2018 Carol Edwards Excellence in Mathematics Contest. Individual Competition Level I

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018 Carol Edwards Excellence in Mathematics Contest Individual Competition Level I (Currently enrolled in Precalculus or higher math course) Name: School Name: Filling out the Scantron: At the top of

1 018 Carol Edwards Excellence in Mathematics Contest Individual Competition Level I (Currently enrolled in Precalculus or higher math course) Name: School Name: Filling out the Scantron: At the top of the scantron as shown here a. Vertically write the ID# from your Student card. Include all zeros. b. Bubble in the number. Along the right edge of the scantron as shown at the right a. In the Name box, neatly print First Name then Last Name. b. In the Subject box, write in the high school. No initials please. c. In the Period box, write 1 for Level I and for Level II. Level I is for students currently enrolled in Precalculus or higher level classes Level II is for students currently enrolled in classes below Precalculus Testing Instructions: a. Do not open the test until told to do so.. No talking. Cell phones are put away.. No sharing of calculators. 4. Use a pencil to fill in the scantron. 5. Be careful when filing out the scantron watch for poorly erased marks, incomplete marks, skipped lines. 6. Scores are based on the number of correct answers. There is no penalty for wrong answers. 7. When finished, turn in the scantron to the proctor, but keep the test. 8. Test lasts one hour.

2 1. Suppose a square is inscribed in a circle of radius one and then a second circle is inscribed inside the square. Now suppose a second square is inscribed in the second circle and then a third circle is inscribed in the second square. If this process is continued without end, what is the sum of the areas of the infinitely many circles including the original circle of radius one? a. 6 b. c. d.. Suppose an isosceles triangle with angles 6, 7, and 7 has a shorter side of length x and longer sides each of length y. Find. a b. 1 + c. 1 + d All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enjas are neither Derfs nor Sivads? a. 5 b. 55 c. 61 d The tune Twinkle, Twinkle, Little Star has seven notes in its first line: C, C, G, G, A, A, G. Assume that all seven notes are held for the same length of time. If the notes are arranged at random, how many different melodies could be composed? a. 190 b. 00 c. 04 d Find the units digit of a. 1 b. c. 7 d. 9 P age

3 6. A 1 and A are the centers of their respective circles. Find the ratio of the shaded area to the unshaded area. A 1 A a. 1: b. 1: c. 14: d. 14: 7. The base of a regular square pyramid is inscribed in the base of a cylinder. The height of the cylinder is triple the height of the pyramid. Find the ratio of the volume of the pyramid to the volume of the cylinder. a. 5 b. 9 c. 6 d. 8. Given = 6 and = =, find the points that the curves = () and = have in common. a. (, ) b. (6, 6) c. (, 6) d. (4, ) 9. Call an integer biprime if it is the product of two distinct prime numbers (thus, 6 and 15 are biprime, but 9 and 1 are not). If N is the smallest number such that N, N + 1, and N + are all biprime, find the largest prime factor of N(N + 1)(N + ). a. 1 b. 17 c. 9 d. 4 P age

4 10. The equation x + y = defines four line segments which enclose a region in the x-y plane. The area of the enclosed region is: a. 4 b. 8 c. 7 d Suppose Mark can harvest 10 acres of grain in days and Greg can harvest 17 acres of grain in 4 days. Working together how long will it take them to harvest 50 acres of grain? a. 6 " " days b. 6 " " days c. 7 " " days d. 7 " " days 1. The rectangle has area 180 and consists of nine congruent subrectangles. Find its perimeter. a. 8 b. 58 c. 60 d Perpendicular tangents " and " are drawn to circle 0 with radius 4. If BE = 1, find AD. C A D O E B a. b. 1 c. d. 4 P age

5 14. Given an equilateral triangle ABC with sides of length x, let CDE be an isosceles triangle with CD = CE = 7 and DE = 1. The segments AD and BE both have length. Find the length of x: C D E A B a. + 8 b. " c. " d When Silvia was born, her grandparents started a college savings fund for her by investing $15,000 in a savings account that compounds continuously. When Silvia finished eighth grade at age thirteen, the account held $71,8.. What will the account s instantaneous rate of change be when she graduates from high school at age 18? a. $14, b. $15, c. $15, d. $16, e. None of these 16. A cylindrical tank with height inches and diameter 18 inches is lying on its side. Water is added to the tank to a depth of 1.5 inches. Use the fact that one gallon is approximately 1 cubic inches to determine the number of gallons of water in the tank. a gal b gal c gal d gal 5 P age

6 17. Sandra is in the smaller building looking out of a window. She sights the top of the taller building at an angle of elevation of 40. She sights the bottom of the taller building with an angle of depression of 0. If the taller building is 00 feet tall, how far apart are the two buildings? a ft b ft c ft d ft 18. The Singapore Flyer is a Ferris wheel constructed on top of a three-story building. The wheel itself has a diameter of 49 feet, but the bottom of the wheel sits nearly 50 feet off the ground. Determine the height from the ground of a person after boarding from the bottom and traveling " of the way around? a ft b ft c ft d ft 19. A spider has one sock and one shoe for each of its eight legs. Assuming that the sock for each leg must be put on before the shoe, in how many different orders can the spider put on its socks and shoes? a. 8 b. 16 c. 16 d. (8) 6 P age

7 0. Two circles with centers and and radii of length 0 and 10, respectively, are tangent to each other (at point D) and to a line (at points B and C), as shown. Find the area of the shaded region. 0 B O 1 D C O 10 a b c d. 400 "# 7 P age

Math is Cool Championships

Math is Cool Championships Individual Contest Express all answers as reduced fractions unless stated otherwise. Leave answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on