Homework Practice

Printable assignment

Exploring Some Geometric Themes: Practice 3

Section A: Core Practice

Question 1mcq

A block model is viewed from the top, front, and side. Which statement is true?

A.All three views must always be identical.

B.A 3D object cannot have 2D views.

C.Top, front, and side views can be different for the same solid.

D.Only the front view matters.

Question 2mcq

Which is Euler's formula for a convex polyhedron?

F+E=V+2

F+V=E+2

F+V=E

E+V=F+2

Question 3mcq

Can a convex polyhedron have

6

faces,

8

vertices, and

12

edges?

A.Cannot be checked using a formula.

B.No, because faces must equal edges.

C.Yes, it satisfies Euler's formula.

D.Yes, because all three numbers are positive.

Question 4mcq

A geometric path has several turns on a grid. What is the best way to describe it accurately?

A.Estimate by looking only at the endpoint.

B.Break the path into simpler straight parts and track direction changes.

C.Use a random line through the figure.

D.Ignore turns and count only shapes.

Question 5mcq

How many faces, edges, and vertices does a triangular prism have?

5

faces,

9

edges,

6

vertices

8

faces,

6

edges,

12

vertices

4

faces,

4

edges,

4

vertices

6

faces,

9

edges,

5

vertices

Question 6mcq

How many faces, edges, and vertices does a square pyramid have?

8

faces,

6

edges,

12

vertices

4

faces,

4

edges,

4

vertices

5

faces,

8

edges,

5

vertices

5

faces,

8

edges,

5

vertices

Section B: Reasoning and Application

Question 7mcq

Which statement about a valid net of a cube is correct?

A.It must include circles for the corners.

B.It can have any five squares.

C.A cube net must have six connected squares arranged so they fold without overlap.

D.Its squares may overlap after folding.

Question 8mcq

A block model is viewed from the top, front, and side. Which statement is true?

A.A 3D object cannot have 2D views.

B.Top, front, and side views can be different for the same solid.

C.All three views must always be identical.

D.Only the front view matters.

Question 9mcq

A block model is viewed from the top, front, and side. Which statement is true?

A.A 3D object cannot have 2D views.

B.Top, front, and side views can be different for the same solid.

C.All three views must always be identical.

D.Only the front view matters.

Question 10mcq

Which is Euler's formula for a convex polyhedron?

F+E=V+2

F+V=E+2

F+V=E

E+V=F+2

Question 11mcq

Can a convex polyhedron have

6

faces,

8

vertices, and

12

edges?

A.Yes, it satisfies Euler's formula.

B.No, because faces must equal edges.

C.Yes, because all three numbers are positive.

D.Cannot be checked using a formula.

Question 12mcq

A geometric path has several turns on a grid. What is the best way to describe it accurately?

A.Break the path into simpler straight parts and track direction changes.

B.Ignore turns and count only shapes.

C.Estimate by looking only at the endpoint.

D.Use a random line through the figure.