1) For point A remember that the curve is this means that the curve has been stretched by scale factor 2 parrallel to the y-axis (i.e. all the y co-ordinates on the curve have been multiplied by 2)
For the equation we have;
Thus due to the graph or CAST diagram or whatever method has been taught;
2) For 2 you have the length BE so imagine the triangle that BEH makes.
Notice that the angle at E is a right-angle thus trigonometry can be used.
We want the angle at B. We have length BE which is adjacent and we have length EH which is opposite hence use
I get the answer to be to 2 decimal places.
3) As stated this question is similar so the information above should help.
4) In this question you need to use the 2 points that are given and sub them into the equation given;
We know that when
Thus giving us;
We also know that when
Now solve and simultaneously.
5) We know the volume of a cone is
So firstly we need to find the area of the larger cone then the smaller cone then minus one from the other to get the volume of the cup.
The question gives the area of the larger cone thus;
We know the height of the larger cone is hence;
To work out the volume of the smaller cone we need the radius so re-arrange the above formula. I get;
Now we have the square of the radius of the smaller cone and the height of the smaller cone which is h. Sub the information into the cone formula;
The and the will cancel out giving the volume to be
Now minus one from the other.
6) This one is similar to the one above. The equation for the volume of a cylinder is
Please ask if there are any more queries and good luck with your exams.