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...

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...

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