NOTA" stands for none of these answers." Figures are not drawn to scale. 1. If Kyle does not do his homework, then he is lazy. Kyle is lazy. Which of the following must be true? a) Kyle never does his homework b) Kyle always does his homework c) If Kyle does his homework, then he is not lazy d) If Kyle is not lazy, then he does his homework 2. If ΔABC has m A=20 o and m B=40 o, then what is the degree measure of C? a) 30 o b) 40 o c) 60 o d) 120 o 3. What is the perimeter in units of an equilateral triangle with side length 2? a) b) 3 c) 6 d) 8 4. In ΔABC, AC=BC=4 and AB=1. E is a point on segment. If P is the maximum value of BE+AE and Q is the minimum value of BE+AE, then what is P-Q? a) 1 b) 3 c) 5 d) 7 5. Find the perimeter in units of a square inscribed in a triangle with side lengths 5, 5, and 6 if one side of the square lies on the side of the triangle with length 6. a) b) c) d) 6. Find the sum of the coordinates of the centroid of a triangle with vertices at (4, ), (5, ), and (6,1). a) 4 b) 5 c) 6 d) 7 1
7. Refer to the diagram below. In equilateral triangle ΔABC with side length 3 inches, points D and E trisect, G is on,, and. Find the perimeter of quadrilateral ADGF in inches. a) 3 b) 4 c) 5 d) 6 8. How many sides does a dodecagon have? a) 10 b) 12 c) 14 d) 20 9. Rectangle ABCD has side lengths 8 and 15 units. A right triangle with a right angle at point B and its legs extending along and is constructed such that point D bisects its hypotenuse. Find the length, in units, of the right triangle's hypotenuse. a) 32 b) 34 c) 36 d) 38 10. Consider the following diagram of unit square ABCD. Point E is on, point G is on, and AE=. Point H on is projected onto at point F, and FG=AE. H is also projected onto at point I. Find the value of IH HF. 2
a) b) c) d) 2 11. In ΔABC, AB=1, AC=3, and BC is an integer. The angle bisector through C intersects at point E. CE can be expressed in the simplest radical form for a,b Z +. Find the value of a+b. a) 32 b) 35 c) 37 d) 40 12. In ΔABC, the angle bisector of A intersects at a right angle. If AC=4 and m B=45 o, then the perimeter of ΔABC can be written in the simplest radical form a+b for a,b,c Z +. Find the value of a + b + c. a) 4 b) 8 c) 14 d) 16 13. Find the sum of all k such that the line through points (7,k) and (2,0) is parallel to the line through points (k-2,3) and (2k,6). a) -2 b) 2 c) -8 d) 8 14. Refer to the diagram below. A quadrilateral is formed by intersecting unit square ABCD with unit equilateral triangle EFG. Point B lies on the centroid of ΔEFG and. intersects with at point Y. Find the length of segment. 3
a) b) c) d) 15. Which of the following statements is always true regarding parallel lines and a transversal? a) Vertical angles are supplementary. b) Consecutive interior angles are congruent. c) Alternate interior angles are congruent. d) Corresponding angles are complementary. 16. Right triangle ΔABC has a right angle at vertex A and AC>AB. Point D is the foot of the altitude from vertex A. If CD-BD=1, then find the value of AC 2 -AB 2 in terms of BC. a) b) c) BC d) BC 17. Which of the following is a polygon with 10 sides? a) dodecahedron b) decagon c) dodecagon d) decahedron 18. Which of the following methods cannot be directly used to prove two triangles are similar? a) SSS b) AA c) SAS d) SSA 19. How many diagonals are in a convex 60-gon? 4
a) 172 b) 1710 c) 1770 d) 10440 20. A convex n-gon is divided into only triangles by segments connecting (not necessarily all) its vertices. Express the fewest number of triangles that can be formed in terms of n. a) n-2 b) n-1 c) n d) n+1 21. A triangle has side lengths 3x+2, x+1, and 2x+3 for real x. Which of the following is the domain of x? a) all reals b) reals strictly greater than -1 c) reals greater than or equal to -1 d) positive reals 22. In right triangle ΔABC, the altitude dropped from A to hypotenuse intersects at point D. Given that BD=5 and CD=4, what is the length in units of? a) 4.5 b) 10 c) 2 d) 20 23. A 30-60-90 right triangle with hypotenuse 1 has an equilateral triangle constructed outwards from each side. Find the side length in units of the equilateral triangle formed by the centroids of the three constructed equilateral triangles. a) 1 b) c) d) 24. Tianbo is on a hoverpad moving straight ahead towards a skyscraper at 10 meters per second, and his eye level is 10 meters above ground. If he spots the base of a skyscraper at an angle of depression of 45 o, then how long from the time the angle of depression is 45 o will it take for him to reach the skyscraper? a) 1 second b) 10 seconds c) 100 seconds d) 1000 seconds 5
25. What is formed when three or more coplanar, nonintersecting line segments of different lengths are connected at their ends to form a closed figure? a) regular polygon b) rhombus c) scalene triangle d) irregular polygon 26. In trapezoid ABCD, m C=m D=60 o. Point E is on segment such that m AEB=30 o. A line through D perpendicular to meets at point G. Given that BG=1 and CD=2, find the length of. a) 3- b) 1+ c) 3+ d) 1+2 27. Find the degree measure of one interior angle of a regular convex hexagon. a) 90 o b) 110 o c) 120 o d) 150 o 6
28. In ΔABC, AC=6 and BC=5. Let M be the midpoint of. Given that is perpendicular to the angle bisector of BAC, then find the perimeter in units of ΔABC. a) 13 b) 14 c) 15 d) 16 29. If p q is always true and q r is always true, then which of the following statements must apply? a) p r is always true b) p r is sometimes true c) p r is never true d) r p is always true 30. Find the maximum height (distance between two parallel sides) in units of a rhombus with side length 1. a) b) c) 1 d) 7