# Which composition of transformations was used?. ~... t (I) R D2 (3) DI R I80 "2 (2) Ryoo0 D2

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1 36 Part nswer all 28 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, record your answer in the space provided. 1. Juliann plans on drawing MBC, where the measure of L can range from 50 to 60 and the measure of LB can range from 90 to 100. Given these conditions, what is the correct range of measures possible for LC? ()20 0 t040 (2) 30 to 50 (3) 680 to [> 90 (4) to n the accompanying diagram ofmbcandwef,b==de, L == LD, and LB == LE. Which D method_can be used to prove MBC = WEF! C B (1) SSS (3)S E (2) SS (4) HL 2 3. n the accompanying diagram, under which transformation will M 'B'C' be the image of MBC? (1) rotation (3) translation (2) dilation (4) glide reflection 4. The lateral faces of a regular pyramid are composed of (1) squares (3) congruent right triangles (2) rectangles (4) congruent isosceles triangles 4 8~ ~8 C' 3 5. Point is located at (4, -7). The point is reflected in the x-axis. ts image is located at (1) (-4, 7) (2)(-4, -7) (3) (4,7) (4)(7, -4) 5 6. n the accompanying diagram of circle 0, chords B and CD are parallel, and BD is a diameter ofit he circle. f md = 60, what is mlcdb? c 0)20 (3)60 (2) 30 (4) What is an equation ofthe line that passes through the point (-2,5) and is perpendicular to the line whose equation is y = ~ x + 5? (l)y=2x+ 1 (2)y=-2x+ 1 (3)y=2x+9 (4)y=-2x fter a composition of transformations, the coordinates (4, 2), B(4, 6), and C(2, 6) become"(-2, -1), B"(-2, -3), and C"(-1,-3), as shown on the accompanying set of axes. ; j ;,-- ' - :~.~~- : t r'... '. Which composition of transformations was used?. ~... t ; ; C" y,.: x () R D2 (3) D R 80 0 "2 (2) Ryoo0 D2 "-' ;;::r= ::~ (4) D1 o~o o 8 "2 9. n an equilateral triangle, what is the difference between the sum of the exterior angles and the sum of the interior angles? (1)180 (2)120 (3)90 (4) What is an equation of a circle with its center at (-3, 5) and a radius of 4? (l)(x - 3)2 + (y + 5)2 = 16 (3) (x - 3)" + (y + 5)2 = 4 (2) (x + 3? + (y - 5)2 = 16 (4) (x + 3)2 + (y - 5)2 = n MBC, ml == 95, mlb == 50, and mlc = 35. Which expression correctly relates the lengths ofthe sides of this triangle? (l)b<bc < C (3)C<BC<B (2)B<C < BC (4)BC<C<B n a coordinate plane, how many points are both 5 units from the origin and 2 units from the x-axis? (1) (2)2 (3)3 (4) What is the contrapositive of the statement, "f am tall, then will bump my head"? (1) f bump my head, then [ am tall. (2) f do not bump my head, then am tall. (3) f am tall, then will not bump my head. (4) 1fT do not bump my head, then am not tall

2 n the accompanying diagram of MBC, Jose found centroid P by constructing the three medians. He measured CF and found it to be 6 inches. fpf= x, which equation can be used to find x? ~F B (l)x+x=6 (3)3x+2x=6? (2) 2x +x = 6 (4) x +"3 x = 6 S. n the accompanying diagram, x the length ofthe legs C and BC of right triangle BC are 6 cm 6 em and 8 cm, respectively. ltitude CD is drawn to the hypotenuse of MBC. What is the length ofd to c Bem B the nearest tenth ala centimeter? (1)3.6 (2)6.0 (3)6.4 (4) 4.0 S B 16. n the accompanying diagram, tangentb and secantcd are drawn to circle 0 from an external point, B = 8, and C = 4. What is the length of CD? () 16 (2) 13 (3) 12 (4) n the accompanying diagram ofmbc and D~B!1EDC, E and BD intersect at C, and LCB == LCED. Which method can be used to show that MBC must be similar to MDC? () SS (2) (3) SSS (4) HL Point P is on line m. What is the total number of planes that are perpendicular to line m and pass through point P? (1)1 (2)2 (3)0 (4) infinite 18 o D C Square LMNO is shown in y the accompanying diagram. What are the coordinates of the midpoint of diagonal LN? (1)(4 2,-2 2 ) (3)(-2 2,32) 1 1 (2)(-3 2,3 2 ) (4)(-2 2,4 2 ) Which graph represents a circle with the equation (x - 5y< + (y + Y = 9?...=::-. +,. y ':'[ n't~i ~X (1) (3) ~ j. ; i ;... +., -. i r -~ l --. ~: +. (2) (4) n the accompanying diagram, 8 inches a right circular cone has a diameter of 8 inches and a height of 12 inches. What is the volume of the cone to the nearest cubic inch? (1) 201 (3) inches (2) 481 (4)

3 circle is represented by the equation x 2 + (y + 3y == 13. What are the coordinates of the center of the circle and the length of the radius? () (0, 3) and 13 (3) (0, -3) and 13 (2)(0, 3) and.jf3 (4)(0,-3) and.jf Given the system ofequations: y == x 2-4x x== 4 The num ber of points of intersection is (1) 1 (2) 2 (3) 3 (4) Side PQ of MQR is extended through Q to point T. Which statement is not always tme? () ml.rqt> ml.r (3) m L.RQT== ml.p + m L.R (2) ml.rqt> ml.p (4) ml.rqt> ml.pqr Part nswer all 6 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. ll answers should be written in pen, except for graphs and drawings, which should be done in pencil. B 29. n the accompanying diagram of MBC, B == 10, BC == 14, and C = 16. Find the perimeter of the triangle fonned by connecting the midpoints of the sides of MBC ~1~6----~~~C 25. Which illustration shows the correct construction of an angle bisector? ~~ (1) (3) ~ (2) (4) Using a compass and straightedge, construct a line that passes through point P and is perpendicular to line m. [Leave all construction marks.] p 26. Which equation represents a line perpendicular to the line whose equation is 2x + 3y = 12? (1)6y=-4x+ 12 (3) 2y == -3x + 6 (2) 2y = 3x + 6 (4) 3y == -2x n MBC, point D is on S, and point E is on BC such that -- DE C. f DB = 2, D == 7, and DE == 3, what is the length ofc? (1) 8 (2) 9 (3) 10.5 (4) ( ~ m 31. Find an equation ofthe line passing through the point (5, 4) and parallel to the line whose equation is 2x +Y == n three-dimensional space, two planes are parallel and a third plane intersects both of the parallel planes. The intersection of the planes is a () plane (3) pair of parallel lines (2) point (4) pair of intersecting lines 28

4 The length ofb is 3 inches. On the diagram below, sketch the points that are equidistant from and B and sketch the points that are 2 inches from. Label with an X all points that satisfy both conditions. _ -8 Part nswer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. ll answers should be written in pen, except for graphs and drawings, which should be done in pencil. 35. n the diagram below, circles X and Y have two tangents drawn to them from external point T. The points of tangency are C,, S, and E. The ratio of T to C is 1:3. f TS = 24, find the length ofse. 43 T 33. Given: Two is an even integer or three is an even integer. Determine the truth value of this disjunction. Justify your answer. 34. n the diagram below, MBC - MFG, mlc = 4x + 30, and mlg = 5x Determine the value ofx. B \' \ F G E s (Not drawn to scale) 36. Triangle BC has coordinates (-6, 2), B(-3, 6), and C(5, 0). Find the perimeter of the triangle. Express your answer in simplest radical form. [The use of the grid below is optional.] i T! i iii -, L '! [ T r: ~-- ~ =-l-----ti, ' ~ -t-j-- i' '. i r---iii J ~'j±' i' W-- T- _-r~~---- " ---r--j--j--rl ----r-m " _ Jj 1+ i!. ' ~ ~ - : -i -f--. -;-f---' H-+ : : +-J!. j flit -(-. +-~~±J~. :. -t--~r-rl~ i!! tllij t--1-: ---'--i---t-.!! T ;! '!! i ' ; i._i-j- +=t-r-+--r-~- t-t-l+-+-1-i ~ ~t m fm-i-- n~-t--tt ~--+--rn-j- -l [j i T.! u ~J L1J.. L-L-L_

5 The coordinates of the vertices of parallelogram BCD are (-2, 2), B(3, 5), C(4, 2), and D(-l, -1). State the coordinates of the veltices of parallelogram "B"C"D" that result from the transformation. 0 ry T 2-3. ax is [The use of the set of axes below is optional.] y [ -T + ~t--; ~+- \-. -.t.. :-t _ iji i---j-t-. t -_.-._. - t ~ ~. ' ~ ~-' U N f~lf1:! ' Part V nswer the question in tbis part. correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen. 38. Given: MBC and MDC, C is the midpoint ofbd and E -- Prove: B DE 'Z J B 0' ::", E

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