Question / Vraag 1: [12]
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1 1 Question / Vraag 1: [12] The following questions are multiple choice questions. There is only one correct answer from the choices given. Select the correct option by marking the option with a cross (X). / Die volgende vrae is veelkeusige vrae. Daar is slegs een korrekte antwoord uit al die opsies gegee. Merk die korrekte antwoord met n kruis (X). 1.1 a; b; c; d is an arithmetic series of four different numbers. Which statement is NOT TRUE? / a; b; c; d bewering is NIE WAAR NIE? a) b a = d c b) c a = d b c) 2b = a + d d) 2b = a + c e) They are all true / Almal is waar is n rekenkundige ry met vier verskillende getalle. Watter 1.2 The coefficient of in the expansion of ( )( ) is: / Die koëffisiënt van in die uitbreiding van ( )( ) is: a) 96 b) 576 c) 32 d) 480 e) None of the above / Geen een van bogenoemde nie 1.3 If a letter is chosen randomly from the word GEOMETRY, the probability that it will be an E is: / As n letter ewekansig gekies word uit die woord GEOMETRY, is die waarskynlikheid dat dit n E is: a) b) c) d) e) None of the above / Geeneen van bogenoemde nie
2 2 1.3 You know that the extension of a telephone number is 343, but you have forgotten the last four digits. You can only recall that the last 4 digits are 3; 6; 8; and 9, but you don t know the order. What is the maximum number of telephone calls you will need to make in order to dial the correct number? / Jy weet dat die uitbreiding van n telefoonnommer 343 is, maar jy het die laaste vier syfers vergeet. Jy kan net onthou dat die laaste 4 syfers 3; 6; 8; en 9 is, maar jy weet nie wat die volgorde is nie. Wat is die maksimum aantal oproepe wat jy sal moet maak om die korrekte nommer te skakel? a) 4 b) 18 c) 20 d) 24 e) None of the above. / Geen een van die bogenoemde. Question / Vraag 2: [10] Give a short answer to the following questions. / Gee n kort antwoord vir die volgende vrae. Question / Vraag Answer / Antwoord Simplify / Vereenvoudig: ( ) If interest is compounded monthly, and the effective interest rate is12,13%, what is the nominal interest rate? As rente maandeliks saamgestel word en die effektiewe rentekoers is 12,13%, wat is die
3 3 nominale rentekoers? True or False? If mean > median, the data is skewed to the right. Waar of Onwaar? As gemiddelde > mediaan is die data skeef na regs. Paul has 1 green shirt, 5 red shirts, and 9 striped shirts. He randomly draws one out of his drawer. What is the probability that the shirt is striped? Paul het 1 groen hemp, 5 rooi hemde en 9 gestreepte hemde. Hy kies een hemp ewekansig uit die laai. Wat is die waarskynlikheid dat die hemp gestreep is? Determine whether the statement is True or False: The 50 th percentile is another term to describe the mean. Bepaal of die bewering Waar of Onwaar is: Die 50 ste persentiel is n ander woord om die gemiddelde te beskryf Question / Vraag 3: [12] 3.1 In the following sketches, shade the appropriate sections: Arseer die gevraagde gebiede in die sketse: A B A B (A B) (A B)
4 4 3.2 The probability that a grade 9 learner chooses Mathematics as a subject is 0,7. The probability that he chooses Geography as a subject is 0,2. The probability that he takes neither is 0,3. /Die waarskynlikheid dat n graad 9 leerder Wiskunde as vak kies is 0,7. Die waarskynlikheid dat hy Aardrykskunde kies is 0,2. Die waarskynlikheid dat hy geen een van die twee vakke kies nie, is 0, Draw a Venn-diagram to represent this information: / Teken n Venn diagram om die inligting voor te stel: (2) (2) Find the probability that he takes both, Mathematics and Geography. / Vind die waarskynlikheid dat hy beide, Wiskunde en Aardrykskunde kies. (2) Find the probability that he takes only one of the two. / Vind die waarskynlikheid dat hy slegs een van die twee kies. (1)
5 5 3.2 In a game of chance you spin the following two spinners. You have to spin the first spinner once to determine whether you have to pay or receive money and the second spinner once in order to determine how much money you pay or receive. / In n kansspel moet jy die volgende twee spinners spin: jy moet die eerste een eenkeer spin om te bepaal of jy geld moet betaal of ontvang, en dan spin jy die tweede een eenkeer om vas te stel hoeveel jy moet betaal of ontvang. PAY R10 R20 RECEIVE R50 R Draw a tree diagram to represent all the possible outcomes. / Teken n boomdiagram om al die moontlike uitkomste voor te stel. (4) Determine the probability of receiving R50 if you play the game once. / Bepaal die waarskynlikheid dat jy R50 sal ontvang as jy die spel eenkeer speel. (1)
6 6 Question / Vraag 4: [18] 4.1 Jean borrows R to buy an apartment. The interest rate is 15,5% per annum, compounded monthly. She will repay the loan with equal monthly instalments at the end of each month over a period of 20 years. / Jean leen R om n woonstel te koop. Die rentekoers is 15,5% per jaar, maandeliks saamgestel. Sy sal die lening terugbetaal in gelyke maandelikse paaiemente, oor n tydperk van 20 jaar Determine her monthly instalments. / Bepaal haar maandelikse paaiemente Calculate the outstanding balance on the loan after 10 years. / Vind die uitstaande balans op die lening na 10 jaar.
7 At the end of 10 years she falls into some financial difficulty and cannot keep up her payments. After 6 months, her situation improves and she starts paying her instalments at the end of the 7 th month. What will her new instalments be if she still intends to settle her loan by the end of 20 years? / Aan die einde van 10 jaar beland sy in finansiële moeilikheid en kan nie meer haar paaiemente betaal nie. Na 6 maande verbeter haar situasie en sy begin teen die einde van die 7de maand weer om haar paaiemente te betaal. Wat sal haar nuwe paaiement wees as sy steeds beplan om die lening teen die eide van 20 jaar af te betaal? 4.2 Mandy takes out a loan of R in order to start a business. She repays R two years later. Four years after starting a business she expands, and borrows a further R Three years later she pays off the total debt in one payment. The rate of the loan was 18% p.a., compounded monthly. Use a timeline to determine Mandy s debt payment at the end of 7 years. Mandy neem n lening uit van R om n besigheid te begin. Twee jaar later betaal sy R terug. Vier jaar nadat sy die lening geneem het, brei sy haar besigheid uit en leen n verdere R Drie jaar later betaal sy die totale skuld in
8 8 een betaling terug. Die rentekoers was 18% p. j., maandeliks bereken. Gebruik n tydlyn om te bereken hoeveel sy aan die einde van 7 jaar terugbetaal het. (5) 4.3 A man buys a TV, costing R7 800, on a hire purchase agreement. He pays a deposit of 20%, and agrees to pay the balance over a period of 2 years in half yearly instalments at 13,5% interest p.a. Determine the amount of each instalment. / n Man koop n TV wat R7 800 kos, op n huurkoop ooreenkoms. Hy betaal n deposito van 20% en stem ooreen om die balans oor 2 jaar terug te betaal in halfjaarlikse paaiemente teen 13,5% rente per jaar. Bereken die bedrag van elke paaiement. (4)
9 9 Question / Vraag 5: [23] 5.1 The first two terms of an infinite geometric sequence are 8 and using a calculator, that the sum of the series to infinity is / Die eerste twee terme van n meetkundige ry is 8 en sakrekenaar, dat die som van die reeks tot oneindig is Prove, without 2 8. Bewys, sonder n (4) 5.2 Consider the sequence: / Beskou die ry: 3; 8; 13; 18; 23; 28; If the sequence continues to behave in the same manner, write down the next two terms. / As die ry so voortgaan, skryf die volgende twee terme neer. (1)
10 Write down a recursive formula for the n-th term of the above sequence./ Skryf neer die rekursiewe formule vir die n-de term van die bogenoemde ry. (2) 5.3 The first and second terms of an Arithmetic series are 161 and 154 respectively. The sum of the first n terms is 0. Find n. Die eerste en tweede terme van n Rekenkundige reeks is 161 en 154 respektiewelik. Die som van die eerste n terme is 0. Vind n. (4)
11 Consider the sequence: / Beskou die ry: 3; a;10; b ; 21;... It is given that the sequence has a common second difference of 1. / Dit word gegee dat die ry n gemene tweede verskil van 1 het Show by calculation that a 6 and b 15. / Toon aan deur berekenunge dat a 6 en b 15. (4) Calculate the n th term of the sequence. / Vind die n de term van die ry.
12 Use the Binomial Theorem to expand and simplify the expression: / Gebruik die Binomiaal Stelling om uit te brei en vereenvoudig die uitdrukking: ( ) (5) Question / Vraag 6: [12] 6.1 The following cumulative frequency graph shows the percentage spent on advertising for a sample of 50 businesses. / Die volgende kummulatiewe frekwensie grafiek toon die persentasie uitgawes op advertensies vir n steekproef van 50 besighede. C u m u l a t i v e F r e q u e n c y Percentage
13 Indicate, on the graph, where you read the values of Q 1, median and Q 3. / Dui aan op die grafiek, waar u die waardes van Q 1, mediaan en Q 3 sal aflees. Now complete:/ Voltooi nou: Q 1 =.. Median/ mediaan = Q 3 = Use the graph to determine how many businesses spend less than 50% on advertising. / Gebruik die grafiek om vas te stel hoeveel besighede spandeer minder as 50% op advertensies. (2) 6.2 A teacher presented the following box and whisker diagrams as part of a staff discussion on learner performance. The diagram shows the percentage test marks in mathematics for a revision test for two class groups. / n Onderwyser het die volgende houer-en-punt diagramme aangebied as deel van n personeelbespreking oor leerder-prestasie. Die diagram toon die toets uitslae vir n hersieningstoets vir albei klasgroepe.
14 In which class was the range of percentage marks greatest? / In watter klas was die persentasie punte die hoogste? (1) What was the median percentage mark for each class? / Wat was die mediaan persentasie punt vir elke klas? (2) What was the interquartile range for each class? / Wat was die interkwartielvariasiewydte vir elke klas? (4) Question / Vraag 7 [13] The following data illustrates the relationship between the annual profit (in thousands of rands) and the annual marketing expenditure (in thousands of rands) of a company. / Die volgende data illustreer die verwantskap tussen die jaarlikse wins (in duisende rande) en die jaarlikse bemarkingsuitgawes (in duisende rande) van n maatskappy. Annual marketing expenditure (x) Jaarlikse bemarkingsuitgawes Annual profit (y) Jaarlikse wins
15 Plot the data in a scatter diagram. / Plot die data in n spreidingsdiagram 7.2 Draw on the above system the line of best fit. / Teken op bostaande die lyn van beste passing. (1) 7.3 Determine the equation of the least squares regression line. / Bereken die vergelyking van die kleinste kwadrate regressielyn. (4) 7.4 Calculate the correlation coefficient. / Vind die korrelasiekoëffisiënt. (2) 7.5 Estimate the annual profit if R15000 was spent on marketing. / Skat die jaarlikse wins as R op bemarking gespandeer is.
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