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MUF0092 Mathematics Unit 2-SEM 1-2025
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It was found that using the least squares regression line for a set of data and , that for a particular data point, the predicted value is 12.6.
The residual value for that data point is 3.9 . What is the actual value for this data point?
The number of incoming phone calls at a Call Centre over a certain number of days is shown on the stem plot below:
Which of the following statement is NOT true about the data?
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 + 1 + 3 = 7 marks
A gym operates a small café for its clients. The owner wants to investigate the costs of ingredients used the cafe. Over a week, she records the daily costs of ingredients used. These are shown in the table below:
Day | Mon | Tues | Wed | Thur | Fri | Sat | Sun |
Cost, $ C | 184 | 254 | 198 | 240 | 261 | 321 | 298 |
a) Give the five point statistics ( five number summary) for the cost data shown above. [2 marks]
b) Draw a boxplot to represent this information. Clearly label your scale and all important features. [2 marks]
The owner realises the cost of preparing meals is probably linearly related to the number of meals prepared. She decides to investigate the cost for various numbers of meals prepared for clients. The data collected is shown below.
Number of meals, N
|
24
|
41
|
30
|
36
|
45
|
54
|
49
|
Cost, $ C
|
184
|
254
|
198
|
240
|
261
|
321
|
298
|
c) Use your calculator to find the equation of the least squares line that relates the cost of preparing meals to the number of meals produced. Give your equation in the form values correct to 2 decimal places. [2 marks]
d) tell us, in terms of
e ) tell us, in terms of
f) Use the equation you obtained in part (a) to predict the cost of producing:
(i) 42 meals. Does this prediction involve interpolating or extrapolating?
(ii) 5 meals. Does this prediction involve interpolating or extrapolating?
(iii) Comment on the reliability of both predictions from (i) and (ii) above. [3 marks]
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 + 2 + 2 + 1 = 7 marks.
A particle is moving in a straight line with velocity , for seconds. Its initial position from a fixed point is 2m.
[Hint : and ]
a. Find the times when the particle is at rest.
b. Find the total distance travelled by the particle in the first 5 seconds.
c. Find an expression for the displacement at time seconds.
d. Find an expression for the accelaration of the particle at time seconds.
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 7 marks.
The graphs of and meet at the point . The area enclosed by the two graphs, the line x = . Find the value of
Estimate the mean for the data below correct to 1 decimal place:
Calculate the mean for the table below: