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Mathematics: Exam workbook 4
Grade 6
1
Geometry
Question 1:
1.
Circle or Highlight the correct answer. Choose A, B, C or D.
A hexagonal shaped pyramid is made up of a number of the following shapes:
a) Hexagons
A:
2.
3.
4.
5.
C: a) and d)
D: All of the above
two equal sides and two equal angles, at least one angle greater than 90º.
B:
no equal sides or angles, at least one angle equal to 90º.
C:
all sides and all angles equal, all angles less than 90º.
D:
no equal sides or angles, at least one angle greater than 90º.
A parallelogram has:
a) 4 equal sides
b) inner angles add up to 360º
c) 2 pairs of parallel sides
A:
B: b) and c)
D: All of the above
a)
C: a) and c)
Which of the following are properties of a pentagonal prism?
a) 6 vertices
b) 10 vertices
c) 15 edges
d) 6 faces
A:
B:
C: a) and b)
D: All of the above
a) and c)
b) and c)
If one more edge is added to a hexagonal pyramid, you will have a __________
Hexagonal pyramid
B:
The following net
Octagonal pyramid
C:
Heptagonal pyramid
C:
Pentagonal pyramid
C:
An obtuse angle
will from a:
Pentagonal prism
B:
Hexagonal prism
An angle which is smaller than a right angle is called:
A:
8.
B: a) and c)
d) Rectangles
A:
A:
7.
a) and b)
c) Squares
An obtuse, scalene triangle is made up of:
A:
6.
b) Triangles
An acute angle
B:
A reflex angle
A closed 2-D shape with equal sides is called a/an ___________ polygon:
A:
Heptagon
Question 2:
B:
Irregular
C:
Regular
Practise drawing the following shapes on the grid paper:
1.
Isosceles, Obtuse triangle
2.
Equilateral, Acute triangle
3.
Scalene, Right-angled triangle
4.
Isosceles, Right-angled triangle
5.
Parallelogram
6.
Hexagon
7.
Trapezium
8.
Rhombus
D:
Closed
Mathematics: Exam workbook 4
2
Grade 6
Mathematics: Exam workbook 4
Grade 6
3
Geometry
Question 3:
Measure the angles, using a protractor, and classify each angle with reasons:
1.  ABC = _________
2.  DEF = __________
____________________
_____________________
_____________________
____________________
_____________________
_____________________
____________________
_____________________
_____________________
Question 4:
1.
3.
 ABC = 76º
3.  GHI = ____________
Construct the following angles and triangles, using a ruler and a protractor:
2.  DEF = 210º
An isosceles triangle ABC, where AB = 5 cm and BC = 6 cm and
 ABC = 53º
Mathematics: Exam workbook 4
Grade 6
4
Geometry
Question 5:
Polygon
Complete the table:
Sum of
inner angles
720º
1 080º
1 440º
Number of
Vertices
Number of
sides
Draw and add diagonals
Mathematics: Exam workbook 4
Grade 6
5
Geometry
Question 6:
a)
Construct the following polygons, following the instructions given;
Construct a rhombus ABCD with line AB = 3cm ^
and A = 52º.
Extend line AB with 3 cm and form a triangle BCE.
Extend line AD to point F and line EC to point F to form another triangle.
Measure the sizes or lengths of the following:
i)
EF = ___________ cm
ii)
DF = ______________ cm
iii)
^
E = _______________
iv)
^
DCF = __________________
v)
Identify the two triangles formed.
Question 7:
Consider the following polygons. Group each polygon under the correct heading
(write only the letter representing the polygon)
A
B
C
E
D
F
Regular
polygon
Quadrilateral
G
H
Concave
polygon
I
Irregular
polygon
Convex
polygon
Mathematics: Exam workbook 4
Grade 6
6
Geometry
Question 8:
Calculate the angles as instructed:
^
1. KJL = ________________________
K
________________________________
________________________________
M
^
^
2. Angles NJL and KJL are called
________________________________,
because _________________________
L
85º
24º
J
________________________________
^
3. KLM = ________________________
135º
N
________________________________
________________________________
^
^
4. JLK and KLM are called _________________________________________, because
______________________________________________________________________________
^
5. JMN = ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
^ = ______________________________________________________________________
6. JLN
______________________________________________________________________________
______________________________________________________________________________
^ = ______________________________________________________________________
7. LNM
______________________________________________________________________________
______________________________________________________________________________
^
9. JKL = ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
10.How many triangles are there in this shape? _____________
Mathematics: Exam workbook 4
Grade 6
7
Geometry
Question 9:
Identify the following shapes, then complete the number of vertices,
edges and faces for each:
Number of
Shape
Vertices
Number of
Shape
Vertices
Number of
Shape
Shape
+
Shape
+
Number of
+
Number of Vertices
+
Number
of
Vertices
Number
of Faces
+
+
Shape
Number of
Edges
Number of
Edges
Number of
Edges
+
Number of Faces
+
Number
of Edges
Number of
Faces
Number of
Faces
Vertices
+
Number of
Edges
Number of
Faces
Vertices
Shape
+
Number of
Faces
Number of Edges
+
Number
of
Vertices
+
Number Number of
of Faces
Edges
Mathematics: Exam workbook 4
Grade 6
8
Geometry
Question 10:
Classification of angles—Draw lines to match the angle with the measurement.
Measure between 0° and 90°.
Right
Revolution
Measure 360°.
Acute
Measure between 180° and 360°.
Question 11:
Obtuse
Reflex
Straight
Measure 180°.
Measure 90°.
Measure between 90° and 180°.
Fill in the missing words to complete the sentences. Choose from the
words in the word bank. The words may be used more than once.
1.
Angles are measured in ________________.
2.
Angles are drawn with ________ which are called the ______ of the angle. degrees
3.
The arms of angles meet at the ______________.
4.
Angles are measured with a ________________.
5.
Angles are classified according to their ______________.
6.
Angles are measured using __________capital letters. The _________
Word bank:
rays
turning
vertex
protractor
letter is always the _____________.
7.
size
three
Angles have to do with how much ____________ has taken place.
middle
arms
Question 12:
Name the following transformations:
__________
__________
__________
__________
Mathematics: Exam workbook 4
9
Geometry
Question 13:
Draw in the lines of symmetry for each shape:
Question 14:
Complete the following to form symmetrical patterns:
Question 15:
Draw a cross through the shapes that can tessellate.
Question 16:
Form your own tessellation using two of the shapes above:
Grade 6
Mathematics: Exam workbook 4
Grade 6
10
Geometry—Memo:
Question 1:
1. A
2. D
3. B
Question 2:
4. B
5. C
6. C
7. A
8. C
Practise drawing the following shapes on the grid paper:
1.
2.
3.
58
60
104
38
38
4.
60
90
32
6.
5.
90
45
45
8.
7.
Question 3:
60
Measure the angles, using a protractor, and classify each angle with reasons:
1. ABC = 28º
2. DEF = 105º
Acute angle
Obtuse angle
Reflex angle
Angle between 0º - 90º
Angle less then 180º,
Angle less than 360º,
more than 90º
more than 180º
Question 4:
1.
3.
3.
GHI = 195º
Construct the following angles and triangles, using a ruler and a protractor:
ABC = 76º
2.
DEF = 210º
An isosceles triangle ABC, where AB = 5 cm and BC = 6 cm and
Not drawn to scale
53º
53º
ABC = 53º
Mathematics: Exam workbook 4
Grade 6
11
Geometry—MEMO:
Question 5:
Complete the table:
Sum of
inner angles
Number of
Vertices
Number of
sides
Hexagon
720º
6
6
Trapezium
360º
4
4
Octagon
1 080º
8
8
Rhombus
360º
4
4
Pentagon
540º
5
5
Parallelogram
360º
4
4
Decagon
1 440º
10
10
Polygon
Draw and add diagonals
Mathematics: Exam workbook 4
Grade 6
12
Geometry—MEMO:
Question 6:
Construct the following polygons, following the instructions given;
Draw a rhombus ABCD with line AB = 3cm and ^
A = 52º. Extend line AB with 3 cm and
a)
form a triangle BCE. Extend line AD to point F and line EC to point F to form another
triangle.
Measure the sizes or lengths of the following:
i)
EF = 5 cm
ii)
DF = 3 cm
iii)
^
E = 64º
iv)
^
DCF = 64º
Identify the two triangles formed:
E
Triangle BEC and DCF are both acute,
isosceles triangles.
30 mm
B
C
52º
52º
A
F
30 mm
Question 7:
D
Consider the following polygons. Group each polygon under the correct heading
(write only the letter representing the polygon)
Regular
polygon
Quadrilateral
Concave
polygon
Irregular
polygon
Convex
polygon
A, E, F, G
C, F, G
B, C, D, H, I
B, C, D, H, I
A, E, F, G
Mathematics: Exam workbook 4
Grade 6
13
Geometry—MEMO:
Question 8:
Calculate the angles as instructed:
1.
K
^ = 66º
KJL
^ = 90º
KJN
^ = 90º - 24º = 66º
KJL
M
^
^
2. Angles NJL and KJL are called
complimentary angles, because they add
up to 90º and form a right angle.
L
85º
24º
J
135º
N
^
3. KLM = 95º
^
KLJ = 85º
^
KLM = 180º - 85º = 95º
^
^
4. JLK and KLM are called supplementary angles, because they add up to 180º and are angles on
a straight line.
^
6. JMN = 180º - (135º + 24º) = 21º (3 angles of a triangle add up to 180º)
^
^
^
7. JLN = 95º (opposing/opposite angle to KLM) or can be calculated using 180º - KLJ
^
8. LNM = 180º - (85º + 21º) = 74º (3 angles of a triangle add up to 180º)
^
9. JKL = 180º - (85º + 66º) = 29º (3 angles of a triangle add up to 180º)
(You can also use triangle KJN to calculate the angle).
10. How many triangles are in this shape? 5
Mathematics: Exam workbook 4
Grade 6
14
Geometry—MEMO
Question 9:
Identify the following shapes, then complete the number of vertices, edges
and faces for each:
Number of
Shape
Vertices
Number of
Faces
Number of
Edges
6
5
9
Triangular prism
Number of
Shape
Vertices
Number of
Faces
Number of
Edges
4
4
6
Triangular pyramid
Number of
Shape
Vertices
Number of
Faces
Number of
Edges
8
8
14
Heptagonal pyramid
Number of
Shape
Square prism
+
+
+
+
Vertices
Number of
Faces
Number of
Edges
8
6
12
+
+
+
Shape
Number of Vertices
Number of Faces
Number of Edges
Hexagonal prism
12
8
18
+
Shape
+
Number
of
Vertices
cylinder
(rectangle
curved with
circles on each
end)
0
+
Number
of Faces
2
Number
of Edges
0
Shape
+
Number
of
Vertices
Triangular
prism
6
+
Number
of Faces
Number
of Edges
5
9
Mathematics: Exam workbook 4
Grade 6
15
Geometry—MEMO
Question 10:
Classification of angles—Draw lines to match the angle with the measurement.
Obtuse
Measure between 0° and 90°.
Right
Measure 180°.
Revolution
Measure 360°.
Acute
Measure 90°.
Reflex
Measure between 180° and 360°.
Question 11:
Straight
Measure between 90° and 180°.
Fill in the missing words to complete the sentences. Choose from the words
in the word bank. The words may be used more than once.
1.
Angles are measured in degrees.
2.
Angles are drawn with rays which are called the arms of the angle.
degrees
3.
The arms of angles meet at the vertex.
rays
4.
Angles are measured with a protractor.
5.
Angles are classified according to their size.
6.
Angles are measured using three capital letters. The middle letter is size
always the vertex.
three
7.
Angles have to do with how much turning has taken place.
Word bank:
turning
vertex
protractor
middle
arms
Question 12: Name the following transformations:
Slide
Flip
Flip
Turn
Mathematics: Exam workbook 4
16
Geometry—MEMO:
Question 13:
Draw in the lines of symmetry for each shape:
Question 14:
Complete the following to form symmetrical patterns:
Question 15:
Draw a cross through the shapes that can tessellate.
Question 16:
Form your own tessellation using two of the shapes above:
Example given, using the triangle and hexagon:
Grade 6