# 1 What is the solution of the system of equations graphed below? y = 2x + 1

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1 1 What is the solution of the system of equations graphed below? y = 2x As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x 3 1) (0, 3) 2) ( 1, 4) 3) ( 3, 0) and (1, 0) 4) ( 2, 3) and (2, 5) 2 What are the coordinates of the midpoint of the line segment with endpoints (2, 5) and (8, 3)? 1) (3, 4) 2) (3, 1) 3) (5, 4) 4) (5, 1) Under this transformation, which property is not preserved? 1) area 2) distance 3) orientation 4) angle measure 4 In the diagram of ABC below, BD is drawn to side AC. If m A = 35, m ABD = 25, and m C = 60, which type of triangle is BCD? 1) equilateral 2) scalene 3) obtuse 4) right 1

2 5 In the diagram below of rhombus ABCD, the diagonals AC and BD intersect at E. 8 In the diagram below of isosceles ABC, the measure of vertex angle B is 80. If AC extends to point D, what is m BCD? If AC = 18 and BD = 24, what is the length of one side of rhombus ABCD? 1) 15 2) 18 3) 24 4) 30 1) 50 2) 80 3) 100 4) What are the truth values of the statement "Opposite angles of a trapezoid are always congruent" and its negation? 1) The statement is true and its negation is true. 2) The statement is true and its negation is false. 3) The statement is false and its negation is true. 4) The statement is false and its negation is false. 9 A student used a compass and a straightedge to construct CE in ABC as shown below. 7 What is the length of a line segment whose endpoints have coordinates (5, 3) and (1, 6)? 1) 5 2) 25 3) 17 4) 29 Which statement must always be true for this construction? 1) CEA CEB 2) ACE BCE 3) AE BE 4) EC AC 10 In ABC, AB = 4, BC = 7, and AC = 10. Which statement is true? 1) m B > m C > m A 2) m B > m A > m C 3) m C > m B > m A 4) m C > m A > m B 2

3 11 A circle whose center has coordinates ( 3, 4) passes through the origin. What is the equation of the circle? 1) (x + 3) 2 + (y 4) 2 = 5 14 The diagram below is a graph of circle O. 2) (x + 3) 2 + (y 4) 2 = 25 3) (x 3) 2 + (y + 4) 2 = 5 4) (x 3) 2 + (y + 4) 2 = Point W is located in plane R. How many distinct lines passing through point W are perpendicular to plane R? 1) one 2) two 3) zero 4) infinite 13 In the diagram below, line is parallel to line m, and line w is a transversal. Which equation represents circle O? 1) (x 5) 2 + (y + 3) 2 = 4 2) (x + 5) 2 + (y 3) 2 = 4 3) (x 5) 2 + (y + 3) 2 = 16 4) (x + 5) 2 + (y 3) 2 = In isosceles trapezoid QRST shown below, QR and TS are bases. If m 2 = 3x + 17 and m 3 = 5x 21, what is m 1? 1) 19 2) 23 3) 74 4) 86 If m Q = 5x + 3 and m R = 7x 15, what is m Q? 1) 83 2) 48 3) 16 4) 9 3

4 16 Triangle ABC is graphed on the set of axes below. 18 Which graph represents a circle whose equation is (x 2) 2 + (y + 4) 2 = 4? 1) What are the coordinates of the point of intersection of the medians of ABC? 1) ( 1, 2) 2) ( 3, 2) 3) (0, 2) 4) (1, 2) 2) 17 Given the statement, "If a number has exactly two factors, it is a prime number," what is the contrapositive of this statement? 1) If a number does not have exactly two factors, then it is not a prime number. 2) If a number is not a prime number, then it does not have exactly two factors. 3) If a number is a prime number, then it has exactly two factors. 4) A number is a prime number if it has exactly two factors. 3) 4) 19 If two sides of a triangle have lengths of 4 and 10, the third side could be 1) 8 2) 2 3) 16 4) 4 4

5 20 The lines represented by the equations 4x + 6y = 6 23 In the diagram below of circle O, m ABC = 24. and y = 2 3 x 1 are 1) parallel 2) the same line 3) perpendicular 4) intersecting, but not perpendicular 21 In the diagram of ABC below, DE AB. What is the m AOC? 1) 12 2) 24 3) 48 4) 60 If CD = 4, CA = 10, CE = x + 2, and EB = 4x 7, what is the length of CE? 1) 10 2) 8 3) 6 4) 4 24 Triangle A' B' C' is the image of ABC after a dilation of 2. Which statement is true? 1) AB = A' B' 2) BC = 2(B' C' ) 3) m B = m B' 4) m A = 1 2 (m A') 22 Parallelogram ABCD with diagonals AC and BD intersecting at E is shown below. 25 In the diagram of the circle below, AD BC, AB = (5x + 30), and CD = (9x 10). Which statement must be true? 1) BE CE 2) BAE DCE 3) AB BC 4) DAE CBE What is mab? 1) 5 2) 10 3) 55 4) 80 5

6 26 The bases of a prism are right trapezoids, as shown in the diagram below. 28 For which diagram is the statement ABC ADE not always true?? 1) Which two edges do not lie in the same plane? 1) BC and WZ 2) AW and CY 3) DC and WX 4) BX and AB 2) 27 In the diagram below, A' B' is the image of AB under which single transformation? 3) 4) 29 Given: BE and AD intersect at point C BC EC AC DC AB and DE are drawn Prove: ABC DEC 1) dilation 2) rotation 3) translation 4) glide reflection 6

7 30 Using a compass and straightedge, construct the perpendicular bisector of side AR in ART shown below. [Leave all construction marks.] 34 The slope of QR is x 1 and the slope of ST is If QR ST, determine and state the value of x. 35 Quadrilateral HYPE has vertices H(2, 3), Y(1, 7), P( 2, 7), and E( 2, 4). State and label the coordinates of the vertices of H"Y"P"E" after the composition of transformations r x axis T 5, 3. [The use of the set of axes below is optional.] 31 Determine and state the measure, in degrees, of an interior angle of a regular decagon. 32 Write an equation of a line that is parallel to the line whose equation is 3y = x + 6 and that passes through the point ( 3, 4). 33 In the diagram below, secants PQR and PST are drawn to a circle from point P. If PR = 24, PQ = 6, and PS = 8, determine and state the length of PT. 7

8 36 On the set of axes below, graph two horizontal lines whose y-intercepts are (0, 2) and (0, 6), respectively. Graph the locus of points equidistant from these horizontal lines. Graph the locus of points 3 units from the y-axis. State the coordinates of the points that satisfy both loci. 38 In the diagram below, right triangle RSU is inscribed in circle O, and UT is the altitude drawn to hypotenuse RS. The length of RT is 16 more than the length of TS and TU = 15. Find the length of TS. Find, in simplest radical form, the length of RU. 37 In the diagram below, a right circular cone with a radius of 3 inches has a slant height of 5 inches, and a right cylinder with a radius of 4 inches has a height of 6 inches. Determine and state the number of full cones of water needed to completely fill the cylinder with water. 8

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