3 Kevin s work for deriving the equation of a circle is shown below.
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1 June A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation? 2 A three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image? 9 inches 2 inches 15 inches 18 inches 3 Kevin s work for deriving the equation of a circle is shown below. STEP 1 STEP 2 STEP 3 STEP 4 In which step did he make an error in his work? Step 1 Step 2 Step 3 Step 4 4 Which transformation of would result in an image parallel to? a translation of two units down a reflection over the x-axis a reflection over the y-axis a clockwise rotation of 90 about the origin [32]
2 5 Using the information given below, which set of triangles can not be proven similar? 6 A company is creating an object from a wooden cube with an edge length of 8.5 cm. A right circular cone with a diameter of 8 cm and an altitude of 8 cm will be cut out of the cube. Which expression represents the volume of the remaining wood? 7 Two right triangles must be congruent if an acute angle in each triangle is congruent the lengths of the hypotenuses are equal the corresponding legs are congruent the areas are equal 8 Which sequence of transformations will map onto? reflection and translation rotation and reflection translation and dilation dilation and rotation 9 In parallelogram ABCD, diagonals and intersect at E. Which statement does not prove parallelogram ABCD is a rhombus? The diagonals do not have to be congruent in a rhombus bisects [33]
3 10 In the diagram below of circle O, and are radii, and chords,, and are drawn. Which statement must always be true? and are isosceles. The area of is twice the area of. 11 A 20-foot support post leans against a wall, making a 70 angle with the ground. To the nearest tenth of a foot, how far up the wall will the support post reach? Line segment NY has endpoints and. What is the equation of the perpendicular bisector of? 13 In shown below, altitude is drawn to at U. If,, and, which value of h will make a right triangle with as a right angle? [34]
4 14 In the diagram below, has vertices,, and. What is the slope of the altitude drawn from A to? 15 In the diagram below,. Which statement is always true? 16 On the set of axes below, rectangle ABCD can be proven congruent to rectangle KLMN using which transformation? rotation translation reflection over the x-axis reflection over the y-axis 17 In the diagram below, and intersect at point C, and and are drawn. If,,,, and, what is the length of? [35]
5 18 Seawater contains approximately 1.2 ounces of salt per liter on average. How many gallons of seawater, to the nearest tenth of a gallon, would contain 1 pound of salt? Line segment EA is the perpendicular bisector of, and and are drawn. Which conclusion can not be proven? bisects angle ZET. Triangle EZT is equilateral. is a median of triangle EZT. Angle Z is congruent to angle T. 20 A hemispherical water tank has an inside diameter of 10 feet. If water has a density of 62.4 pounds per cubic foot, what is the weight of the water in a full tank, to the nearest pound? 16,336 32, , , In the diagram of, points D and E are on and, respectively, such that. If,, and, what is the length of? [36]
6 22 Triangle RST is graphed on the set of axes below. How many square units are in the area of? The graph below shows, which is a chord of circle O. The coordinates of the endpoints of are and. The distance from the midpoint of to the center of circle O is 2 units. What could be a correct equation for circle O? 24 What is the area of a sector of a circle with a radius of 8 inches and formed by a central angle that measures 60? Free Response: Show all work 25 Describe a sequence of transformations that will map onto as shown below. [37]
7 26 Point P is on segment AB such that is. If A has coordinates, and B has coordinates, determine and state the coordinates of P. 27 In as shown below, points A and B are located on sides and, respectively. Line segment AB is drawn such that,,, and. Explain why is parallel to. ABllBC because there is a dilation from point E because the sides are in proportion. 28 Find the value of R that will make the equation true when. Explain your answer. 29 In the diagram below, Circle 1 has radius 4, while Circle 2 has radius 6.5. Angle A intercepts an arc of length, and angle B intercepts an arc of length. Dominic thinks that angles A and B have the same radian measure. State whether Dominic is correct or not. Explain why. Yes both angles are equal [38]
8 30 A ladder leans against a building. The top of the ladder touches the building 10 feet above the ground. The foot of the ladder is 4 feet from the building. Find, to the nearest degree, the angle that the ladder makes with the level ground. 31 In the diagram below, radius is drawn in circle O. Using a compass and a straightedge, construct a line tangent to circle O at point A. [Leave all construction marks.] 32 A barrel of fuel oil is a right circular cylinder where the inside measurements of the barrel are a diameter of 22.5 inches and a height of 33.5 inches. There are 231 cubic inches in a liquid gallon. Determine and state, to the nearest tenth, the gallons of fuel that are in a barrel of fuel oil. [39]
9 33 Given: Parallelogram ABCD,, and diagonal Prove: Statement Reason Parallelogram ABCD, EFG, Given Diagonal BFD <DFE=<BFG Vertical angles are congruent ABllCD in a parallelogram opposite sides are parallel <EDF=<GBF if parallel lines are cut by a transversal alternate interior angles are congruent DEF BGF AA=AA 34 In the diagram below, is the image of after a transformation. Describe the transformation that was performed. Explain why. A dilation of 2.5 was performed and the triangles are similar because dilations preserve angle measure but not distance [40]
10 35 Given: Quadrilateral ABCD with diagonals and that bisect each other, and Prove: is an isosceles triangle and is a right triangle Given ABllCD ABCD is a parallelogram the diagonals of a parallelogram bisect each other Opposite sides of a parallelogram are parallel <1=<3, <2=<4 if parallel lines are cut by a transversal alternate <2=<3, <1=<4 Substitution ACD is isosceles AD=DC ABCD is a rhombus AEl BE <BEA is a right angle interior angles are congruent The base angles of an isosceles triangle are congruent in a triangle, opposite sides of congruent angles are congruent A rhombus has consecutive sides congruent in a rhombus the diagonals are perpendicular perpendicular lines form right angles AEB is a right triangle right triangles have one right angle 36 A water glass can be modeled by a truncated right cone (a cone which is cut parallel to its base) as shown below. The diameter of the top of the glass is 3 inches, the diameter at the bottom of the glass is 2 inches, and the height of the glass is 5 inches. The base with a diameter of 2 inches must be parallel to the base with a diameter of 3 inches in order to find the height of the cone. Explain why. Determine and state, in inches, the height of the larger cone. Determine and state, to the nearest tenth of a cubic inch, the volume of the water glass. [41]
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