78150 Age 65 to 75 121 000 Older than 75 135 300 REBATES Primary rebate Under ager 65 R 14067 Secondary rebate Age 65 to 75 R7713 Tertiary rebake Older than 75 R 2574 2.1 Using the tax table for the 2018/2019 tax year calculate Bongani’s annual tax payable. Solution 2.1 Step 1: Find the correct tax bracket according to his annual taxable income of R236 700 § Use the tax bracket to calculate his annual tax payable. =R 35 253 + (26% of 236 700 – 195 850) =R 35 253 + (26% x R 40 850) =R 35 253 + (R 10 621) = R 45 874 Step 2:Deduct the PRIMARY rebate = R 45 874 – R 14 067 = R 31 807 is Bongani’s annual tax payable 30

Worked example 4 Cally is a 55 year old woman who earns an annual taxable income of R350 000. She pays medical aid for herself and her daughter. Using the tax table for the 2018/2019 tax year calculate Cally’s monthly tax payable. Solution Step 1: Taxable Income = R350 000 Step 2: Identify Bracket: R63 853 + 31% ( 350 000 – 305 850) = R63 853 + 31% of R 44 150 = R63 853 + R13 686,50 = R77 539,50 Step 3: Now subtract the rebate/s: Cally is under 65 yrs of age, thus only 1 rebate Thus: R77 539, 50 – R14 067 = R63 472,50 Step 4: Medical rebates: R310 + R310 = R620 × 12 = R7 440 Step 5: Thus Tax Payable for the year R63 472, 50 – R7440 = R56 032, 50 Step 6: Monthly tax = R56 032, 50 ÷12 = R4 669,38 Always use the Tax table given to you to work from. Remember they are not all the same! 31

Practice Questions Question 1 All employers have an obligation to provide their employees with a payslip monthly. Use the payslip provided to answer the questions that follow: 1.1 Explain the term gross income. (2) 1.2 Write down the name of the employee. (2) 1.3 Calculate the values of M and N on the payslip. (4) 1.4 What percentage of his basic salary was paid toward pension fund contribution? (3) 1.5 Determine the employee’s annual taxable income. (4) 1.6 Use the tabel below to identify the employee’s tax bracket. (5) 2019 tax year (1 March 2018 – 28 February 2019) Taxable income (R) Rates of tax (R) 1 – 195 850 18% of taxable income 195 851 – 305 850 35 253 + 26% of taxable income above 195 850 305 851 – 423 300 63 853 + 31% of taxable income above 305 850 423 301 – 555 600 100 263 + 36% of taxable income above 423 300 555 601 – 708 310 147 891 + 39% of taxable income above 555 600 708 311 – 1 500 000 207 448 + 41% of taxable income above 708 310 1 500 001 and above 532 041 + 45% of taxable income above 1 500 000 Source: https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals 32

Question 2 Precious is a 40 year old temporary worker at ABC trading. She earns R5 500 per month. Use the table below to answer the questions that follow: Source: https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals) 2.1 Determine, by means of calculations, whether she qualifies to pay tax. (3) 2.2 Show how the value of R 35 253 in the second tax bracket was calculated . (3) Question 3 Yamkela, a 64-years-old employee, receives a gross salary of R37 537,50 per month. • He contributes 7,5% per month towards the Government Employees Pension Fund (GEPF) which is tax deductible. • He also donates R575 per month to a charity organisation, the donation is tax deductible. (adapted from EC Paper 2 September 2020) Use the 2019/2020 Tax Table in question 2 above. 3.1 Calculate the total amount that Yamkela pays towards the pension fund and donations for the year. (6) 3.2 Hence, calculate Yamkela’s annual taxable income. (3) 3.3 Verify, with the necessary calculations, that Yamkela’s tax that he pays permonth is more than R6 850. (7) 3.4 Explain why people who are aged 75 years and older pay less tax than people younger (2) than 75 years and earning the same taxable income. 3.5 The monthly gross salary of Yamkela increased by 6,4% in 2019. Calculatewhat his gross (2) salary was in 2018. 33

Question 4 Pierre (28 years old) started a new job on 1 March 2020 at Expert Systems with a starting salary of R168 000 per year. His letter of appointment states that he is not entitled to a bonus. Refer to his incomplete payslip below and the tax table on ANNEXURE A to answer the questions that follow. Expert Systems Salary advice Tax number:00654321 Employer: Pierre Tolken Date employed: 01/03/2020 Pay period: 01/03/2020 – 31/03/2020 ID number: 8704020035081 ITEM Earnings Deductions A Pension Fund 1 050 UIF employee contribution B Net tax payable C Total deductions D Net salary (R) E 4.1 Write down Pierre’s surname. (2) 4.2 Determine the number of days that Pierre was employed by 28 February 2021. (2) 4.3 On what day of every month is Pierre getting paid? (2) 4.4 What is the name of the company Pierre is working for? (2) 4.5 Calculate A, his monthly salary. (2) 4.6 What percentage of his monthly salary is his contribution to the pension fund? (2) 4.7 Calculate B, his contribution to the UIF at 1% of his monthly salary. (2) 4.8 Calculate his taxable income. (3) 4.9 Calculate C, the monthly tax payable. (4) 4.10 Calculate D, the total deductions from his salary. (2) 4.11 Calculate E, his net monthly salary. (net salary = salary after all deductions) (2) 34

Question 5 Joy is a 52-year-old nurse who earns a salary of R286 500 per annum. She contributes 7% of her annual salary to a pension fund. She only has her 2 daughters listed as a dependents on her medical aid. She is concerned that the R4000 monthly income tax deduction is too much. Use the ANNEXURE A below to verify if this concern is warranted. (9) ANNEXURE A Rates of tax for individuals 2021 tax year (1 March 2020 - 28 February 2021) Taxable income (R) Rates of tax (R) 1 – 205 900 18% of taxable income 205 901 – 321 600 37 062 + 26% of taxable income above 205 900 321 601 – 445 100 67 144 + 31% of taxable income above 321 600 445 101 – 584 200 105 429 + 36% of taxable income above 445 100 584 201 – 744 800 155 505 + 39% of taxable income above 584 200 744 801 – 1 577 300 218 139 + 41% of taxable income above 744 800 1 577 301 and above 559 464 + 45% of taxable income above 1 577 300 Tax Rebate 2020/2021 2019/2020 2018/2019 Primary R14 958 R14 220 R14 067 Secondary (65 and older) R8 199 R7 794 R7 713 Tertiary (75 and older) R2 736 R2 601 R2 574 Tax Thresholds Age 2021 2020 2019 Under 65 R83 100 R79 000 R78 150 65 an older R128 650 R122 300 R121 000 75 and older R143 850 R136 750 R135 300 Monthly medical tax credits Main Member R319 First dependent R319 Each additional member R 215 35

Interest and Hire-purchase Objectives By the end of this section, learners must be able to: 1. Distinguish between “interest rate” values and “interest” values. 2. Investigate through calculation how interest values are calculated using interest rate values. 3. Perform simple and compound interest calculations manually. 5. Interpret and use tables showing compounded values. 6. Represent simple interest growth scenarios using linear graphs. 7. Represent compound interest growth scenarios using graphs showing compound change. 8. Investigate the following scenarios: 8.1 Hire-purchase agreement and loans (e.g. personal, car, house) where a repayment is made every month. 8.2 Other investments (e.g. retirement annuities, funeral plans) where a fixed deposit is made every month. SUMMARY Ø Interest is money paid regularly at a particular rate for the use or loan of money. • It can be paid to you by a financial organisation or bank (in case of savings); or • It may be payable by you to a financial organisation on money you borrowed from the organisation or invested at the organisation. Ø Interest rate is the percentage used to calculate the amount of interest that is charged from you or paid to you. Ø Interest value is the actual rand amount of interest that will be added to your loan or investment. In this section we are going to deal with the following type of interest: SIMPLE INTEREST COMPOUND 36

Simple interest Ø Simple interest is calculated only on the principal amount, and is the same each time Note: it is paid. Principal is the original amount of money initially invested or borrowed Calculating the amount of interest Ø If we know what the interest rate is, we can calculate the amount of interest quite simply. \ The amount of interest payable depends on the interest rate. Ø The lower the interest rate, the lesser the payment and, Ø The higher the interest rate, the more the payment. Worked example 1 Jan wants to buy a bicycle. He then borrowed R800 from his uncle and promised to pay it back in 3 months at a simple interest rate of 5%. 1.1 Write down the principal amount. 1.2 Determine the total amount Jan has to pay. Solutions 1.1 R800 1.2 Table illustration Month Principal Interest Total amount 1 R800 5 R800 + R40 ´ R800 100 = R840 =R40 2 R800 5 R840 + R40 ´ R800 100 = R880 =R40 3 R800 5 R880 + R40 ´ R800 100 = R920 =R40 Principal stays the same Interest also stays the same 37

Now that we have realised that the principal and interest stays the same, we can do the above solution this way: 5 Interest = ´ R800 100 =R40 Then total interest = R40 ´ 3 = R120 \ Total to be paid = R800 + R120 = R920 Calculating the interest rate Ø If you are given the final amount, then you follow these steps to find the interest rate: • Find the difference between the final amount and the original amount, this gives you the amount of interest. • Work out what percentage the amount of interest is of the principal amount. Worked example 2 Jan paid his uncle a total amount R920 after borrowing R800 to buy a bicycle. Determine the interest rate that was charged. Solution Total interest amount = R920 – R800 = R120 First calculate the total interest R120 Interest per month = 3 = R40 Then calculate the interest per month Interest amount \ interest rate = ´ 100 Principal amount R40 = ´ 100 R800 = 5% Lastly calculate the percentage of interest on the principal amount Representing simple interest Ø Simple interest will always be represented by a straight line graph, where interest represent a constant increase. 38

Worked example 3 The table below represents simple interest on R800 borrowed at 5% interest over a period of 3 months. Month Principal Interest Total amount 1 R800 5 R800 + R40 ´ R800 100 = R840 =R40 2 R800 5 R840 + R40 ´ R800 100 = R880 =R40 3 R800 5 R880 + R40 ´ R800 100 = R920 =R40 Draw a graph of the above information. Solution 940 920 900 Total amount 880 860 840 820 800 1 2 3 Number of years Simple interest graph will always be a straight line graph, where the constant increase of R40 represents the interest. 39

Compound interest Ø Unlike simple interest, Compound interest is calculated on the total/accumulated amount. Note: Ø Interest increases constantly. Total/Accumulated Ø It yields more interest over time than simple amount is the principal amount plus the interest. interest. Worked example 4 Jan wants to buy a bicycle. He then borrowed R800 from his uncle and promised to pay it back in 3 months at a compound interest rate of 5%. Determine the total amount Jan has to pay. Solution Table illustration Month Starting Interest Total amount amount 1 R800 5 R800 + R40 ´ R800 100 = R840 =R40 2 R840 5 R840 + R42 ´ R840 100 = R882 =R42 3 R882 5 R882 + R44,10 ´ R882 100 = R926,10 =R44,10 Starting amount Interest also increases increases Ø It is therefore safe to say that in compound interest, you also earn interest on interest. The above calculation can also be done this way: 1st month starting amount = R800 5 1st month interest = ´ R800 100 =R40 Total amount = R800 + R40 = R840 nd 2 month starting value = R840 40

5 2nd month interest = ´ R840 100 = R42 Total amount = R840 + R42 = R882 3rd month starting value = R882 5 3rd month interest = ´ R882 100 = R44,10 \ Total to be paid = R882 + R44,10 = R926,10 Ø In Mathematical Literacy, compound interest is calculated using the step by step method used above. Ø NO COMPOUND INTEREST FORMULA. Worked example 5 The table below represents compound interest on R800 borrowed at 5% interest over a period of 3 months. Month Starting Interest Total amount amount 1 R800 5 R800 + R40 ´ R800 100 = R840 =R40 2 R840 5 R840 + R42 ´ R840 100 = R882 =R42 3 R882 5 R882 + R44,10 ´ R882 100 = R926,10 =R44,10 Draw a graph of the above information. 41

Solution 1400 1300 1200 Total amount 1100 1000 900 800 1 2 3 4 5 6 7 8 9 10 Number of years Compound interest graph will not be a straight line graph, but an exponentially curved graph as the interest constant increases. In compound interest, interest can be compounded: Ø Daily Ø Monthly Ø Quarterly Ø Half yearly Ø Annually Hire Purchase Agreement Ø Most people don't have the cash up front to purchase items such as TVs, fridges, coaches etc., so they buy them on a hire purchase agreement. Ø A hire purchase agreement is therefore a financial agreement between the shop and the customer about how the customer will pay for the desired product. Ø The interest on a hire purchase loan is always charged at a simple interest rate and only charged on the amount owing. Ø Most agreements require that a deposit is paid before the product can be taken by the customer. Ø The principal amount of the loan is therefore the cash price minus the deposit. Ø The total loan amount is then divided into monthly payments over the period of the loan. Ø Payment period is usually 12, 24, 36, 48, 60, and 72 months 42

Worked example 6 Me Tsie decided to buy the following lawn-mower which was advertised as follows: BRILLIANT LAWN-MOWER ON SPECIAL Now only R 23 099 SAVE R900 Deposit: R2 300 Instalments: R975 x 36 months 2.1 Write down the special cash price of the lawn-mower. 2.2 Determine the price of the lawn-mower before the special. 2.3 What percentage of the original cash price is the SAVED amount? 2.4 Me Tsie decided to buy the lawn-mower on hire purchase. Calculate the total amount that she will pay for the lawn-mower. 2.5 Calculate how much Me Tsie would have saved, had she bought the lawn-mower cash. Solutions 2.1 R23 099 2.2 R23 099 + R900 = R23 999 2.3 R900 ´ 100 R23 999 =3,75 % 2.4 Total amount = Deposit + monthly instalment = R2 300 + (R975 × 36) = R2 300 + R35 100 = R37 400 2.5 Saving = R37 400 – R23 099 = R14 301 43

Practice Questions Question 1 Tumi has set aside R800 per month for the last two years. He then decided to invest this money in a bank in order to put down a deposit to buy a house. Tumi approached a bank that offered him 12,5 % p.a. simple interest for a period of 36 months. 1.1 Calculate the amount that Tumi will be able to invest in the bank, if he is going to invest the total amount he has set aside. (3) 1.2 Determine the interest he will earn from the bank. (4) 1.3 What is the total amount that he will receive at the end of the investment period? (2) Question 2 Tumi managed to find the house of his dreams, the price of the house was R549 000. He then applied for a home loan at the bank because he did not have the entire amount. Tumi decided to pay 11,5% deposit. 2.1 Calculate how much Tumi had to put down as a deposit for the house. (2) 2.2 If Tumi uses the money he received from the bank at the end of his investment term, will he have enough to pay for the deposit? Show by (3) means of calculations. 2.3 Tumi learns that he will have to pay a monthly instalment of R5 380 over a period of 20 years. 2.3.1 If the interest rate does not change, Show with calculations that the total amount paid, including the deposit will be R1 354 335. (3) 2.3.2 How much more money would Tumi have paid by the end of the 20 years? (2) 2.3.3 Calculate the percentage interest that Tumi would have paid by the end of 20 years if the monthly instalment did not change. Round your answer off to one decimal place. (3) 44

Question 3 Study the advert below and then answer the questions that follow. Months InterestVehicle Deposit *Residual Monthly Total rate Price instalments Payment 60 10,5% R221 11% R99 218 R2 991 R303 007,80 180 *Residual is an amount that must be paid at the end of the term after all the monthly payments have been made. 3.1 What is the cash price of the NISSAN NP 300? (2) 3.2 If a person decide to pay for the vehicle in instalments, determine the number of years (2) it will take to pay for the vehicle. 3.3 Calculate the amount of the deposit needed. (3) 3.4 Show by means of calculations how the Total Payment of R303 007,80 was calculated. (3) 3.5 How much will the person paying cash save compared to the person paying in (2) instalments? 3.6 What method of payment is the best value for money? Explain. (3) Question 4 Mr Moleko has two options for borrowing money: • His uncle has offered to loan him R16 000 for five years at 18% per annum, simple interest. • His bank will offer him a personal loan of R16 000 for five years at 16% compound interest per annum. Showing all calculation, determine the option that will be best for Mr Moleko. (10) 45

Question 5 Mrs. Mhlaba is planning on doing a baking course and therefore decided to buy a food processor.While browsing the internet, she came across the following special promotion: Kenwood-Titanium Chef Food Processor Was: R7 139,99 Special price now: R6 499,00 Mrs. Mhlaba doesn’t have enough cash to pay for the Kenwood – Titanium Chef food processor.She then decided to buy it on a hire-purchase agreement deal. The hire-purchase deal entails the following: • 15% deposit • 18,5% annual simple interest rate on the remaining balance • 3 years to repay 5.1 Define the term hire-purchase. (2) 5.2 Calculate the discount amount on the Kenwood Titanium Chef. (2) 5.3 Mrs Mhlaba paid R974,85 as a deposit on the food processor. Show how the deposit (2) was calculated. 5.4 Identify the interest rate charged on the financed amount. (2) 5.5 Calculate the amount payable after three years, excluding the deposit. (5) Income and Expenses; Profit and Loss Objectives: At the end of this section, you should be able to: 1. Identify and perform calculations involving income and expenses, profit and loss. 2. Identify and work with fixed and variable expenses for businesses and personal use. 3. Analyse income and expense statements 4. Identify costs involved with manufacturing or producing an item 5. Draw graphs on the same set of axes in order to do a break even analysis. 46

Summary: Income and Expenses: Income is exactly as the word states, money that comes in, while expenses is money that leaves an account or business. Income and expense statements allow us to keep track of our finances. This shows exactly how much money comes into or leaves your business or account. Fixed and Variable Expenses Profit/Loss Fixed and Variable Income Fixed vs Variable Expenses/Income Fixed vs Variable Expenses: Those expenses that do not change are called fixed, while those who change are called variable. Eg. Rent or salaries could be fixed for a business while insurance or car instalments could be fixed for an individual. Fixed vs variable Income: Fixed income is income that is constant, while variable income can change monthly. 47

Budget vs Income and Expense Statement Budget is a list of expected income and expenses while a statement lists the actual income and expenses. NB: Profit /Loss = Income - Expenses 9:#;(& Profit Margin = <%)#"= × 455 A quotation can be given for any goods or services to be delivered in the future. A quotation always has certain conditions which apply and is only valid for a certain period of time. An invoice is issued after work has been done/article(s) is/are sold/services were delivered. The invoice specifies the amount that the consumer has to pay the service provider. What to do when given Income and Expenditure Statement. Worked example 1 Cally is the owner of Cally’s Corner Shop. She pays rent monthly and draws her own salary. She has three people working for her. One in the deli, one in the bakery and one cleaner. The income and expenditure statement for Cally’s Corner Shop is shown on the table below. (All values given are in rand) Source: adapted from www.eclassroom.co.za 48

Use the information on the previous page to answer the questions that follow. 1.1 Show how the total income for March was calculated 1.2 Show how the net profit for February was calculated. 1.3 Calculate the profit made from General sales over the three-month period? 1.4 The property owner has decided to increase rental by 9,8 %. Calculate the new rental amount for the store each month. 1.5 Cally, the owner of the shop, wants to increase his advertising budget by R300 in May. Calculate the new total as a percentage of the total expenses for April 1.6 Is the amount of money spent on advertising every month justifiable? Suggest a reason for your answer. 1.7 Suggest an example of what may be included in ‘Maintenance’ expenses. 1.8 Calculate the percentage increase in profit from February to April 1.9 Which expenses decreased from February to March? 1.10 How can Freddy use this income and expense statement to budget his expenses for May? Worked example 2 The following is the income and expenditure statement for Ally’s Boutique for a specific month: EXPENDITURE INCOME OPERATING COSTS PRODUCTION COST Rental R5 000,00 Fabric used R25 000,00 Dresses made R60 000,00 Electricity R450,00 Other R10 000,00 material used Water R120,00 Fittings R3 850,00 Telephone R900,00 Seamstress E and internet wage Total R6470 Total R42 550 Total F Source: adapted from grade 12 Math Lit revision workbook Use the information above to answer the questions that follow. 2.1 Calculate the value of E. 2,2 Calculate the value of F. 2.3 Provide two fixed costs for the business 2.4 What percentage is the fabric used of the production cost? 2.5 Did Ally make a profit or a loss during this month? Verify your answer showing all calculations. 2.6 A supplier offers Ally fabric that is 10% cheaper than her current supplier. In addition to this the supplier also offers her 5% discount. What would she pay for fabric if she decided to make use the new supplier’s offer? 49

Solutions 1.1 R9678 + R7854 + R12976 = R30 508 1.2 Profit = R29586 –R23965 = R5621 1.3 GSI: R13450 + R12976 + R 13450 = R39876 GSE: R4989 + R4125 + R 5055 = R14169 Thus: R 39876 – R 14169 = R25 707 1.4 R4000 × 1,098 = R4392 1.5 R1300 × 100 = 4,8% R26920 1.6 Yes, there could be several other stores in competition with her. OR No her sales have increase and she is making a profit already 1.7 Equipment repairs; cleaning or general fixing or painting of structure 1.8 7856 − 5621 × 100 = 39,76% 5621 1.9 General good; electricity; water 1.10 She can make decisions around the performance for the next month based on the trends she noticed over the last three months. Question 2 2.1 R42550 – R 25 000 – R 10 000 =R 7550 2.2 R60 000 + R3850 = R 63850 2.3 Rental; Seamstress wage 2.4 R25 000 × 100 = 58,75% R42550 2.5 Profit = R63850 – (R42550 + 6470) = R 14830 2.6 $25 000 × 0,1 = $2500 $25 000 − $2500 = $ 22 500 Discount: $22 500 × 0,05 = $1125 New Price: $22 500 − $1125 = $21 375 50

Practice Questions Question 1 Study Layla’s Delicious Sea Food business budget given below and answer the questions that follow: DELICIOUS SEA FOOD Budget for the year ending 29 February 2021 Income Expenditure Income from sales: R385 000 Fixed expenses: Rent R 25 000 Salaries R A Repayment (Delivery scooter) R 9 500 Variable Expenses: Electricity & water R 8 200 Consumables R 120 000 Total Income: R385 000 Total Expenditure: R327 700 Source: adapted from grade 12 Math Lit revision workbook 1.1 Assist Layla to complete the budget and calculate the profit or loss. 1.2 The business had a profit of R28 000 during the previous year. Layla has a partner with whom she shares the profit in the ratio 3:1, where the biggest share goes to Layla. Calculate each partner’s share of the profit of R28 000. 1.3 Their rent for the next year will increase by 7,5%. What will their total rent be for the following year? 1.4 Calculate the value of A? 1.5 13.5% of their total salaries bill is usually paid to casual delivery personnel. Calculate the average monthly amount paid out to casual workers. 51

Question 2 The table below shows the summary of Income and Expenses statement with notes of the South African National Blood Service (SANBS) for the financial year ending 31 March 2016. Some of the amounts have been omitted. source: adapted from SANBS annual report Use the table and he information above to answer the questions that follow: 2.1 Communication costs decreased by 4,402% from 2015 to 2016. Calculate, to the nearest thousand rand, the communication costs for 2016. (4) 2.2 The SANBS expects a 17,5% increase in the costs of its product testing materials and consumables. Explain what possible impact this could have on their profit for the year. (2) 2.3 Compare, showing all calculations, the 2015 and 2016 percentage profit for the SANBS. (5) Question 3 52

Callan invites Lauren to Shezam Cinema to watch a 3D Movie. The table below shows the pricelist at the cinema. He decides to go on Friday and buys two large cooldrinks and two boxes of popcorn. Shezam Cinema Prices Cooldrink prices Ticket 2D Movie 3D Movie Small R15 250ml Normal R50 R75 Medium R20 340ml Budget R25 R35 Large R25 500ml Tuesday Combo deal on Tuesday: 1 popcorn + 1 large cooldrink for R40 3.1 If the popcorn costs R15 each. Calculate the total amount that David paid. Use the formula: Costs = Cost of movie tickets + Cost of cooldrinks+ Cost of popcorn. (3) 3.2 Calculate the amount that David would save if he went on Tuesday and got the Tuesday combo deal. Use the formula: Savings = Cost of Friday – (Cost of movies + Tuesday Refreshments) (3) 3.3 Which size cooldrink is the most value for money in your opinion? (2) 3.4 Provide a reason why the budget deal is on a Tuesday? (2) 53

Cost and Selling Price; Break Even Analysis Cost and Selling Price Adjust Income and strategy Expenses Profit and Break even Loss Analysis In order for a business to show a profit, the Income needs to exceed the expenses. For this to happen, the owner needs to know how much to sell the goods for. For this we need to set up equations that can help us project how the business will perform What are equations and how are they used? A business can use formula/equations, tables and graphs to determine profit or loss. An equation is a mathematical expression that shows the relationship between two items. It contains letters (variables) and an equal sign ¶ Variables − a variable is a symbol or letter used to describe the relationship being represented by the equation. Variables do not have a fixed value and their value can vary or change. ¶ The equal sign shows how the variables and/or numbers are related to each other. Variables can be dependent or independent ¶ The value of the dependent variable is dependent on the value of other variables. ¶ The independent variable(s) is a variable whose value is not dependent on the value of any other variable. 54

Finding the Break Even Point Follow these steps when doing break-even point questions: Formulate Draw Summarise equations Complete graphs Analyse the the for Cost the table using the graph situation and table Income ¶ When you run a small business, you must be able to calculate the number of items you need to sell in order to make a profit. ¶ Two graphs are drawn on the same grid, the point where these two lines intersect is called the BREAK-EVEN POINT. ¶ You must be able to read the profit or loss from the graph Break-Even Analysis Model VARIABLE COST source:https://www.freepik.com/free-vector/break-even-point-graph_4489537.htm 55

Break-Even Analysis Model Application: Skills: Find the number of units? You must be able to draw a graph; read information off Show changes over time the graph, explain what each Find break even point area means Break Even Analysis: Break even : when income = expenses Profit: above break even point Loss below break even point Cost per unit= Total Costs divided by no. of items Worked examples Example 1 Maddy’s needs to know how her new business is performing. She has set up a pop-up hamburger stall outside the mall. She has a fixed cost of R500 per month for the stall. The cost price of the ingredients is R10 per hamburger. She sells the hamburgers for R25 each. The table below shows her income and expenses for the sale of the hamburgers. Use the information above, as well as the table to answer the questions that follow: Number of hamburgers made 0 10 20 40 50 C Cost (in rand) 500 600 700 A 1000 1250 Income (in rand) 0 250 B 1000 1250 1875 STEP 1: Finding the costs and determining the income Solution: Your first equation will be constructed based on the Total Expenses for the hamburgers. • Expenses: Fixed Cost = R500.00 Variable Cost = R10.00 X no. made (Use N as the variable) Total Costs (TC)= Fixed cost + Variable costs TC= R 500 + (R10 x N) The second equation will be constructed based on the Total Income of the hamburgers. Income = R25 x number sold (Use N as the variable) I = R25 x N 56

STEP 2: Using a table A table is a useful way of summarizing information. Use the table below and the equations to answer the following questions. Number of hamburgers made 0 10 20 40 50 C Cost (in rand) 500 600 700 A 1000 1250 Income (in rand) 0 250 B 1000 1250 1875 1. Use the following equation to calculate the value of A TC = R 500 + (R10 x H) 2. Use the following equation to calculate the value of B I = R25 x N 3. Use the Income equation to determine C, the number of hamburgers that are made. Income = R25 x N R1875 = 25 X N >25?4 Thus N = 74 = 75 Hamburgers Step 3: Drawing a Graph We can now plot these values on a set of axes to give two graphs − one to represent the income and the other for the total costs. 4. Draw a graph indicating the income and expenses for Maddy’s hamburgers sales. 57

Solution: Income & Expenditure for Maddy's Hamburgers 1400 1200 1000 Amount in Rands 800 600 400 200 0 0 10 20 30 40 50 No. of hamburgers Income Expenses Step 3: Analysis of the Graph 5. Determine what the total cost would be if Maddy sold 45 hamburgers for the month. 6. Calculate the total income if Maddy sold 45 hamburgers. 7. Verify with the necessary calculations that Maddy has made a profit of R175 if he sold 45 hamburgers a month. 8. Use the graph to determine how many burgers she would have to sell to cover her expenses? 9. What do we call this point? Solutions: 6. Costs/Expenses = R 500 + (R10 x H) = R500 + (R10 x 45 ) = R 950 7. Income = R25 x 45 = R1125 8. Profit = Income – Expenses = R1125 -950 = R175 Therefore it is correct. 9. Approximately 33 hamburgers 10. Break Even Point. LOOK OUT for questions which ask,” how many products must be sold to start showing a profit.” The answer is NOT the break-even point, but 58 actually the first integer AFTER the break-even point.

Worked example 2 (Using real life examples to make decisions) Let us consider the school approaching a printing company to lease new photocopier machines. The invoice below shows the costs involved for three different contracts with a particular company. DRAFTWORX Photocopier Suppliers Tel: 011 7567 536 26 Lances Lane, Florida, 7576 26 January 2021 Quote valid for 14 days Proposed Rental Options Description Contract 1 Contract 2 Contract 3 Machine XP 121 XP 122 XP 123 Monthly Rental R500 R650 R1050 Per page fee 35c 25c 10c Allocation of free copies 0 500 1000 Adapted from: Via Africa Mathematical Literacy 2.1 Provide equations for the cost involved with renting from each of the companies above. 59

Solution: Setting up the equations for the costs involved Contract 1: Has a Fixed monthly fee and a further 35c per page. Thus, Costs= R500 + R0.35 X every page copied(P) Contract 2: Has a fixed charge of R650 per month, but only starts charging for prints after 500 free pages have been copied. Thus, Costs = R650 + 25c X (number of pages above 500) = R650 + 25c X (number of pages copies – 500) Fixed Costs Tariff Variable Amount. for Contract 2 for Contract 2 You only start paying after 500 copies so we need to subtract Contract 3: Has fixed cost of R1050 and only charges after 1000 copies Thus, Costs = R1050 + 10c X (every page above 1000) = R1050 + 10c X (number of pages copied – 1000) Using these formulae we can complete the following table: 2.2 Complete the table below using the equations above. Solution: Complete a table to analyse the data In the following example shows the data for various photocopier contracts Always try to First Charging point Charging point include this value to after 500 free after 1000 free copies ground the graphs copies 0 100 200 400 500 501 1000 1001 3500 Copie s R500 R535 R570 R640 R675 R675,3 R850 R850,35 R1750 Contract 1 5 R650 R650 R650 R650 R650 R650,2 R775 R775,25 R1400 Contract 2 5 R1050 R1050 R1050 R1050 R1050 R1050 R1050 R1050,1 R1300 Contract 3 0 60

Notice that the table includes 501 and 1001 copies. On contract 2 the page fee only applies for more than 500 copies (i.e 501 and more). So the cost on this contract will change after 500 copies. A similar situation happens on contract 3 when there are more than 1000 copies (i.e. 1001 or more) No look again at the invoice presented by the company. NOTICE how IMPORTANT it is to complete an analysis of the costs involved before you choose a contract? 2.3 Draw a graph to illustrate the three different contracts. Solution: Draw a graph to give you a visual idea of what is happening Camparison of 3 Contracts Crossing point 1800 for contract 1&3 1600 1400 1200 Cost in Rand 1000 Crossing point for 800 contract 2 & 3 600 400 200 0 0 100 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 Number of copies Contract 1 Contract 2 Contract 3 Source: adapted from Via Africa grade 12 61

2.4 Analyse the graph and provide the school with a recommendation as to which option would be best. Now to Interpret the data •The graph starts at R500 on the vertical axis, Contract representing the fixed cost of rental 1 •The increase is constant since the amount increases with a constant tariff •The graph starts at R650,00 on the vertical axis, indicating the fixed monthly rental fee. Contract •The graph stays horizontal up to 500 copies since the first 2 500 copies are free. •The graph then increases sharply as you are now charged another 25 c per page. •The graph starts at R1050 on the vertical axis. This is the monthly rental fee. Contract •The graph is a horizontal up to 1000 copies since the first 3 1000 are free •The graph then increases sharply as you are now chargedanother 10c per page Now you are ready to make a decision based on the above information Region 1 Region 2 Region 3 From 0 – about 430 From 430 to 2850 Any amount of copies pages contract 1 is the copies contract 2 is the above 2850 Contract 3 cheapest cheapest will be best Solution: Thus if the school makes more than 3500 copies in a month, contract 3 would be cheaper, even though it is more expensive initially. However, if the contracy was for home use where between 400 and 3000 copies were made a month, contract 2 would be best. 62

Practice Questions Question 1 Tally High School tuckshop sells pears during lunch to raise funds for a sports tour. They bought a crate of 250 pears for R255,00. They sold them at R3.00 each. 1.1 Explain what is meant by Break-even point? (2) 1.2 Calculate the cost price for one pear. Round your answer up to nearest 10 cents. (3) 1.3 The Selling Price for one pear is R 3,00. Explain the meaning of the term Selling Price in the (2) given context. 1.4 Calculate the profit they made, if 250 pears were sold (3) 1.5 They normally sell 120 pears per day: 1.5.1 Calculate the income for that day (2) 1.5.1 How many days did they take to raise an amount of R14 400,00 for the function? (2) Question 2 Shelly manufactures (makes) cute bags in her spare time. She decides to sell her product at the Willow Dam Sunday Market. To rent a stall (space) at the market costs R 80,00 per day. The production costs of a bag is R75,00. Shelly wants to sell her bags at R100,00 each. 2.1 What is Shelley’s selling price for one bag? (2) 2.2 What is Shelly’s cost price for one bag? (2) 2.3 Identify Shelly’s fixed costs . (2) 2.4 Complete the following tables for INCOME and COSTS for Shelley’s business: Expenses: No. of Bags 0 1 5 10 20 Costs A 155 B 830 1580 Income: No. of Bags 0 1 D 10 20 Income C 100 500 1000 2000 (4) 63

2.5 Use the information provided in the tables to draw line graphs for (6) COSTS and INCOME on the set of axes provided below. Label your graphs appropriately. 2.6 What is the point of intersection of the graphs called? (2) 2.7 Explain what is meant by this point of intersection. (2) 2.8 How many bags must Shelly sell to start showing a profit? (2) 2.9 Calculate the amount of profit on 17 bags. Show all your calculations. (3) Income and expenses for Shelley's Bags 3500 3000 2500 Money in Rand 2000 1500 1000 500 0 0 5 10 15 20 25 30 Number of bags sold 64

Question 3 Mary intends selling cups of coffee at the local taxi rank for extra money. She has organised to set up her stall at R40 per day and her travelling costs are R14,20 per day. Mary decided to exclude the cost of water when calculating the cost price per cup of Coffee. The table below shows how Mary calculated the cost price of ONE cup of Coffee. QUANTITY BOUGHT COST OF AMOUNT USED FOR COST PER CUP OF INGREDIENTS ONE CUP COFFEE 1 kg Coffee R97,95 0,04 kg A 1 ℓ milk R11,99 B R1,20 2,5 kg sugar R33,20 0,01 kg R0,13 25 foam cups R1.78 ONE R1,78 50 spoons R12,75 ONE R0,26 TOTAL COST C 3.1 Explain the meaning of the word cost price. (2) 3.2 Now calculate the values A, B and C. (6) 3.3 Determine the selling price of one cup of coffee if she wants to have a profit margin (3) of 25% 3.4 Determine Mary’s fixed costs per day (3) 3.5 Provide an equation for the expenses of selling coffee per day (3) 3.6 Mary decides to sell the coffee at R10,00 per cup. Her income and expenses graphs are provided below. Use the graphs to answer the questions that follow: 1200 Mary's Income and Expenses 1000 A 800 Money in Rand B 600 400 C 200 0 0 20 40 60 80 100 120 No. of cups sold 65

Use the information on the previous page to answer the questions that follow. 3.6.1 Provide the labels for graph A and B and point C (3) 3.6.2 Explain the value given by C in this context. (2) 3.6.3 Approximately how much profit is made when she sells 50 cups of coffee? (4) 3.6.4 Explain whether you believe that Mary should continue with the business if she is able to sell (3) at least 40 cups a day? Question 4 Lester rents a hall on the private farm at a fixed cost of R3600 per function. He then hires out the hall and charges R50 per person (per ticket). Number of tickets sold 0 10 D 100 Amount received 0 500 2500 5000 (Income) Use the table and the information above to answer the questions that follow: 4.1 Calculate the value of D. (2) 4.2 Determine the cost that Lester will have to pay if the hall is rented out to 120 people. (2) 4.3 The income graph has been drawn on the annexure below. Draw the cost graph for renting the (3) hall on the same set of axes. 4.4 Use your graph, or otherwise, to determine the difference between the income and costs for (3) renting the hall for a function for 60 people. Indicate whether it is profit or loss. 4.5 Explain the meaning of break even in this context. (2) 4.6 The cost for renting the hall is VAT inclusive (at 15%). Calculate the amount of VAT. (3) 66

Question 5 Meikhe and his friends plan a tour across South Africa. The tour is set to stretch from Port Elizabeth down the Garden route to Cape Town. They investigate the rates for GoGo Car hire and eNIGMA Car Rental. The distance from Port Elizabeth to George is 335km and from George to Cape Town is 434km. TABLE 1. FEES FOR CAR RENTAL COMPANIES eNIGMA CAR RENTAL BOOKING DEPOSIT None R2000 FREE KILOMETERS None First 350km TARIFF R3,50 PER KM R1,50 Use the tables above to answer the questions that follow. 5.1 Provide equations for the cost for both options. (4) 5.2 Show, by calculation, which option would be the best rental for the boys to tour with? (5) 5.3 The table below gives the cost for the two rental options. Provide the values for A and B. COMPANY O km 50km 100km B km 1000km 2000km GOGO CAR HIRE 0 175 375 1400 3500 7000 ENIGMA CAR A 2000 2000 2075 2975 4475 HIRE (4) 5.4 Use the table to complete the graphs for both companies on the same set of axes (5) 5.5 Provide the amount of kilometers you could travel when both companies cost the same. (2) 5.6 With the aid of your graph, explain which company you would recommend if the boys decide (3) to go to George instead? 67

COMPARISON OF TWO RENTAL COMPANIES 8000 7000 6000 5000 MONEY (IN RAND) 4000 3000 2000 1000 0 0 500 1000 1500 2000 2500 NO OF KILOMETERS GOGO ENIGMA 68

3.2 SOLUTIONS TO PRACTICE QUESTIONS 3.2.1 Tariffs Q Solution Explanation T/L 1.1 2 PMA PMA 1MA multiplying 50 by the correct rate Amount = (50 x R0,76) + (200 xR0,97) 1MA multiplying 200 by the correct rate = R38,00 + R194,00 1CA amount to be paid (3) = R232,00 PCA 1.2 Amount for January = 2 PMA PMA PMA 1MA multiplying 50 by the correct rate (50 x R0,76) + (300 x R0,97) + (1 x R1,16) 1MA multiplying 300 by the correct rate 1MA multiplying 1 by the correct rate = R38,00 + R291,00 + R1,16 1CA January payment = R330,16 PCA 1CA difference (5) Difference = R330,16 – R232,00 = R98,16 PCA PA 2.1 Basic Charge is a compulsory monthly amount that one 1A compulsory monthly amount 1 1A whether you use electricity or not. must pay whether you use electricity or not. (2) 2.2 PA 2 11 1MA calculating percentage × 17 PMA 100 1M adding values PM = 1,87 + 17 (No mark for R18,87 as it was given) (2) = R18,87 2.3 3 First 6kℓ x R7,46 = R44,46 PMA 1MA calculating cost for 6kℓ Next 9kℓ x R17,39 = R156,51 PMA 1MA calculating cost for 9kℓ \R44,46 + R15,51 = R200,97 1M calculating the difference PM Then R205,24 – 200,97 = R4,27 1M dividing by R18,87 PM Remaining kℓ = R4,27÷R18,87 = 0,23kℓ 1CA number of kℓ Kilolitres used = 6kℓ + 9kℓ + 0,23kℓ = 15,23 kℓ PCA (5) 2.4 PMA 2 133kℓ - 53,7kℓ 1MA subtracting correct values 1A amount of water used = 79,3kℓ PA (2) 69

Q Solution Explanation T/L 3.1 Total cost (in rands) = 2 1A fixed cost PA PA 1A variable cost 300 + (the number of persons - 15) x 50 (2) 3.2.1 2 PA 1A substituting total cost (900) 900 = 300 + (n – 15 persons) x 50 PM (n – 15 persons) x 50 = 600 1M subtracting 300 from 900 n – 15 persons = 12 PM 1M getting 12 n = 27 PCA 1CA number of passengers (4) 3.2.2 2 PA 1A group 1 Group 1 = 10 learners + 1 teacher Group 2 = 10 learners + 1 teacher PA Group 3 = 4 learners + 1 teacher 1A group 3 24 learners and 3 teachers 24:3 PM 1M ratio of learners to teachers 1CA ratio in the simplest form 8:1 PCA (4) 4.1 Total cost (in rands) = 1A R300 2 1A R0,50 × number of minutes more PA PA R300 + R0,50 × number of minutes more than 500 than 500 (2) 4.2 2 PMA Total cost = R300 + R0,50 x (510 - 500) 1MA subtracting minutes PM 1M multiplying by the tariff = R300 + R0,50 x 10 1M adding values 1CA total cost = R300 + R5,00 PM = R305,00 PCA (4) 4.3 CALL PACKAGE 1 PMA 4 Total cost = R150 + R0,50 x (300 - 100) 1MA subtracting minutes 1M multiplying by the tariff PM = R150 + R0,50 x 200 1M adding values 1CA total cost = R150 + R100,00 PM = R250,00 PCA CALL PACKAGE 2 Total cost = R300 + R0,50 x (0) = R300 + R0,00 1A total cost = R300,00 PA 1O conclusion (6) PO Call Package 1 will be cost effective 70

5.1 PA 3 From 7:30 of 06 Jan to 7:30 of 10 Jan it is four full days 1A 4 days / 48 hours From 7:30 to 09:15 it is 1 hour 45 minutes. PA Expect to pay = 100× d + R44 for part thereof 1A basic R100 = R100 × 4 + R44 = R444 PCA 1CA amount (3) 5.2.1 If stopping for a short time you pay much more than the 2O reason 4 amount due. PPO (2) 5.2.2 PSF 3 Open parking: R67 × d + R29 = R500,00 1SF substituting into correct formula 1A number of days d = 7,03 days PA 1A five days » 8 days 1A more than 5 days PA Shaded parking: 5 days = R500. PA (4) So, more than five days you win. 5.2.3 4 The cost escalates quickly. PPA 2O rate of increase. OR It is costing more after just 15 minutes than in any other type of parking. PPA (2) 71

3.2.2 Tax VAT Q Solution Explanation T/L 1.1 2 PMA 1MA multiply by 15% 24 1A Answer ABC: 233 × $79,99 = R12,00 PA (2) 1.2 PMA 1MA adding values 2 Final Price : $79,99 + $12 = $ 91,99 PA 1A Answer (2) 2 PMA 2 @28A43 1 MA divide by 1,15 2,24 = $12130,43 PA 1A Answer (2) 3.1 1MA divide by 1,15 2 >43 1CA Answer 2,24 PMA 1 CA VAT = R43,48 PCA (3) R50 – R43,48 = R 6,52 PCA 3.2 20 April 3 PRT PCMA 2 x R150 = R300 x 50% = R150 PRT 1RT correct tarrif 1x R50 = R50 x 50% = R25 PCMA 1CMA correct discounted amount 1RT correct tarrif 1 x R50 = R50 1CMA correct discounted amount 1 x R20 = R20 1M adding all values PM 1CA simplification Total: R150+R25+R50+R20 = R245 PCA 23 April 2 x R150 = R300 1 x R50 = R50 1 x R50 = R50 1 x R20 = R20 PM PCA 1M adding all values Total : R300 +R50+R50 +R20 = R420 1CA simplification R420 – R245 = R175 PCA 1CA difference 1MA dividing by 420 R175 1CA answer R420 PMA 1O Conclusion = 0,4167 PCA (12) PO A quarter is 0,25 thus the statement is correct. 3.3 Pensioners often live only on a pension or a grant, thus 2O Opinion 4 the discounts allow them to also enjoy some of the fruits (2) of their labour. PPO 72

Income Tax Q Solution Explanation T/L 1.1 All the money earned before deductions üüO 2O explanation 1 (2) 1.2 Mr KIVIDO üüA 2RT answer 1 (2) 1.3 M = Gross – Deductions 1 RT correct values 2 üM 1 M subtracting values üRT 1CA answer = R31 221,25 − R9 362,62 = R21858,63 üCA üM üRT N = R9 362,62 – (R4 736,90 + R2251,59 + R245,23 + R192,70 + 90,25) 1 RT correct values 1 M adding and subtracting values = R1 845,95 üCA 1CA answer (6) 1.4 1MA divide by correct values 2 >7 742,4A ü MA × 100% 1M multiply by 100 >83 372,74 PM 1CA percentage = 7,5% PCA (3) ü MA 1MA subtracting pension fund 2 üM 1.5 Taxable Income= (R31 221,25 – R1 151,59) X 12 1M multiply by 12 1CA answer = R360 835,92 PCA (3) 1.6 Tax Bracket: 63 853 + 31% of taxable income above 305 2RT correct bracket 2 850 üüRT (2) PMA 4 2.1 R 5 500 × 12 = R66 000 PA 1MA multiply by 12 1A simplification Threshold for tax year is R 79 000, thus she will not pay 1O conclusion tax PO (3) 2.2 The fixed value in the tax bracket is usually the maximum 4 amount of tax payable from the previous tax bracket. PM PRT Thus, 18% of R195 850 1RT R195 850 = 0,18 × R195 850 1M calculating 18% 1A simplification = R 35 253 PA (3) 73

Q Solution Explanation T/L 3.1 3 PMA 7,5 Pension = ⨉ 37 537,75 1MA calculating 7,5% 100 = R2 815,33125 ⨉ 12 PMA 1M multiply by12 = R33 783,98 PCA 1CA pension amount Donation = 575 ⨉ 12 PMA 1MA multiplying by 12 1A donation = R6 900 PA Total = R33 783,98 + R6 900 1CA total amount = R40 683,98 PCA (6) 3.2 CA from 3.1 2 PMA 1MA multiply by 12 Taxable income = (37 537,75 × 12) – R40 683,98 MCA subtract pension and = R450 453 – R40 683,98 PMCA donations 1CA taxable income = R409 769,02 PCA (3) 3.3 Tax payable = 63 853 + 31% of taxable income above 305 850 CA from 3.2 4 ü SF = 63 853 + 0,31 × (409 769,02 – 305 850) PRT 1RT correct tax bracket = 63 853 + 0,31 × 103 919,02 = 63 853 + 32 214,90 1SF amount above = R96 067,90 PCA 1CA simplification 1M subtract rebate = R96 067,90 – R14 220 PM 52 5B?,A3 PM 1M divide by 12 = 27 1CA monthly tax = R6 820,66 PCA Invalid OR less than R6 850 PO 1O conclusion (7) 3.4 They receive 3 rebates PPO 2O Explanation 4 OR Their total rebate is higher PPO (2) 8? 48?,?4 1MA divide by1,064 2 3.5 Gross monthly salary in 2018/2019 = 2,36B PMA 1CA simplification = R35 279,84 PCA OR 100 Gross monthly salary in 2018 = 37537,75 ´ PMA 1MA calculating percentage 106,4 1CA simplification (2) = R35 279,84 PA 74

Q Solution Explanation T/L 4.1 Tolken PPRT 2RT correct surname (2) 1 4.2 365 days PPRT 2RT Answer (2) 1 4.3 On the last day of the month PPRT 2RT Answer (2) 1 4.4 Expert systems PPRT 2RT Answer (2) 1 4.5 Monthly salary = R168 000 ÷ 12 PM 1MA divide by 12 2 = R14 000 PA 1A Answer (2) 4.6 Percentage contribution A CA from 4.5 2 1 050 = 14 000 x 100% 1M calculating percentage PM 1CA answer = 7,5% PCA (2) A 4.7 UIF contribution CA from 4.5 2 = 0,01 x R14 000 PM 1M calculating 1 % = R140 PCA 1CA Answer (2) 4.8 2 Monthly taxable income = R14 000 – R1050 PM 1M subtracting pension = R12 950 PCA 1CA answer Annual Taxable income = R12 950 × 12 =R155 400 PCA 1CA annual taxable income (3) 4.9 Annual tax payable 3 = 18% of R155 400 PRT 1RT Correct bracket = R27 972,60 PCA 1CA simplification = R27 972,60 – R14 958 1CA annual tax payable = R13 014 PCA 1CA monthly tax payable Monthly tax payable >28 32B = 27 = R1 084, 50 PCA (4) 4.10 Total deductions 1 = R1 050 + R140 + R1 084,50 PM 1M adding all values = R2 274,50 PCA 1 CA answer (2) 4.11 Net monthly salary 1 = R14 000 – R2 274,50 PM 1M subtracting values 1 CA Answer (2) = R11 725,50 PCA 75

Solution Explanation T/L 5 Joy: 4 Age:52; Salary: R286 500 per annum ; 7% pension; 1 dependent on Medical Aid Taxable income = Annual Income − Pension Pension = 0.07 × R 286 500 = R20 055 PA 1A correct pension amount PCA 1CA taxable Income Taxable income = R286 500 – R20 055 = R 266 445 PRT 1RT correct tax bracket Tax payable: R37062 + 26% × (R266 445 – R205 900) = R37 062 + 0,26 (R60 545) 1CA simplification = R52 803,70 PCA PM PM 1M subtract tax rebate Now: R52 803,70– (R14 958+(319×2+215) × 12) 1M subtract MTC 1CA simplification = R 27 609,70 PCA Monthly = R27 609,70 ÷ 12 1CA monthly tax = R2 300,81 PCA 1O conclusion Yes she is correct üO (9) 76

3.2.3 Interest and Hire-purchase Q Solution Explanation T/L 1.1 PM 1A calculating 24 months 1 R800 x 24 PA 1M multiplying by R800 1CA amount saved =R19 200 PMA (3) 1.2 2 12,5 PMA Interest per year = ´ R19 200 1MA calculating percentage 100 1A interest per year PA =R2 400 1A for 3 years PA Interest for 3 years = R2 400 x 3 CA total interest (4) =R7 200 PCA PM 1.3 2 R19 200 + R7 200 1M adding correct values 1CA total amount =R26 400 PCA (2) 2.1 1 11,5 PMA 1MA calculating percentage ´ R549 000 100 1A interest per year PA (2) =R63 135 2.2 Amount received from investment = R26 400 4 1M subtracting amounts Deposit needed = R63 135 1CA difference PM Difference = R63 135 – R26 400 1O explanation PCA (3) =R36 735 PO No, he will not have enough, he will run short of R36 735. 2.3.1 Number of months = 20 ´ 12 3 PA 1A number of months = 240 PMA PM 1MA multiplying instalment by months Total paid = (R5 380 x 240) + R63 135 1M adding the deposit =R1 354 335 (No mark here) (3) 2.3.2 PM 2 Difference = R1 354 335 – R549 000 1M subtracting amounts =R805 335 PM 1CA difference (2) 2.3.3 R1 354 335 - R549 000 1M calculating percentage 2 % interest = ´ 100 PM 1CA percentage R549 000 1R correct rounding = 146,6912568% PM (3) =146,7% PM 77

Q Solution Explanation T/L 3.1 1 R221 180 PPA 2A correct amount (2) 3.2 1 60 Number of years = PMA 1MA dividing 60 by 12 12 1A number of years = 5 years PA (2) 3.3 2 11 PA PM 1A correct percentage Deposit needed = ´ R221 180 1M multiplying by the amount 100 1CA deposit needed = R24 329,80 PCA (3) 3.4 3 Total payment = Deposit + monthly instalment + residual PMA = R24 329,80 + (R2991 x 60) + R99 218 1MA multiplying 2991 by 60 1M adding deposit amount PM PM 1M adding residual = R24 329,80 + R179 460 + R99 218 (3) = R303 007,80 (no mark here) 3.5 2 PMA 1MA subtracting correct values Saving = R303 007,80 – R221 180 1CA saving amount (2) = R81 827,80 PCA 3.6 4 1A method of payment Cash Payment. PA PPA 1O reason A customer will not have to pay 10,5% interest rate OR There will be no residual/balloon. (3) 78

Q Solution Explanation T/L 4 Uncles option 4 1MA calculating percentage 18 PMA 1A amount of interest Interest = ´ R16 000 ´ 5 100 1CA total amount = R14 400 PA Total amount = R16 000 + R14 400 = R30 400 PCA Personal loan option 1MA calculating percentage st 16 PMA 1 year interest = ´ R16 000 100 = R2 560 PCA 1CA 2nd year amount 2nd year amount = R16 000 + R2 560 = R18 560 16 2nd year interest = ´ R18 560 100 = R2 969,60 PCA rd 3 year amount = R18 560 + R2 969,60 = R21 529,60 1CA 3rd year amount 16 3rd year interest = ´ R21 529,60 100 = R3 444,74 th PCA 4 year amount = R21 529,60+ R3 444,74 = R24 974,34 1CA 4th year amount 16 4th year interest = ´ R24 974,34 100 = R3 995,89 PCA 5th year amount = R24 974,34 + R3 995,89 = R28 970,23 1CA 5th year amount 16 5th year interest = ´ R28 970,23 100 = R4 635,24 Total amount = R28 970,23 + R4 635,24 1CA total amount = R33 605,47 PCA 1O correct option The personal loan is be best PO (10) 79

Q Solution Explanation T/L 5.1 Hire purchase agreement is a financial agreement between the 2O explanation 1 shop and the customer about how the customer will pay for the desired product. PPO (2) 5.2 1 PMA 1MA subtracting correct values Discount = R7 139,99 – R6 499,00 1CA discount amount = R640,99 PCA (2) 5.3 2 1A correct percentage 15 PA PMA 1MA multiplying by correct amount Deposit = ´ R6 499,00 100 = R974,85 (No mark here) (2) 5.4 1 2A correct percentage 18,5% PPA 5.5 3 PM 1M subtracting amounts Balance after deposit = R6 499,00 – R974,85 = R5 524,15 PCA 1CA balance after deposit 18,5 PM Interest charged = ´ R5 524,15 ´ 3 1M calculating the interest 100 = R3 065,90 PCA 1CA interest Amount payable = R5 524,15 + R3 065,90 PCA 1CA amount payable = R8 590,05 (5) 80

3.2.4 Income and expenses; Profit and loss Q Solution Explanation T/L 1.1 1M subtraction 2 PM 1A answer P = R385 000 – R327700 = R 57 300 PA 1.2 Ratio is 3:1 3 1A correct Fraction 2PA PCA 1CA simplification Thus × R28 000 = R7 000 Partner B PCA 1 CA Layla’s portion 8 × R28 000 = R21 000 B OR Ratio is 3:1 2PA PCA Thus B × R28 000 = R7 000 Partner PCA R28 000 – R 7000 = R21 000 1.3 2 23?,4 PMA PA 1MA calculating a percentage × R25 000 = R26 875 233 1A answer 1.4 PM 2 A: R 327 700 – (R25 00 + 9 500 + 8 200 + 120 000) 1M adding and subtraction 1CA answer = R 165 000 PCA D 1.5 28,4 1M calculating a percentage 2 × R165 000 PM 233 1CA Answer = R22 275 PCA D 2.1 Decrease amount in thousands 3 = R 32 187 × D4,402% 1M % calculation PM 1CA decreased amount = R 1416, 871 PCA Communication costs in thousands 1M subtracting = R32 187 – R1416,87 1R rounding PM = R30 770,13 = R30 770 PR OR = R32187 000 – R1416870 = R30 770 000 2.2 Profits would possibly decrease if income does not change 2 O Explanation 4 drastically. PPO 81

2.3 For 2015: 1RT Correct values 4 PRT 1SF substitution Percentage profit = 8B7 48B × 100 PSF 1A percentage for 2015 7743 3B2 = $ 15,22345593% PA 1A Percentage for 2016 1O Comparison For 2016: 863642 Percentage Profit = 7B3843A × 100 = $ 15,00518617% PA The profits decrease slightly PO 3.1 1RT Correct values 2 PRT 1SF substitution Friday Costs = 2(R75) + 2(R15+ R25) PSF 1A Answer = R230 PA 3.2 1RT Correct values 2 PRT 1SF substitution Savings = R230 – 2(R35 + R40) PSF 1A Answer = R80 PA 3.3 2M Division 4 433 1A Opinion The large cooldrink 74 = 20ml/R PM The medium 8B3 = 17ml/ R PM 73 PO Thus large is best 3.4 Tuesdays are slow business days, thus they are trying to draw 2O Opinion 4 customers PPO 82

3.2.5 Cost and selling price; Break-even analysis. Q Solution Explanation T/L 1.1 Break-even is when the expense is equal to the income received. 2A Explanation 1 There is no profit and no loss. PüM (2) 1.2 Cost price for one pear 1MA Divide by 250 2 = (255 ÷ 250) 1A Answer üMA = R 1,02 1R Rounding üA = R 1,10 üR (3) 1.3 The selling price is the amount that the customer is paying for the 2A Definition 1 item/product. üüA (2) 1.4 Profit 1SF Profit 2 = (R 3,00 × 250 pears) - R 255,00 üSF 1S Simplification = R 750,00 - R 255,00 1A answer üS = R 495,00 (3) üA 1.5.1 Income 1MA Multiply by R3,00 2 = 120 apples × R 3,00 üMA 1A Answer = R 360,00 üA (2) 1.5.2 Number of days 1A Numerator 2 1A Denominator üA = R 14 400,00 ÷ R 360,00 üA 1A Answer = 40 days üA (3) 83

Q Solution Explanation T/L 2.1 Selling price 2 RT 1 (2) = R 100,00 per bag üüA 2.2 Cost price 2MA Adding fixed costs 1 üüMA (2) = R 75,00 2.3 Fixed Costs = Rent at R 80,00 2 RT 1 üüA (2) 2.4 A. Cost for 0 bags 1SF Substit. 0 2 1A answer = R 80,00 + (R 75,00 × 0) üSF = R 80,00 (2) üA B. Cost for 5 bags 2 1SF Substit correct values = R 80,00 + (R75,00 × 5) üSF 1A answer = R 455,00 üA (2) C. Income for 0 bags 2 = R 100,00 × 0 = R 0,00 üüRT 2RT T (2) D. Number of bags 1SF Correct values 2 @433 1A Answer = @233 üSF (2) = 5FGHI üA 2.5 2A Labels for cost 2 Income and Expenses for Shelley's and income 1A starting value of Bags üA costs 1 A Any other 3500 correct value 3000 income costs Money in Rand 2500 üA Any 2 values for 2 Income 2000 üA (6) 1500 üA costs 1000 üA 500 üA 0 0 5 10 15 20 25 30 Number of bags sold Costs Income 2.6 Break-even point üüRG 2 RG (2) 2 2.7 The number of bags she needs to sell to cover her expensesüüEG 2 E Explanation (2) 1 2.8 Approximately 4 bags 2RT (2) 2 üüRT 84

Q Solution Explanation T/L 2.9 Profit = Income – Expenses üA 1A Profit equation 3 üSF üSF Profit = (R100,00 × 17) – (R80,00 + (R75,00 × 17) 1SF Income Profit = R 1 700,00 – R 1 355,00 1SF Costs 1CA Answer Profit = R 345,00 üCA (4) 3.1 Cost price of an item is the cost of making that item/ OR/OF 2A Explanation 1 This is the amount that it costs per unit to either manufacture, purchase the item or to prepare for a service that will be delivered. This amount is pure cost, no markup or profit added yet üüA (2) G 3.2 A: 1M division 2 üM @A?,A4 1A Answer A: ×4 2333 B: 1M Division = $3,92 üA 1 A Answer @22,AA üM C: 1 Addition of correct B: @2,73 = 9,99JK LM 10JK üA values 1CA Answer C: R3,92 + R 1,20 + R0,13 + R1,78 + R0,26 üA = R7,29 üCA (6) 3.3 74 1M 25% of R7,29 only 2 Cost = R7,29 × 233 üM 1M adding = R1,83 + R7,29 1CA simplification üM 1R rounding = R9,11 üCA Accept R9,15 and R9,20 = R9,15 OR R9,20 üR (4) 3.4 Fixed Costs = R40 + R14,20 üA 1 A Correct values 2 1CA Answer = R54,20 üCA (2) 3.5 1SF Fixed cost 2 üSF üSF 1SF Variable costs Cost = R54,20 + R7,29 × NL. LP QRSI (2) 3.6.1 A= Income 1A per label 2 üA (3) B = Costs/Expenses üA C= Break even point üA 3.6.2 The number of cups she needs to sell to cover her costs üüA 2A answer 1 (2) 3.6.3 For 50 cups: 1RT correct values 2 1M subtraction Profit = Income – expenses 1 CA Answer üRT üM = R500 – R418,70 = R81,30 üCA (3) 4 üO üO 1O conclusion 3.6.4 Yes, she will make a profit if she sells more than 20 cups per day. 1 O justification (2) 85

Question 4 Q Solution Explanation T/L 4.1 1MA Division by correct values 2 üMA 1CA (2) 7433 D = 43 = 50 TUQVWTI üCA 4.2 R3600 2 Reading from information. 1 üüA 4.3 1A plotting Cost 2 2 Any two points for cost Hall Rental Income and expenses 1 A Graph 12000 1A starting point Hiring 10000 Money in Rand 8000 6000 4000 2000 (5) 0 0 50 100 150 200 No. of people Rental Hire Out 4.4 üMA 4 1MA subtracting correct values Difference = R3000 - R3600 1A Answer = - R 600 üA 1O Conclusion It is a loss üO (2) 1 4.5 2O explanation When the income from the number of tickets sold is equal to the cost of renting the hall. üüA (2) 4.6 1MA divide by 1,15 3 üMA 1 CA Answer @8633 = $3130,43 1 MCA subtraction 2,24 üCA 1CA Answer üMCA (4) R3600 – 3130,43 = R469,57 üCA 86

Question 5 Q Solution Explanation T/L 5.1 3 üSF üMA 1SF correct Fixed cost Enigma: Cost = R2000 + R1,50 X (distance -350) 1MA variable cost GoGo: Cost = R3,50 X distance üMA 1MA equation (3) 5.2 Distance: 769km 3 üSF Enigma: R2000 + R1,50 X (769km – 350km) 1SF correct values = R 2628 üA 1A answer GoGo = R3,50 X 769 = R 2961,50 üCA 1CA answer ∴ Enigma is the best option üO 1O conclusion (4) 5.3 A: R2000üA 1A Fixed Costs 2 B: 8,4 üMA 2 B33 = 400km üA 1MA Division by 3,5 1A Answer (3) 5.4 2 1M Starting point for Enigma COMPARISON OF TWO RENTAL COMPANIES 2 Any two points 8000 2 Any two points for GoGo 7000 MONEY (IN RAND) 6000 1 A Graph is a straight line 5000 4000 3000 2000 1000 0 0 500 1000 1500 2000 2500 NO OF KILOMETERS GOGO ENIGMA (6) 5.5 2RT 2 üüRT approximately 750 km (2) 5.6 George Distance = 335 km üRT 1RT distance 4 2 O opinion Thus GoGo is cheaper as the graph is lower üüO NOTE: Even though you are given free km, the fixed cost for Enigma is still R2 000 (3) 87

4. EXAMINATION GUIDANCE PAPER 1 Weighting Finance 60% (±5) oftopics Data Handling 35% (±5) Probability 5% Including Growth Charts (CAPS page 65) assesses application of measures of spread in data handling. Structure and Question 1:30 marks ± 5 marks scope of Level 1 questions from Finance and contentand/or Data Handling skills Question 2 Finance Question 3 Data Handling Question 4 Integrated context on Finance and Data Handling Including Growth Charts (CAPS page 65) assesses application of measures of spread in data handling. WEIHTING Question 5 Finance, data handling or integrated question Probability will be examined in thecontext of one or more of the other questions. Each question can contain more than one context. N.B Each paper may have 4 or 5 questions Topics % 150 marks Taxonomy levels Finance 60% 90 Level 1: Knowing 30% (±45 marks) Data 35% 53 Level 2: Applying routine proceduresin 30% (±45 marks) handling familiar contexts PAPER 1 Probability 5% 7 Level 3: Applying multi-step procedures 20% (±30 marks) in a variety of contexts 100% 150 marks Level 4: Reasoning and reflecting 20% (±30 marks) 88

Time and mark allocation Paper 1 Duration Marks 3 hours 150 Marks Time management for Examination preparation: If you have 100 hours to prepare for the examination, the following can be used as a guide on how to use your hours: Application Topics Number of hours Finance 60 Data handling 35 Probability 5 Order of the questions in the question paper Each paper may have 4 or 5 questions. Paper 1: QUESTION 1 (30 marks ± 5 marks ONLY taxonomy Level 1.) Short context – mixed questions(Finance and Data Handling.) QUESTION 2 – Finance QUESTION 3 – Data Handling QUESTION 4 – Finance and Data Handling QUESTION 5 – Finance, Data Handling or integrated Probability will be integrated in all five questions, where it is appropriate. GUIDANCE Set a goal (marks you would like to see on your Matric Certificate) at the beginning of the term, If for example your aim is to achieve 60% for Mathematical Literacy. One way of getting it is as follows: Paper 1: 90 marks out of a possible 150 Paper 2: 90 out of a possible 150 A total of 180 out of 300 = 60% 89

5. GENERAL EXAMINATION TIPS 1. Study the matric timetable. Know when you are going to write the papers you have registered for. There are sometimes two exams on one day so you will have to be super sharp and alert. Be sure to check the final timetable in case there are any changes. 2. There are less than 123 days to the start of the final exams. This includes all weekends and holidays. Start today and work every day. Set targets for achievement. 3. Do not miss one day of studying between now and your exams. Work at least two to three hours per day. Keep healthy and alert. 4. Reading is a hot skill. Reading will change your life. Read at least 1000 words every day. Read everything you can get your hands on. Read accurately and quickly. 5. Writing is power, but it requires practice. We are all judged, every day, on our writing. We can inspire, impress, persuade, congratulate and express love in writing. Write at least 400 words every day carefully, accurately and beautifully. 6. Resources are an essential student companion. Work systematically through your question papers and Self Study Guide. Don’t wait for your face-to-face classes or broadcasts to explain it all. Look at what you have to cover for the subject and plan accordingly. 7. Your BMI can help you in matric. Your Body mass Index (BMI) is an indication of how healthy you are. Calculate your BMI and then exercise and eat healthy throughout the year to keep an optimum BMI. 8. Academic work requires concentration and focus. Every day you should be engaged in intensive, focused, individual academic work. Turn off iPods, music centres, the TV, the cell phone and have an intensive and rewarding academic work out every day. Except of course if you are using it to access the resources. Be diligent and don’t be tempted to watch or access non – academic material. Technology is a fabulous platform to learn and prepare for the examinations but it can also be a deterrent if you are not focused and dedicated. Build your brain cells and be the envy of all your friends. 9. Good vibes are good for success. Surround yourself with positive people who want you to succeed. Your family and friends will be important ibn supporting you in the next 123 days. Be grateful for their support. 10. Matric success requires Planning and hard work. Start planning and working today. Read every day. Write and calculate every day. Stick to your year plan. 90

6. References 1. DBE NSC Math Literacy, Paper 1, May/June 2019 2. DBE NSC Math Literacy, Paper 2, November 2019 3. Free State Training Manual, Mathematical Literacy, 2015 4. Gauteng Mathematical Literacy Grade 12 SSIP Project, 2013 5. Grade 12 Math Literacy Revision Workbook (Wejeje, 2014) 6. https://www.freepik.com/free-vector/break-even-point-graph_4489537.htm 7. https://www.google.co.za/search?q=tax+definition&sxsrf=ALeKk01viSzlu8kwMKClRHJpXVWUa87g3g%3 A1619012342993&source=hp&ei=9iqAYPOFOoKdlwSG25r 8. https://www.sars.gov.za/tax-rates/income-tax/rates-of-tax-for-individuals 9. JENN winter school material 2020 10. Learn Xtra Live, Mathematical Literacy, Grade 10 – 12. 11. Mathematical Literacy Grade 12, Pg.227 First ed. Via Afrika Publishers 2013 12. NSC Mathematical Literacy, Eastern Cape Paper 1 June 2018 13. NSC Mathematical Literacy, Eastern Cape Preparatory exam P2, 2019 14. NSC Mathematical Literacy, Eastern Cape Preparatory exam P2, 2020 15. NSC Mathematical Literacy, Exampler P1, 2014. 16. NSC Mathematical Literacy, Exampler P2, 2014. 17. NSC Mathematical Literacy, Free State Grade 10 November exam, 2011 18. NSC Mathematical Literacy, Free State June P2, 2014. 19. NSC Mathematical Literacy, Free State March Test, 2014. 20. NSC Mathematical Literacy, Free State November P1, 2019 21. NSC Mathematical Literacy, Free State Preparatory exam P1, 2015 22. NSC Mathematical Literacy, Free State Preparatory exam P2, 2015 23. NSC Mathematical Literacy, Free State Preparatory exam P1, 2016 24. NSC Mathematical Literacy, Free State Practise Paper Grade 12 P1, 2018 25. NSC Mathematical Literacy, Free State Preparatory exam P2, 2019 26. NSC Mathematical Literacy, Mpumalanga November exam P1, 2019 27. Mathematical Literacy, Bright ideas 28. Platinum, Mathematical Literacy, Grade 12. 29. Siyavula, Mathematical Literacy, Grade 12 30. Spot on Mathematical Literacy, First ed, Heinamann Publishers Pty Ltd. 2012, page 222 31. The Answer Series, Mathematical Literacy, Grade 12 32. UFS Schools Partnership Programme, Mathematical Literacy, Grade 12 33. Via Afrika Mathematical Literacy Grade 11, (2014) 34. Via Afrika Mathematical Literacy Grade 12, First Ed 2013 35. www.e-classroom.co.za 36. www.sars.gov.za/tax rates/income tax 91

7. Acknowledgements The Mathematical Literacy Second Chance Self Study Guide Booklet was developed by the following Subject Specialist: • Ms Arden Ellie (Eastern Cape Education Department) • Ms Thembeka Nethe (Free State Education Department) • Mr Nzimeni Koba (Free State Education Department) • Mr Peter Kekana (Gauteng Education Department) • Mrs Zandile Mdiniso (KwaZulu – Natal Education Department) • Ms Mary Sebela (Limpopo Education Department) • Mr Kwazinkosi Gwate (Northern Cape Education Department) The Department of Basic Education (DBE) gratefully acknowledges these officials for giving up their valuable time, families and knowledge to develop this resource for the children of our country. It was also reviewed by the following Subject Specialist: • Ms Luleka Nombombo (Eastern Cape Education Department) • Dr Reinette van der Merwe ((Free State Education Department) • Ms Nikiwe Zulu (Gauteng Education Department) • Ms Lorraine Govender (KwaZulu – Natal Education Department) • Ms Saloshni Pillai (KwaZulu – Natal Education Department) A special mention must be made to Ms Masirheni Gladys Nkwinika, the DBE curriculum specialist who, in addition to her contribution to the development of the booklet, co-ordinated and finalised the process. The development of the Study Guide was managed and coordinated by Ms Cheryl Weston and Dr Sandy Malapile 92

ie basic education Department: ¢ ))} Basic Education as REPUBLIC OF SOUTH AFRICA ISBN :978-1-4315-3509-5 High Enrolment Self Study Guide Series This publication is not for sale. © Copyright Department of Basic Education www.education.gov.za| Call Centre 0800 202 993