Exam Questions

Below is a list of samples of the type of  questions that are likely to be part of the Leaving Certificate exam.  Try to complete the exam and see how you get on.

 

(1) Verify (2,6) is on the line 3x-y=0?                    

 

 

Work this out on paper. 
Move the pointer over the clue if you need a hint.
Click on the answer  when you are ready to check your work.

 

 

 

 

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Answer

(2) Where does the line 2x - 4y =6 intersect the x axis?     

 

 

Work this out on paper. 
Move the pointer over the clue if you need a hint.
Click on the answer  when you are ready to check your work.

 

 

 

 

 

 

Clue.

Answer

(3)  If  x(1,6)   y(-3,-1)  z(2,-2) are vertices (points) of a triangle.  Find what type of triangle it is?               

 

 

 

Work this out on paper. 
Move the pointer over the clue if you need a hint.
Click on the answer  when you are ready to check your work.

 

 

 

 

Clue

Answer

(4)  What is the slope of the line  perpendicular to a line with the slope 1/5?    

 

 

 

 

 

 

 

 

 

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(5) What is Sx(2,3)?           

 

 

 

 

 

 

 

 

 

 

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6. What is Sy(3,4)?            

 

 

 

 

 

 

 

 

 

 

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7. What is S0(2,1)?                

 

 

 

 

 

 

 

 

 

 

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8. Find the image of (2,3) under the translation (0,4) --> (3,3)?

 

 

 

 

 

 

 

 

 

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9. Sketch the line x-y-4=0?

 

 

 

 

 

 

 

 

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(1) Plug x and y values into equation. 


                              3x-2y=0 => 3(2)-6=0 => 6-6=0    
                                                                      
                                 True so point must be on line

 

 

 

 

 

 

 

 

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(2)    The equation for the x axis is y=0 so any po
int that is on the x axis must have a y coordinate of  0.  

So 2x - 4(0) =6  

=> 2x=6 

=> x=3

=> the point is (3,0)

 

 

 

 

 

 

 

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 (3)  Find the length of each line.  

      

 

There are two sides equal.  That means that it must be an isoceles triangle.

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(4)  Lines that are perpendicular  have opposite slopes so you must flip one and change the sign to get the  slope of a perpendicular line to it. 

We flip 1/5 to get 5/1.

Change the sign to get -5

 

 

 

 

 

 

 

 

 


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 (5) Count the distance to the x axis from the point and continue the same distance again.

 

 

 

 

 




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 (6)   Count the distance to the y axis from the point and continue the same distance again.  Sy(3,4) go to y axis and same distance again to give (-3,4)

 

 

 

 


 

 

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 (7)    Go to the origin and continue the same distance again

(2,1) ------> (0,0) --------> (-2,-1)

 





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 (8)A translation is a movement in space.  
If (0,4) gets moved to (3,3) which is 3 spaces across and 1 space down where will the point (2,3) end up.  
3 spaces across will give us 2+3=5 and 1 space down will give us 3-1=2  the point is then (5,2) 

 

 

 

 

 

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 (9)   In order to plot any line you need two points.  The most common way to find two points on a line is to use the X axis intercept and the Y axis intercept.  
To find the X axis intercept 
Plug in Y=0 into equation.
              x-y-4 = 0
              x-0-4 = 0
              x = 4   
===> (4,0)
 

To get the Y axis intercept 
Plug X=0 into equation
          x-y-4 = 0
          0-y-4 = 0
           y= -4  
===> (0, -4)

 

 

 

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