Maths Lit PROGRESSED (SECOND CHANCE)

Mathematical Literacy JIT Term 2 Progressed learners Mathematical Literacy JIT Term 2 Progressed learners SECOND CHANCE MATRIC PROGRAMME KZN DEPARTMENT OF EDUCATION KZN DEPARTMENT OF EDUCATION MATHEMATICAL LITERACY JUST IN TIME MATERIAL MATHEMATICAL LITERACY GRADE 12 JUST IN TIME MATERIAL PROGRESSED LEARNERS GRADE 12 PROGRESSED2020LEARNERS 2020 • This document has been developed to assist Progressed Learners • in Thisimproving documenttheir hasperforma nce in the been developed to NSC Examination assist Progressed 2020. Learners • It in is a compilation improving their of levels nce performa 1 andin2the questions NSC in all topics. Examination 2020. • It is Learners a must use tofhis compilation document levels 1 and 2conjunction questions inwith all the Grades 12 topics. • JIT documents Learners must for term 1 and use this term 2. document conjunction with the Grades 12 • It JITisdocuments further recommended for term 1 andthatterm progressed 2. learners also work with • It is the grades 10 further and 11 JIT recommended thatdocuments. progressed learners also work with the grades 10 and 11 JIT documents. 1 1

Mathematical Literacy JIT Term 2 Progressed learners TABLE OF CONTENTS TOPIC PAGE NO. MEASUREMENT Terminologies 3 Activities 5 FINANCE Terminologies 7 Activities 11 DATA HANDLING Terminologies 15 Activities 17 MAPS AND PLANS Terminologies 20 Activities 21 This document has been compiled by the FET Mathematical Literacy Subject Advisors together with Lead Teachers. It seeks to unpack the content and to give more guidance to teachers. 2

Mathematical Literacy JIT Term 2 Progressed learners MEASUREMENT 1. TERMINOLOGY/VOCABULARY Area: The amount of two-dimensional (2-D) space occupied by a 2-D shape. The area of a shape is the size of its surface. It is measured in square units. 2-D drawings: A diagram or picture that has length and width only. 2-dimensional plans: A plan or design that has length and width only, but possibly represents 3- dimensionalobjects. 3-dimensionalmodels: A dimensional construction of a real-life object. It is a solid, and it has length, breadth/width and height. Body mass index(BMI): A number calculated from an adult’s weight and height, expressed in units of kg/m2 Capacity: The amount of space available to hold something. ORA measure of the volume a hollow object can hold - usually measured in litres. Circle: A closed curve that is everywhere the same distance from the fixed middle point. Circumference: Distance around a circle / the perimeter of a circle. Context: A real-life situation. Conversion: A change from one system /unit to another. Conversion factor: Values used to convert/ change quantities from one measuring system to another. Cylinder: A 3-dimensional object with congruent parallel circles and bases that are joined by a curved surface. Degrees Celsius: Units used to measure temperature in most countries. Diameter: A straight line passing through the centre of a circle and touching the circle at both ends, thus dividing the circle into two equal halves. Distance: How far it is from one place to another, e.g. from one town to another. It is usually measured in kilometres and does not have to be measured in a straight line. Elapsed time: Time that has passed since the start of an event. Estimate: The approximation, prediction or projection of a quantity based on experience or information available at the time. Grid: A network of parallel and perpendicular lines that form rectangles. Growth charts: Graphs consisting of a series of percentile curves that show the distribution of the growth measurements of children. Imperial System: A system of measurement using inches, pounds, feet, gallons and miles. Length: The measurement between two points, in a straight line, e.g. the length of a room. Mass: An indication of how heavy an object is. (Also known as weight.) Measure: Using an instrument to determine size, weight, etc. Measuring: Determining the value of a quantity directly, e.g. reading the length of an object from a ruler or the mass of an object from a scale. Metric System: A system of measurement that uses metres, litres, kilograms, etc. Perimeter: The total distance around the boundary or edge that outlines a specific shape. 1

Mathematical Literacy JIT Term 2 Progressed learners Radius: The distance from the centre of the circle to any point on the circumference of the circle. Result: Something that follows on from an action- Rounding off: To decide to cut off a number at a certain digit to make it simpler but keeping its value close to what it was. Scale: An instrument that is used to measure the mass (weight) of an object. Surface area: The area of all the faces/ surfaces of an object added together. Volume: The amount of 3-D space occupied by an object. It is measured in cubic units. 2

Mathematical Literacy JIT Term 2 Progressed learners 2. ACTIVITIES QUESTION 1 1.1 Thando and Andile are planning for their wedding. They want a two-layer red velvet cake. The radius of the bottom layer is 8,5cm. Use the picture below and the given information to answer the following questions. 1.1.1 How many layers does the cake have? (2) 1.1.2 Define the term radius. (2) 1.1.3 Calculate the diameter of the bottom layer in mm. (2) 1.1.4 Calculate the total height of the cake. (3) 1.1.5 Calculate the volume (cm3) of the bottom layer. You may use the following formula: Volume of a cylinder = π × (radius × height, using π = 3.142. (2) 1.2 Andiswa will bake the red-velvet cake using the recipe below. 2½ ℓb soft butter 375g castor sugar 30g baking powder 4 eggs 200mℓ full cream milk 10mℓ vanilla 625mℓ of flour Note: 1kg = 2,25 pounds (ℓb) 1mℓ flour = 0.7g flour. 1.2.1 Determine the mass of butter in kilograms. (2) 1.2.2 The cake must be baked at 180ᵒC. Determine to what ᵒF the oven should be turned. You may use the following formula: ᵒF = (1.8 × ᵒC) + 32ᵒ (2) TOTAL [15] 3

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 2 2.1 Goodhope is building a house. First he digs the rectangular foundation for the house. The foundation is filled with cement, the dimensions of the foundation are Length = 8m; Breadth =0,5m and Height=50cm 2.1.1 Calculate the volume of the foundation in metres. You may use the formula: Volume = l × b × h (3) 2.1.2 If the concrete for the foundation costs R180/m3, what is the total cost of the concrete for the foundation? (3) 2.1.3 Goodhope finds a cheaper concrete at a total cost of R320 for 2m3. Calculate the cost per m3. (2) 2.2 Goodhope starts cooking dinner at 6:00 p.m. he has to leave for his choir practice in 1 hour and 45 minutes. 2.2.1 What time must he leave? (give your answer in the 12-hour format) (2) 2.2.2 Convert your answer to the 24-hour format. (2) 2.3 The distance travelled by Goodhope from home to work is 126km for 62minutes. Calculate his average speed in (km/h).  The formula may be used. Average speed = (3)  TOTAL [15] QUESTION 3 Mlindo wants to buy a rectangular water storage tank at Samoosa Hardware. The following table shows the different sizes of rectangular water storage tanks they sell, each one having a volume of 2 000 000cm3. Tank Length (cm) Breath (cm) Height (cm) Surface area (cm2) A 160 100 125 97000 B 128 125 125 95250 C 200 100 100 100000 D 200 125 80 A E 160 156.25 80 100 600 NB:1000cm3 = 1000mℓ = 1ℓ Area = Length × Breath 4

Mathematical Literacy JIT Term 2 Progressed learners Surface Area = 2(Length × Breath) + 2(Length × Height) + 2(Breath × Height) Volume = Length × Breath × Height 3.1 Write down the Length of the tank A. (2) 3.2 Write down the Breath of the tank E. (2) 3.3 Write down the Height of the tank C. (2) 3.4 Write down the Surface Area of the tank B. (2) 3.5 What is the volume of the tank in litres? (2) 3.6 Calculate the area of the base of tank A in cm2. (2) 3.7 Calculate the missing value A. (3) TOTAL [15] QUESTION 4 Mrs Sefoloko uses this recipe every time she prepares turkey. Use the recipe and the conversion rates provided to answer the questions below. Roast Turkey With Tasty Chestnut Stuffing "Simple but seriously yummy." Number of servings: 8 Preparation time: 45 minutes Cooking time: 4 hours 30 minutes Ingredients 2 pounds chestnuts 2 cups butter 2 cups minced onion 2 cups minced celery 10 cups dried bread crumbs 1 teaspoon dried thyme 12 pounds whole turkey, neck and giblets removed salt and freshly ground black pepper to taste Preheat oven to 3470F INGREDIENT 5 ml 15ml 25ml 100ml 250ml Baking powder 4g 10g 20g 80g 200g Cake flour 3g 8g 15g 60g 150g Butter 5g 12,5g 25g 100g 250g 5

Mathematical Literacy JIT Term 2 Progressed learners Salt 5,5g 14g 28g 110g 280g Sugar 4g 10g 20g 80g 200g Conversion rates 1 cup = 250 ml 1 tablespoon = 15 ml 1 teaspoon = 5 ml 1 kg = 2,205 pounds (lb) 4.1 Convert the weight of the turkey to kilograms. (2) 4.2 Write the ratio of chestnuts to the number of servings in simplified form. (2) 4.3 How many millilitres of dried thyme will be needed when preparing this dish? (2) 4.4 How many grams of butter will Mrs Sefoloko use for this recipe? (2) 4.5 Convert the preparation time to hours. (2) 4.6 Write the cooking time as minutes only. (3) 4.7 Express the cooking temperature in degrees Celsius (0C) using the formula:0C = (3) (0F – 320) ÷ 4,8. 4.8 Mrs Sefoloko starts preparing her recipe at eleven minutes to nine in the (3) morning . What is the earliest time that the meal will will be ready to be served? 4.9 What information on the recipe would make a person want to try using the (2) recipe? TOTAL [21] 6

Mathematical Literacy JIT Term 2 Progressed learners FINANCE 1. TERMINOLOGY/VOCABULARY 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: When someone or an organisation takes money out of your account. An entry in an account showing a payment made from an 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. Gross income: The total amount of all an individual’s income before deductions. 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 maybe 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. Interest value: This is the actual rand amount of interest that will be added to your loan. Invest: 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. Invoice: A comprehensive document that details all the work done or items sold, and what costs are due. Net pay: The amount an employee “takes home” after income tax has been deducted. 7

Mathematical Literacy JIT Term 2 Progressed learners 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 or item or earning that has tax applied 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. 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). 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. Zero rated VAT items: These are goods that are exempt from VAT . Groceries that are basic foodstuffs are zero-rated in South Africa, e.g. brown bread, milk, mielie meal, samp, rice, 8

Mathematical Literacy JIT Term 2 Progressed learners 2. ACTIVITIES QUESTION 1 1.1 Karishni is a 35 year old teacher and her budget for ONE month is given in the table. TABLE 1: Karishni’s Budget Income Salary per month R 12000,00 Expenses Housing R2 000 Motorcar and fuel R2 300 School fees R 500 Food R1 500 Insurance R 275 Water and electricity R 350 Medical aid R 250 Clothes account R 460 1.1.1 Determine Karishni’s total expected expenditure for one month. (2) 1.1.2 What is Karishni’s salary per year? (2) 1.1.3 How much will Karishni have after paying ALL her expenses? (2) 1.2 Use the Income tax table and tax rebate table below to answer the questions that follow. TABLE 2: Income tax table for the year 2008/09 Income Tax Table Individuals (including special trust) Taxable Income Rates of tax R0 – 112 500 18% of each R1 R112 501 – 180 000 R20 250 + 25% of the amount above R112 500 R180 001 – 250 000 R37 125 + 30% of the amount above R180 000 R250 001 – 350 000 R58 125 + 35% of the amount above R250 000 R350 001 – 450 000 R93 125 + 38% of the amount above R350 000 R450 001 and more R131 125 + 40% of the amount above R450 000 Tax Rebates Persons under 65 R7 740 Persons 65 and older R12 420 1.2.1 Define taxable income (2) 1.2.2 Calculate Karishni’s annual pension contribution if it is 7,5% of her basic salary. (2) 1.2.3 Calculate Karishni’s annual taxable income (2) 1.2.4 Which tax bracket will be used by her employer to calculate her tax? (2) 1.2.5 How much discount will she receive from for her tax? (2) TOTAL [16] 9

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 2 2. Zinathi is a fashion designer from Kokstad. In 2019 she bought material to design wedding gowns and dresses for her clients. She paid R2 375.50 for the material. 2.1 The price of material increased by 9% percent. Calculate how much she would (3) have to pay for the material after the increase. 2.2. Explain the term “inflation’. (2) 2.3. Do you think Zinathi`s business would be affected by this change in prices? (2) Explain. 2.4. The material cost R 2000.00 in 2018. Calculate the inflation rate for 2018. (3) You may use the following formulae: Inflation rate= ( new price – old price) x 100 Old price 2.5. Mention a word for “price decrease” (2) TOTAL [12] QUESTION 3 Mandisa and Andile are friends. They work as fashion designers for the same company. Mandisa is 41 years old and Andile is 66 years old. Each employee earned a basic monthly income of R22 170.00 in the 2019/2020 financial year. They both contribute 7.5% of their basic salary towards a pension fund scheme every month. Mandisa is married and has a child. She contributes monthly towards a medical aid scheme for herself and her two dependents. Andile does not belong to a medical aid scheme. Study the income tax tables, Financial year 2019/2020, below and answer the questions. Tax Taxable Income Tax Rate Bracket 1 0 – 195 850 18% of taxable income 2 195 851 - 305 850 35 253 + 26% of taxable income above 195 850 3 305 851 - 423 300 63 853 + 31% of taxable income above 305 850 4 423 301 - 555 600 100 263 + 36% of taxable income above 423 300 5 555 601 - 708 310 147 891 + 39% of taxable income above 555 600 6 708 311 - 1 500 207 448 + 41% of taxable income above 707 000 310 7 1 500 001 and 532 041 + 45% of taxable income above above 1 500 000 Primary Rebate 14 220 Secondary Rebate (Persons 65 and older) 7 794 Tertiary Rebate ( Persons 75 and older) 2 601 3.1 State the day, month and year when the 2039/2020 financial year ended. (2) 3.2 Explain what is meant by the term tax rebate. (2) 3.3 Which tax rebate/s did Andile qualify for in the 2039/2020 financial year? (2) 3.4 Calculate Mandisa’s gross annual salary. (3) 3.5 Determine the monthly pension fund contribution by Mandisa. Pension Fund Contribution = . x Basic Monthly Salary (3)  10

Mathematical Literacy JIT Term 2 Progressed learners 3.6 Calculate the annual pension fund contribution paid by Mandisa. (3) 3.7 Determine the annual taxable income of each person. Taxable Income = Gross Salary - Pension Fund Contribution (3) 3.8 Which tax bracket will be used to calculate the income tax for Mandisa and (2) Andile for the financial year 2019/2020. TOTAL [20] QUESTION 4 A client received the financial document as shown on ANNEXURE A which showed the water and electricity consumption for a certain period. Study the financial document and answer the questions that follow. 4.1 Write name of the client to whom the statement is addressed. (2) 4.2 How many units (kWh) of electricity were used? (2) 4.3 Which period does this statement cover? (2) 4.4 Write the payment date. (2) 4.5 What will happen if the account holder does not pay on the amount due? (2) 4.6 What does the minus(-) sign before R453,65 mean? (2) 4.7 Calculate the missing values: 4.7.1 A (2) 4.7.2 B (3) 4.7.3 C (3) TOTAL [20] ANNEXURE A QUESTION 4 Miss K. Ndlovu 21 Short Street Durban 4036 Type Metre Previous reading Current reading Usage Period Number Electricity 47332 15 654 16 144 490 24/01/2020 – Water 476132 4 312 4 349 A 23/02/2020 24/01/2020 – 23/02/2020 Type Reference Consumption Basic VAT Amount (R) Opening ………….. 453.65 balance Receipts 5432A -453.65 Electricity 490 341,50 51,23 392,73 Charged Rates (Monthly) 243G3 237,59 Refuse 534Ru B 61,04 Sewage 534S 9,20 C Balance 752,69 Due Total VAT 90 DAYS + 60 DAYS + 30 DAYS + Current Amount 0,00 0,00 0,00 DUE DATE 05/03/2020 ARREARS 0,00 TOTAL 752,69 AMOUNT DUE VAT rate is 15% 11

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 5 Naledi owns a spaza shop in KwaMadlala. She buys her stock from a wholesaler in Port Shepstone. Below is a table showing some stock she buys weekly. She buys two packs of beans every week. The cost and selling prices shown already include 15% VAT. 10 kg Aunt 5 litres Cooking oil Caroline rice 400 g tin Koo Baked beans Cost price : R 89,99 Cost price : Cost price: R 9,99 Selling price per 750 119,99 Selling price: R 13,40 ml Profit : R R 17,98 48,27 5.1 Calculate the cost per gram of baked beans. (2) 5.2 What is the maximum number of 750 ml bottles cooking oil that she can sell (4) from the amount of oil that he buys per month. 5.3 Calculate the selling price of Aunt Caroline rice. (2) 5.4 How many grams of baked beans does Lesedi buy per fortnight if a pack has a (5) dozen tins? 5.5 Calculate the VAT exclusive price of rice. (3) 5.6 Use calculations to show that Naledi needs R449.74 to pay for her weekly (3) supplies. TOTAL [19] 12

Mathematical Literacy JIT Term 2 Progressed learners DATA HANDLING 1. TERMINOLOGY/VOCABULARY Bar graph: 900 graph using bars to show frequency (horizontal and vertical graph). Box-and-whisker plot: A diagram that statisticians use to show the distribution of data along a numberline divided into quartiles. Certain: Something is definitely going to happen, e.g. getting heads or tails when tossing a coin is certain. Classify: Identify the category or class. Continuous Data: Numerical data (e.g. measurements like weight or age). Data: Information, a series of observations, measurements, facts; collecting and recording information for purposes of statistical investigation. Discrete data: Numerical data (fixed numbers, like size of family); data that can have only certain values (quantities that can be counted, usually whole numbers) Equivalent: Quantities that have the same value. Frequency (f): The number of times a data value is recorded. Frequency table: A table showing frequencies in an organised form; a table that summarises the frequencies of all the data values in a data set. Histogram: 900 graph using adjacent bars to show the frequency of numerical data grouped into intervals; where areas of rectangles (continues; no gaps between them) show frequency of classes of data (breadth 5 class; height 5 frequency). Mean: The average of the values in a data set; sum of all the observed values divided by the number of observations. Average: The sum of all data values divided by the number of data values. Measures of central tendency: Numbers that tell more about the balance (middle values) in a data set (mode; median; mean). Measures of spread: Numbers that tell how far apart data values in a data set lie; the spread of a numerical data set (range, quartiles, percentiles). Median: The middle value in an ordered data set. Median- of a set of data The value that cuts an ordered data set in half. Mode: The value or values appearing most often in a data set. Mode of a set of data: The most common data value in a data set. Quartiles: The values that divide a list of numbers into four equal parts. Range [of a data set]: The difference between the highest and lowest values in a data set Outcome: Result of a trial (experiment). Outcome [fair]: All outcomes are equally likely to occur. Outliers: A data value that lies an abnormal distance from the other data values in a dataset. 13

Mathematical Literacy JIT Term 2 Progressed learners Population: The entire source of data involved in an investigation; all the subjects included in a study or survey from which conclusions will be drawn about that population as a whole. Possible outcome: The chance that an event will occur. Prediction: A statement describing the chance of an outcome happening, based on given information. Probability (Mathematical): The results of a trial or experiment expressed as a fraction; the number of favourable outcomes divided by number of all possible outcomes. Probability [of an outcome]: The likelihood of a particular outcome occurring, expressed as a number between zero and one. Questionnaire: A list of questions that can be used to collect data. Sample: A sub-set (small group) chosen from the population to represent the population. Survey: Collect data from a group of people or objects. Survey [biased]: Survey containing factors that produce answers that do not represent a truthful picture of the situation. Tree diagram: A diagram that uses using branches to display all the outcomes of a series of trials. Unlikely: The chance of something happening is less than the chance of it not happening. Variable: A number or quantity that can have different values in a situation. Very likely: The chance of something happening is much greater than the chance of it not happening. Very unlikely: The chance of something not happening is much greater than the chance of it 14

Mathematical Literacy JIT Term 2 Progressed learners 2. ACTIVITIES QUESTION 1 Mr Langa of Swelihle High School recorded marks for his learners for Mathematical literacy Grade 11, the test was out of 100. The pass mark for the test is 40% Grade 11 A 25 , 18 , 92 , 33 , 78 , 42 , 35 , 44 , 81 , 86 , 39 , 74 , 65 , 50 , 49 , 52 , 80 , 42 , 43 , 42 , 98 1.1 Arrange the test scores in ascending order. (2) 1.2 How many learners failed the test? (2) 1.3 What is the value of the median mark? (2) 1.4 Determine the 3rd quartile mark. (3) 1.5 Calculate the range for grade 11 A. (2) 1.6 Explain the difference between a discrete and continuous data. (4) 1.7 Determine the modal value (2) TOTAL [17] QUESTION 2 Study the graph below, which represents the monthly expenses for the Jacobs’ family household. 2.1 Identify the type of graph used to represent the expenses of the Jacobs' family household. (2) 2.2 Identify the minimum and maximum values spent that month. (2) 2.3 Is the food expense a fixed expense, a variable expense, or an occasional expense? (2) 2.4 Write the ratio of the cost for water and electricity to rent. (3) 2.5 Arrange the expenses in ascending order. (2) 2.6 Determine the median expense for the month. (2) 2.7 Calculate the mean expense for the month. (3) 2.8 Determine the modal expense for the month. (2) 2.9 Name an expense that could fall in the category ‘other'. (2) TOTAL [20] 15

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 3 Learners from a Life Sciences class planted bean seeds as an investigation. Their task was to watch the seeds grow and record the height of the bean plants in cm. Study the tally and frequency table and answer the questions. 3.1 Identify the method that was used to collect data on the bean plants. (2) 3.2 What was the total number of plants used in the investigation? (2) 3.3 What was the minimum height category of the bean plants? (2) 3.4 Identify the modal height of the bean plants. (2) 3.5 State the number of bean plants in the modal height. (2) 3.6 Complete the tally in the table. (6) TOTAL [36] QUESTION 4 The following marks, as whole percentages, were obtained by Miss Maduna’s grade 12 learners for their first assessment task. Refer to the marks and answer the questions that follow. 42 18 11 32 29 58 47 44 45 18 24 18 33 62 9 97 32 14 18 37 4.1 How many learners wrote the test? (2) 4.2 Arrange the marks in descending order. (2) 4.3 Calculate the mean mark for the class. (3) 4.4 Calculate the median mark for the learners’ marks. (2) 4.5 Determine the range of the marks. (2) 4.6 The mark 97 is too big compared to the rest of the marks that other learners obtained. (2) What is the special name for such a value in the dataset? 4.7 Use ANSWER SHEET 4 to complete the frequency table for the marks. (3) 4.8 Determine the modal interval for the marks. (2) TOTAL [48] 16

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 5 Asanda tossed a coin THREE times. The incomplete tree diagram below represents the possible outcomes. Study the tree diagram and answer the questions that follow. HEADS H,H,H HEADS TAILS H,H,T HEADS HEADS H,T,H A TAILS H,T,T EVENT B T,H,H HEADS TAILS T,H,H TAILS HEADS T,T,H TAILS TAILS C 5.1 Find A, B and C to complete the tree diagram. (3) 5.2 How many possible outcomes are there in this tree diagram? (2) 5.3 Calculate the probability of tossing two heads and one tails. Write your answer as a (3) fraction in a simplified form. 5.4 Calculate the Probability of tossing a 6. (2) TOTAL [50] 17

Mathematical Literacy JIT Term 2 Progressed learners MAPS AND PLANS 1. TERMINOLOGY/VOCABULARY Bar scales: Presented as a picture, it means that if you placed a ruler next to this scale, you could determine how many centimetres represent the specified kilometers. Compound bar graphs: Graphs that contain multiple bars for each category of data, with each bar representing a different component of each category of the data. Elevation map: Information about the profile of a route as seen from the side. Elevation plans: Shows the design and dimensions of the outside of a building from a side view. Floor plans: Shows the design and dimensions of the inside of a building, from a top view. Number scale: A number scale such as 1 : 50 000 means that 1 unit on the map represent 50 000 units in real life. Route map: Shows a specific route, for instance for an event, as seen from above. Scale: Determines how many times smaller an object shown on a plan or map is that its actual size. Scale drawing: A diagram of a real-life object drawn in proportion. Scaled elevation plans: Show the design and dimensions of the outside of a building from aside view using a specific scale. Street map: A map of a small area such as a town or city. Strip map: A map of a section of a travelling route. 18

Mathematical Literacy JIT Term 2 Progressed learners 2. ACTIVITIES QUESTION 1 Mr Ramafole and his family decided to visit Sodwana Bay to relax during the upcoming Easter holidays Use the map below to answer the following questions. 1: 4 500 00 1.1 Define the given scale on the map in words (2) 1.2 Give the names of game reserves situated in Sodwana in this map (2) 1.3 Measure the distance from Vryheid to Sodwana Bay, use the given scale to calculate the actual (4) distance from Vryheid to Sodwana Bay in km 1.4 Give the general direction of Sodwana Bay from Vryheid? (2) 1.5 Suppose the distance from Vryheid to Sodwana Bay via Jozini is 295km .Calculate the time in hours (5) and minutes if the travelling speed is 97,3km/h. May use formula: Time = TOTAL [15] 19

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 2 Two Oceans is one of the best worldwide marathon which takes place annually. The map below shows this Two Oceans marathon. Study the map below and answer the following questions: 2.1 How many water points are present in this map? (2) 2.2 What is the difference in kilometres between the second water point and the finishing point (3) 2.3 Explain why this type of map is regarded as an elevation map. (2) 2.4 How long im metres is the Two Ocean marathon. (3) 2.5 Give a reason why there are medics avaliable in this map (3) 2.6 George Ntshiliza is one of South African runners who broke the record in the Two (4) Oceans Marathonfinishing the race in a time of3:38:58. Calculate at whatspeed  George ran to be winner . Use the formula Time =  TOTAL [17] QUESTION 3 Miss Dludla , an educator from Nongoma decided to use the map which shows the part of Kwazulu Natal and Mpumalanga to let her learners understand different types of maps. Study the map and answer the following questions. 3.1 Write down the Grid reference of Vryheid (2) 3.2 Use both of the given scales to calculate the actual distance from Ermelo to Manzini. (3) 20

Mathematical Literacy JIT Term 2 Progressed learners 3.3 What is the difference between the two scales given and which one is more reliable and why? (4) 3.4 On a particular month ,Miss Dludla used the same map to travel from Nongoma to (4) Ermelo to go Mr Ramafole’s wedding. Give the shortest route to arrive at the wedding on time. TOTAL [13] QUESTION 4 The map below was used Lekhanyane Church to travel around South Africa to visited some of the church members across the Country 4.1 Write down the two cities or town on the N2 linking Durban and East London. (2) 4.2 What type of the scale is used on this map? (2) 4.3 Name one advantage of using this type of scale. (2) 4.4 Write the scale of the map as a number scale in the form of 1:........ (3) 4.5 Calculate the actual distance between Mossel bay and Port Elizaberth (3) TOTAL [12] 21

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 5 Mr Madiba is going to drive from Durban to Port Elizabeth for the family wedding .He finds the strip map to help him plan his trip to Port Elizabeth. Use the strip map to answer the following questions 5.1 How many national are present in map (2) 5.2 Calculate the distance from Durban to Umtata (2) 5.3 Give the name of the national from Durban to Port Elizabeth (2) 5.4 Mr Madiba wanted to visit a friend .He them drove in the southerly direction from Durban along the N2 • At Komga, he travelled 104km in the easterly direction to East London • Then he continued for 158 km in the south direction to his destination. 5.4.1 What is the name does his friend live? (2) 5.4.2 What is the general direction of Madiba’s friend place from Underberg (2) TOTAL [10] 22

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 6 Mr Rankhakile’s family, his wife and two children lives in Port Elizabeth and he planned to take his family on holiday trip to Durban that will last for the weekend. The following questions are based on the strips map that shows the distance between Durban and Port Elizabeth and national roads map given below. 6.1 How many members does Mr Rankhakile’s family have (2) 6.2 Mr Rankhakile lives in Port Elizabeth town, how many km are they going to travel to Durban? (2) 6.3 Name the route that they will use to travel from Umtata via Port St John’s (2) 6.4 Use the national roads map below the strip in the annexure A to answer the following questions 6.4.1 How many national roads are shown on the map (2) 6.4.2 Which national road is the longest? (2) 6.5 There is one national park close to where Mr Rankhakile lives, give the name of the National park (2) 6.6 If the family intends to have a break after every two hundred kilometres, how many times are they going to stop before they get to Durban (4) 6.7 On their to Durban, they travelled 84km from the national road, just to take a quick short break besides the one they planned for every two hundred kilometres. Mention the national road they were 23

Mathematical Literacy JIT Term 2 Progressed learners on and their destination after 84km (2) 6.8 Calculate the distance in km between Cradock and Durban (2) 6.9 If they left Port Elizabeth at 04:30 and arrived at 15:45, at what average speed were they travelling? Give your in km/hour You may use the formula: (5) 6.10 Write their departure and the arrival times in the 12 hour format. (2) 6.11 Give a possible explanation why the distances between Port Shepstone, Margate and Port Edward are not equal whereas they appear to be equal on the map. (2) 6.12 The vehicle they using has an average fuel consumption of , if their car has a fuel tank of 60litres how many km will they travel in a full tank? (3) 6.13 If the petrol price of the coastal regions is R15,80 per litre, calculate how much is he going to need for the number of litres of petrol he needs to fill in the car to get to Durban. (6) TOTAL [43] QUESTION 7 Use the strip map of the that shows the cape town to port Elizabeth route below to answer the questions that follow. 7.1 How many national roads are shown on the map? (2) 7.2 Name two national parks from the map, which are closer to N2. (2) 7.3 If you travel 458km from cape town on the N2, then travel 360km on the N12 in which city or town 24

Mathematical Literacy JIT Term 2 Progressed learners are you? (2) 7.4 You stay in Ladysmith and you meet a lost tourist in your town, he wants to ADDO NATIONAL PARK. Give the tourist the directions that will take him to the park. (5) 7.5 If you travelling from Paarl to Ladysmith, which of the following routes is the shortest, Paarl via Worcester or Paarl via cape town? Show calculations to support the decision. (5) TOTAL [16] QUESTION 8 8.1 Mr Ramafole, mathematical literacy educator used the picture below to explain the advantage of using the below scale. 8.1.1 Name type of scale illustrated above? (2) 8.1.2 Convert the given scale to number scale (3) 8.1.3 What is the difference between above scale and the one calculated. (4) 8.2 Mr Ramafole was invited to a wedding which was held recently in Waterwheel, a popular wedding place in Vryheid. Below is the picture of the trouser he bought from Twizz Boutique . 1:50 8.2.1 Measure the length of the trouser in mm. (2) 8.2.2 How many pockets does this trouser have? (2) 8.2.3 Calculate the actual length of the trouser. Express your answer in metres (3) TOTAL [16] 25

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 9 Miss Dludla is interested in building a new house for herself. The architect gave her number of floor plans to help decide. She chose the below floor plan. Use the floor plan above to answer the following questions. 9.1 Define the term floor plan? (2) 9.2 Write down the compass direction of guest from the master bed room. (2) 9.3 Identify the scale of the floor plan. (2) 9.4 Explain what the scale means in terms of the measurements on the plan and actual dimensions. (2) 9.5 Calculate the actual length of the north side of the house (3) TOTAL [11] QUESTION 10 Study the following diagram which shows the top view for an old styled plan of the house and use it to answer the questions that follow 26

Mathematical Literacy JIT Term 2 Progressed learners 10.1 Identify the type of scale used in the above given plan (2) 10.2 Explain what is meant by the scale outlined in question 10.1 (2) 10.3 How many rooms does the plan have including the pantry and server but exclude the passage? (2) 10.4 Give the general direction of the bedroom 2 from study (2) 10.5 What is the probability that the kitchen will receive the sunlight during the sunrise? (2) TOTAL [10] QUESTION 11 Study the following diagram which shows the top view for an modernised plan of the house and use it to answer the questions that follow N KEY: Door: Window: 0 3m 11.1 Identify the type of the scale used and give one advantage of the identified scale (2) 11.2 What length does the above mentioned scale represent? (2) 11.3 Which bedrooms will receive the sunlight or sunrays when the sun is about to set? (2) 11.4 How many doors and windows does the plan have? (2) 11.5 Is the door of bedroom 3 a left-hand or right-hand? Explain. (3) 11.6 Write down the ratio of the bathrooms to the bedrooms (2) 11.7 If the length of the east-facing wall is measured to be 8cm on the plan, use the given scale to calculate the length of the east-facing wall in reality (4) TOTAL [17] 27

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 12 Thato and his friends decided to go out to have fun and they visited a playhouse theatre. The following is the seating plan of the play house theatre which shows how the spectators are allocated seats. Study the plan and answer the questions that are based on it. 12.1 How many seats are reserved for disabled people (2) 12.2 Determine the maximum number of people who can be accommodated in the theatre if all seats are occupied. (2) 12.3 If Thato short sighted and prefers to sit nearer and directly to the stage, write down ANY 2 seats that are likely to be chosen by Thato? (2) 12.4 All disabled were occupied on the day Thato and his friends visited the theatre. Calculate the probability (as a percentage) of picking up the disabled person from the front row if five of the front seats were not occupied. (3) 12.5 One of Thato’s friends was seating at seat number E22 wanted to be close to Thato. He moved 3 rows down the aisle and 2 seats to the left. Give the row and the seat number of his new position. (2) TOTAL [11] 28

Mathematical Literacy JIT Term 2 Progressed learners QUESTION 13 The floor plan of Mr Khoza’s house is shown below. 13.1 How many rooms are shown in the floor plan? (2) 13.2 How many windows are shown on the plan? (2) 13.3 How many doors are shown on the plan? (2) 13.4 Give the general direction of the master bedroom from the toilet. (2) 13.5 Give the name of the room(s) that will receive the sunshine as the sun rises. (2) 13.6 If the measured distance of the southern wall is 92mm and the actual distance is 16m, determine the (3) scale. 13.7 What is the probability of finding a door that opens towards the right in the plan from the outside? (3) Give your answer as a decimal. TOTAL [16] 29