Department of Mathematics and Applied Mathematics Departement Wiskunde en Toegepaste Wiskunde

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1 Department of Mathematics and Applied Mathematics Departement Wiskunde en Toegepaste Wiskunde MATHEMATICS COMPETITION WISKUNDE KOMPETISIE GRADES 0 AND GRADE 0 EN SEPTEMBER 04 SEPTEMBER 04 TIME: HOURS TYD: URE 0 OUTEURSREG VOORBEHOU, UNIVERSITEIT VAN PRETORIA 0 COPYRIGHT RESERVED, UNIVERSITY OF PRETORIA

2 INSTRUCTIONS INSTRUKSIES No calculators or other calculation Geen sakrekenaars of ander aids are allowed. rekenhulpmiddels word toegelaat nie. Mark allocation Puntetoekenning Every question counts mark. Elke vraag tel punt. Random guessing is not advisable, Raaiery word nie aanbeveel nie, as the mark allocated to a question aangesien die punt toegeken aan die may be deducted for a wrong answer. vraag afgetrek mag word vir n n verkeerde antwoord. Every question has five possible Elke vraag het vyf moontlike answers, (A) to (E). antwoorde, (A) tot (E). Only ONE answer is correct. Slegs EEN antwoord is korrek. Colour in the rectangle of the correct Kleur die reghoek van die korrekte answer on the answer sheet. antwoord op die antwoordvel in. Do not colour outside the rectangle. Moenie buite die reghoek inkleur nie. Use a soft pencil. Gebruik n sagte potlood. Example: Voorbeeld: Suppose Question reads: Gestel Vraag is: The smallest integer larger than is Die kleinste heelgetal groter as is (A) 0 (B) (C) (D) (E) 3 The correct answer is, which is answer (D). On the answer sheet you must colour in the rectangle (D) against Die korrekte antwoord is, en dit is antwoord (D). Op die antwoordvel moet jy die reghoek (D) inkleur teenoor Question. Vraag. Question / Vraag (A) (B) (C) (D) (E)

3 Question Vraag Calculate Bereken (A) (B) (C) 0.35 (D) (E) Question Vraag If x = and y = then (x + )(y ) is 3 equal to? (A) 7 (B) 5 (C) 5 As x = en y = dan is (x + )(y ) 3 gelyk aan? (D) 7 Question 3 Vraag 3 The sum of nine numbers is 46. If one of the nine numbers is changed from 654 to 456, what is the new sum? (E) 9 Die som van nege getalle is 46. As een van die nege getalle verander word van 654 na 456, wat is die nuwe som? (A) 98 (B) 654 (C) 8 (D) 46 (E) 64 Question 4 Vraag 4 Arrange the numbers x, x+, x 4, x+5 and x 3 from biggest to smallest. What is the middle number? Rangskik die getalle x, x+, x 4, x+5 en x 3 van grootste na kleinste. Watter getal is in die middel? (A) x 4 (B) x + (C) x 3 (D) x + 5 (E) x Question 5 Vraag 5 Cindy thinks of a positive number. She squares it and add to it. Then she halves the number and gets 38. What number did Cindy think of? (A) 8 (B) 9 (C) 0 (D) 36 (E) 64 Question 6 Vraag 6 Suppose the operation is given by the rule x y = xy + x + y. Solve for x if x 3 = 6. (A) 3 (B) 7 3 (C) 4 (D) 7 4 Question 7 Vraag 7 Cindy dink aan n positiewe getal. Sy kwadreer dit en tel by. Dan halveer sy die getal en kry 38. Aan watter getal het Cindy gedink? Veronderstel die bewerking word gegee deur die reël x y = xy + x + y. Los op vir x as x 3 = 6. (E) 5 The cube root of 4 3 is Die derdemagswortel van 4 3 is (A) 4 (B) 64 (C) 56 (D) 8 (E) 04

4 Question 8 Vraag 8 The diameter of a circle is 4π. What is the area of the circle? Die middellyn van n sirkel is 4π. Wat is the oppervlak van die sirkel? (A) 4π (B) 4π (C) 8π (D) 4π 3 (E) 8π 3 Question 9 Vraag 9 Solve for x if + x = 5. Los op vir x as + x = 5. (A) 4 5 (B) 5 (C) 5 4 (D) 5 (E) 4 Question 0 Vraag 0 A container has 3 red, 4 blue and 5 green marbles. A marble is drawn from the container, and without putting it back, a second marble is drawn. What is the chance that they are both blue? n Houer het 3 rooi, 4 blou en 5 groen albasters. n Albaster word getrek uit die houer, en sonder om dit terug te plaas, word n tweede albaster getrek. Wat is die kans dat albei blou albasters getrek is? (A) 0 (B) (C) (D) 3 (E) 4 Question Vraag Make x the subject of the formula if Maak x die onderwerp van die formule as z + y = x + y. (A) (B) (C) (D) (E) x = z + 4z y + 4y x = z + z y + 4y x = z + 4z y + 3y x = z + z y + 3y none of these/geen van die

5 Question Vraag Find k if the slope of the line passing through points A(, ) and B(k + k, k + 3k) is. (A) (B) 0 (C) (D) 4 (E) 6 Question 3 Vraag 3 How many numbers in this arithmetic sequence, 8, 5,, 9, 36,... is between 00 and 500? (A) 56 (B) 57 (C) 58 (D) 59 (E) 60 Question 4 Vraag 4 The vertex (turning point) of the parabola y = x +8x+c will be a point on the x-axis if the value c is : (A) 6 (B) 4 (C) 4 (D) 8 (E) 6 Question 5 Vraag 5 The lengths of two adjacent sides of a parallelogram is and 3. The sum of the squares of the diagonals of the parallelogram is : (A) (B) 4 (C) 6 (D) 8 (E) 30 Question 6 Vraag 6 What is a + b + c if a + b + 3c = 6, 3a + b + c = and a + 3b + c = 7? (A) (B) (C) 3 (D) 4 (E) 5 Bepaal k as die helling van die lyn wat deur punte A(, ) en B(k +k, k +3k) gaan is. Hoeveel terme in die rekenkundige ry, 8, 5,, 9, 36,... is tussen 00 en 500? Die draaipunt van die parabool y = x + 8x + c sal op die x-as lê indien c gelyk is aan : Die lengtes van twee aangrensende sye van n parallelogram is en 3. Die som van die kwadrate van die diagonale van die parallelogram is : Wat is a + b + c as a + b + 3c = 6, 3a + b + c = en a + 3b + c = 7?

6 Question 7 Vraag 7 Calculate 4 n+ 36 n 45 n+ 5 if n = 04. Bereken 4n+ 36 n as n = 04. n 45 n+ 5n (A) 4 9 (B) 5 9 (C) 9 5 (D) 9 4 (E) None of these/geen van die Question 8 Vraag 8 If f(x) = x g(f(x)). x + and g(x) = x, find As f(x) = x g(f(x)). x + en g(x) = x, bepaal (A) x (B) x + (C) x + x (D) 3x (E) x x + Question 9 Vraag 9 Solve for x if x + x + Los op vir x as x + x +... = 5. (A) 7 (B) 9 (C) 5 4 (D) 7 4 (E) 5 Question 0 Vraag 0 Inside a circle of radius, three mutually tangent circles are drawn with the same radius. Determine the radius of the smaller three circles if they are all tangent to the big circle. Binne n sirkel met radius, word drie sirkels geteken met dieselfde radius. Bereken die radius van die kleiner sirkels as al die sirkels aan mekaar raak. (A) (B) 3 (C) (D) (E) 3 3 4

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