Assignment:
Q1. Solve graphically the following simultaneous equations:
y = 10 - 2x
y = x - 1
Q2. Plot the graph of: y = x^2 - 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 x^2 - 2x - 4 = 0.
Q3. The following grouped frequency table shows the compressive strength of 30 concrete cubes at age 7 days.
Compressive Strength (NM/m^2) 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
Q4. 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/mm^2) 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
Provide complete and step by step solution for the question and show calculations and use formulas.