Graad/Grade 12 Februarie/February

Toets/Test Totaal/Total: 55 punte/marks

Eksaminator: Tyd/Time: 1 uur/hour

Moderator:

INSTRUKSIES INSTRUCTIONS

1. Beantwoord ALLE vrae.2. Sakrekenaars mag gebruik word.3. Dit is tot jou eie voordeel om netjies en

volledig te werk.4. Rond alle antwoorde af tot 2 desimale syfers.5. Trek ‘n lyn na elke vraag.6. Geniet die vraestel.

1. Answer ALL questions.2. Calculators may be used.3. It is to your advantage to work neatly and show

all workings.4. Round off all answers to two decimal places.5. Draw a line after each question.6. Enjoy the paper.

Vraag 1/Question 1

Onderstaande is twee getalpatrone:

een is rekenkundig een is meetkundig

Below is two number sequences:

one is arithmetic one is geometric

A: -1; 4; -16; 64; …..

B: 10; 8,75; 7; 5,75; …..

1.1 Skryf die een wat meetkundig is neer. Identify and write down the geometric sequence. (1)

1.2 Verduidelik hoekom die som tot oneindigheid van dié reeks nie bereken kan word nie. Explain why the sum to infinity of this sequence cannot be found. (1)

1.3 Bepaal die som van die eerste 11 terme van die meetkundige ry. Determine the sum of the first 11 terms of the geometric sequence. (4)

1.4 Bepaal watter term van die rekenkundige ry is -35. Determine which term of the arithmetic sequence is equal to -35. (4)

1.5 Skryf die rekenkundige ry in sigma notasie as dit 110 terme bevat. Write the arithmetic sequence in sigma notation if it has 110 terms. (3)

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Vraag 2/Question 2

2.1 Bewys dat die som van ‘n rekenkundige ry bereken kan word deur die formule

Sn=n2[2a+(n−1 )d] te gebruik.

Prove that the sum of a arithmetic sequence can be calculated by using the formula

Sn=n2[2a+(n−1 )d] (4)

2.2 Bereken k as/Determine k if:

∑n=1

k

(3n+4 )=282

(6) [10]

Vraag 3/Question 3

Bewys dat die terme 2a−13

; 2a−12

; 2(2a−1)3

‘n rekenkundige ry vorm.

Prove that the terms 2a−13

; 2a−12

; 2(2a−1)3

form an arithmetic sequence.

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Vraag 4/Question 4

4.1 Gegee/Given: Sn=3n+2−9.

Bewys dat Tn gegee word deur T n=2¿.

Prove that Tn is given by T n=2 ¿. (5)

4.2 Die tweede en vierde terme van ‘n konvergerende ry is 36 en 16 respektiewelik. Bepaal die som tot oneindigheid van die reeks as al die terme nie positief is nie. The second and fourth terms of a convergent series are 36 and 16 respectively. Find the sum to infinity of this series, if all terms are not positive. (6)

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Vraag 5/Question 5

Aanvaar dat die bostaande patrone só bly toeneem. Assume that the patterns above continue to behave consistently.5.1 Bepaal ‘n formule vir die aantal blokke in die nde patroon.

Determine a formula for the number of blocks in the nth pattern. (4)5.2 Gebruik jou antwoord in 5.1 om jou te help om die waarde van T50 + T51 in die

onderstaande ry te vind:2; 2; 4; 5; 7; 8; 11; 11,….Use your answer in 5.1 to assist in finding the value of T50 + T51 in the sequence below:2; 2; 4; 5; 7; 8; 11; 11,…. (5)

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Vraag 6/Question 6

‘n Man is beseer in ‘n ongeluk by die werk. Hy verdien ‘n ongeskiktheidstoelae van R4800 in die eerste jaar. Die toelae word jaarliks met dieselfde hoeveelheid vermeerder. A man was injured in an accident at work. He receives a disability grant of R4800 in the first year. This grant increases with a fixed amount each year.

6.1 Wat is sy jaarlikse verhoging indien hy na 20 jaar ‘n totaal van R143 500 ontvang het? What is the annual increase if, over 20 years, he would have received a total of R143 500. (4)

6.2 Sy aanvanklike uitgawes is R2 600 en dit vermeerder teen R400 per jaar. Ná hoeveel jaar is sy uitgawes meer as sy inkomste? Aanvaar dat sy inkomste elke jaar met R250 styg. His initial annual expenditure is R2 600 and increases at a rate of R400 per year. After how many years does his expenses exceed his income? Accept that his grant increases with R250 per year. (4)

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