ASIAN MATHS OLYMPIAD

Transcription

1 ASIAN ATHS OLYPIAD Full Name: Date: School Name: IC No.: Time: Class: Rules and Regulations (Please read the following rules and regulations carefully) 1. Please fill in your FULL name correctly, IC No., school name, class and the date and time of contest clearly in the spaces above. Those who do not fill in the required particulars will be disqualified automatically. 2. Do not open the question booklet until you are told to do so. You may use only 2B pencil when answering the questions. 3. No calculators and any unauthorised electronic devices (including mobile phones) are allowed during the contest. 4. Strict silence must be observed at all times in the examination hall and please be reminded that you AY NOT leave your seat without permission. 5. If you have any request or enquiry, please raise your hand and wait for an invigilator. 6. Only one candidate is allowed to leave the hall at a time. You are required to return to the hall within 10 minutes or else you will automatically be disqualified from the contest. 7. All questions in the contest have been verified by experienced trainers, thus no further explanation will be given. 8. The time allowed for the paper is 120 minutes. You must stop writing when you are told to do so. 9. You UST fill in your answers in the answer sheet on the second page of this question booklet. Any answers written elsewhere in the question booklet will not be awarded marks. 10. Please be reminded that this is a contest and not an examination, do not expect to answer all questions. Just answer as many questions as possible. 11. Please tear off the answer sheet carefully and return it to the invigilator along with the contest paper. Contestants are allowed to collect the contest papers only a week later. 12. Please be reminded that NO SUBSTITUTE for a contestant who can t attend the contest is acceptable. The contestant who violates this rule will be disqualified automatically. Scoring System 1. For Questions 1 10, 3 marks will be awarded for each correct answer. For Questions 11 20, 4 marks will be awarded for each correct answer. For Questions 21 25, 6 marks will be awarded for each correct answer. However, you will NOT be penalised for any incorrect answer. 2. The organiser reserves the rights to disqualify the event of malpractice to differentiate between those outstanding students. 3. A disqualified team or contestants will not be allowed to participate in other contest of the same year.

2 2016 ANSWER SHEET ASIAN ATHS OLYPIAD

3 ASIAN ATHS OLYPIAD 1. (- 2016) (- 2015) (-2014) (2014) (2015) (2016) = sin 2016⁰ -- cos 2034⁰ = 4. (log 2) 3 + (log 5) 3 + (log 2)(log 5) = 5. The function f(x) is defined in domain of integer with the following definition: Calculate the value of

4 ASIAN ATHS OLYPIAD The function f(x) is defined as Simplify the following terms 8. Thirteen positive integers are written in order as following: 1,3,4,4,a,a,b,c,c,c,10,12,13 If the mean for this set of numbers is 7, the mode for this set of numbers is 9 and the median for this set of numbers is 7, calculate value of a+b+c. 9. Calculate the area enclosed by y = x 2 and y = x 3 in a Cartesian plane. 10. Evaluate 11. The function f(x) is defined by the following equation Calculate f(2016) - f(-2016)

5 ASIAN ATHS OLYPIAD 12. ( x 2 x + 1) 16 = a 0 + a 1 x +a 2 x 2 + a 3 x a 32 x 32 Calculate the value of a 0 + a 1 + a 2 + a 3 + a The following diagram shows a triangle ABC. Point P subdivides triangle ABC into 3 small triangles PBC, PCA and PAB such that the area S PAB :S PBC :S PCA =3:5:4. If, what is the value of h+k Seven different presents are all given to Ali, uthu and Ah Chong. If Ali must be given one present, how many way(s) can the presents be given out?

6 ASIAN ATHS OLYPIAD 16. Given that a 2 + b 2 = c 2.What is the value of 17. A meteorological station has a weather forecast accuracy of 75%. Calculate the probability of only 2 out of 5 weather forecasts from this station are correct. 18. Given that the average of the first 9 terms of an arithmetic progression is 10 and the average of the first 10 terms of the same arithmetic progression is 11. What is the value of common difference of this arithmetic progression? 19. The diagram shows a circle with centre O. Line PA and PB are tangent to the circle at point A and B respectively. Line PO intersects circle at point C. Given that PB = 10cm and PC = 5cm, calculate the perpendicular distance from point C to line AB. 20. A triangle ABC has the following characteristics: i. A = 2C ii. a + c = 2b iii. c = 4cm Calculate the perimeter of ABC.

7 ASIAN ATHS OLYPIAD 21. Evaluate the value of tan 20º + 4 tan 20º 22. Two roots of the quadratic equation x 2 +x+1=0 is α and β. Calculate α β How many ways are there to use paper notes of R1, R2, R5 and R10 to prepare R16? 24. A positive integer is divisible by 5 and 49. If it is known that this integer has exactly 10 factors, what will be the value of this integer? 25. The following diagram shows a cube ABCD-EFGH with length of edge equal to 6cm. Calculate the distance between lines BE and GC. THE END