4

FAT / Activity/Form / Learner’s mark / Learner’s %
4.1 / INVESTIGATION
TOTAL

4

MATHEMATICS GRADE 9 FORMAL ASSESSMENT TASK (FAT) 4.1:

INVESTIGATION - Geometry of 3D objects

Total: 60 Marks Time: 1 period in the class

Name: ______Date: ______

______

Instructions:

1)  Write your name and date in the spaces provided.

2)  Show calculations as requested on question paper.

3)  You may use a calculator.

4)  It must be your own work.

5)  Check your answers.

Question 1: Match the definitions to the correct term in the Object – column. Write only the letter ( from the definition column) in the blank column.

Object / Answer / Definition
1 / Regular polygon / A) A perfectly rounded solid in three dimensional space
2 / Platonic solid / B) Identical circular ends that are flat and parallel to each other
3 / Polyhedron / C) A 3D solid that consists of a polygon as a base and all the side faces meet at a single vertex.
4 / Face / D) A shape where all sides are of equal length and all angles are equal in size
5 / Edge / E) Two faces meet in a straight line segment
6 / Vertices / F) A solid in which every face is a polygon
7 / Pyramid / G) The flat plane surface on a polyhedron
8 / Cylinder / H) A solid in which all faces are regular polygons and the same number of faces meet at each vertex.
9 / Sphere / I) A corner where a number of edges and faces meet

[9]

Question 2: Platonic Solids :

Facts: There are only five geometric solids that can be made using a regular polygon and having the same number of these polygons meet at each corner.

2.1 Complete the table by writing the correct answer to the letters ( a – s). (17)

Platonic Solid / Picture / Number of Faces
(F) / Shape of Faces / Number of Faces at each Vertex / Number of Vertices
(V) / Number of Edges
(E) / Unfolded Polyhedron (Net)
Tetrahedron / / 4 / Equilateral Triangle
(3-sided) / i / 4 / 6 /
Cube / / a / e / 3 / l / o /
Octahedron / / b / f / 4 / m / p /
Dodecahedron / / c / g / j / n / q /
Icosahedron / / d / h / k / 12 / 30 /

2.2 Euler's formula:V – E + F = 2, where V = number of vertices; E = number of edges; F = number of faces:

Use the general formula to check your answer at the Icosahedron

(3)

[20]

Question 3: Match the correct net with the correct 3D object. Only write the letter of the net next to the object.

Matc

A ___

____ B

____ C

____ D

____ E

___ F

[6]

Question 4:

Calculate the volume of the cylinder with a height of 2m and a radius of 1,5m. [3]

Question 5:

Complete the table using your knowledge of real life objects:

Object / Name of solid / Number of faces / Number of vertices / Number of edges
1 / Block of margarine
2 / A dice
3 / Tin of paint
4 / Marble

[16]

Question 6: Draw the net of a square pyramid [2]

Question 7: Sally has drawn an incomplete net for the 3D object shown.

a) Copy her incomplete net four times and show four different ways that she could

complete it. [4]

Mathematics Grade 9