2017 SACAI WINTER SCHOOL MATHEMATICAL LITERACY NOTES

Transcription

1 2017 SACAI WINTER SCHOOL MATHEMATICAL LITERACY NOTES 1

2 EXAMINATION PAPER Example of the instruction Read the following instructions carefully before answering the questions: 1. This question paper consists of 5 questions. Answer ALL the questions. 2. Question and Question must be answered on ANNEXURE A and ANNEXURE B. Write your exam number in the space provided and attach the ANNEXURES to your ANSWERBOOK. 3. Number the answers correctly according to the numbering system used in this question paper. 4. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 5. All calculations must be clearly shown. 6. Round all final answers appropriately according to the context, unless stated otherwise. 7. Write clearly and legibly. Time: 3 hours Marks: 150 marks 2

3 Weightings of topics Topic Weighting (%) Interpreting and communicating answers Basic Skills Topics and calculations Numbers and calculations with numbers Patterns, relationships and representations Finance 35% (±5%) Application Topics Measurement 20% (±5%) Maps, plans and other representations of the physical world 15% (±5%) No weighting is provided for these topics. It will be assessed in an integrated way in the Application Topics. Data Handling 25% (±5%) Probability Minimum of 5% Taxonomy levels: The four levels of the Mathematical Literacy assessment taxonomy Paper 1 Paper 2 Overall allocation Level 1: Knowing 60% ± 5% 30%± 5% Level 2: Applying routine procedures in familiar contexts Level 3: Applying multi-step procedures in a variety of contexts Level 4: Reasoning and reflecting 35% ± 5% 25%± 5% 5% minimum 35% ±5% 40% ± 5% 30% ± 5% 20% ±5% 20% ± 5% 3

4 Questions Intention Paper 1 Paper 2 Basic Skills Paper: Applications Paper: To Assess proficiency of To Assess the ability to content and/or skills use both mathematical and non-mathematical techniques/ considerations to explore familiar and unfamiliar Paper 1 consists of 5 questions contexts. Paper 2 consists of 4 or 5 questions Structure and scope of content and/or skills Four Questions deal with contexts relating to each of the following topics: Finance Measurement Maps, plans and other representations of the physical world. Data Handling The Fifth question integrates content from across all of these Topics. Probability will be examined in the context of one or more of the other questions. NB Each question can contain more than one context. Each question deals with contexts drawing integrated content from across all of the following topics: Finance Measurement Maps, plans and other representations of the physical world. Data Handling Probability will be examined in the context of one or more of the other questions. NB Each question can contain more than one context. 4

5 ERRORS IN PAPERS: Common mistakes: Appendix B and C was not handed in. You write so ugly, you yourself do not know what you have written (e.g. 6 seen as 0 or 0 seen as 6). Make certain you don t cross out the memo correct answer, because then the wrong answer is being marked. Write correctly from question paper and/or calculator. Unnecessary mistakes/unnecessary marks lost because: Steps not shown: zero points for no action/operation. Rounded within sum, makes answer incorrect. Incorrect normal rounding. Not rounded as asked. Writing down wrongly from calculator. Numbers on answer sheet and typed in on calculator not the same. Work out interquartile range, without showing the quartiles. Wrong unit for area (or volume, or circumference). Interquartile range is NOT the same as range! No unit in answer for BMI. Write something in the asked ration: there must not be units and the order does matter! Ratio/Scales: must be whole numbers. Draw graphs in pencil, and when you are 100% certain it s correct, THEN use pen/highlighters etc. Using the wrong formulae = Max 1 mark with CA. 5 is not the same as 5 hours. Pietermaritzburg is not the same as Pietersburg. When doing calculations, you need to give the answer too! 2 2 is not the same as x. 5

6 3 3 is not the same as x. Converting mm to cm has ONE ZERO. Converting cm to m has TWO ZERO s. Converting m to km has THREE ZERO s. 1st answer is marked, so do not write OR (/)... we only mark the 1st answer. Cannot do calculations with different units. Money is always 2 decimal rounding; rates can be up to 6 decimal rounding. Dates must be complete. DAY MONTH YEAR 1 kg =1 000 grams. 1 km =1 000 meters. Order matters when working with data to calculate median and quartiles. Do what is asked: if they ask gold, do not give silver; if they ask milk, do not use flour measurements. If something is free, you lose marks if you don t mention it. It should be written as "it s free (etc.)". Probability: fraction must be written in its simplest form, although it is not specified; AND as decimal and percentage. If only decimal is asked DO NOT give the percentage (and vice versa). o The calculation fraction should be given to get marks for simplification. Account works out to R69,99 then there may NOT be rounding to R70... it is always rounded down. Use chart to read something, if you do a calculation, it cannot be marked because you didn t do as the question asked! "Use graph" = NO CALCULATION. Do not round off something if they do not say so... e.g. R6 don t round it off to R10. 1st answer is marked! Do not give two answers, no OR". Any map that is measured: if memo says 19 mm then 29 mm is too far! 20 mm or 18 mm etc. will be marked correctly, but not 25 mm or 15 mm. Something discreet, must be calculated with whole numbers. E.g. make recipe 5,4 times is impossible! 5 times is not enough, then it must be 6 times. [depends of course on the situation! Sometimes the answer really can only be 5 not 6 (e.g. if asked how many times you can make the recipe, and the calculation is 5,4 then it can only be 5 times, a 6th time will not have enough ingredients)]. 6

7 Numbers are being interchanged. It should be 80 (as on the paper), then candidates write 08. It is wrong! And follow-up then will be with 08 and not 80 as it is entered on the calculator. Do specifically as asked. E.g. give only name, then do not give the numbers; give only the numbers, don t give the name. Ask yourself if you can make sense of the answer: o 2 eggs are enough for a recipe that makes 25 muffins. Question: how many eggs are needed for 500 muffins?, then an answer of 6250 eggs for 500 muffins does not make sense!! o Is it possible to have a closet height calculated as 185 m? It cannot be 185 meters; it is 185 cm! o A map of South Africa: the scale can NOT be 1:17! "What is the percentage?" The answer has a % sign! It's not RAND or CENT! "Give ONE reason" do not give more than one reason. Only your first reason will be marked, and if he is wrong, you lose the marks. Know the difference between discrete values and continuous values. Know the difference between independent and dependent variables. Know the difference between numbers scale vs bar scale. Do not make "stupid" mistakes. E.g. to say = 6. Single trip vs. Return o Single trip is not the same as a return trip o Johannesburg to Cape Town is not the same as Cape Town to Johannesburg. The correct order of towns when you drive is important. Attention needed, as you WILL get these and its easy marks: Scales VAT included, work to VAT excluded BMI IQR Write something in the required ratio Distance Speed Time Write an equation from info given Draw graphs: know when to draw a certain graph 7

8 Technical aspects of the paper: Do not number in the middle of the page. Write the question number on the left, before the red line. Make a definite space between the question number and the beginning of an answer, so that the marker can clearly see what is the question number and where the answer starts. Between each question, leave a line open. It just makes it easier for the marker to mark. Draw graphs with a pencil! If you make a mistake, it s easy to correct it with the use of an eraser, but if you make a mistake with pen, you are NOT allowed to use Tipp- Ex! Irregularity! Tips for the day of the exam: If your paper is handed out and everyone is going through it, make sure your paper is complete and that you have all pages. Read the instructions carefully! Read your paper first and make mental notes on questions which are easy and which will be difficult. You can answer the paper in any order, if you do full question at a time. This means Question 5, then Question 2, then Question 1 etc.... but you cannot change the order within a main question (i.e then then 2.1.3, not then then 2.1.2!!!) Look at the paper's marks. You have 3 hours; it means you have to be done with 50 marks every hour. If you complete 50 marks in less than one hour, you have more time to spend on a difficult question. Do not apply this guideline 100 % with easier questions, because then you get stuck with the difficult questions and you will not be finished in time. Write neatly!! Show all calculations. Check your answers, make sure you have typed the correct keys on your calculator. It is very easy to, under stressful conditions, type the wrong keys and thus to get the wrong answer. Do a sum twice on your calculator and make sure you get the same answer. 8

9 Do not waste time on questions that do not count a lot of marks. If you are struggling with a question for 1 or 2 marks, rather go on and come back to this question. Try to be done at least 15 minutes before the time to go through your paper. Make sure the parts that should not be mark, is drawn out. If you finish early, check everything more than 1 time. Make sure everything is completed. Make sure you do not miss a question. Especially a question with many questions, it's easy to miss one. If you did not complete your paper in chronological order, make sure all questions are done! Make sure any appendix is torn off and stapled to your paper. Get enough sleep the night before the paper. You can t think logically if you are tired! To pull an all-nighter the night before, is the recipe for failure! Eat breakfast. Research showed that you can t concentrate when you are hungry. EXCHANGE RATES Standard Bank Exchange rate indicators for Forex at close of business on May 16, 2017 as at 16:08 Bank buys Bank sells Money unit T/T Cheques Notes Cheques & T/T Notes Exchange rate based on Rand per unit foreign currency British pound (GBP) 16, , , , ,2220 Euro 14, , , , ,7817 American-dollars (USD) 12, , , , ,2488 Exchange rate based on foreign currency per R1 Botswana pula (BWP) 0,8444 0,8498 0,8444 0,7288 0,7288 Kenia shieling (KES) 8,8151 8,8962 6,9436 Mozambique metical (MZN) 4,9292 4,4014 4,3490 Namibian dollar (NAD) 1,0000 1,0000 1,0000 1,0000 Nigerian naira (NGN) 30, , ,1245 Swaziland lilangeni (SZL) 1,0000 1,0000 1,0000 1,0000 9

10 The following table should be known by heart. It will NOT be given in the papers 1 cm = 10 mm 1 m = 100 cm 1 km = m 1 = m 1 ton = kg 1 kg = g 1 gram = milligram 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hour 1 week = 7 days 1 month = 4 weeks 1 year = 52 weeks 1 year = 12 months 1 year = 365 days 1 = cm 3 1 m = 1 cm m = cm 3 The following information will be provided in the examination: 1 cm = 0, foot 1 cm = 0, Inch 1 foot = 30,48 cm 1 foot = 0,3048 meters 1 inch = 2,54 cm 1 km = 3280,84 foot 1 km = 39370,1 inch 1 m = 3,28084 foot 1 m = 39,3701 inch 1 mile = 5280 foot 1 gallon =3,78541 liters 1 ounce =28,3495 gram 1 pound =0, kg 1 m 3 = cm 3 1 m 3 = m 1 m 3 = m 2 = cm 2 1 km 2 = m 2 10

11 How to work out Income Tax: Step 1: Annual taxable income (monthly x 12) Step 2: Use the Tax Threshold to determine whether you should continue to pay taxes Step 3: Identify tax bracket Step 4: Identify the "tax formula" Step 5: Work out the provisional tax (before rebates) Step 6: Less Primary rebate Step 7: Less Secondary rebate Step 8: Less Tertiary rebate Step 9: Less Medical rebate Step 10: This annual income tax Step 11: Get monthly income tax by dividing annual by 12 11

12 Person younger than 65 years Person years Person over 75 years Step 1-6 Step 1-6 Step 1-6 Step 9 and further Step 7, 10 and further Step 7, 8, 10 and further 12

13 2018 tax year (1 March February 2018) Taxable income (R) Rates of tax (R) % of taxable income % of taxable income above % of taxable income above % of taxable income above % of taxable income above % of taxable income above and above % of taxable income above tax year (1 March February 2017) Taxable income (R) Rates of tax (R) % of taxable income % of taxable income above % of taxable income above % of taxable income above % of taxable income above and above % of taxable income above tax year (1 March February 2016) Taxable income (R) Rates of tax (R) % of each R % of the amount above % of the amount above % of the amount above % of the amount above and above % of the amount above tax year (1 March February 2015) Taxable income (R) Rates of tax (R) % of each R % of the amount above % of the amount above % of the amount above % of the amount above and above % of the amount above

14 2014 tax year (1 March February 2014) Taxable income (R) Rates of tax (R) % of each R % of the amount above % of the amount above % of the amount above % of the amount above and above % of the amount above tax year (1 March February 2013) Taxable income (R) Rates of tax (R) % of each R % of the amount above % of the amount above % of the amount above % of the amount above and above % of the amount above Tax Rebates Tax Rebate Tax Year Primary R R R R R R Secondary (65 and older) R7 479 R7 407 R7 407 R7 110 R6 750 R6 390 Tertiary (75 and older) R2 493 R2 466 R2 466 R2 367 R2 250 R2 130 Tax Thresholds Tax Year Person Under 65 R R R R R R an older R R R R R R and older R R R R R R Medical Tax Credit Rates from 2013 tax year onwards Per month (R) For the taxpayer who paid the medical scheme contributions R303 R286 R270 R257 R242 R230 For the first dependant R303 R286 R270 R257 R242 R230 For each additional dependant(s) R204 R192 R181 R172 R162 R154 14