[PDF] SASMO 2014 Round 1 Secondary 1 Problems.pdf | Plain Text

SASMO 2014 Round 1 Secondary 1 Problems1. Find the next term of the following sequence: 2, 1, 3, 4, 7, …2. Find the product of the highest common factor and the lowest common multiple of 8 and 12. 3. Solve for x and y in the following equation . 4. The last day of 2013 was a Tuesday. There are 365 days in 2014. In what day of the week will 2014 end? 5. What is the maximum number of parts that can be obtained from cutting a circular disc u sing 3 straight cuts? 6. A man bought two paintings and then sold them for $300 each. He made a profit of 20% for the first painting, but a loss of 20% for the second painting. Overall, did he make a profit, a loss or break even? If he did not break even, state the amount of profit or loss. 7. Solve = 2. 8. Given that xyz = 2014, and x, y and z are positive integers such that x < y < z, how many possible triples ( x, y, z) are there? 9. At a workshop, there are 27 participants. Each of them shakes hand once with one another. How many handshakes are there? 10. A perfect number is a positive integer that is equal to the sum of its proper positive factors. Proper positive factors of a number are positive factors that are less than the number. For example, 6 = 1 + 2 + 3 is a perfect number because 1, 2 and 3 are the only proper positive factors of 6. Find the next perfect number. 11. The dimensions of a rectangle are x cm by y cm, where x and y are integers, such that the area and perimeter of the rectangle are numerically equal. Find all the possible values of x and y . 12. If a and b are positive integers such that a < b and ab = ba , find a possible value for a and for b . 13. Find the value of             11 21 1 21 1 . 14. Find the last digit of 2014 2014 . 15. The diagram shows 9 points. Draw 4 consecutive line segments (i.e. the start point of the next segment must coincide with the endpoint of the previous segment) to pass through all the 9 points. Свалено от Klasirane.Com

16. What are the last 5 digits of the sum 1 + 11 + 111 + … + 111…111? 17. What is the least number of cuts required to cut 10 identical sausages so that they can be shared equally among 18 people? 2014 digits 18. Divide the following shape into 4 identical parts. 19. Solve the following equation: x5 + 2 x 3  x2  2 = 0. 20. Find the value of . 21. In the following cryptarithm, all the letters stand for different digits. Find the values of A, B, C and D. A 8 B C  3 D 9 8 2 0 1 4 22. Find the sum of the terms in the nth pair of brackets: (1, 2), (3 , 4), (5, 6), (7, 8), … 23. In the diagram, PQ is parallel to RS, PA = PB and RB = RC . Given that BCA = 60, find BAC . P Q R S A B C 60  Свалено от Klasirane.Com

24. Find the remainder when 2 2014 is divided by 7. 25. The diagram shows a triangle ABC where AB = AC , BC = AD and BAC = 20  . Find  ADB . A B C D 20  Свалено от Klasirane.Com