Randomly Generated Mathematics multiple choice Practice Exam
Grade: 12
Number of questions: 10

1. Suppose that a circle C has equation x2 + y2 -4x - 6y + 9 = 0.
What is the equation of the image of C after it has been reflected
about the line l: y=x + 3?
   ( x - 1) 2 + ( y - 4)) 2 = 4   
   x2 + y2 - 10y + 21 =0   
   x2 + y2 - 4x - 6y + 9 = 0  
   (x - 2) 2 + (y - 3) 2=9   

2. If a translation T takes the point (1,3)to the point
, then what is the image of the origin under T?
   (0,0)   
   (-2,3)   
   (-3,-1)   
     

3. , for x > 1, then which one of the following is the inverse of f?
     
     
     
     
     

4. a rectangular field of length 1 and width w meters for w < 1 has perimeter 400 meters. If a circular region of area w2 is to be reserved for
office purpose , what should be the length of the field so that the area of
the remaining region is maximum?
   150 meters  
   120 meters   
   50 meters   
   100 meters   

5. f(x)=xe3x-cos(2x), then f '(0) is equal to
   0   
   2   
   6   
   10  

6. You are given a data on the age of students, in a primary school.
Age 8 10 11 12 13
Number of students 5 15 8 10 2

Which of the following is NOT true about the data?
   The median is 10.5   
   The mode is 10   
   The mean is 10.5   
   The range is 5  

7. Let A and B 3x3 matrices such that

Which of the following is equal to |ABT|?
   400  
   100   
   1   
   4   

8. Consider an airplane that flies in straight line from Addis Ababa to city X in a planned time. If it flies at a speed of 1000 km/hr, it will reach at X 30 minutes before the planned time. On the other hand, if it flies at 900 km/hr, it will reach there 20 minutes after the planned time. Which of the following is the distance between Addis Ababa and city X?
   8000km   
   7250km  
   8500km   
   7500km   

9. Let
What is the value of a if f is continuous at x =1?
   4   
   0   
   8  
   2   

10. Consider a gate whose shape is a parabolic arch of height 3m and base
width 3m as shown in the figure below. If the origin of the coordinate
system is at the vertex, the equation that represents the edge of the gate is
   3y2-4x=0  
   y=-3x2+1   
   3x2+ 3y = 0   
   4X2+ 3y = 0   



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