1. In the figure below, angle A is a right angle. Find the sum x + y (degrees).

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1 1. In the figure below, angle is a right angle. ind the sum x + y (degrees). y x What is the ratio x:y in the right triangles shown below? The figures are not drawn to scale. x 0º y 0º 1. : 1 : 4. 8 :. 1 : 1. In the figure below, m m, 8,, and 14. ind. The figure is not drawn to scale ind the apothem length of the regular hexagon whose area is VHHS 008

2 5. There is a group of twenty penguins standing in line for a movie. Polly Penguin and Paul Penguin are part of the group. Polly has six penguin buddies in the group and Paul has five penguin buddies in the group, three of whom are also Polly s penguin buddies. Polly and Paul are penguin buddies. How many penguins in the group are not penguin buddies with Polly or Paul? and are both tangent to circle O at and. If m 15, m 80, and m 0, find m (in degrees). The figure is not drawn to scale.. O There are two similar cones, one with half the volume of the other one. If the larger cone has a height of 7, then what is the height of the smaller cone? Square is inscribed in circle X. ircle X is inscribed in square GH. If square has an area of 7 square millimeters, then what is the length of the diagonal of square GH (in millimeters)? The region bounded by the lines y 0, x 0, and y x 8 is rotated about the y- axis. What is the volume of the resulting figure (in cubic units)? The faces of a right rectangular prism have areas of 1, 4, and 14. ind the volume of the prism VHHS 008

3 11. ind the area of a regular octagon with side length In the figure below, 4and 15. If and is perpendicular to each of these line segments, what is the length valuate 0 tan40 tan50 tan70 tan ind JH given the following: J = the height of if 1 = the area of the circle x y x y 10 1 H = Three couples (rnie and bby, arney and renda, and huck and laudia) are seated around a hexagonal table. No husband is sitting next to his wife. rnie and arney, being good friends, are seated next to each other, but bby and laudia, being mortal enemies, are not seated next to each other. huck is allergic to arney s aftershave and cannot sit next to him. laudia is sitting across from either arney or bby. Who is sitting across from arney?. bby renda. huck. laudia 1. quadrilateral with side lengths, 5, 8, and 1 units is inscribed in a circle. ind the area of the quadrilateral (in square units) VHHS 008

4 17. In how many ways can you move from the bottom left of the diagram below to the upper right of the diagram if you can only move up or right along the lines of the diagram? ind the surface area (in square inches) of the frustum with base areas 4 and 9 square inches if the height of the frustum is 5 inches has point on, point on, and point on.,, and intersect at point G. The ratio : is :5 and the ratio : is 8:. ind the ratio G : G. 7: 4:49. 19:7. 15:8 0. falcon is tied to the upper corner of a cube house with an edge length of 10 yards by a 0 foot rope. ind the volume of the region (in cubic feet) in which the falcon can fly..,5 7,000. 1,500., Two circles intersect each other at 10º arcs. The radius of both circles is 1 centimeters. ind the area (in square centimeters) of the intersection of the circles ind the area of the circle inscribed in the triangle formed by the centroids of Δ, Δ, and Δ given the points below. (-4, 5) (-, 7) (-9, 0) (7,1) (5,8) (-4,-5) VHHS 008

5 . In the figure below quadrilaterals and GH are both squares. The lengths of sides and differ by one and are multiplicative inverses of each other. What is the length of side G? The drawing is not to scale. G H Given the regular octagon GH with side length 1, find the length of the diagonal dartboard is made from four concentric circles of radii 7, 5,, and 1. dart that lands in the innermost circle scores 5 points. dart that lands in the ring surrounding the innermost circle scores points, a dart that lands in the next ring scores points, and a dart than lands in the outermost ring scores 1 point. If the probability of hitting the dartboard is 1, then what are the odds of scoring higher than a in one throw?. 9:40 9:49. 9:89. 5:49 T1 There are 81 balls and a balance on a table. ll of the balls weigh the same except for one, which weighs more. What is the least number of times you need to use the balance to accurately determine and guarantee the heaviest ball? T ind the altitude to the side of length 11 of the triangle below T What is the greatest number of triangles that can be formed by arranging 45 toothpicks tip to tip in a single design? VHHS 008