MU123: Discovering Mathematics The Coordinates - Mathematics Assignment Help

Assignment Task:

Task:

Question 1 – 10 marks
This question is based on your work on MU123 up to and including Unit 6.
(a) Figure 1 shows two points A and B with a straight line drawn through them.

(i) Write down the coordinates of the points A and B. [1]
(ii) Find the gradient of the line that passes through the points A and B, clearly showing each step of your method. [2]
(b) (i) Find the equation of the line that passes through the point (5, −2) and has slope 3 4
. [3]
(ii) Determine whether or not the point (4, −3) lies on the line found in part (b)(i), clearly showing each step of your method. [2]
(iii) Find the x-intercept of the line found in part (b)(i), clearly showing each step of your method. [2]

Question 2 – 15 marks
This question is based on your work on MU123 up to and including Unit 6.
(a) Describe in your own words how you would expect the data points on a scatterplot to be distributed if the following features were present.
(i) An outlier [2]
(ii) A positive correlation between the x and y variables [2]
(iii) A correlation coefficient of r = −0.4 [2]
(b) This question investigates the relationship between the time taken to upload a file to the eTMA system and the number of students using the eTMA system at a particular time. A sample of 20 students were asked to record the time at which their eTMA submission was received and the time taken to upload their eTMA file. The researcher then checked to see how many students were logged on to the eTMA system at the recorded submission times. The results were displayed on a scatterplot with the regression line included. The number of students logged on at the submission time was displayed on the horizontal axis and the time taken to upload the file (in seconds) was displayed on the vertical axis.

The number of students logged on to the system at the times recorded ranged from approximately 1500 to 4500.
(i) The regression line for the investigation is y = 0.0062x + 6.54.
i. What does the variable x represent here? [1]
ii. What does the variable y represent here? [1]
(ii) The correlation coefficient r for the investigation is 0.93. What does this tell you about the relationship between x and y? [2]
(iii) Use the regression equation from part (b)(i) to predict the time it takes to upload a file when there are 3750 students logged on to the eTMA system. Give your answer to the nearest whole second. [2]
(iv) Can you conclude from this investigation that the number of students using the eTMA system at a particular time determines the time it takes to upload a file? Explain your answer. [2]
(v) If the correlation coefficient for this investigation had been 0.99, would this have changed the answer that you gave to part (b)(iv)? Explain your reasoning. [1]

Question 3 – 5 marks
This question is based on your work on MU123 up to and including Unit 7. Make k the subject of the following two equations. Show each step of your working.
(a) 7t = 5k 9 + 13 [2]

(b) 5k = 7k 12t + 8t

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