Сагс хоосон байна
Mixed exercises
{{exercise_number}}. Look for words that, when written in upper case, contain
a) straight lines only;
b) curved lines only.
{{exercise_number}}. Which of the following figures can be drawn without lifting the pencil or going over the same line twice?
a)
b)
c)
d)
e)
{{exercise_number}}. Which of the following statements are true and which are false?
If two rays are not on the same line, then
a) they do not have any common points;
b) they may have one common point;
c) they may have an infinite number of common points;
d) they cannot have more than one common point.
b) they may have one common point;
c) they may have an infinite number of common points;
d) they cannot have more than one common point.
{{exercise_number}}. In a park there are five molehills lined up along a straight path. The third molehill is \latex{ 4 } \latex{ metres } from the first one, the second molehill is \latex{ 8 } \latex{ metres } from the fifth one, the fourth molehill is \latex{ 3 } \latex{ metres } from the third one, and the third molehill is \latex{ 1 } \latex{ metre } from the second one. How far is the first molehill from the last?
{{exercise_number}}. What is the length of segment \latex{ EC } if all the following points are situated on a straight line and \latex{ AB = 2\,cm }; \latex{ AC = 3\,cm }; \latex{ AE = 4\,cm }; \latex{ DB = 12\,cm? }
{{exercise_number}}. How many triangles or quadrilaterals are there in each image?
a)
b)
c)
d)
{{exercise_number}}. Does a hexagon exist where any two adjacent sides are perpendicular to each other?
{{exercise_number}}. Does a quadrilateral exist whose adjacent sides are perpendicular to each other but have no parallel sides?
{{exercise_number}}. Segment \latex{ AB } is \latex{ 6\,cm } long. Draw a point that is
a) \latex{ 4\,cm } from the end of segment \latex{ AB };
b) \latex{ 3\,cm } from point \latex{ A } and \latex{ 5\,cm } from point \latex{ B };
c) \latex{ 4\,cm } from one end of segment \latex{ AB } and \latex{ 5\,cm } from the other end.
b) \latex{ 3\,cm } from point \latex{ A } and \latex{ 5\,cm } from point \latex{ B };
c) \latex{ 4\,cm } from one end of segment \latex{ AB } and \latex{ 5\,cm } from the other end.
{{exercise_number}}. Segment \latex{ AB } is \latex{ 5\,cm } long. Colour the parts of the plane that are at most \latex{ 3\,cm } from point \latex{ A } but no further than \latex{ 4\,cm } from point \latex{ B }.
{{exercise_number}}. A goat and a lamb are tethered in a field \latex{ 7\,m } apart from each other. The lamb's rope is \latex{ 3\,m } long and the goat's is \latex{ 5\,m } long.
a) Draw the possible position of the two animals in your notebook. Draw \latex{ 1\,m } as \latex{ 1\,cm } in your notebook.
b) Colour the areas red where both animals can graze. Colour the area where only the lamb can graze blue, where only the goat can graze yellow and green where neither one of them can graze.
b) Colour the areas red where both animals can graze. Colour the area where only the lamb can graze blue, where only the goat can graze yellow and green where neither one of them can graze.
{{exercise_number}}. Draw a triangle. Then, draw a line through each vertex that is parallel to the opposite side. What figure do these lines draw out?
{{exercise_number}}. Draw a pentagon with all its diagonals without lifting the pencil or going over any lines twice.
{{exercise_number}}. Draw a quadrilateral that has
a) perpendicular but not parallel sides;
b) has parallel but not perpendicular sides.
b) has parallel but not perpendicular sides.
{{exercise_number}}. A solid bounded by polygons has \latex{ 8 } vertices and \latex{ 8 } faces. \latex{ 7 } of its \latex{ 8 } faces are congruent. What type of polygon is the \latex{ 8^{th} } face?
{{exercise_number}}. Funny Pepe's car has been stolen from his home by thieves. Detective Hunch knows that the car alarm was on for more than \latex{ 20 } \latex{ minutes } but less than \latex{ 30 } \latex{ minutes } before it was switched off. As the alarm can only be turned off at a service workshop, Detective Hunch suspects that one of the thieves works at one of the four services in the area. Which service should he send the police car to if the stolen car can travel \latex{ 1\,km } \latex{ per } \latex{ minute }\latex{ ? } (→)
Pepe's house
service
\latex{ 10 } \latex{ km }
