Task 1. Solve graphically the following simultaneous equations:
y=10-2x
y = x-1
Task 2. Plot the graph of y =x2 - 2x - 4 for values of x from x = -2 to x = +4 at intervals of 1 and use the graph to solve the quadratic equation x2 - 2x - 4 = 0
Task 3. The following grouped frequency table shows the compressive strength of 30 concrete cubes at age 7 days.
|
Compressive strength.
(NM/m2)
|
Frequency.
|
|
21.0-22.9
|
3
|
|
23.0-24.9
|
6
|
|
25.0-26.9
|
14
|
|
27.0-28.9
|
5
|
|
29.0-30.9
|
2
|
a. Draw a histogram to represent this data.
b. Calculate the mean and the standard deviation of the data to 2 decimal places
c. Draw the cumulative frequency graph for the data.
d. Find from the graph the median of the data.
Task 4. In small groups of 3 carry out a presentation of examples of the use of statistics in the construction industry. Select a variety of forms (at least 3 different types) and include advantages and disadvantages of the forms of statistical representation.
Comment on how the data has been calculated, presented and used to aid effective decision making.
Task 5. Ten concrete cubes were prepared and tested by crushing in compression at 28 days from different sites A and B. The table below shows the following crushing strengths (in N/mm2) were obtained.
Find and compare the mean and standard deviations and comment, on the results.
|
Site A:
|
Site B:
|
|
43.3
|
44.6
|
|
46.2
|
46.2
|
|
41.1
|
42.2
|
|
38.5
|
40.4
|
|
46.2
|
47.4
|
|
45.6
|
46.3
|
|
42.7
|
44.7
|
|
48.6
|
48.5
|
|
44.1
|
45.3
|
|
41.6
|
42.8
|
This task provides evidence for grading criteria M3.
Task 6. Using alternative mathematical methods, carry out tasks 1 and 2 and make appropriate judgment on the outcome (this needs to include at least the relevancy, practicality and ease of use of the methods).
In addition to the above calculate task 5 develop a spreadsheet tool to solve this and multiple standard deviation calculations and compare to your manual workings in task 5 drawing conclusions on the practicalities of this as a tool.