Which of the following is the converse of the following statement?

Sample Item 1

MA.912.D.6.2

Lessons 2-2 and 2-3

The circle shown below is centered at the origin and contains the point (-4, -2).

Which of the following is closest to the length of the diameter of the circle?

Sample Item 2

MA.912.G.1.1

A. 13.41B. 11.66C. 8.94D. 4.47

Chapters 1, 5, 6, and 12

€

radius = dis tance from (0,0) to (−4,−2)

r = (−4 − 0)2 + (−2 − 0)2

= 16 + 4 = 20 = 2 5

€

diameter = 2(radius)

d = 2(2 5)

d = 4 5 ≈ 8.94

On a coordinate grid, AB has end point B at (24, 16). The midpoint of AB is P(4, -3). What is the y-coordinate of Point A?

Sample Item 3

MA.912.G.1.1

Chapters 1, 5, 6, and 12

Read Carefully!

€

x + 24

2= 4

€

y +16

2= −3

€

x + 24 = 8

x = −16

€

y +16 = −6

y = −22

Response Attributes: Fill in response items may require that students provide the length of a segment or the x or y-coordinate of a point of interest.

On a coordinate grid, AB has end point B at (24, 16). The midpoint of AB is P(4, -3). What is the y-coordinate of Point A?

In the figure below, AB is parallel to DC.

Which of the following statements about the figure must be true?

Sample Item 4

MA.912.G.1.3

Lessons 3-2, 3-3, and 3-4

If parallel lines are cut by a transversal, then same side Interior angles are supplementary.

Highlands Park is located between two parallel streets, Walker Street and James Avenue. The park faces Walker Street and is bordered by two brick walls that intersect James Avenue at point C, as shown below.

What is the measure, in degrees, of ∠ACB, the angle formed by the park’s two brick walls?

Sample Item 5

MA.912.G.1.3

Lessons 3-2, 3-3, and 3-4

€

60°

If parallel lines are cut by a transversal, then alternate Interior angles are congruent.

€

m∠ABC = 60°

€

m∠ACB = 180° − (60° + 36°)

= 84°Triangle Sum Theorem

€

?

A regular hexagon and a regular heptagon share one side, as shown in the diagram below.

Which of the following is closest to the measure of x, the angle formed by one side of the hexagon and one side of the heptagon?

Sample Item 6

MA.912.G.2.2

Lessons 3-5 and 6-1

Measure of one interior angle of a heptagon (7 sides)

€

180(7 − 2)

7=900

7≈ 129°

Measure of one interior angle of a hexagon (6 sides)

€

180(6 − 2)

6=720

6≈ 120°

€

129°

€

120°

€

x ≈ 360 − (129 + 120)

≈ 111°

Claire is drawing a regular polygon. She has drawn two of the sides with an interior angle of140°, as shown below.

When Claire completes the regular polygon, what should be the sum, in degrees, of the measures of the interior angles?

Sample Item 7

MA.912.G.2.2

Lessons 3-5 and 6-1

Method 1:

€

180 n − 2( )n

= 140

n = 9

140 × 9 = 1260°

Method 2:

€

Exterior∠ = 180 − 140 = 40

360 ÷ 40 = 9

9 × 140 = 1260°

The owners of a water park want to build a scaled-down version of a popular tubular water slide for the children’s section of the park. The side view of the water slide, labeled ABC, is shown below.

Sample Item 8

MA.912.G.2.3

Chapters 4, 7, and 10

Points A', B' and C ', shown above, are the corresponding points of the scaled-down slide. Which of the following would be closest to the coordinates of a new point C ' that will make slide A'B'C 'similar to slide ABC ?

Sample Item 8 (Continued)

MA.912.G.2.3

€

AB

A'B'=AC

A'C'60 ft

20 ft=140 ft

x ft

3

1=140

x

€

3x = 140

x = 462

3

€

x coordinate of C'

= 462

3+ 30 ≈ 77

C'(77,20)

Malik runs on the trails in the park. He normally runs 1 complete lap around trail ABCD. The length of each side of trail ABCD is shown in meters (m) in the diagram below.

Sample Item 9

If trail EFGH is similar in shape to trail ABCD, what is the minimum distance, to the nearest whole meter, Malik would have to run to complete one lap around trail EFGH ?

MA.912.G.2.3

Chapters 4, 7, and 10

EFGH is similar in shape to trail ABCD

€

perimeter of EFGH

perimeter of ABCD=GH

CD

x m

282m=100m

90mx

282=10

9

€

9x = 2820

x = 3131

3x ≈ 313m

Sample Item 10 MA.912.G.2.4A top view of downtown Rockford is shown on the grid below, with Granite Park represented by quadrilateral ABCD. The shape of a new park, Mica Park, will be similar to the shape of Granite Park. Vertices L and M will be plotted on the grid to form quadrilateral JKLM, representing Mica Park.

Which of the following coordinates for L and M could be vertices of JKLM so that the shape of Mica Park is similar to the shape of Granite Park?

A. L(4, 4), M(4, 3)B. L(7, 1), M(6, 1)C. L(7, 6), M(6, 6)D. L(8, 4), M(8, 3)

Lesson 4-1 and Chapter 9

A. L(4, 4), M(4, 3)B. L(7, 1), M(6, 1)C. L(7, 6), M(6, 6)D. L(8, 4), M(8, 3)

€

DA

CB=6

3=2

1

Sample Item 11

MA.912.G.2.4

Pentagon ABCDE is shown below on a coordinate grid. The coordinates of A, B, C, D, and E all have integer values. If pentagon

ABCDE is rotated 90º clockwise about point A to create pentagon A'B'C'D'E', what will be the x-coordinate of E'?

Lesson 4-1 and Chapter 9

B

A

E

D

C

B

A

E

D C

€

E −6,−3( ) →E' −3,6( )

90° rotation about the origin

€

x,y( ) →(y,−x)

Sample Item 12

MA.912.G.2.5

Marisol is creating a custom window frame that is in the shape of a regular hexagon. She wants to find the area of the hexagon to determine the amount of glass needed. She measured diagonal d and determined it was 40 inches. A diagram of the window frame is shown below

Which of the following is closest to the area, in square inches, of the hexagon?

A. 600 B. 849 B. C. 1,039 D. 1,200

Lesson 1-8 and Chapter 10

€

A =1

2a p

20

10

€

10 3

€

A =1

210 3( ) 120( )

A = 600 3 ≈1039 in2

Method 1

A hexagon is made up of 6 equilateral triangles….

Area of equilateral triangle:

If the diagonal = 40 inches then each side of the equilateral triangle = 20 inches

Area of one Triangle =

Area of Hexagon=

€

s2 3

4

€

202 3

4=100 3

€

6 100 3( ) ≈1039in 2

Method 2

A. 600 B. 849C. 1,039 D. 1,200

20

€

Area of circle

= π 20( )2

= 400π

≈1257 in2

Method 3

Sample Item 13

MA.912.G.2.5

A package shaped like a rectangular prism needs to be mailed. For this package to be mailed at the standard parcel-post rate, the sum of the length of the longest side and the girth (the perimeter around its other two dimensions) must be less than or equal to 108 inches (in.). Figure 1 shows how to measure the girth of a package.

What is the sum of the length, in inches, of the longest side and the girth of the package shown in Figure 2?

Figure 1

Figure 2

Lesson 1-8 and Chapter 10

Girth= 2(11 in.)+2(19 in.)= 60 in.

Longest Side= 42 in.

1 0 2

Sample Item 14

MA.912.G.3.3

On the coordinate grid below, quadrilateral ABCD has vertices with integer coordinates.

Quadrilateral QRST is similar to quadrilateral ABCD with point S located at (5, -1) and point T located at (-1, -1). Which of the following could be possible coordinates for point Q?

A. (6, -4) B. (7, -7) C. (-3, -7) D. (-2, -4)

Lessons 6-7, 6-8, and 6-9

TS = 2 DC

Segment DA has slope=3, ThereforeSegment TQ also has to haveSlope 3, however TQ = 2 DAQ

A. (6, -4) B. (7, -7) C. (-3, -7) D. (-2, -4)

Sample Item 15

MA.912.G.3.4

Figure ABCD is a rhombus. The length of AE is (x + 5) units, and the length of EC is (2x - 3) units.

Which statement best explains why the equation x + 5 = 2x - 3 can be used to solve for x?

A. All four sides of a rhombus are congruent.B. Opposite sides of a rhombus are parallel.C. Diagonals of a rhombus are perpendicular.D. Diagonals of a rhombus bisect each other.

Chapter 6

Sample Item 16

MA.912.G.3.4

Four students are choreographing their dance routine for the high school talent show. The stage is rectangular and measures 15 yards by 10 yards. The stage is represented by the coordinate grid below. Three of the students—Riley (R), Krista (K), and Julian (J)—graphed their startingpositions, as shown below.

Let H represent Hannah’s starting position on the stage. What should be the x-coordinate of point H so that RKJH is a parallelogram?

Chapter 6

Segment KJ has slope=¼, therefore Segment RH also has to have slope ¼.H

€

H 9,4( )

9

Sample Item 17

MA.912.G.4.6

Nancy wrote a proof about the figure shown below.

In the proof below, Nancy started with the fact that XZ is a perpendicular bisector of WY and proved that LWYZ is isosceles.

Which of the following correctly replaces the question mark in Nancy’s proof?

A. ASA B. SAA C. SAS D. SSS

Chapters 4 and 7

MA.912.G.4.6€

ΔWXZ ≅ ΔYXZ

by SAS

Sample Item 18

MA.912.G.4.7

A surveyor took some measurements across a river, as shown below. In the diagram, AC = DF and AB = DE.

The surveyor determined that m∠BAC = 29 and m EDF = 32. Which of the ∠following can he conclude?

A. BC > EFB. BC < EFC. AC > DED. AC < DF

Lessons 5-6 and 5-7

29°

32°

B. BC < EF

Sample Item 19

MA.912.G.4.7

Kristin has two dogs, Buddy and Socks. She stands at point K in the diagram and throws twodisks. Buddy catches one at point B, which is 11 meters (m) from Kristin. Socks catches the otherat point S, which is 6 m from Kristin.

If KSB forms a triangle, which could be the length, in meters, of segment SB?

A.5 mB. 8 mC. 17 mD. 22 m

Lessons 5-6 and 5-7

x

€

x +11 > 5

x > −6

€

x + 6 > 11

x > 5

€

11 + 6 > x

x < 17

X actually needs to be greaterThan zero because it is a length.Further more, from the first Inequality we see that x must be greater than 5, Therefore x > -6 is not valid. Which leaves us with:5 < x < 17.

€

B. 8 m

Sample Item 20

MA.912.G.5.4

In ΔABC, BD is an altitude. What is the length, in units, of BD?

€

A. 1

B. 2

C. 3

D. 2 3

Chapters 4, 7, and 8

€

x

3=

1

x

x 2 = 3

x 2 = 3

x = ± 3x

€

C. 3

Sample Item 21

MA.912.G.5.4

Nara created two right triangles. She started with LJKL and drew an altitude from point K to sideJL. The diagram below shows LJKL and some of its measurements, in centimeters (cm).

Based on the information in the diagram, what is the measure of x to the nearest tenth ofa centimeter?

Chapters 4, 7, and 8

s

€

s 3 = 5

s =5

3

€

5

3

⎛

⎝ ⎜

⎞

⎠ ⎟2

+ x 2 =122

€

x 2 =144 −25

3

x =407

3≈11.6

Sample Item 22

MA.912.G.6.5

Allison created an embroidery design of a stylized star emblem. The perimeter of the design is made by alternating semicircle and quarter-circle arcs. Each arc is formed from a circle with a 2½ -inch diameter. There are 4 semicircle and 4 quarter-circle arcs, as shown in the diagram below.

To the nearest whole inch, what is the perimeter of Allison’s design?

A. 15 inchesB. 20 inchesC. 24 inchesD. 31 inches

Lessons 1-8, 10-6, 10-7, and 10-8

4 half circles + 4 quarter circles = 2 circles + 1 circle= 3 circles

To the nearest whole inch, what is the perimeter of Allison’s design?

€

d = 21

2in

C = 21

2π in.

€

P = 3(21

2π) in.

= 7.5π in

≈ 23.6 in

C. 24 inches

Sample Item 23

MA.912.G.6.5

Kayla inscribed kite ABCD in a circle, as shown below.

If the measure of arc ADC is 255° in Kayla’s design, what is the measure, in degrees, of ADC ?∠

Lessons 1-8, 10-6, 10-7, and 10-8

€

measure arc ABC

= 360° − 255°

=105°

€

€

m∠ADC

=1

2105°( )

= 52.5°

5 2 . 5

Sample Item 24

MA.912.G.6.6

Circle Q has a radius of 5 units with center Q (3.7, -2). Which of the following equations defines circle Q?

A. (x + 3.7)2 + (y - 2)2 = 5

B. (x + 3.7)2 + (y - 2)2 = 25

C. (x - 3.7)2 + (y + 2)2 = 5

D. (x - 3.7)2 + (y + 2)2 = 25

Lesson 12-5

Euler’s Formula

€

V =Vertices

E = Edges

F = Faces

V − E + F = 2

Sample Item 25

MA.912.G.7.1

Below is a net of a polyhedron.

How many edges does the polyhedron have?

A. 6B. 8C. 12D. 24

Lessons 1-1 and 11-2

Sample Item 26

MA.912.G.7.1

How many faces does a dodecahedron have?

1 2

Sample Item 27

MA.912.G.7.5

Abraham works at the Delicious Cake Factory and packages cakes in cardboard containers shaped like right circular cylinders with hemispheres on top, as shown in the diagram below.

Abraham wants to wrap the cake containers completely in colored plastic wrap and needs to know how much wrap he will need. What is the total exterior surface area of the container?

A. 90π sq. in.B. 115π sq. in.C. 190π sq. in.D. 308π sq. in.

Chapter 11

€

LA(cylindar) + Area(circle) +1

2SA(sphere)

Total Exterior Surface Area:

€

10π • 4

€

+ π 5( )2

€

+1

24 5( )

2[ ]

€

=40π + 25π + 50π

A. 90π sq. in.B. 115π sq. in.C. 190π sq. in.D. 308π sq. in.

Sample Item 28

MA.912.G.7.5

At a garage sale, Jason bought an aquarium shaped like a truncated cube. A truncated cube can be made by slicing a cube with a plane perpendicular to the base of the cube and removing the resulting triangular prism, as shown in the cube diagram below.

What is the capacity, in cubic inches, of this truncated cube aquarium?

Capacity of Truncated Cube:

€

Volume cube( ) −Volume triangular prism( )

€

24( )3

1515

24 €

− 241

215( ) 15( )

⎡ ⎣ ⎢

⎤ ⎦ ⎥

€

=13,824 − 2700

=11,124 cubic in

1 1 1 2 4

Sample Item 29 MA.912.G.7.7

Kendra has a compost box that has the shape of a cube. She wants to increase the size of the boxby extending every edge of the box by half of its original length. After the box is increased insize, which of the following statements is true?

A.The volume of the new compost box is exactly 112.5% of the volume of the original box.

B. The volume of the new compost box is exactly 150% of the volume of the original box.

C. The volume of the new compost box is exactly 337.5% of the volume of the original box.

D. The volume of the new compost box is exactly 450% of the volume of the original box.

Chapter 11

€

1.5x( ) 1.5x( ) 1.5x( )x 3

=3.375x 3

x 3

= 3.375

C. The volume of the new compost box is exactly 337.5% of the volume of the original box.

x

x

x

1.5x

1.5x

1.5x

Sample Item 30

MA.912.G.7.7

A city is planning to replace one of its water storage tanks with a larger one. The city’s old tank isa right circular cylinder with a radius of 12 feet and a volume of 10,000 cubic feet. The new tankis a right circular cylinder with a radius of 15 feet and the same height as the old tank. What isthe maximum number of cubic feet of water the new storage tank will hold?

Chapter 11

12 ft 15 ft

h hV=10,000 ft3

€

π • 12( )2

• h =10,000

h =10,000

144π

h =625

9πft.

€

V = π • 15( )2 625

9π

⎛

⎝ ⎜

⎞

⎠ ⎟

V =140625π

9π

V =15,625 ft 3

Sample Item 31 MA.912.G.8.4

For his mathematics assignment, Armando must determine the conditions that will makequadrilateral ABCD, shown below, a parallelogram.

Given that the m∠DAB = 40°, which of the following statements will guarantee that ABCD is a parallelogram?

A.m∠ADC + m DCB + m ABC + 40°= 360°∠ ∠

B. m∠DCB = 40°; m ABC = 140°∠

C. m∠ABC + 40°= 180°

D. m∠DCB = 40°

Lesson 2-1 and MULTIPLE Concept Bytes

Sample Item 32

MA.912.T.2.1

A tackle shop and restaurant are located on the shore of a lake and are 32 meters (m) apart. A boat on the lake heading toward the tackle shop is a distance of 77 meters from the tackle shop. This situation is shown in the diagram below, where point T represents the location of the tackle shop, point R represents the location of the restaurant, and point B represents the location of the boat.

The driver of the boat wants to change direction to sail toward the restaurant. Which of thefollowing is closest to the value of x?

A. 23 B. 25 C. 65 D. 67

Lessons 8-3, 8-4, and 10-5

€

Tan x =32

77

x = tan−1 32

77

⎛

⎝ ⎜

⎞

⎠ ⎟

x ≈ 22.6°

A. 23

Sample Item 33

MA.912.T.2.1

Mr. Rose is remodeling his house by adding a room to one side, as shown in the diagram below.In order to determine the length of the boards he needs for the roof of the room, he must calculatethe distance from point A to point D.

What is the length, to the nearest tenth of a foot, of AD ?

Lessons 8-3, 8-4, and 10-5

x

€

Sin 25° =7

x

x =7

Sin 25°≈16.6 ft.

1 6 . 6