Name: ____________________________________ NJASK Prep Part BGeometry and Measurement

Part I. Multiple Choice1) The floor of the lobby of a theater is shaped like a rectangle, as shown below.

Before a performance starts, a velvet rope is stretched diagonally across the lobby. Which of the following best describes the diagonal length of the lobby?

A Between 8 and 9 metersB Between 9 and 10 metersC Between 10 and 11 metersD Between 11 and 12 meters

2) Intersecting sidewalks surround a playground shaped like a quadrilateral, as shown in the diagram below.

Based on the angle measures in the diagram, what is the value of x?

A 70B 80C 120D 150

3) In the figure below, quadrilateral PQRS is congruent to quadrilateral VUTW.Which of the following pairs of angles must be congruent?

A ∠P and ∠TB ∠Q and ∠UC ∠R and ∠VD ∠ S and ∠T

4) Madelyn had a square piece of cardboard that was 10 inches in length. She cut one 3-inch square from each corner, as shown below.

The shaded part represents the remaining cardboard. What is the area of the remaining cardboard?A 36 sq. in.B 48 sq. in.C 64 sq. in.D 80 sq. in.

5) Massachusetts has 4230 miles of rivers. Which of the following measures is closest to the length, in kilometers, of the rivers in Massachusetts? (1 mile ≈ 1.609 kilometers)A 2629 kilometersB 3804 kilometersC 5839 kilometersD 6806 kilometers

6) A parallelogram and some of its dimensions are shown below.

What is the area of the parallelogram?A 100 square inchesB 200 square inchesC 300 square inchesD 600 square inches

7) A square pyramid is shown below.

What is the total number of edges in a square pyramid?A 4B 5C 6D 8

8) Jessica has one piece of ribbon that is 623 yards long and one piece that is 5

13 yards long.

What is the total length, in feet, of the two pieces of the ribbon?

A 33 23 feet

B 34 feet

C 34 12 feet

D 36 feet

9) One of the largest statues of a cow in the United States is 38 feet tall. What is the height of the statue in meters, to the nearest tenth of a meter? (1 meter ≈ 3.28 feet)A 11.6 metersB 12.5 metersC 115.9 metersD 124.6 meters

10) A rose garden is in the shape of a circle with a circumference of approximately 37.7 feet. Which of the following is closest to the diameter of the rose garden? (Use 3.14 for π).A 6.0 feetB 11.8 feetC 12.0 feetD 18.9 feet

11) A box is in the shape of a rectangular prism and has a volume of 360 cubic inches. The box has a width of 6 inches and a length of 10 inches. What is the height of the box? A 6 inchesB 10 inchesC 23 inchesD 36 inches

12) If you slide the figure up 4 units, what are the coordinates of the vertices of the new figure?

A A' (5,5 ); B' (6,8 );C ' (9,8 ); D '(9,6)B A' (1,5 ); B' (2,8 );C ' (5,8 ) ; D ' (5,6)C A' (5,1 ); B' (6,4 ) ;C ' (9,4 ) ; D' (9,2)D A' (1,1 ); B' ( 4,2 );C ' ( 4,5 ); D ' (2,5)

13) Lainey drew Figure P on a coordinate grid. Then she did a one-step transformation of Figure P to draw Figure Q, as shown below.

Which of the following one-step transformations of Figure P could Lainey have done to draw Figure Q?A reflection over the x-axisB reflection over the y-axisC rotation 180° clockwiseD translation to the right

14) Anne is using tape to mark off sections of a gameboard. About how much tape will she need if she wants to place it across both diagonals of the gameboard?

A about 17 inchesB about 24 inchesC about 34 inchesD about 144 inches

15) The width of a classroom door is indicated in the picture below.

Which of the following is most likely the width of the door?

A 0.1 kilometersB 10 metersC 100 centimetersD 10,000 millimeters

16) A porch has a total floor area of 2,856 ft2. If the width of the porch is 42 feet, what is the length of the porch?A 58 ft B 63 ft C 68 ft D 73 ft

17) Phyllis made the stack of blocks shown below.

Which of the following figures shows the front view of the stack of blocks?

18) Which of the following will always be similar?A two different squaresB two different rectanglesC two different rhombusesD two different parallelograms

19) A right triangle is shown below.

Based on the measures in the triangle, what is x?

A 15° B 30° C 45° D 60°

20) A hexagon and the measures of some of its angles are shown below.

What is the measure of ∠N?A 129°B 121°C 111°D 102°

21) The measure of each of the smaller angles of a parallelogram is 30°. What is the measure of each of the larger angles?A 30°B 60°C 150°D 165°

22) Look at this diagram.

Which triangle is the image of Triangle 1 after it is rotated 90 degrees clockwise about the origin?A Triangle AB Triangle BC Triangle CD Triangle D

23) A round clock on a classroom wall has a diameter of 12 inches. What is the approximate area of the clock? A 38 square inchesB 113 square inchesC 226 square inchesD 452 square inches

Part II. Extended constructed response24) The saguaro cactus can grow to a maximum height of 12 meters. What is the maximum

height to the nearest foot of a saguaro cactus? (1 meter ≈ 3.28 feet)

25) A triangle and some of its dimensions are shown in the diagram below.

Based on the dimensions in the diagram, what is x, the height in feet of the triangle?

26)

26) The figure below shows ∆ PQR and two of its angle measures.

What is the degree measure of ∠P?

27) In the figure below, parallel lines l and m are intersected by transversal p.

If the measure of ∠1 is 50°, what is the degree measure of ∠2?

28)

28) Rectangle ABCD is similar to rectangle EFGH. The rectangles and some of their dimensions are shown in the diagram below.

Based on the diagram, what is the length, in inches, of side FG?

29) A shipping box is in the shape of a rectangular prism, as shown below.

It has a length of 12 inches. It has a width of 6 inches. It has a volume of 288 cubic inches.

What is the height, in inches, of the shipping box?

30) Roger leans a 13-foot ladder against his home to wash the windows on the second floor. If the window is 12 feet from the ground, how far away from the house should Roger place the ladder?

31) The net for a prism is shown. What is the surface area of the prism?

32) For an art project, Calvin drew a rectangle inscribed in circle C, as shown below. The rectangle is 8 centimeters long and 6 centimeters wide.

What is the diameter, in centimeters, of circle C?

33) Parallelogram PQRS and the coordinates of point Q are shown on the coordinate plane below.

What are the coordinates of the image of point Q after parallelogram is translated 6 units to the left?

34) David drew ∆ ABC on a coordinate plane, as shown below.

David reflected ∆ ABC over the x-axis. What are the coordinates of the image of point A?

Part III. Open-Ended Response35) Mora bought a box of cereal that was a rectangular prism with a length of 7.5 inches, a

width of 2.5 inches, and a height of 11 inches, as shown below.

a. What is the total number of vertices of Mora’s cereal box? Show or explain how you got your answer.

b. What is the total number of faces of Mora’s cereal box? Show or explain how you got your answer.

c. In your Student Answer Booklet, draw a net (flat pattern) that can be folded to form a box with the same dimensions as Mora’s cereal box. Be sure to label your drawing of the net with the lengths, in inches, of the line segments.

36) A rancher has two water tanks. Each water tank is in the shape of a cylinder. The base of each water tank is in the shape of a circle.

Diagrams of the two water tanks are shown below.

a. What is the circumference, in feet, of the base of Water Tank 1? Show or explain how you got your answer. (Use 3.14 for π.)

b. The circumference of the base of Water Tank 2 is 6.28 feet longer than that of Water Tank 1. What is the diameter, in feet, of the base of Water Tank 2? Show or explain how you got your answer. (Use 3.14 for π.)

c. How many more square feet does the base of Water Tank 2 cover than the base of Water Tank 1? Show or explain how you got your answer. (Use 3.14 for π.)

37) Michael stacked cubes to make the structure shown below.

a. Draw a right side view of Michael’s structure. Be sure to label your drawing “right side view.”

Michael used a total of 14 cubes to make his structure.

b. Draw the front view of Michael’s structure. Be sure to label your drawing “front view.”

c. Draw one possible top view for Michael’s structure. Be sure to label your drawing “top view.” Show or explain how you got your answer.

38) Erika has a cylindrical container with a diameter of 6 inches and a height of 1.5 feet, as shown below.

a. What is the height, in inches, of the container? Show or explain how you got your answer.

b. What is the volume, in cubic inches, of the container? Show or explain how you got your answer. (Use 3.14 for π.)

c. Erika filled the container with 250 cubic inches of sand. What is the approximate height, in inches, of the sand that Erika put in the container? Show or explain how you got your answer.

39) A cafeteria has a recycling container for cans. The recycling container has a lid that is in the shape of a circle with an opening in the center that is also in the shape of a circle. The lid and some of its dimensions are shown in the diagram below.

The shaded part of the diagram represents the opening in the lid.a. What is the circumference, in inches, of the lid of the recycling container? Show or

explain how you got your answer. (Use 3.14 for π.)

b. What is the area, in square inches, of the lid, including the opening? Show or explain how you got your answer. (Use 3.14 for π.)

c. What is the area, in square inches, of the lid, not including the opening? Show or explain how you got your answer. (Use 3.14 for π.)

40) Danielle measured two of the computer screens in her school’s computer lab. The two screens and some of their dimensions are shown below.

a. What is the area, in square inches, of Screen 1? Show or explain how you got your answer.

b. What is x, the diagonal length in inches of Screen 1? Show or explain how you got your answer.

c. Which computer screen, Screen 1 or Screen 2, has the greater area? Show your work or explain how you got your answer.