Exam Questions

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.		Clue		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?		Clue		Answer
(5) What is S_x(2,3)?		Clue		Answer
6. What is S_y(3,4)?		Clue		Answer
7. What is S₀(2,1)?		Clue		Answer
8. Find the image of (2,3) under the translation (0,4) --> (3,3)?				Answer
9. Sketch the line x-y-4=0?				Answer





Answers
(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		Question
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(2) The equation for the x axis is y=0 so any point 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)		Question Next Question
(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			Question
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(5) Count the distance to the x axis from the point and continue the same distance again.			Question
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(6) Count the distance to the y axis from the point and continue the same distance again. S_y(3,4) go to y axis and same distance again to give (-3,4)			Question
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(7) Go to the origin and continue the same distance again (2,1) ------> (0,0) --------> (-2,-1)			Question
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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)			Question
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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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