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MUF0092 Mathematics Unit 2-SEM 1-2025
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The area shaded in the diagram below is closest to which of the following?
If a curve has a stationary point at and a gradient is a constant. The equation of the curve is:
This question is a hybrid question. Please clearly label a blank piece of paper with this question number and write your response to this question.
(In the examination you may be required to take a photo of your response at the end of the examination to upload).
___________________________________________________________________This question is worth 4 + 3 + 6 = 13 marks
[Note : This is an examination style REVISION question. In an actual examination question, there would not be as many parts]
The librarian is conducting an audit.
The table below summarises the number of pages of 200 books.
Number of pages
|
100 - 199
|
200 - 299
|
300 - 399
|
400 - 499
|
500 - 599
|
600 - 699
|
700 - 799
|
Frequency
|
12
|
36
|
42
|
53
|
33
|
20
|
4
|
To encourage the love of reading among the students, the librarian organised a reading competition. The data is summarised below. The mean of the data in the table is 8.6875 and the range is 15.
Number of pages read | Number of students |
3 | 6 |
8 | |
10 | 2 |
2 |
Mean number of pages read :
|
14.29
|
Mean time spent in the library :
|
0.90
|
Standard deviation of the number of pages read :
|
3.78
|
Standard deviation of the time spent in the library
|
0.21
|
Correlation Coefficient :
|
0.45
|
c. i. Which variable is the dependent variable?
ii. Calculate the value of for the regression line. Interpret this value in terms of the variables.
iii. Calculate the value of for the regression line. Interpret this value in terms of the variables.
iv. Use your line to predict the number of pages read by a student who spends 45 mins in the library. [Give your answer to the nearest page]
This question is a hybrid question. Please clearly label a blank piece of paper with this question number and write your response to this question.
(In the examination you may be required to take a photo of your response at the end of the examination to upload).
_____________________________________________________________________This question is worth 2 + 1 + 4 + 7 + 2 + 2 = 18 marks
[Note : This is an examination style REVISION question. In an actual examination question, there would not be as many parts]
In nature, the leaves of a certain variety of succulent plants are arranged in a spiral. [NB: The picture is for reference only]
Counting the number of leaves in the successive circles starting from the centre and moving outwards, the following number of leaves were counted.
Circle Number ( C )
|
1st
|
2nd
|
3rd
|
4th
|
5th
|
6th
|
7th
|
8th
|
9th
|
10th
|
Number of leaves ( N )
|
3
|
5
|
8
|
13
|
20
|
31
|
50
|
79
|
126
|
200
|
a. Find the value, correct to 2 decimal places,
of the correlation coefficient. What does this mean?
b. Use your graphics calculator to draw a residual plot. Briefly explain if a linear model is appropriate for this data set.c. Apply a squared transformationto transform the data.
i. Find the least square regression line for this transformation. [Give all coefficients to 2 decimal places]ii Find the correlation coefficient.iii. Is there any improvement? Why?
iv. Comment on the residual plot that is obtained with this transformation.d. Now apply a ) transformation to the original data set.i. Find the least square regression line for this transformation.
[Give all coefficients to 2 decimal places]
ii Find the correlation coefficient. [Give your answer to 4 decimal places]iii. Is there any improvement from the model in c.? Why?iv. Comment on the residual plot that is obtained with this transformation.v. Calculate, correct to 4 decimal places, the coefficient of determination. How
does this explain variation?
vi. Rewrite the equation in the form [Give all coefficients to 2 decimal places]e. Predict the number of leaves (to the nearest number) in the 11thcircle using the three different regression equations. How do they
compare with each other?
f. Find the residuals for the 7th circle using the three regression equations. Comment on your findings.