January 2002 TRINITY MATH TRIATHLON

1.  What is 40% of 300?

2.  Simplify: 10 ÷ [9 - (2 * 2)]

3. What is ?

4.  How many rectangles are in the following figure? 

5.  If A = 7, D = 2C + B, C = A  -  B, and B = 3, what is D?

6.  Mrs. Smith lost Sarah's test after she graded it.  There are 5 students in the class.  The four known scores are 86, 94, 73, and 82.  Mrs. Smith knows the average of the tests was 85.  What does Sarah's missing test score have to be?

 
7.  An isosceles right triangle with legs of length 8 is partitioned into sixteen congruent triangles as shown.  What is the area of the shaded section?

8.  Al wants to jog a circular track for an hour. He starts at A and reaches B in 10 minutes. He then doubles his speed and continues at this speed. At the end of the hour where will he be?

9.  During a mathematics test, 18 students answered question 1 correctly, 23 students answered question 2 correctly, 8 of them got them both correct and 11 students answered incorrectly on both questions. How many students took the test?

10.   The number of chickens and hogs in the barnyard adds to 18. They have a total of 50 legs. How many chickens are in the yard?

11.   The planar figure shown is composed of four semicircles, three of which have their diameters shown in centimeters.  Find the perimeter of the figure.  (Leave your answer in terms of .) 

12.  There are six people at a party.  Each person shakes hands with every other person there.  How many handshakes occur altogether?

13.  Amy and Jamie are taking a road trip for spring break.  They travel 80 miles east to see a waterfall, then 50 miles north to a restaurant.  They then travel 140 miles west to see a cave and finally 95 miles south to a music concert.  What distance are they now from their starting point?

14.  Ted the tortoise and Harry the hare are having a 100 meter race. Harry can bound along at 15 meters per minute. But after five minutes, he stops for 6 minutes to eat some tender shoots in the nearby carrot patch, before continuing at the same speed as before. Slow and steady Ted travels at 8 meters per minute, but does not stop for anything. Who wins the race, and how much later does the loser cross the finish line?

15.  Bob, Dave, Joan, Anne and Fred were all invited to a mysterious mansion to spend the weekend. One night Bob was found murdered. The guests were alone at the mansion, so one of them must have committed the crime. When questioned by the investigating officer, Anne said that a man killed Bob, Dave said that a woman did it, Joan said that she was not the murderer and  Fred claimed that Dave was lying. If only the murderer is lying, who did it?

16.  Basil and Hazel are playing a game in which either player is equally likely to win any given point.  Basil currently has four points and Hazel has three points.  If the object of the game is to obtain five points, what is the probability that Basil will win?

17.  On ITV's Homework Hotline, it's time for "Rudolph's Rules."  If you guess what rule "Rudolph" is using you get a prize.  Someone puts golf balls into a miniature-golf display called "Rudolph," then "Rudolph" sends back a certain number of golf balls.  Today "Rudolph" responses are in the table below.  If n represents the number of balls initially given to "Rudolph," write an expression to represent how many balls will be sent back
 

Number of balls into "Rudolph"	6	8	15	25
Number of balls "Rudolph" returns	0	6	27	57

18.  What is the area of the shaded area if the circles each have a radius of 3?  (Leave your answer in terms of .)

19. The Caesar Cipher is a simple crypto system. Using this crypto system the text: 

J U L I U S     C A E S A R 

Becomes: 

M X O L X V   F D H V D U

 Now decode the following: P D W K   L V   I X Q

20.  What is the remainder when 1999 raised to the 2002 power is divided by 5?