maths o level Questions
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can anyone help me with these questions?
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Originally posted by Reynard lee:
For 21 (b) (i), the bisector of angle PSR will be a line drawn through the point S which will divide angle PSR into 2 equal angles.
For 21 (b) (ii), use your ruler to find the midpoint of the line SR, and draw a line perpendicular to SR through that point.
For 11 (b) (ii), area of triangle TRW / area of triangle VSR = RW /RS = 1/3
For 11 (a) and 20 (b) , it seems that you are new to graph drawing and venn diagrams, so instead of just giving you the answers this time round, I will suggest that you discuss with us here on how to draw the various type of graphs and venn diagrams.
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i dun understand 11bii, and for the venn and graph drawing i jus cnt do it
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Are calculator allowed in both paper 1 and paper 2 of this year's A and E Maths papers?
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yea
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Originally posted by Reynard lee:
i dun understand 11bii, and for the venn and graph drawing i jus cnt do it
For Q. 11(b)(ii), triangle TRW and triangle VSR are similar triangles, hence you could use this simple and direct method.
For venn diagrams and graph drawings, I am afraid it is a bit hard to teach you without drawing it out for you to see.
For 11 (a), the graph you drawn is actually y = 1, which is a straight line through y and parallel to the x-axis. y = x + 1 is a straight line graph too, but it is a constant increasing graph.
The 1st thing you should do when you deal with this kind of straight line graph is to find their points on the x-axis and y-axis.
On the x-axis, y = 0, and on the y-axis, x = 0. In short, you will have to sub in y = 0 and x = 0 respectively into the original equation to find the points on the two axis.
In this case, the point on the x-axis will be ( -1 , 0 ) and the point on the y-axis will be ( 0 , 1 ). Now, draw a straight line through this two important points, and that line will be y = x + 1.
For 11 (b), it will be slightly tougher, as you will need to find something called the turning point. For graphs like this which has x^2 in their equation, it will be a U-shaped or a n-shaped graph.
It is a good thing that you have find the 3 major points on the x-axis and y-axis, and the next thing you must do is to find the turning point. The turning point is also known as the maximum or the minimum point, depending on the shape and equation of the graph.
Using differentiation on the equation y = 1 - x^2, you will get dy/dx = -2x
One thing you must know is that at the turning point, dy/dx = 0.
Hence, -2x = 0, and the turning point is at x = 0.
At x = 0, you will find that y = 1, as shown in your unfinished graph. With these, you can conclude that y = 1 - x^2 is a n-shaped graph which passes through the 3 points you marked on the 2 axis, with ( 0, 1 ) being the maximum point.
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For the venn diagrams, since you can find the answers already, it means that you have a rough idea of how it goes about.
For 20 (b) (i) and (ii), you will need to draw 2 circles, with one circle representing the amount of people who went for the morning run, and another circle representing the amount of people who went for the afternoon swim.
In 20 (b) (i), you need to draw the venn diagram representing the least amount of people going for both events, hence you should draw two circles which barely intercept each other, with only a small amount of cross-over area.
The cross-over area will represent 5 people ( People who went for both events ), and the two areas which are separated on each circle will represent 21 people ( People who went for morning run only ) and 24 people ( People who went for afternoon swim only ), and thus one area must be drawn to be slightly bigger than the other.
For 20 (b) (ii), you need to draw the venn diagram representing the most amount of people going for both events. Hence, you should draw one circle within the other, with the smaller circle representing the people who went for both the morning run and the afternoon swim, and the area of the larger circle which did not cross-over with the smaller circle representing the amount of people who went for the afternoon swim only.
A very important thing to note is that you must write down the number 21 in the venn diagram on the area not touched by both circles. This is to represent that 21 people went for neither the morning run nor the afternoon swim.