Choose the best answer

1. Use dimensional analysis to determine which of
   the following equations is dimensionally
   correct
   
   1. acceleration * distance = speed ² ⁄ time
      
   2. acceleration * distance = speed ²
      
   3. acceleration * distance = time ⁄ speed
      
   4. acceleration * distance = speed ⁄ time ²
      
   5. acceleration * distance = speed ⁄ time
      
   Answer: B
   

2. Approximate the order of magnitude of the
   following product: 7 * 867 * 452 * 78 * 3 * 5432
   
   1. 1e9
      
   2. 3486833348544
      
   3. 1e10
      
   4. 1e13
      
   5. 1e12
      
   Answer: E
   

3. Convert 3 mm is equal to
   
   1. 3e-6 km
      
   2. 3e-3 km
      
   3. 3e5 km
      
   4. 3e-5 km
      
   5. 3e6 km
      
   Answer: A
   

4. 6 cm ⁄ min is equal to
   
   1. 3600 m ⁄ s
      
   2. 0.1 m ⁄ s
      
   3. 0.001 m ⁄ s
      
   4. 0.006 m ⁄ s
      
   5. 360 m ⁄ s
      
   Answer: C
   

5. 4 cm ² is equal to
   
   1. 4e4 m ²
      
   2. 4e-1 m ²
      
   3. 4e2 m ²
      
   4. 4e-4 m ²
      
   5. 4e-2 m ²
      
   Answer: D
   

6. 1 km ⁄ hr ² is equal to
   
   1. 6.48e3 m ⁄ s ²
      
   2. 6.48e4 m ⁄ s ²
      
   3. 5e-5 m ⁄ s ²
      
   4. 7.716e-4 m ⁄ s ²
      
   5. 7.716e-5 m ⁄ s 2
      
   Answer: E
   

7. The two legs of a right angled triangle are 19 m and 18 m long.
   Calculate the length of the hypothenus.
   
   1. 37.933 m
      
   2. 16.348 m
      
   3. 4.517 m
      
   4. 43.324 m
      
   5. 26.173 m
      
   Answer: E
   

8. The hypothenus of a right angled is 100 m. Calculate the length of one of the legs
   if the angle between this leg and the hypothenus is 10 degrees.
   
   1. 47.323 m
      
   2. 87.043 m
      
   3. 151.986 m
      
   4. 98.481 m
      
   5. 125.715 m
      
   Answer: D
   

9. The hypothenus of a right angled triangle is 30 m long.
   Calculate the length of one of its legs,
   if the angle opposite to this leg is 70 degrees.
   
   1. 33.177 m
      
   2. 23.263 m
      
   3. 28.191 m
      
   4. 37.698 m
      
   5. 3.6 m
      
   Answer: C
   

10. One of the legs of a right angled triangle is 80 m.
    The angle opposite to this leg is 70 degrees.
    Calculate the length of the other leg.
    
    1. 47.488 m
       
    2. 25.623 m
       
    3. 29.118 m
       
    4. 32.837 m
       
    5. 9.464 m
       
    Answer: C
    

11. The legs of a right angled triangle are respectively 3 m and 18 m.
    Calculate the angle formed between the former leg and the hypothenus.
    
    1. 8.972 deg
       
    2. 29.632 deg
       
    3. 49.29 deg
       
    4. 80.538 deg
       
    5. 123.168 deg
       
    Answer: D
    

12. The cartesian coordinates of a certain point are ( x, y ) = ( 75, 20 ) m.
    Calculate the polar coordinates ( r, θ ).
    
    1. (77.621 m, 27.91 deg )
       
    2. (77.621 m, 14.931 deg )
       
    3. (132.348 m, 14.931 deg )
       
    4. (132.348 m, 27.91 deg )
       
    5. (35.817 m, 11.758 deg )
       
    Answer: B
    

13. The polar coordinates of a certain point are ( r, θ ) = ( 12 m, 20 deg ).
    Calculate its cartesian coordinates ( x, y ).
    
    1. (11.276 m, 1.874 m )
       
    2. (12.943 m, 4.104 m )
       
    3. (11.276 m, 4.104 m )
       
    4. (10.074 m, 6.248 m )
       
    5. (12.943 m, 1.874 m )
       
    Answer: C