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simultaneous eqns & concrete strength

1. Solve graphically the following simultaneous equations:
y = 10 - 2x
y = x - 1

2. 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.

3. 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

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/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

This task provides evidence for grading criteria M3.

Solution Preview

Task 1. see attachment (540000_1.jpeg)
From the graph, intersection point: (3.7,2.7)

Task 2: see attachment (540000_2.jpeg)
From graph, solution to x^2 - 2x - 4 = 0:
x = -1.2, ...

Solution Summary

Solution to simultaneous equations using graphical method. statistical methods to observe strength data of concrete. Also, comparison of strength of two concrete mixes.

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