math exercises

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If A is a set with 5 elements, how many are the subsets of A ?

 


Find the lateral area, the total area and the volume of a circular cone that is circumscribed to a sphere of radius and whose axial cut is an equilateral triangle.

 


In the following picture: is the diameter of the sphere whose center is , é is the center of a intersection with a plane perpendicular to . Also the measures are and . Calculate the area of the cicle whose center is .

 


In the picture the line r is parallel to the line s . Find the value of .

 


Knowing that in the picture r // s, the value of is:

a) 90°
b) 100°
c) 110°
d) 120°
e)

None of the above.


 


Given the following picture, find the value of :

 


In the given picture, if r // s , we can say that the value of is:

a) 90°
b) 100°
c) 110°
d) 120°
e) 22°40'


 


Determine the quadrants in which the points are located.

a)
b)
c)


 


Plot in the following xOy plane the points A(4; 3) , B(-2; 5) , C(-4; -2) , D(3; -4) , E(2; 0) , F(0; -3) , G and H(; -4).

 


Solve the following inequalities:

a)
b)
c)
d)
e)
f)


 


What is the measure of the smaller angle between the hour hand and the minute hand on a clockface at 12:20?

 


The numbers , and are arranged:

a) in descending order
b) in ascending order
c) in non-descending order
d) the value of the last term is half of the sum of the first term and the second term
e) none of these


 


Considering the following functions

and ,

the value of is:

a) b) c) d) e)


 


After subtracting from the result is:

a)
b)
c)
d)
e) none of these are correct.


 


The expression , where and are positive numbers, is equivalent to:

a)
b)
c)
d)
e)


 


A machine working 6 hours each day produces 3000 hair clips in 5 days. How many hair clips will be produced if the machine is working 4 hours each day during 8 days?

 


What is the vertical height (altitude) of the right cone whose radius of the circular base is equal to centimeters and the slant height is 5 centimeters ?

 


A tap can fill a tank in 16 hours. How much time is needed for five identical taps to fill the same tank?

 


A small spur gear with 30 teeth drives another gear with 25 teeth. When the first gear has made 450 revolutions, how many revolutions has the second one made?

 


A workman makes U$ 4000,00 each 16 days of hard work; how much money is he going to make working hard 20 days?

 


Three points are given in the (x,y)-plane: , and . The equation of the line passing through the point and the midpoint of the segment is:

a)
b)
c)
d)
e)


 


The length of the two parallel sides of a right trapezoid are 6 cm and 8 cm, respectively top and bottom bases, and the altitude is 4 cm. The distance between the intersection of the two straight lines that contain the non-parallel legs and the midpoint of the major base is:

a) cmb) cm
c) cmd) cm
e) none of these


 


The lantern shown in the picture is suspended by two strings perpendicular to each other. Knowing the length of each string is 1/2 and 6/5 , respectively, what is the distance between the lantern and the ceiling?

a) 1,69b) 1,3c) 0,6
d) 1/2 e) 6/13


 


If the length of the legs of a right triangle are and , the length of the hypotenuse is:

a) b) c) d)
e)


 


In the picture below, ABCD is a rectangle, , and . The length of is:

a) b) c)
d) e)


 


In the picture below, ABFG and BCDE are squares and their each one sides measures, respectively, a and b. Knowing that and the perimeter of the triangle ACG is 12, we can assure that a e b are both inside the interval:

a) ]1; 5[b) ]0; 4[c) ]2; 6[
d) ]3; 7[e) ]4; 8[