[PDF] SASMO 2014 Round 1 Secondary 2 Problems.pdf | Plain Text

SASMO 2014 Round 1 Secondary 2 Problems1. The first day of 2014 was a Wednesday. There are 365 days in 2014. In what day of the week will 2015 begin? 2. What is the maximum number of parts that can be obtained from cutting a circular cake using 3 straight cuts? 3. Evaluate 2014  2014  2013  2015. 4. Solve = 3 . 5. Find the exact value of 1  0.99999… 6. Mersenne primes are prime number s of the form M p = 2 p  1, where p is a prime. For example, 3 = 2 2  1 is a Mersenne prime. Find the 4 th largest Mersenne prime. 7. S im plify ( x  a) ( x  b) ( x  c) … ( x  z). 8. How many squa r es are there in a 5  5 square grid? 9. If x and y are positive integers, find the values of x and y which satisfy the equation x 2  4y2 = 41. 10. Find the dimensions of all the rectangles with integral sides whose area and perimeter are numerically equal. 11. A whole number is between 40 and 70. When it is divided by 3, the remainder is 1. When it is divided by 7, the remainder is 2. Find the number. 12. Find the value of             22 12 2 2 12 2 2 . 13. Find the value of . 14. Find the sum of the terms in the nth pair of brackets: (1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), … 15. In the diagram, PQ and RS are parallel, PA = PB and RA = RC . Find BAC . P R S A B C Свалено от Klasirane.Com

16. There are 367 students in the school hall. What is the probability that two of the students have their birthday falling on the same day of the year? 17. Let x be a number such that5 1   x x . Find the value of 3 3 1x x  . 18. Divide the following shape into 4 identical parts. 19. Find all the solutions to the trigonometric equation sin 2 x  cos 2 x = 1 for 0  x  360 . 20. The diagram shows a square AEFG with an inscribed circle. ABCD is a rectangle such that AB = 2 cm and AD = 4 cm. Find the radius of the circle. A B D C E F G 21. In the following cryptarithm, all the letters stand for different digits. Find the final four-digit product. H E  E H * 8 + * * * * * * 22. A farmer wants to plant 10 trees in 5 rows such that there are exactly 4 trees in each row. Draw a diagram to show how the trees should be planted. 23. Find the last three digits of 25 25 . 24. Find the remainder when 3 2014 is divided by 5. 25. Find the largest number of composite numbers less than 2014 that are relatively prime to one another, i.e. the highest common factor of any two of them is 1. Свалено от Klasirane.Com