12/18/2013. Directions

Transcription

1 Directions You will have 4 minutes to answer each question. The scoring will be 16 points for a correct response in the 1 st minute, 12 points for a correct response in the 2 nd minute, 8 points for a correct response in the 3 rd minute, 4 points for a correct response in the 4 th minute. A sliding scale will be used. Once your hand has been raised with the answer sheet, it must stay up. If you put your hand down, your answer will be disqualified for that question. Your answer must be submitted on the official answer sheet that has been correctly filled out. Otherwise your answer will be disqualified. Your answer must be in the specific form that the question asks for. 1

2 Directions If not otherwise noted, the answers should be in one of the following generally accepted forms: Denominators rationalized Simplest radical form Fractions, improper fractions, or mixed numbers in simplest form Equations should have integral coefficients in standard form No units are necessary Calculators are not allowed in any division except Statistics. Headphones, beepers, cell phones, or electronic devices are not permitted. Sunglasses and hats are not to be worn during the competition. 2

3 1) Let P be a point on the circumference of a circle. Perpendiculars PA and PB are drawn to points A and B on two mutually perpendicular diameters. If AB=36in, what is the diameter of the circle? 3

4 2) Find the number of diagonals in a convex decagon (a polygon with ten sides). 4

5 3) From 2:30pm to 2:50pm, how many degrees does the hour hand cross? 5

6 4) A convex polygon is inscribed in a circle with radius 1. If every side of the polygon is bigger than 1 but less than the square root of 2, how many sides does this polygon have? 6

7 5) Given two spheres, the volume of the larger sphere is 27 times the volume of the smaller one. What is the ratio of the surface area of the smaller sphere to the surface area of the larger sphere? 7

8 6) A quadrilateral has these properties: 3 of its angles are congruent to one another, no set of three vertices are co-linear, and its largest angle is three times as large as its smallest one. What is the measure of the smallest angle? 8

9 7) Twice the measure of the supplement of an angle is added to three times the measure of the complement of the same angle. The sum is the measure of an interior angle of a regular nonagon. What is the measure of the supplement of the angle? 9

10 8) A 25 foot ladder is placed against a vertical wall of a building. The foot of the ladder is 7 feet from the base of the building. If the top of the ladder slips 4 feet down the wall, how far will the foot of the ladder slide away from the wall? 10

11 9) A company sells peanut butter in cylindrical jars. Research suggests that using wider jars will increase sales. If the diameter of the jars is increased by 25% (without altering the volume), by what percent must the height be decreased? 11

12 10) How many axes of symmetry does a nonsquare rhombus have? 12

13 11) A cube is 100 inches on each side. The cube is painted red and then cut into 1,000,000 small cubes with 1 inch sides. How many of the small cubes have no red paint on them? 13

14 12) How many times in one 24-hour day do the hands of a clock form a right triangle? 14

15 13) The sizes of the angles of a quadrilateral are x, x+10, x+20, and x+30 degrees. How many degrees is the largest angle? 15

16 14) If in a regular hexagon the diagonals are increased by 30%, how much is the total area of the hexagon increased by? 16

17 15) It takes 5 seconds for a clock to strike 6 o clock beginning at 6:00 o clock precisely. If the strikes are uniformly spaced, how long (in seconds) does it take to strike 12 o clock? Answers 1) 72 in. 2) 35 3) 10 4) 5 5) 1 : 9 6) 36 deg. 7) 82 deg. 8) 8 ft. 9) 36% 10) 2 11) 941,192 12) 44 13) ) 69% 15) 11 sec. 17