Discrepancy in Week 4 Tutorial questions between Video and PDF versions

[CG]

There are a few discrepancies in the Tutorial questions for Week 4 between the PDF version and the video version. Here are a few that caught my attention.

Question 3  Week 04 Tutorial 3

Question in PDF : 3. A train goes along a path x2 − 6x + 8. There are two stops on the line y = 0 and Arav’s home is at the origin. How much minimum distance will Arav have to cover in order to catch the train?

Question in Video : A train goes along a path y2 − 6y + 8. There are two stops on the line y = 0 and Arav’s home is at the origin. How much minimum distance will Arav have to cover in order to catch the train?

The solution to the above questions would differ only in axis of symmetry and being parallel to x instead of y axis and curve being right opening.

Question 6 b Week 04 Tutorial 6

Question in PDF : 6. Consider the functionf1 = −x2 + 8x + 6. Two points P and Q are on the resulting parabola such that they are two units away from the axis of symmetry. If V represents the vertex of the curve, answer the following.

(a) If the triangle P V Q is rotated around its axis of symmetry then what is the curved surface area of the resulting cone? Given that the curved surface area of a cone is πrl, where r is the radius of the base and l is the slant height of a cone?

(b) Consider another curve representing function f2 such that f2 = (x − 4)2 . Now let A be the set of all points inside the region bounded by these curves (including the curves), what is the range of X − coordinate of the points in A ?

Question in Video : 6. Consider the functionf1 = −x2 + 8x + 6. Two points P and Q are on the resulting parabola such that they are two units away from the axis of symmetry. If V represents the vertex of the curve, answer the following.

(a) If the triangle P V Q is rotated around its axis of symmetry then what is the curved surface area of the resulting cone? Given that the curved surface area of a cone is πrl, where r is the radius of the base and l is the slant height of a cone?

(b) Consider another curve representing function f2 such that f2 = (x − 4)2 . Now let A be the set of all points inside the region bounded by these curves (including the curves), what is the range of Y − coordinate of the points in A ?

In the above question it is quite straight forward to get the range of Y coordinate points in A. However I found it a bit challenging to get the X coordinate points in a A, as per the PDF version of the question. Could someone please help me in this question.

[CG]

Solving the PDF version of the Week 4 tutorial question number 6 b

For X coordinates the solution I get is (4±√11,11) 

ie (0.68,11) and (7.32,11)

So the range would be [0.68,7.32] or [4-√11,4+√11]

This is obtained by equating the functions that define the 2 parabolas, since they will have the same y value when they intersect

-x²+8x+6 = x²-8x+16

or

2x²-16x+10 = 0

Factorise using [-b ± √(b² - 4ac)]/2a 

this gives 4±√11 

Substitute 4+√11 as x in y = x²-8x+16 to get y = 11

[Mathematics 1 Support 2]

Dear learner,

Thank you for pointing out those errors we will make changes accordingly in the pdf and update it in the portal. However the tutorial videos are good and no changes will be done in that.

Thanks and regards 

Vicky Kumar Sharma 

Maths_1 instructor

IITM Online Degree 

[Malabika Guha Mustafi]

HI CG, you are absolutely right .