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SOUTH AFRICAN MATHEMATICS OLYMPIAD
Organised by the

SOUTH AFRICAN MATHEMATICS FOUNDATION

2012 FIRST ROUND
SENIOR SECTION: GRADES 10, 11 AND 12 19 March 2012 Time: 60 minutes Number of questions: 20

Instructions 1. This is a multiple choice question paper. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct. 2. Scoring rules: 2.1. Each correct answer is worth 5 marks. 2.2. There is no penalty for an incorrect answer or any unanswered question. 3. You must use an HB pencil. Rough work paper, a ruler and an eraser are permitted. Calculators and geometry instruments are not permitted. 4. Figures are not necessarily drawn to scale. 5. Indicate your answers on the sheet provided. 6. Start when the invigilator tells you to do so. 7. Answers and solutions will be available at www.samf.ac.za

Do not turn the page until you are told to do so. Draai die boekie om vir die Afrikaanse vraestel.

PRIVATE BAG X173, PRETORIA, 0001 TEL: (012) 392-9323 Email: ellie@samf.ac.za Organisations involved: AMESA, SA Mathematical Society, SA Akademie vir Wetenskap en Kuns

PRACTICE EXAMPLES

1. As a decimal number 6.28% is equal to (A) 0.0628 (B) 0.628 (C) 6.28 (D) 62.8 (E) 628

2. The value of 1 +

1 3+ 1 2 7 6

is

(A)

6 5

(B)

(C)

9 2

(D)

6 7

(E)

9 7

3. The tens digit of the product 1 × 2 × 3 × · · · × 98 × 99 is (A) 0 (B) 1 (C) 2 (D) 4 (E) 9

PLEASE DO NOT TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO

1. The value of

1 + 0.025 is 4 (B) 1 2 (C) 0.375 (D) 3 8 (E) 11 40

(A) 0.05

2. In a country with a population of 60 000 000 people, 1% of the population is over 2 metres tall. How many people are over 2 metres tall? (A) 6 000 000 (B) 600 000 (C) 60 000 (D) 6 000 (E) 600

3. The value of 20122 − 20112 is (A) 1 (B) 2011 (C) 2012 (D) 2013 (E) 4023

4. The mean of five numbers is 12. If one number is removed, the mean of the remaining four numbers is 14. The number that was removed is (A) 2 (B) 4 (C) 6 (D) 8 (E) 10

5. Two circles of radius 2 touch each other and are inscribed in a large circle as shown. The area of the shaded region is 9π 2

(A)

(B) 12π

(C) 24π

(D) 4 + 4π

(E) 4π

6. The unit square in fig 1 is surrounded by 8 unit squares to form fig 2. These 9 unit squares are then surrounded again to form fig 3. If this pattern continues, then how many unit squares in total would there be in figure 10? (A) 169 (B) 225 (C) 289 (D) 361 (E) 441

7. A mountain path has a gradient of 3 : 4. If I walk 15 m up the path, then how many metres higher am I than at my original position? (A) 4 (B) 6 (C) 9 (D) 10 (E) 15

8. If your watch loses 5 minutes each hour and you set the time correctly at 07:00, what is the actual time when your watch shows later that morning that it is 09:45? (A) 09:55 (B) 10:00 (C) 10:05 (D) 10:10 (E) 10:15

9. A pack of 52 cards is dealt out to 10 people seated around a circular table in such a way that the first person gets the 1st card, the fourth person gets the 2nd card, the seventh person gets the 3rd card, the tenth person gets the 4th card, the third person gets the 5th card and so on. Which person gets the last card? (A) 2nd (B) 4th (C) 5th (D) 6th (E) 7th

10. A straight line passes through the points (2,3) and (4,7). Which one of the following points is also on the line? (A) (0, 2) (B) (1, 2) (C) (2, 4) (D) (3, 5) (E) (4, 5)

11. The value of 1 + 2 + 3 − 4 + 5 + 6 + 7 − 8 + . . . + 97 + 98 + 99 − 100 is (A) 4010 (B) 5050 (C) 3050 (D) 2450 (E) 1206

12. How many pairs of parallel edges are there in the rectangular box shown?

(A) 18

(B) 12

(C) 24

(D) 8

(E) 16

13. A ball is dropped from the roof of a tall building. Which one of the following graphs best represents the height h of the ball above the ground with respect to time t?

14. In a set of numbers there are 5 even numbers and 4 odd numbers. If 2 numbers are chosen at random from the set, without replacement, then the...
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