AB EXAM 1. During the first four days of Arthur s new job, he had to wake up at 5:30, 5:30, 7:10 and 7:30. On average, at what time did he have to wake up each morning? 2. When the first 2003 positive odd primes are multiplied together, what is the units digit of the product? 3. The College of Hard Knox belongs to a six-school league in which each school plays four games with each of the other schools. No tied games ever occur, and the other five schools finished the season having won, respectively, 20%, 30%, 35%, 60% and 80% of the league games they played. What was the The College of Hard Knox s final winning record in the league this season (expressed as a percent)? 4. When a dealer learned that the price of a certain product was about to increase by $3 per barrel, he bought a number of barrels of the product for $300. If he would have received five fewer barrels at the new price, how many barrels did he buy? 5. Pretend that you are the owner of a candy store. You have twenty pounds of cashews, which cost $3.55 a pound, and you have some peanuts, which cost $2.50 a pound. How many pounds of peanuts would you have to mix with the cashews to get a mixture that costs $3.20 per pound? 1
6. A survey of 50 students found that 30 had cats, 25 had dogs, 5 had mice, 16 had both dogs and cats, 4 had both dogs and mice, 2 had both cats and mice and only 1 had all three kinds of pets. How many students had no pets of these types? 7. The difference between the squares of two consecutive odd integers is 128. What is the product of the two integers? 8. If x y x + y = 5 2, find x y. 9. There are eight circles in the picture below. The shaded circles are congruent. If each circle in the picture is tangent to each of its neighbor circles, what is the ratio of the total area of the seven shaded regions to the area of the largest circle? Express your answer as a common fraction. 10. When its digits are reversed, a particular positive two-digit integer is increased by 20%. What is the original number? 2
11. Each point in the rectangular grid below is one unit from its nearest horizontal and vertical neighbors. Which point is exactly 10 units from point P? A B C D E F G H I J P 12. Two cylindrical cans have the same volume. The height of one can is triple the height of the other. If the radius of the narrower can is 12 units, how many units are in the length of the radius of the wider can? Express your answer in simplest radical form. 13. Positive integers B and C satisfy B 2 BC 23 = 0. What is the value of C? 14. A parallelogram has vertices at (0, 0), (2, 5), (m, n) and (10,0), where m and n are both positive numbers. How many units are in the length of the longest diagonal of the parallelogram? 15. For how many positive integers x does there exist a positive integer y such that xy x + y =10? 3
16. A certain 90-mile trip took 2 hours. Exactly 1/3 of the distance traveled was by rail and this part of the trip took 1/5 of the travel time. What was the average rate, in miles per hour, of the rail portion of the trip? 17. The following instructions to a computer are carried out in the order specified. 1. LET S=0 2. LET X=5 3. LET THE NEW VALUE OF S EQUAL THE OLD VALUE OF S PLUS THE VALUE OF X 4. INCREASE THE VALUE OF X BY 2 5. IF X<8, GO BACK TO INSTRUCTION 3. OTHERWISE GO ON TO INSTRUCTION 6 6. WRITE THE FINAL VALUE OF S What value of S should be written in instruction 6? 18. Of the following statements, the one that is false is: a. The product of two integers is an integer. b. The sum of two natural numbers is a natural number. c. The product of two irrational numbers is an irrational number. d. The difference of two rational numbers is a rational number. e. None of these. 19. If the sum of 5 consecutive positive integers is w, write the sum of the next 5 consecutive positive integers in terms of w. 4
20. If the five-digit number 5DDDD is divisible by 6, then determine the digit D. 21. The sum of 101 consecutive integers is equal to 101. What is the largest integer in the sequence? 22. What is the probability that four randomly selected points on the geoboard shown below are vertices of a square? 5