1. In the diagram below, a sequence of rigid motions maps ABCD onto JKLM.

If m\angle A = 82^{\circ}, m\angle B = 10^{\circ}, and m\angle L = 121^{\circ}, the measure of \angle M is

(1) 53^{\circ}
(2) 82^{\circ}
(3) 104^{\circ}
(4) 121^{\circ}

2. Parallelogram HAND is drawn below with diagonals \overline{HN} and \overline{AD} intersecting at S.

Which statement is always true?

(1) HN = \dfrac{1}{2}AD
(2) AS = \dfrac{1}{2}AD
(3) \angle AHS \cong \angle ANS
(4) \angle HDS \cong \angle NDS

3. The graph below shows two congruent triangles, ABC and A'B'C'.

Which rigid motion would map \triangle ABC onto \triangle A'B'C'?

(1) a rotation of 90 degrees counterclockwise about the origin
(2) a translation of three units to the left and three units up
(3) a rotation of 180 degrees about the origin
(4) a reflection over the line y = x

4. A man was parasailing above a lake at an angle of elevation of 32^{\circ} from a boat, as modeled in the diagram below.

If 129.5 meters of cable connected the boat to the parasail, approximately how many meters above the lake was the man?

(1) 68.6
(2) 80.9
(3) 109.8
(4) 244.4

5. A right hexagonal prism is shown below. A two-dimensional cross section that is perpendicular to the base is taken from the prism.

Which figure describes the two-dimensional cross section?

(1) triangle
(2) rectangle
(3) pentagon
(4) hexagon

6. In the diagram below, \overline{AC} has endpoints with coordinates A(-5,2) and C(4,-10).

If B is a point on \overline{AC} and AB:BC = 1:2, what are the coordinates of B?

(1) (-2, -2)
(2) (-\dfrac{1}{2}, -4)
(3) (0, -\dfrac{14}{3})
(4) (1, -6)

7. An ice cream waffle cone can be modeled by a right circular cone with a base diameter of 6.6 centimeters and a volume of 54.45\pi cubic centimeters. What is the number of centimeters in the height of the waffle cone?

(1) 3\dfrac{3}{4}
(2) 5
(3) 15
(4) 24\dfrac{3}{4}

8. The vertices of \triangle PQR have coordinates P(2,3), Q(3,8), and R(7,3). Under which transformation of \triangle PQR are distance and angle measure preserved?

(1) (x,y) \rightarrow (2x,3y)
(2) (x,y) \rightarrow (x + 2, 3y)
(3) (x,y) \rightarrow (2x, y + 3)
(4) (x,y) \rightarrow (x + 2, y + 3)

9. In \triangle ABC shown below, side \overline{AC} is extended to point D with m\angle DAB = (180 - 3x)^{\circ}, m\angle B = (6x - 40)^{\circ}, and m\angle C = (x + 20)^{\circ}.

What is m/angle BAC?

(1) 20^{\circ}
(2) 40^{\circ}
(3) 60^{\circ}
(4) 80^{\circ}

10. Circle O is centered at the origin. In the diagram below, a quarter of circle O is graphed.

Which three-dimensional figure is generated when the quarter circle is continuously rotated about the y-axis?

(1) cone
(2) sphere
(3) cylinder
(4) hemisphere

11. Rectangle A'B'C'D' is the image of rectangle ABCD after a dilation centered at point A by a scale factor of \dfrac{2}{3}. Which statement is correct?

(1) Rectangle A'B'C'D' has a perimeter that is \dfrac{2}{3} the perimeter of rectangle ABCD
(2) Rectangle A'B'C'D' has a perimeter that is \dfrac{3}{2} the perimeter of rectangle ABCD
(3) Rectangle A'B'C'D' has an area that is \dfrac{2}{3} the area of rectangle ABCD
(4) Rectangle A'B'C'D' has an area that is \dfrac{3}{2} the area of rectangle ABCD

12. The equation of a circle is x^{2} + y^{2} - 6x + 2y = 6. What are the coordinates of the center and the length of the radius of the circle?

(1) center (-3,1) and radius 4
(2) center (3,-1) and radius 4
(3) center (-3,1) and radius 16
(4) center (3,-1) and radius 16

13. In the diagram of \triangle ABC below, \overline{DE} is parallel to \overline{AB}, CD = 15, AD = 9, and AB = 40.

The length of \overline{DE} is

(1) 15
(2) 24
(3) 25
(4) 30

14. The line whose equation is 3x - 5y = 4 is dilated by a scale factor of \dfrac{5}{3} centered at the origin. Which statement is correct?

(1) The image of the line has the same slope as the pre-image but a different y-intercept.
(2) The image of the line has the same y-intercept as the pre-image but a different slope.
(3) The image of the line has the same slope and the same y-intercept as the pre-image.
(4) The image of the line has a different slope and a different y-intercept from the pre-image.

15. Which transformation would not carry a square onto itself?

(1) a reflection over one of its diagonals
(2) a 90^{\circ} rotation clockwise about its center
(3) a 180^{\circ} rotation about one of its vertices
(4) a reflection over the perpendicular bisector of one side

16. In circle M below, diameter \overline{AC}, chords \overline{AB} and \overline{BC}, and radius \overline{MB} are drawn.

Which statement is not true?

(1) \triangle ABC is a right triangle
(2) \triangle ABM is isosceles
(3) m\widehat{BC} = m\angle BMC
(4) m\widehat{AB} = \dfrac{1}{2}m\angle ACB

17. In the diagram below, \overline{XS} and \overline{YR} intersect at Z. Segments XY and RS are drawn perpendicular to \overline{YR} to form triangles XYZ and SRZ.

Which statement is always true?

(1) (XY)(SR) = (XZ)(RZ)
(2) \triangle XYZ \cong \triangle SRZ
(3) \overline{XS} \cong \overline{YR}
(4) \dfrac{XY}{SR} = \dfrac{YZ}{RZ}

18. As shown in the diagram below, \overline{ABC} \| \overline{EFG} and \overline{BF} \cong \overline{EF}.

If m\angle CBF = 42.5^{\circ}, then m\angle EBF is

(1) 42.5^{\circ}
(2) 68.75^{\circ}
(3) 95^{\circ}
(4) 137.5^{\circ}

19. A parallelogram must be a rhombus if its diagonals

(1) are congruent
(2) bisect each other
(3) do not bisect its angles
(4) are perpendicular to each other

20. What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x - 6y = 15?

(1) y - 9 = -\dfrac{3}{2}(x - 6)
(2) y - 9 = \dfrac{2}{3}(x - 6)
(3) y + 9 = -\dfrac{3}{2}(x + 6)
(4) y + 9 = \dfrac{2}{3}(x + 6)

21. Quadrilateral ABCD is inscribed in circle O, as shown below.

If m\angle A = 80^{\circ}, m\angle B = 75^{\circ}, m\angle C = (y + 30)^{\circ}, and m\angle D = (x - 10)^{\circ}, which statement is true?

(1) x = 85 and y = 50
(2) x = 90 and y = 45
(3) x = 110 and y = 75
(4) x = 115 and y = 70

22. A regular pyramid has a square base. The perimeter of the base is 36 inches and the height of the pyramid is 15 inches. What is the volume of the pyramid in cubic inches?

(1) 180
(2) 405
(3) 540
(4) 1215

23. In the diagram below of \triangle ABC, \angle ABC is a right angle, AC = 12, AD = 8, and altitude \overline{BD} is drawn.

What is the length of \overline{BC}?

(1) 4\sqrt{2}
(2) 4\sqrt{3}
(3) 4\sqrt{5}
(4) 4\sqrt{6}

24. In the diagram below, two concentric circles with center O, and radii \overline{OC}, \overline{OD}, \overline{OCE}, and \overline{ODF} are drawn.

If OC = 4 and OE = 6, which relationship between the length of arc EF and the length of arc CD is always true?

(1) The length of arc EF is 2 units longer than the length of arc CD.
(2) The length of arc EF is 4 units longer than the length of arc CD.
(3) The length of arc EF is 1.5 times the length of arc CD.
(4) The length of arc EF is 2.0 times the length of arc CD.