12/15/2015. Directions

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Alvin Garrett
5 years ago
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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) The points 0,8, 5,3, 1, 1 and 4,4 are vertices of a rectangle. Determine the coordinates of the midpoints for each side and determine if the midpoints are vertices of a rectangle. 3

4 2) Find the area of equilateral AMO given that DG = 5, FG = 3, and BG = 7. 4

5 3) If a rectangle has diagonal length c and perimeter p, which of the following is an expression for the area of the rectangle. A. p2 4c 2 2 B. p 2 + 2c 2 C. p 2 +2c 2 2 D. p2 4c 2 8 5

6 4) Let ABCD be a rectangle with AB = 5 and BC = 2. Let E be a point on AB. Let diagonal AC intersect line DE at F. Find the distance AE if the area of AEF is

7 5) The four vertices of a rectangle are 5,6, 1,6, 1, 4, and 5, 4 What is the slope of the line that passes through the origin and divides the rectangle into two congruent trapezoids? 7

8 6) In triangle ABC, the point D lies on BC, and AD is the bisector of angle BAC. If AB = c, AC = b, and m CAD = w, find the value of AD. 8

9 7) In the equilateral triangle ABC, PM BC, PN AC and AB = a, then CM + CN =? 9

10 8) British Flag Theorem: Consider some rectangle ABCD and a point P chosen on the same plane. Then the following is satisfied: AP 2 + CP 2 = BP 2 + DP 2 a. Consider a square ABCD and a point P chosen on its interior. If AP = 5, BP = 3, and CP = 4, compute the length of DP. b. Consider some rectangle ABCD such that AB = 8 and BC = 6. A square EBDF is drawn such that it has diagonal BD as a side and contains point A. Compute the value of EA FA EA + FA 10

11 9) Rectangle ABCD has area 96. Parallelogram ACEF is drawn such that EF passes through D. What is the area of ACEF? 11

12 10) A parallelogram has 3 of its vertices at 0,1, 2,7, and 3,0. There are 3 possible points for the fourth vertex. Let k be the sum of the coordinates of the fourth point. Determine the sum of all possible k. 12

13 11) The interior angles of a polygon are in arithmetic progression. The least angle is 120 and common difference is 5. Find the least number of sides that this polygon can have. 13

14 12) Graph the points A 5,0, B 8,5, D 0,3, and E 3,8. Draw AB, AE, BD, and DE. Label point C, the intersection of AE and BD. a. Find the slopes of AE and BD. Find the measure of the angles ACB and ECD? b. Write equations for AE and BD. What are the coordinates of C? 14

15 13) In the given figure, all adjacent sides meet at right angles. If the area of the figure is 50u 2 and 4 < x < 5, find the smallest value a and the largest value b such that a < h < b. 15

16 14) In the given parallelogram ABCD, AB = BE = ED = 2 and ABE = 90. Find the ratio of the area of the trapezoid BEDC to the area of the triangle ABE. 16

17 15) Jack and Rose each order a pizza. The circumference of Jack s pizza is 20% greater than the circumference of Rose s pizza. The area of Jack s pizza is what percentage greater than the area of Rose s? Answers 1) 5, ) ) D 4) 1, 3,1, 3 2, 3 2, 2,6 ; No 9) 96 10) 13 11) 9 12) 4, 1, 4 90, y = 4x + 20, y = 1 x + 3, 4 4,4 5) 1 2 6) 7) bc cos w b+c 13) 5 < h < ) ) 44% or 2.5< h < ) 4 2, 28 17

12/18/2013. Directions

12/18/2013. Directions 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