AVM Higher Secondary School Maths Quiz Pre-Qualifying Round Class: 9 and 10 Subject: Mathematics 1. If n is an odd integer, which one of the following is an even integer? n (a) n 3 (b) (c) 2n? 3 (d) n ? n? 3? (e) ? n 4 2. If x and y are perfect squares, then which of the following is not necessarily a perfect square? (a) x2 (b) xy (c) 4x (d) x + y (e) x5 3. Let P = ( x + y ) k . If P = 10 and k = 3, what is the average of x 1 5 10 7 and y? (a) 0 (b) (c) (d) (e) 2 3 3 2 4. A square with sides of length 3 cm is intersected by a line at S and T. What is the maximum possible distance between S and T? a) ? 6 (b) 2 ? 3 (c) 3 ? 2 (d) (e) 9 2 ? 5 5. If w is 10 percent less than x, and y is 30 percent less than z, then wy is what percent of less than xz? (a) 10% (b) 20% (c) 37% (d) 40% (e) 100% 6. The average of five numbers is 6. 9. If one of the numbers is deleted, the average of the remaining numbers is 4. 4. What is the value of the number deleted? 7. John is 20 years older then Steve. In 10 years, Steve’s age will be half that of John’s. What is Steve’s age? (a)2 (b) 8 (c) 10 (d) 20 (e) 25 8. Joe takes three-fifths of a bag of candy. Bob has three fourths of Pete’s share of the remaining candy.

What fraction of the total number of pieces of candy does Pete have? 9. Arrange the four squares below to create five squares of the same size. You cannot interlock or overlap the squares. 10. One- fifth of a pound of chocolate is balance perfectly by two-fifth of a block of the same chocolate. What is the weight of the whole block of chocolate? ? Page 1 of 3 ? 11. Six hours ago, it was two hours later than three hours before midnight. What time is it? (a) 5 a. m. (b) 7 a. m. (c) 5 p. m. (d) 8 p. m. (e) 10 p. m. 12. Draw a square as shown and divide the square into four equal congruent parts with three straight lines.

None of the lines may cross each other within the square r . 13. At a reception, one-third of the guests departed at a certain time. Later, two-fifths of the remaining guests departed. Even later, twothirds of those guests departed. If six people left, how many were originally at the party? (a)25 (b) 80 (c) 45 (d) 50 (e) 55 1 . 2 1 14. If x? =3 , then find x ? 2 x x 15. If xy = 12 ,yz = 20 and zx = 15 , the find the value of xyz. 16. Joan and Jane are sisters. Jean is Joan’s daughter and 12 years younger than her aunt is. Joan is twice as old as Jean. Fours years ago, Joan was the same age as Jane is now, was twice as old as her niece was.

How old is Jean? 17. A farmer knows that 20 of his hens, housed in 3 coops, will hatch 30 eggs in 18 days. How long will it take 30 hens, housed in 4 coops to hatch the same number of eggs? 18. What is the area of a circle whose radius is the diagonal of a square whose area is 4? 19. If @ is defined for all positive numbers a and b by a @ b = 2ab – b2, then find the value of 5 @ 2 . 20. There are five teams. Each team plays one game against each of the other teams. How many games are played together? 21. The length of a square is increased by 10% and breadth is decreased by 10%.

Now the area of the new rectangle is ______ (a) remain same (b) 1% less than the square (c) 1% more than the square (d) 5% greater by the square 22. Lily has a book of 125 pages. On how many pages will the sum of the digits be greater than or equal to 10? 23. Which of the proportions is correct if 12 = pq ? (a) 2:p = 6:q (b) 4:p = 3:q (c) 6:p = 2:q (d) 4:q = p:3 24. An equilateral triangle inscribed in a circle having ? 2 (b) 2 radius 2, what is the area of the triangle? (a) a ? 2 (c) ? 3 (d) 3 ? 3 (e) 10 ? 3 ? Page 2 of 3 ? 25. A car travels across Texas ‘ m ’ miles at the rate of ‘t’ miles per a hour. How many hours does the trip take? 6. How can I get the answer 24 by only using the numbers 8,8,3,3. You can use the main signs add, subtract multiply and divide. 27. If the two circles are concentric and the radius of larger circle is . twice that of the smaller circle, what is ratio of the region . between two circles’ area to the area of the smaller circle? . . (a) . 10:1 (b) 9:1 (c) 3:1 (d) 2:1 (e) 1:1 28. Find the mode of 2 , 4 ,5 , 7 , 10 , 27 ,15 ,36 29. Ram agreed to give Shyam some money for 10 days regulation in a . condition that the money to be given next day would be double of . that given on the previous day. If Ram gave Re 1 on the first day, . how much money did Shyam get on the 10th day? 30. From a bag with 80 chocolates, Ram got 20% from his uncle and from a bag with 20 chocolates, Ram got 80% from his aunt. Who gave him more chocolates? 31. Brandon is taking pictures of Mariah, Tobias and Mike. He asks them, “How many different ways could you three stand in a line? ” a) 3 b) 4 c) 5 d)6 e) 9 f) not any Answers 1) d 2) d 3) c 4) c 5) c 6) 16)9 7) c 8) 10)? 11) a 12) 8 35 9) 13) 45 14) 7 15) 60 16) 16 years 17) 18 days 18) 8 ? 19) 16 20) 10 8 m 8 27)c 28) no mode 29) Rs 21) b 22)48 23) d 24) d 25) 26) ? 3? ? t 3 512 30) equal 31) d ? Page 3 of 3 ?