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maths ocr c3 june 2011 q9

i am stuck on part (ii). could someone please help?


Expand the numerator and denominators separately according to the standard formulae for cos and sine (A -B). You will s find that some of he resulting factors cancel out in each case. From the numerator take sine theta as a common factor and use cos from the denominator. Put one result over the other and hey presto!
Ian S.
09 June 2013
got it, thanks!
10 June 2013
It's very simple. If you take a factor of 4 out of the numerator and a factor of 3 out of the denominator and bring it out to the front, you'll have 4/3 multiplied by the original function that was worked out to be tan(theta). You can see theta is equal to 150. So it is tan150 multiplied by 4/3. So the answer is (4tan150)/3.
27 April 2016
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Total marks for this assignment are 100; this contributes 25% of the module. Task 1: (30 marks)

A student measured the data in the tables below by recording the time, t, it took two different cylinders (one solid and one hollow) with the same dimensions to roll, from rest, down a slope for a fixed distance.

Theory suggests that the hollow cylinder should take longer to travel the same distance as the solid cylinder. Hollow Cylinder times, t/s Solid Cylinder times, t/s 2.08 2.03 1.88 1.88 2.07 2.07 1.79 1.87 2.05 2.01 1.80 1.90 2.04 2.16 1.85 1.78 2.03 2.03 1.90 1.81 2.12 2.01 1.76 1.74 2.06 2.05 1.62 1.73 2.07 2.08 1.72 1.79 1.97 2.11 1.77 1.87 1.99 2.12 1.77 1.82 2.10 2.00 1.81 1.79 2.06 2.01 1.77 1.84 2.07 2.02 1.81 1.83 2.06 1.99 1.84 1.77 2.13 2.07 1.86 1.80 1.98 2.10 1.80 1.73 2.04 2.02 1.78 1.77 2.05 2.11 1.76 1.84 2.03 2.08 1.82 1.95 2.02 2.08 1.81 1.87 2.00 2.07 1.67 1.79 1.97 2.12 1.84 1.89 2.10 2.03 1.74 1.87

To analyse the data it is suggested to the student that she groups the data and produces a histogram for each cylinder showing the distribution of rolling times. The student consults her lecturer who suggests the following class intervals, where t is the rolling time in seconds: A B C 1.50

a.The student decides to use the class intervals shown in column C in the table, explain why this is an appropriate choice for the data from this experiment.

  1. Construct histograms for the experimental data using the class intervals shown in column C of the table above.

  2. Calculate the mean rolling time for each of the cylinders.

  3. Produce a spreadsheet to calculate the standard deviation in the rolling time for each cylinder – the spreadsheet table should show the additional columns required and a print out including the formulae you have used in each cell is required.

  4. Use the “Comparison of Means Test” (Shown below) to determine whether there is significant difference in the rolling time between the two cylinders.

Comparison of means test (i) Calculate the difference between the mean values of each data set.

(ii) Calculate the “Standard error of the difference” using the formula below:

Standard error of difference = √((S1/n1)+ ) (S2/n2) (the frist one is S1 2 and next is S2 2 )

Where: s1 is the standard deviation of data set 1, n1 is the number of measurements in data set 1, s2 is the standard deviation of data set 2 and n2 is the number of measurements in data set 2.

If the difference between the mean values of each data set is greater than twice the standard error of the difference then you can be 95% confident that there is a significant difference between the two sets of data i.e. whatever has been changed between one data set and the other has influenced the results.